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EMPIRES OF TIME

Einstein' s CLOCKS,tbo~Poincare-'s MAPS'

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Advance praise for Einstein's Clocks, Poincare's Maps

"This is how twentieth-century science really began-not just in

abstractions but in machines; not just in Einstein's brain but

in coal mines and railway stations. Peter Calison's book is

engaging, original, and absolutely brilliant."

-James Gleick, author of Chaos

"Peter Galison provides a masterful and exciting account of the

revolution in our understanding of time that occurred at the

beginning of the twentieth century. Galison places Einstein and

Poincare at the crossroads of physics, philosophy, and technology I

where the problem of coordinating distant clocks played a crucial

role in both the new physics and the new technology."

-David Gross, Frederick W Gluck Professor of Theoretical Physics

"In what amounts to a stroke of genius, Peter Galison employs his

unmatched ability to depict historical events on many levels and

from many vantage points, as well as his unique com~~tion

of historical, scientific, and philosophical sophistication, to shed

fresh light on the revolution in physics that we associate with the

word relativity. This is simultaneously an indispensable book

for the specialist and a wonderful read for anyone."

-Hilary Putnam, Cogan University Professor Emeritus,

Harvard University

SClENCE

ISBN 0·393-02001-0

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EINSTEIN'SCLOCKS,

POINCARE'SMAPS

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Al.SO BY PETER GAUSO

How Experiments End

Image and Logic: A Material Culture of Microphysics

COEDITED VOLUMES:

Big Science: The Growth of Large-Scale Research

The Disunity of Science

Atl1losfJhericFlight in the Twentieth Century

Science in Culture

Picturing Science, Producing Art

'1 'heArchitecture of Science

Scientific Autlwrshif): Credit and Intellectual Property in Science

EINSTEIN'SCLOCKS,

POINCARE'SMAPS

Empires of Time

Peter Galison

W. W. Norton 6 COI11/)(I1lY New Yorl: London

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For Sam and Sarah,who have taught me the right use of time

Copyright © Z003 Peter Calison

All rights reserved

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First Edition

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Calison, Peter I.ouis.

Einstein's clocks und Poillcare', maps: empires of time I by Peter Galison.-Ist ed.p.Clll.

Includes bibliographical references and index.

ISBN 0-393-02()OI-O

I. Time. 2. Relativity (Physics) i. Einstein, Albert, IR79-1955. 4. Poincare, Henry,

1854-1912.1. Title.

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CONTENTS

Acknowledgments 9

CHAPTER I. SYNCHRONY

Einstein's Times 14

A Critical Opa/eocence 26

Order ofArgllmelll 41

CIIAPTER 2. COAL, CHAOS,

AND CONVE TIO 48

Coal 54

Chaos 62

Convention 76

t

CHAPTER 3. THE ELECTRIC WORLDMAP 84

Standards ofSfJace and Time 84

Times, Trains, and Telegrabhs <)8Marketing Time 107

Measuring Society 113

Time into Space 128

Battle over Neutrality 144

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CHAPTER 4. POINCARE'S MAPS 156

Time, Reason, Nation 156

Decimalizing Time 162

Of Time and Maps 174

Mission to Quito 191

Etherial Time 198

A Triple Coniuncticm. 211

CHAPTER 5· EINSTEIN'S CLOCKS 221

Materializing Time 221

Theory-Machines 227

Patent Truths 243

Clocks First 263

Radio Eiffel 271

CHAPTER 6.THEPLACEOFTIME

Without Mechanics 294

Two Modernisms j03

Looking Up, Looking Down 322

294

(Notes 329

Bibliography 355

Index 371

ACKNOWLEDGMENTS

I have benefited enormously from discussions with many studentsand colleagues. It is a privilege to be able in particular to thankDavid Bloor, Graham Burnett, Jimena Canales, Dehbie Coen,Olivier Darrigol, Lorraine Daston, Arnold Davidson, James Gleick,Michael Gordin, Daniel Gowff, Cerald Holton, Michael Janssen,Bruno Latour, Robert Proctor, Hilary Putnam, Juergen Renn,Simon Schaffer, Marga Vicedo, Scott Walter, and especially Caro-line Jones, for their many thoughtful comments. Over the years ithas been a pleasure to have learned as well from many discussionswith Einstein scholars Martin Klein, Arthur Miller, and JohnStachel. Though short ill pages, the manuscript and picture prepa-ration were long and certainly could not have been done withoutthe help of research assistants Doug Campbell, Evi Chantz, RobertMacdougall, Susanne Pickert, Sam Lipoff, Katia Scifo, HannaShell, and Christine Zutz. Particular thanks go to my orton cdi-tor, Angcla von clerLippe, and my agent, Katinka Matson, for goodideas and much encouragement. Amy Johnson and Carol Roseoffered many editorial improvements. Finally, I owe a great deal tothe many archivists who graciously helped in my research-espe-cially at the Observatoire de Paris, the Archives Nationales, theArchives de la Ville de Paris, the New York Public Library, the U.S.National Archives, the National Archives of Canada, the Burger-bibliothek Bern, and the Stadtarchiv Bern.

EINSTEIN'S

CLOCKS,POINCARE'S

MAPS

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Chapter 1

SYNCHRONY

r--j(!!'¥RUE TIME WOULD never be revealed by mere clocks-of..I this Newton was sure. Even a master clockmaker's finest

..i'~.. work would offer only pale reflections of the higher,absolute time that bclonged not to our human world, but to the"sensorium of Cod." Tides, planets, moons-everything in the Uni-verse that moved or changed-did so, Newton believed, against theuniversal background of ,1 single, constantly flowing river of time.In Einstein's clcctrotcchnical world, there was ]]0 place for such a"universally audible tick-lock" that we can call time, no way todefine time meaningfully except in reference to a definite system oflinked clocks. Time flows at different rates for one clock-system inmotion with respect to another: two events simultaneous for a clockobserver at rest arc not simultaneous for one in motion. "Times"replace "time." With that shock, the sure foundation ofNcwtonianphysics cracked; Einstein knew it. Late in life, he interrupted hisautobiographicalnotcs to apostrophize Sir Isaac with intense inti-macy, as if the intervening centuries had vanished; reflecting on theabsolutes of space and time that his theory of relativity had shat-tered, Einstein wrote: "Newton, forgive me ['Newton, vcrzeih' mir'[;you fonnd the only way which, in your age, was just about possiblefor a man of highest thought-and creative power.":

At the heart of this radical upheaval in the conception of time layan extraordinary yet easily stated idea that has remained dead-centerin physics, philosophy, and technology ever since: To talk abouttime, about simultaneity at a distance, you have to synchronize yourclocks. And if you want to synchronize two clocks, you have to start

EINSTEIN'S CLOCKS, POINCARE'S MAPS

with one, flash a signal to the other, and adjust for the time that theflash takes to arrive. What could be simpler? Yet with this proce-dural definition of time, the last piece of the relativity puzzle fellinto place, changing physics forever.

This book is about that clock-coordinating procedure. Simple asit seems, our subject, the coordination of clocks, is at once loftyabstraction and industrial concreteness. The materialization ofsimultaneity suffused a turn-of-the-century world very different fromours. It was a world where the highcst reaches of theoretical physicsstood hard by a fierce modern ambition to lay time-bearing cablesovcr thc whole of the planet to choreograph trains and completemaps. It was a world where engineers, philosophers, and physicistsrubbed shouldcrs; where the mayor of New York City discoursed Oil

the conventionality of time, where the Emperor of Brazil waited bythe ocean's edge for the telegraphic arrival of European time; andwhere two of the century's leading scientists, Alhert Einstein andHenri Poincare, put simultancity at the crossroads of physics, phi-losophy, and technology.

Einstein's Times

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For its cnduring echoes, Einstein's 1905 article on special relativity,"On the Electrodynamics of Moving Bodies," became the best-knownphysics paper of the twentieth century, and his dismantling of absolutetime is its crowning feature. Einstein's argument, as usually under-stood, departs so radically from thc older, "practical" world of classicalmechanics that the paper has become a model of revolutionarythought, seen as fundamentally detached from a material, intuitiverelation to the world. Part philosophy and part physics, Einstein'srethinking of simultaneity has come to stand for the irresolvable breakbetween modern physics and all earlier framings of time and space.

Einstein began his relativity paper with the claim that there wasan asymmetry in the then-current interpretation of electrodynam-

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ics, an asymmetry not present in the phenomena of nature. Almostall physicists around 1905 accepted the idea that light waves-likewater waves or sound waves-must be waves in something. In thecase of light waves (or the oscillating electric and magnetic fieldsthat constituted light), that something was the all-pervasive ether.Most late-nineteenth-century physicists considered the ether to beone of the great ideas of their era, and they hoped that oncc prop-erly understood, intuited, and mathematizcd, the ether would leadscience to a unified picture of phenomena from heat and light tomagnetism and electricity. Yet it was the ether that gave rise to the

asymmetry that Einstein rejected.'In physicists' usual interpretation, Einstein wrote, a moving mag-

net approaching a coil at rest in the ether produces a current indis-tinguishahle from the current gencrated when a moving coilapproaches a magnet at rest in the ether. But the ether itself couldnot be observed, so in Einstein's view there was but a single obscrv-able phenomenon: coil and magnet approach, producing a currentin the coil (as evidenced by the lighting of a lamp). But ill its then-current interpretation, electrodynamics (the theory that includedMaxwell's equatio\ls-describing the behavior of electric and mag-netic fields-and a force law that predicted how a charged particlewould move in these fields) gave two different explanations of whatwas happening. Everything depended on whether the coil or themagnet was in motion with respect to the ether. If the coil movedand the magnet remained still in the ether, Maxwell's equationsindicated that the electricity in the coil experienced a force as theeleetricity traversed the magnetic field. That force drove the elec-tricity around the coil lighting the lamp. If the magnet moved (andcoil stayed still), the explanation changed. As the magnetapproached the coil, the magnetic field near the coil grew stronger.This changing magnetic field (according to Maxwell's equations]produced an electric field that drove the electricity around the sta-tionary coil ancllit the lamp. So the standard account gave two

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explanations depending on whether one viewed the scene from thepoint of view of the magnet or the point of view of the coil.

As Einstein reframed the problem there was one single phe-nomenon: coil and magnet approached each other, lighting thelamp. As far as he was concerned, one observable phenomenondemanded one explanation. Einstein's goal was to produce that sin-gle account, one that did not refer to the ether at all, but insteaddepicted the two frames of reference, one moving with the coil andone with the magnet, as offering no more than two perspectives onthe same phenomenon. At stake, according to Einstein, was a

founding principle of physics: relativity.. Almost three hundred years earlier, Galileo had similarly qucs-

boned frames of reference. Picturing an observer in a closed ship'scabin, borne smoothly across the seas, Galileo reasoned that nomechanical experiment conduded in a below-deck laboratorywould reveal the motion of the ship: fish would swim in a bowl justas they would were the bowl back on land; drops would not deviatefrom their straight drip to the floor. '1'here simply was no way to useany part of mechanics to tell whether a room was "really" at rest or"really" moving. This, Calileo insisted, was a basic feature of themechanics of falling bodies that he had helped create.

Building on this traditional use of the relativity principle inmechanics, Einstein in his 1905 paper raised relativity to a princi-ple, asserting that physical processes are independent of the uni-forrnly moving frame of reference in which they take place.Einstein wanted the relativity principle to include not only themechanics of drops dripping, balls bouncing, and springs springingbut also the myriad effects of electrieity, magnetism, and light.

This relativity postulate ("no way to tell which unaccelerated ref-e.rence frame was 'truly' at rest") gave rise to an additional assump-bon that proved even more surprising. Einstein noted thatexperiments did not show light traveling at any speed other than300,000 kilometers per second. He then postulated that this was

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Synchrony

always so. Light, Einstein said, always travels by us at the same mea-sured speed- 300,000 kilometers per second-no matter how fastthe light source is traveling. This was certainly not how everydayobjects behaved. A train approaches and the conductor throws amailbag forward toward a station; it goes without saying that some-one standing on the station platform sees the bag approach at thespeed of the train plllS the speed at which the conductor habituallyhurls mail. Einstein insisted that light was different: stand, yourlantern raised, at a fixed distance from me and I see the light travelby me at 300,000 kilometers per second. Hurtle toward me on atrain, even one moving at 150,000 kilometers per second (half thespeed oflight), and I still see the light from your lantern go by me at300,000 kilometers per second. According to EillSlein's second pos-tulate, the speed of thc source docs not matter to the velocity of light.

Both of these postulates would have secmcd reasonable (at leastin part) to Einstein's contemporaries. 111 the science of mechanics,not only had the principle of relativity been around since Calileo,but for some ycars Poincare (among others) had also 'IJlaly/.cd therelativity principle's problems and prospects ill electrodynamics.' Iflizht moreover was nothing but an excitation of waves in a rigid,b ., ., '--'

all-pervasive ether, then ill the frame of reference ill which theether was at rest, it was plausihle to assume that the speed of lightwould not depend on the speed of the light source. Aftcr all, for rca-sonable source speeds, the speed of sound docs not depend on thevelocity of the source: once a sound wave is started, it movesthrough air at a fixed speed.

But how could Einstein's two postulates be reconciled? Supposein the ether rest frame a light was shining. 'Io an observer movingwith respect to the ether, wouldn't the light appear to travel eitherfaster or slower than normal, depending Oil whether the movingobserver was approaching or retreating from the light? And if a dif-ference in the velocity of light was observable, thcn wouldn't thatviolate the principle of relativity, since that observation would indi-


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cate whether one was truly moving with respect to the ether? Yet nosuch difference could be measured. Even precise optical experi-ments failed to detect the slightest hint of motion through the ether.

Einstein's diagnosis: "insufficient consideration" had been paid tothe most fundamcntal concepts of physics. He elaimed that if thesebasic concepts were properly understood, the apparent contradictionbetwecn the relativity and the light principles would vanish. Einsteinproposed, therefore, to begin at the very beginning of physical rea-soning, asking, What is length? What is time? And especially. Whatis simultaneity? Everyone kncw that the physics of electromagnet-ism and optics dcpended on making measurements of time, length,and simultaucity, but as filr as Einstein was concerned, physicists had110tpaid enough critical attention to the basic procedures by whichthese fUlldamental quantities were determined. How could rulersand clocks yieldullambiguous space and time coordinates for thephenomena of the world? In l<instein's judgment, the predominantview that physicists should eOllcern themselves first with the com-plex forces that held matter together had it backward. Instead, kine-IIWtiCS had to come fir~t, that is, how clocks and rulers behaved inconstaut, force-frce motion. Only then could the problem of dynam-ics (for example, how electrons behaved in the presence of electri-cal and Illagnetic forces) be usefully addressed.

J<:inst·eil\believed that physicists would only find consistency bysorling 011[· the measurcments of space and time. To make spatial

measurcments, a coordinate system is necded-by Einstein's lights,a system of ordinarv rigid measuring rods. For example: this point istwo feet along the x-axis, three along the y, and fourteen up the z-axis. So far, so good. Then came the surprising part, the reanalysis oftime that contemporaries like the mathematician and mathematicalphysicist Hermann Minkowski saw as the crux of Einstein's argu-ment.' As Einstein put it: "We have to take into account that all ourjudgments in which time plays a role are always judgments of simul-taneous events. If, for instance, I say, 'That train arrives here at 7

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Synchrony

0'clock,' I mean something like this: The pointing of the small handof my watch to 7 and the arrival of the train are simultaneousevents' .'" For simultaneity at one point, there is no problem: if anevent located in the immediate vicinity of my watch (say, the trainengine pulling up beside me) occurs just when the small hand ofthe watch reaches the seven, thcu those two events are obviouslysimultaneous. The difficulty, Einstein insisted, comes when we haveto link events separated ill space. What docs it mean to say two dili-font events are simultaneous? Ilow do Icompare the reading of mywatch here to a train's arrival at another station there at 7 o'clock?

For Newton the question of time hcld an absolute component;time was not and coulclnot he merely ,1 question of "common"clocks. From the instant EillStein demanded a l)Tocedure ill order togive meaning to the term "simultaneous," he split from the c1,octrilleof absolute time. In ,111 appmelltly philosophical register, 1',llls/eJl1established this definillg procedure HHOUgh a thought experimentthat has long seemed Elr from the play of laboratories and industry.How, \':instein asked, should we synchronize our distant clocks?"We could in principle content ourselves to time events by nsing aclock-hearing observer located at the origin of the coordinate sys-tem, who coordinates the arrival of the light signal originating fromthe event to be timed ... with the hands of his clock." Alas, Eill-stein noted, because light travels at ,1 finite speed, this procedure isnot independent of the place of tlic central clock. Suppose I standnext to A and far from B; you stand exactly halfway between A and B:

A-l11e--you----B

Both A and B flash light signals to me, and both arrive in front ofmy nose at the same moment. Can I conclude that they were sentat the same time? Of course not. It is obvious that 13'ssignal had amuch lonzer way to travel to me than A's signal, and yet they arrivedat the sam: time. So B's signal must have been launched before A's.

20 EINSTEIN'S CLOCKS, POINCARE'S MAPS

Suppose I stubbornly insist that A and B must have launched theirsignals simultaneously; after all, I got the two signals at the samemoment Immediately I run into trouble, as you can bear witness:if you were standing exactly halfway between A and B, then youwould have received B's light before A's. To avoid ambiguity, Ein-stein did not want to make the simultaneity of the two events "Asends light" and "B sends light" depend on where the receiver hap-

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Figure 1.1 Central Clock Coordination. In his 1905 pa/Jer Oil s/JeI:ial rela-tivity, Einstein introduced - and rejected - a scheme of clock coordination inwhich the central clock sent a signal to all other clocks; these secondary clocksset their times when the signal arrived. For example, if the central clod: sentits time signal at 3:00 P.M., each secondary clod: synchronized its hands to thatsame 3:00 P.M. when the /ndse arrived. Einstein's objection: the secondaryclocks were at different distance« from the center so close clocks would he setby the arriving signal before distant ones. This made the simultaneity of twoclocks depend (unacceptably to Einstein) on the arbitrary circumstance ofwhere the time-setting "central" clock happened to be.

Synchrony 21

1 LightSecond 1 Light

Figure 1.2 Einstein's Clocl: Coordination. ":illsieill. argued ilia! a betterand nonarbttrarv solulion to the simultaneity question was this: set cloc/,s no!to the time that the signal was launched, hut to the lime of the initial clockplus the time it took fen the signal to travel the distance limn the initial clockto the clocl: being uvnclironizo]. S/Jeciflcall)', he advocated sending a roiuul-trip signal from the initial cloci: to the distant clock cuul then seUing the c/is-tant clock to the initial clocl:« time plus half the round-trip time. III this waythe location of the "central" clock made no cliITerel1ce--olzccould start the /Jro-cedure at an)' point and 1l1wmbigllollsly Fixunnultaneii».

pens to be standing. As a procedure for defining simultaneity,"simultaneous receipt of signals by me" is a disaster, an epistcmicstraw man who cannot tell a consistent story.

Having knocked the straw out of this straw mall, young Einsteinproposed a better system: let one observer at the origin A send alight signal when his clock says 12:00 to B at a distance d from A;


the light signal reflects off B and returns to A. Einstein has B set herelock to noon plus half the round-trip time. A two-second round-trip? Then Einstein has B set her clock to noon plus one secondwhen she gets the signal. Assuming that light travels just as fast inone direction as the other, Einstein's scheme amounts to having Bset her clock to noon plus the distance between the two clocksdivided by the speed of light. The speed of light is 300,000 kilome-ters per second. So if B is 600,000 kilometers from A when Breceives the light signal, she sets her clock to 12:00:02, noon plustwo seconds. If B were 900,000 kilometers away from A, B would scther clock to 12:00:03 when she gets the signal. Continuing ill thisway, A, B, and anyone else participating in this coordination exer-cise can all agree that their clocks are synchronized. If we now movethe origin, it makes no difference: every clock is already set to takeinto account the time it takes for a light signal to arrive at the clock'slocation. Einstein liked this: no privileged "master clock," and anunambiguous definition of simultaneity.

With the clock coordination protocol in hand, EillSlcin hadcracked his problem. By relentlessly applying the simple procedureof coordination and his two starting principles, he could show thattwo events that were simultaneous in one framc of reference werenot simultaneous in another. Consider: the length measurement ofa moving object always depends on making simultaneous positionmea~urements of two points (if you want the length of a movingbus, It behooves you to measure the position of the front and backat the same time). Because the determination of length requires thesimultaneous measurements of front and back, the relativity ofsimultaneity led to a relativity of lengths-my frame of referencewill measure a meter stick moving by me as lcss than a meter long.

Astonishing in and of itself, this relativity of times and lengths ledto many other consequences, some more immediate than others.Because speed is defined as distance covered in a certain timecombining the motion of objects had to be reconsidered in Ein-

Synchrony

stein's theory. A person running in a train at a speed of 1/2 the speedof light (with respect to the train) while the train barreled along at3/4 the speed oflight would, in Newtonian physics, be moving rel-ative to the ground at 1 1/4 times the speed of light. But by rigor-ously following the definition of time and simultaneity, Einsteinshowed that the actual combined speed would be less than that-indeed always less than the speed oflight no matter what the speedof the train or the runner in the train. Nor was that all: Einsteincould explain previously puzzling optical experiments and makenew predictions about the motion of electrons. Finally, Einstein'sstarting assumptions about light speed and relativity, coupled withhis clock coordination scheme, helped show that there weren'treally two different explanations of the coil, magnet, and lamp butjust one: a magnetic field in one frame was an electric ficlcl inanother. The difference was one of perspective-the view from clif-ferent frames of reference. And all without a whiff of ether. A shorttime later, Einstein was to use relativity to produce that mostfamous of all scientific equations, ],; ::::me'. With consequences thatat first seemed restricted to the most sensitive of barely possibleexperiments to the utter transformation of the military-politicaldomain forty YCclfSlater, Einstein had found mass and energy to heinterchangeable.

Much lies behind Einstein's relativity besides the coordinationof clocks. Without exaggeration, one could say that the collectivemastery of electricity and magnetism was the great accomplishmentof nineteenth-century physical science. Theoretically, Cambriclgephysicist James Clerk Maxwell had produced a theory that showedlight to be nothing other than electric waves and so unified elec-trodynamics and optics. Practically, dynamos had brought electriclighting to cities, electric trams had altered cityscapes, andtelegraphs had transformed markets, news, and warfare. By the cen-tury's end physicists were making precision measurements oflight-staggeringly accurate attempts to detect the elusive ether; they


were refining work in electricity and magnetism to dissect the behav-ior of the newly accepted electron. All this led many of the leadingphysicists (not just Einstein and Poincare) to consider the problemof an electrodynamics of moving bodies to be onc of the most diffi-cult, fundamental, and acute problems on the scientific agenda.'

By Einstein's own account, the recognition that synchronizingclocks was necessary to define simultaneity was the final conceptualstep that let him conclude his long hunt, and that-time coordi-nation -; is the subject of th is book. Indeed, Einstein judged thealteration of time in relativity theory to be that theory's most strik-ing fcature. But his assessment did not immediately carry the day,even among those who counted themselves as Einstein's backers.SOIIle embraced relativity after experiments on the deflcction ofelectrons seemed to lend it support. There were those who used thetheory only when physicists auc] mathematicians had reworked itinto more familiar terms that did not put so much stress Oil the rel-ativity of time. 'f 'hrough tense mcetings, exchanges of letters, arti-clcs and responses, by 1<) 10 a growi lIg number of F instcin'seollcagues were pointing to the revision of the time concept as thesalient feature. In the years that followed, it became canonical forhoth philosophers and physicists to hail clock synchronization ,IS atriumph in both disciplines, a beacon of modern thought.

Younger physicists, including Werncr Hcisenbcrg, began in the1920s to pattern the new quantum physics 011 what they took to beEinstein's tough stance against concepts (like absolute time) thatreferred to nothing observable. In particular, Heisenberg admiredEinstein's insistence that simllltaneity refer exclusively to clockscoordinated by a definite and observable procedure. Heisenbergand his colleagues pressed their insistence on observability hard: ifyou want to speak about the position of an electron, show the pro-cedure by which that position can be observed. If you want to saysomething about its momentum, then display the experiment thatwill measure it. Most dramatically, if even in principle you could

Synchrony

'" Ii measure both position and momentum simultaneously, thent" ».ition and momentum simply did not both exist at the same lime.t'.llls/ein famously bridled at that conclusion, even as his quantum, ,>llcagues pleaded with him to acknowledge that they had onlyI\lcnded to atoms Einstein's own acute criticism of time, and simul-t.iueity. It was far too late for Einstein to call his relativistic genic1);lck into the bottle, but he worried the new physics carried too farIllc spirit of his insistence on observable procedures -and so under-,·.,timated the formative role of theories in fixing what could be«-cn. As Einstein wryly observed, "A good joke should not he

repeated too often."The good joke spread. Psychologist Jean Piagd made the inves-

tigation of the "intuitive" time cone cpt ill the child into an impor-tant research area. 1'~illStein's time coordination hegan serving as amodel-and soon the model-s-for a new era of scientific philoso-

phy. Gathering in the Austrian capital to founcl ,I new antiincta-physical philosophy, tho physicists, sociologists, aud philosophers ofthe Vienna Circle hailed synchronized clock simultaneity as theparadigm of a proper, verifiable scientific concept. Ebewhere inEurope and ill the United Stales, other self-consciously modemphilosophers (as well as physicists) joined in hailing signal exchangesimultaneity as an example of properly grounded knowledge thatwould stand proof against idle metaphysical speculation." ToWillard Van Orman Quine, one of the most influential Americanphilosophers of the twentieth century, all knowledge was ultimatelyrevisable (he even held that logic might eventually need alteration).Yet as Quine surveyed the whole of scientific understanding, hechose as most durable Einstein's definition of simultaneity throughclocks and light signals, judging that it was Einstein's time conceptthat we "should be most inclined to preserve when called upon tomake future revisions of ... science.?" For a philosophical centurymarked by vast ehangcs in knowledge, in a climate hostile to eter-

nal, unbending truths, there was no higher praise.


Of course not everyone admired the relativity of time. Some lam-pooncd it, others tried to rescue physics from it. But very broadly bythe 1920s, both physicists and philosophers recognized that Ein-stein's question, What is time? set a standard for scientific conceptsthat demanded something more finite, more humanly accessiblethan Newton's metaphysical, absolute time. Einstein himsclf sug-gcsted that he had drawn an effective philosophical sword againstabsolute lime from thc cightecnth-ccntnry critical work of DavidII rune, who had forcefully argued that the statement "A causes B"meant nothing more than the regular sequence, A then B. Key for1':illStein, too, was the Viennese physicist-philosopher-psychologistI<mst Mach's work lambasting conccpts disconnected from pcr-ccption. AlIlong Mach's (sometimes excessive) roundup of idleabstractions, none figured as a grcater offender than Newton's"medieval" notions of absolute spacc and absolute timc. 1':iI1Steinalso studied time through the microscope of other scientists'inquiries, among them thosc of Hcndrik A. I .orcntz and Poincare.

I':<lch of these lines of philosoph ical reasoning - and othcrs that wewill encounter - [onu part of our story oftime and timepieces. Yeta purely intellectual hist-ory leaves I<instein hovering in a cloud ofabstractions: the philosopher-scientist brandishing thought cxpcri-iucnts agaimt the dusty Newtonian dogma of absolute time. Ein-stein con fouJlding a contemporary scientific-technical cadre toosophisticated to ask basic questions about time and simultaneity.But is this cerebral account sufficicnt?

A Critical Opalescence

Certainly Einstein and Poincare often looked back on their work asif it originated entirely outside the material world. In this respect, itis useful to reflect on a speech Einstein delivered in early October1933 to a massive rally organized to aid refugees and displacedscholars. Scientists, politicians, and the public jammed London's

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I()y;d Albert Hall. Hostile demonstrators threatened to stir things

1 1 ." 1 "'J"IIJ': ;1 thousanc stue ents came to serve as protective stewarc S.',lll-.lri n warned of the imminence of war, of the hatred and violence1,)[ lllling over Europe. He urged the world to resist the drivc toward-Livcry and oppression, and pleaded with governments to halt theuupending economic collapse. Then, suddenly, the poli tical thread,>i Einstein's speech snapped. There was a sudden pullillg backIIom worldly crisis, as if the calamity of current events had stretcher]

IIim beyond his limits. In a different register he began to reflect onsolitude, creativity, and quiet, on moments he had spent lost in;1 bstract thought surrounded only by the productive monotony ofthe countryside. "There arc certain occupations, even in modernsociety, which cntailliving in isolation and do not require greatphysical or intellectual effort. Such occupations as the service of

lighthouses <Indlightships come to mind."!'Solitude was perfect for a young scientist engaged with philo-

sophical and rnathcmatical problems, I':insteill insisted. Ilis ownyouth, wc arc tempted to speculate, might be thought of this way:we might read the Bern patent office where he had earned a livingas no more than such a distant oceanic lightship. Consistent withEinstein's gardcn of otherworldly contemplation, we haveenshrincd Einstein as the philosopher-scientist who iglloredtheclutter of the patent office and the chatter of the hallway to rethinkthe foundations of liis discipline, to topple the Newtonian absolutesof space and time. N cwton to Einsteill: it is easy enough to rcprc-sent this transformation of physics as a coufrontation of theoriesfloating above the world of machines, inventions, and patents. Ein-stein himself contributed to this image, emphasizing in manyplaces the role of pure thought in the production of relativity:"[T]he essential in the being of a man of Illy type lics precisely inwhat he thinks and how he thinks, not in what he docs or suffers.':"

The picture we so often see is of an Einstein otherworldly, orac-ular, communing with the spirits of physics; Einstein pronouncing

...._---_ .._----------------_.- -


on the freedom of God in the creation of the Universe; Einsteinshucking off patent applications as so much busywork between himand the philosophy of nature, Einstein summoning a world of purethought experiments featuring imaginary clocks and fantasticaltrains. Roland Barthes explored this imagined persona in his "Brainof Einstein," where the scientist appears as nothing but his cere-brum, an icon of thought itself, at once magician and machinewithout body, psychology, or social existence."

Barthes would have known that alllong those scientists imagincdto float above the material world was Henri Poincare, the extraor-dinary French mathematician, philosopher, and physicist who pro-duced, quite independently of Einstein, a detailed mathematicalphysics incorporating the relativity principle. In elegantly wordedessays, Poincare offered these results to the wider cultured world, atthe same time prohing the limits and accomplishments of bothmodern and classical physics. Like Einstein, Poincare presentedhimself as a mind unbound. In one of the most famous accountsever written hy a scientist of his own creative work, Poincarerecounted his steps toward a thcory of a new set of functions thatwere important for several domains of mathematics:

For fifteen clays [ strove to prove there could not he any functionslike those Jihad in mind]. I was then vcry ignorant; every clay Iseated myself at my work table, stayed an hour or two, tried a greatnum her of combinations and reached no results. One evening,contrary to my custom, 1 drank black coffee and could uot sleep.Ideas rose in crowds; I felt them collide until pairs interlocked, soto speak, making a stable combination .... 1 had only to write outthe results which took but a few hours. )'1

Not just in his account of his newly invented functions, butthroughout his remarkable philosophical and popular essays, Poin-care dissected physics and philosophy by way of metaphorical

Synchrony

worlds detached from the here and now, suspending imaginary sci-entists in idealized alternate universes: "Suppose a man were trans-lated to a planet, the sky of which was constantly covered with aIhick curtain of clouds, so that he could never see the other stars.On that planet he would live as if it were isolated in space. But hewould notice that it revolves .... "IS Poincare's sp8ce traveler mightexhibit the rotation by showing that the planet bulged around itsequator, or by demonstrating that a free-swinging pendulum grad-ually rotates. As always, Poincare here used an invented world tomake a real philosophical-physical point.

It certainly is possihle-even productive= to read Einstein andPoincare ,15 ifthey were abstract philosophers whose goal was toenforce ph ilosophical distinctions hy fabricating hypotheticalworlels rich ill imaginative metaphors. Poincare (it might bethought) hac! ill mind such a world when he spoke of such wildlyvarying temperatures that objects altered their lengths dramaticallyas one moved up or clown. Poincare and Einstein's attacks on New-ton's absolute siuniltaucity could be taken to be just such metaphor-ical musing», ones that employed imaginary trains, fantastical

clocks, and ahstraclldegraphs.Let's return 10 Einstein's central inquiry. Invoking what may

seem a quaintly mclaphotica] thought experiment, Einstein wantedto know what was meant hy the arrival of a train in a station at 70' clock. 1 have long read th is as an instance of Einstein asking aquestion that (as Kinstciu put it) was normally posed "only in earlychildhood," a matter that he, peculiarly, was still asking when hewas "already grown up.")!' Was this the naivete of the isolatedgenius? Such riddles about time and space appear, on this reading,to be so elementary as to lie below the conscious awareness of pro-fessional scientists. But was the problem of simultaneity, in fact,below the threshold of mature thought? Was no one else in1904-1905 in fact asking what it meant for an observer here to saythat a distant observer was watching a train arrive at 7 o'clock? Was

...--_ .._,,_ ...._---


the idea of defining distant simultaneity through the exchange ofelectric signals a purely philosophical construct removed from theturn-of-the-century world?

Relativity was certainly far from my mind when, not long ago, rwas standing ill a northern European train station, absentmindedlystaring at the elegant clocks that lined the platform. They all readthe same to the minute. Curious. Good clocks. Then Inoticed that,as far as I could see, even the staccato motion of their second handsclicked ill synchrony. These clocks arc not just running well, I

thought; these clocks arc coordinated. 1':iIlStein must also have hadcoordinated clocks in view while he was grappling with his 1905paper, trying to undcrst.md the lllc<llling of distant simnltancity.Indeed, across tho street from his Bcrn patent office was the oldtrain station, sporting a spectacular display of clocks coordinatedwithin the statiou, alollg the tracks, and on its facade.

'I 'he origins of coordinated clocks, like much in our tcchnologi-cal past, remains obscure. Which of the many pari's of a tcchnolog-ical system docs ClIlC count as its defining feature: the IISC orelectricity? the branchiJlg of llJallY clocks? [he continuous coulro]of tlic distant clocks? However one reckons, alrcady by tho I rrwsand I k40s Britain's Clwrlcs Wheatstone and Alexander Buin, audsoon thereafter Switzcrland's M;lIhias I ripp and a myriad of otherI':mopean and American inventors, hegan constructing electricaldistr ibution systems to hind numerous far-flung clocks to a singlecentral clock, callecl in their respective languages the "liorloge-mere"[mother clock], "Pruniiie Nomwluhr"lprilluuy standard clock], and

the "master clock.?" In Germany, I ,eipzig was the first city to installelectrically distributee! time systems, followed by Frankfurt in 1859;Hipp (then director of a telegraph workshop) launched the Swisseffort in the Federal Palace ill Bern, where a hundred clock facesbegan marching together ill 1890. Clock coordination quicklyembraced Ceneva, Basel, Neuchatcl, and Zurich, alongside theirrailways."

:1

'J..',

IIII

Synchrony

Figure 1. 3 Bel'//. Train Station (circa 1860-6'» i u«: oftlie first huildingsin Bem 10 he /Jrovided with the /lell' coordillated clocks. '}\I'O clocl:«are (h(lIdy)visible [u«! o)'(:.rthe ova! arches 0/1 the (J/Jellside of/he station. S(lIIHCI';: COI'Y-

RIGHT BClHCI·:ltBIIII.IOTIIEK ilEHN, NI';C. '~'i7~.

Einstein, therefore, was not only surrounded by the technologyof coordinated clocks, he W<lS also in one of the great centers for theinvention, procluctiou, ;lIIcl patenting of this burgeoning Icclmo]-

ogy. Were any other major scientist» whose concern was with basicphysical laws of clcctromuguctism LInd the nature of philosophicaltime also in the midst of this vas! effort to synchronize clocks? Therecertainly was atleast one.

Some seven years before the twenty-six-year-old patent officerredefined simultaneity in his 1905 relativity p,lper, Henri Poincarehad advanced strikingly similar ideas. A cultured intellectual, Poin-

care was widely acclaimed as one of the greatest of nineteenth-century mathematicians for his invention of a great part of topology,

EINSTEIN'S CLOCKS, POINCARf:'s MAPS

Figure 1.4 Neucluitel Master Clocl«. Heau(ilit/ly decorated master docks

were ohjeds of enomum« value and civic {nide. This one, in the center or thedodnllo/':ing regio1l oFSwi(;::erlalld, received its iiuie (rom (/1/ o!Jserwllory atu!then launched its .~igl1(/lsalong telegraflfl Iines. SOIJRCI':: I';WAR(;I-:R, , :';;1.1-:( :n(/(:,.,.,:;

(1<)24),1'· 4'+

his celestial mechanics, his cnormons contributions to the electro-dynamics of moving bodies. Engilleers lauded his writings on wire-less telegraphy. The wider pub] ic devoured his best-selling books Oil

the philosophy of conventionalism, science and values, and hisdefense of "science for science."

For our purposes, one of the most remarkable essays Poincarepublished appeared in January 1898 in a philosophical journal, theReview ofMetaf)hysics and Morals, under the title "The Measure ofTime." There Poincare blasted the popular view, espoused by theinfluential French philosopher Henri Bergson, that we have an

\

Svnclironv 33

Figure 1. 'i Berlin Masler C/()d~. This clod" residi/lg at (lie Silcsischcr ncdlll-

ho(ill Berlill, sent it« tune down 'he 111(11)' tracks emanating [ann (he station.S(lIIRCI':: / :/;;1.1.;( :T/(/( :n":; ("F+), 1'.47' l.

intuitive uuclcrstaucling of time, simultaneity, and duration. Poin-care arcucd instead that simultaneity was irreducibly a convention,

b

an agreement among people, a pact chosen not because it wasinevitably ill truth, but because it maximized human convenience.As such, simultaneity had to be defined, which one could do hyreading clocks coordinated by the exchange of electromagneticsignals (either telegraph or light flashes). Like Einstein ill 1905,Poincare in 1898 contended that ill llwkillg simultaneity a proce-dural concept, the time of transmission would have to be taken intoaccount in allY telegraphically communicated time signal.

Had Einstein seen Poincare's paper of 1898 or a crucial subse-quent one of 1900 before he wrote his 1905 paper? Possibly. While

--------------------------- r-----------------------------


there is no definitive evidence one way or the other, it will, nonethe-less, prove worthwhile to explore the question both narrowly andmore widcly. For as we will see, Einstein need not have read justthose lines of Poincare. Clock coordination appeared in the pages ofphilosophy journals, and even occasionally in physics publications.In fact, clectromagnetic clock coorclination was so fascinating to the[ate-nineteenth-century public that thc subject came ill for close dis-cussion in one of Einstein's favorite childhood books Oil science."In 1904-05, clock-coordinating cables were th ick OIl the ground andunder the seas. Synchronized timepieces were everywhere.

Just as couuncntators have grown used to interpreting Einstein'stalk of trains, signals, and simultaneity as all extended metaphor, aliterary-philosophical thought experiment, there is a similarly rou-tine metaphorical reading of Poincare's obscrvatious.Hcrc too, sup-posedly, stands philosophical speculation, an anticipatory note toEiJlstein's special theory of relativity, a brilliant move by an authorlacking the intellectual courage to purslle it to its logical, revolu-tionary end. So familiar is this story thai it has become a COlllJllO\l-place 10 treat Poincare's insight into eoordinatcd time as if il wereentirely isolated, a philosophical abetcu disconnected from hisplace ill the world. But neither Poincare nor EillStein was speakingin a vacuum about lime.

What, Poincare asks, arc the rules hy which scientists judgesimultaneity? What is simultaneity? His final, most forceful exam-ple turned Oil the determination oflongitude. He begall by notingthat when sailors or geographers determine longitude, they mustsolve precisely the central problem of simultaneity that governedPoincare's essay: they must, without being in Paris, calculateParisian time.

Finding latitude is simple. If the north star is straight overhead,you are on the North Pole; if it is halfway to the horizon, you are atthe latitude of Bordeaux; if it is on the horizon, you are at the lati-tude of Ecuador, on the equator. It does not matter at all what time

Synchrony 35

YOll make latitude measurements- in any particular location theangle of the pole star is always the same. Finding the longitude dif-ference between two points is famously more difficult: it requirestwo distant observers to make astronomical measurements at thesame time. If the earth did not rotate, there would be no problem:you and I would both look up and check which stars were directlyunder the North Star (for example). By checking a map of the starswe could easily find our relative longitudes. But of course the earthdoes turn, so to fix longi lucie differences accurately we must be surethat we arc measuring the position of the overhead stars (or sun orplanets) at thc same time. For example, suppose a map-makingteam ill North America knew tile time in Paris and saw that at theteam's location the SIlII rose exactly six hours later than it had in theCity of Light. Since the earth lakes 24 hours to rotate, the teamwould know that it was soru owhere along a longitude line 6/24(one-fourth or equivalently <)0 degrees) of the way around the worldto the west of Paris. Bul how could the explorers know what time it

was hack in Paris?As Poincare says ill his" Measure of Time," the roving eartogra-

phcr could know Paris lime simply by carrying a precision time-keeping device (r.lirouomctcr] on the expedition, having set it toParis lime. But transporting chronometers led to problems both inprinciple and in practice. The explorer and his Parisian colleaguescould observe an instantaneous celestial phenomenon (such as theemergence of a moon of [upitcr from behind the planet) from theirtwo different locations and declare that their observations weresimultaneous. But this seemingly simple procedure isn't. Therewere practical problems ill using Jovian eclipses. Even as a matterof principle, as Poincare noted, the time would need to be correctedbecause light from Jupiter travels over different paths to reach thetwo observation points. Or-and this is the method Poincare pur-sues - the explorer could use all electric telegraph to exchange

time-signals with Paris:


It is clear first that the reception of the [telegraph 1 signal at Berlin,for instance, is after the sending of the same signal from Paris. Thisis the rule of cause and effect. ... But how much after? In gcneral,the duration of the transmission is neglected and the two eventsare regarded as simultaneous. But, to be rigorous, a little correc-tion would still have to be made by a complicated calculation; inpractice it is not made, because it would be well within the errorsof observation; its theoretic necessity is none the less from ourpoint of view, which is that of a rigorous definition."

Direct intuitions about time, Poincare concluded, are incompe-tent to settle questions of simultaneity. To believe so is to fall into illu-sion. Intuitions must be supplemented by rules of measurement: "Nogeneral rule, no rigorous rule; a multitude of little rules applicable toeach particular casco These rules arc not imposed upon us by them-selves, and we might amuse ourselves in inventing others; but theycould not be cast aside without greatly complicating the laws ofphysics, mechanics, and astronomy. We choose these rules, therefore,not because they arc true, but because thcy are the most conve-nient.'?' All these concepts-simultaneity, time order, equal dura-ticms-were defined to make the expression of natural laws as simpleas humanly possible. "In other words, all these rules, all these defin-itions are nothing but the fruit of an unconscious opportunisrn.l'"Time, according to Poincare, is a convention-not absolute truth.

What time do the map makers make it out to be in Berlin whenit is noon in Paris? What time is it down the line when the trainpulls into Bern? In posing such questions, Poincare and Einsteinseem, at first glance, to be asking questions of stunning simplicity.As was their answer: two distant events are simultaneous if coordi-nated clocks at the two locations read the same - noon in Paris,noon in Berlin. Such judgments were inevitably conventions of pro-cedure and rule: to ask about simultaneity was to ask how to coor-dinate clocks. Their proposal: Send an electromagnetic signal from

Synchrony 37

one dock to the other, taking into account the time the signal takesto arrive (at approximately the speed of light). A simple idea ofbreathtaking consequences for concepts of space and time, for thenew relativity theory, for modern physics, for the philosophy of con-ventionalism, for a world-covering network of electronic navigation,

for our vcry model of secure scientific knowledge.This is my quarry: how, at the turn of thc century, was simul-

taneity actually produced? How did Poincare and Einstein bothcome to think that simultaneity had to bc defined in terms of a con-ventional procedure for coordinating clocks by electromagnetic sig-nals? Addressing these questions demands far too wide a scope tobc captured by a biographical approach, though there are, to besure, too many biographics of Einstein and nol cnough of Poincare.Nor is this book a history of philosophical ideas of time, a task thatcould easily takc us back before Aristotle. It is not a comprehensiveaccount of the in tricatc development of timepieces, even electricones. And it is not a complete history of the Illany broadly sharedconcepts of ninetccuth-century electrodynamics that Poincare andEinstein appropriated as each strugglcd to reformulate the electro-

dynamics of moving boclies.Instead, this is a slice through layers of physics, technology, and

philosophy that cuts high and low, an exploration of synchronizedclocks crisscrossing back and forth between the wiring of the oceansto marching Prussian armies. It reaches into the heartland ofphysics, through the philosophy of conventionalism, and backthrough relativistic physics. Take hold of a wirc in the late-nine-teenth-century telegraph system and begin to pull: it takes take youdown and across the North Atlantic, up onto pebbled beaches ofNewfoundland; it tracks from Europe into the Pacific and up intoHaiphong Harbor; it slides along thc ocean floor the length of WestAfrica. Follow the land-based wires and the iron and copper cables;they lead lip into the Andes, through the backeountry of Senegal,and clear across North America from Massachusetts to San Fran-


cisco. Cables nm along train lines, under oceans, and between thebeachfront shacks of colonial explorers and the chiseled stone ofgreat observatories.

But wires for time did not arrive on their own. They came withnational ambitions, war, industry, science, and conquest. They werea visihle sign of the coordination among nations in conventionsabout lengths, times, and electrical measures. Coordinating clocksin the nineteenth and twentieth centuries was never just about a lit-tle procedure of signal exchange. Poincare was an administrator ofthis glohal network of electrical time,Einstein an expert at the cen-tral Swiss clearinghouse for the new clcctrotcclmologics. Both werealso riveted by the electrodynamics of moving bodies and fascinarcrlhy philosophical reflections on space and time. Unclerstanding thisworld-ern bracing synchronization will take us some way towardunderstanding what is modern about modern physics and abouthow Einstcin and Poincare stood at crossing points of their respec-tive ruodcrnitics.

Surely, we learn from the astonishing contrast between Newlon'sdistant seventeenth- and Einstein and Poincare's turn-of-the-twentieth century concepts of time. Their two conceptions stand asmonuments to a clash between the early modern and the modcru:on the one hand, space and time as modifications of the sensoriumof Cod; 011 the other, space and time as given hy rulers and clocks.But the distance between 1700 and 1900 should not eclipse thenear at hand. It is the near at hand that interests me-the dailyworld of 1900 in which it became usual, a]J(1not just for Poincare

and Einstein, to see time, conventions, engineering, and physics asof a piece. For those decades it made perfect sense to minglemachines and metaphysics. A century later that propinquity ofthings and thoughts seems to have vanished.

Perhaps one reason for the difficulty we have in imagining scienceand technology so caught up with one another is that it has becomehabitual to divide history into separate scales: intellectual history for

;1

Synchrony 39

id".I'> that are or aim to be universal; social history for more localizedcb·,:;cs, groups, and institutions; biography or microhistory for indi-viduals and their immediate surround. In telling of the relationlxIwcen the pure and applied, there are narratives that track abstractill,:IS down through laboratories to the machine-shop floor and intoeve-ryday life. There are also stories that run the other way, in whichtlH daily workings of technology are slowly refined as they shed theirmateriality on the way up the ladder of abstraction until they reachtlHOly-from the shop floor to the laborat-ory to the blackboard, andeve-ntually to the arcane reaches of philosophy. Indeed, science oftendocs function this way: from the purity of ;1Il etherial vapor, ideasnuy seem to condense into everyday matter; conversely, ideas seemto sublime from the solid, quotidcan world into air.

But here neither picture will do. Philosophical and physicalreflections did not cause the deployment of coordinated train andtelegraph time. The technologies were not derivative versions of anabstract set of ideas. Nor did the vast networks of electro-coordinatedclocks of the late nineteenth century cause or force the philoso-phers and physicists to adoptthe new convention of simultaneity.No, the present narrative of coordinated time fits neither of thesemetaphors of progressive evaporation or condensation. Another

image is needed.Imagine an ocean covered hy a confined atmosphere of water

vapor. When this world is hot enough, the water evaporates; whenthe vapor cools, it condenses and rains down into the ocean. But ifthe pressure and heat arc such that, as the water expands, the vaporis compressed, eventually the liquid and gas approach the samedensity. As that critical point nears, something quite extraordinaryoccurs. Water and vapor no longer remain stable; instead, allthrough this world, pockets of liquid and vapor begin to flash backand forth between the two phases, from vapor to liquid, from liquidto vapor-from tiny clusters of molecules to volumes nearly the sizeof the planet. At this critical point, light of different wavelengths


begins reflecting off drops of different sizes-purple off smallerdrops, red offlarger ones. Soon, light is bouncing off at every possi-ble wavelength. Every color of the visible spectrum is reflected as iffrom mother-of-pearl. Such wildly fluctuating phase changes reflectlight with what is known as critical opalescence.

This is the metaphor we need for coordinated time. Once in agreat while a scientific-technological shift occurs that cannot beunderstood in the cleanly separated domains of technology, science,or philosophy. The coordination of time in the half-century follow-ing 1860 simply does not sublime ill a slow, even-paced processfrom the technological field upward into the more rarified realmsof science and philosophy. Nor did ideas of time synchronizationoriginate in a plUe realm of thought and then condense into theobjects and actions of machines and factories. In its fluet-uationsback and forth between the abstract and the concrete, ill its varie-gated scales, time coordination emcrges in the volatile phasechanges of critical opalescence.

"lo dig into the records of <II most allY town in Europe or NorthAmerica - indeed, far beyond both - reveals the struggle 10 coordi-nate time during these years of the late nineteenth century, Therelie the yellowing data of railroad superintendents, navigators, andjewelers, but also of scientists, astronomers, cngineers, and entre-preneurs. Time coordination was an affair for individual schoolhuildings, wiring their classroom clocks to the principal's office, butalso an issue for cities, train lines, and nations as they soldered align-ment into their public clocks and often fought tooth-and-nail overhow it should be done. Step back to the archives of central govern-ments and the cast of characters grows wider and wilder: anarchists,democrats, internationalists, generals.

Amidst this cacophony of voices, this book aims to show how thesynchronizing of clocks he came a matter of coordinating not justprocedures but also the languages of science and technology. Thestory of time coordination around 1900 is not one of a forward

Synchrony

111.111"11 of ever more precise clocks; it is a story in which physics,'"1',illeering, philosophy, colonialism, and commerce collided. At1 In)' moment, synchronizing clocks was both practical and ideal:;',1111 a-percha insulator over ironclad copper wire and cosmic time.:;() variously construed was time regulation that it could serve in( .crrnany as a stand-in for national unity, while in France at thes.une moment it embodied the Third Republic's rationalist institu-

Iionalization of the Revolution.My aim is to pursue coordinated time through this critical

opalescence, and ill particular to set l Icnri Poincare and Alhert }':ill-stein's revamped simultaneity in the thick of it. I<nlering the sites oflime production <\11(1 the lanes of its distribution will bring us repeal-edly to two crucial locations in the binding of clocks that joinedEinstein's and Poincare's transcendent metaphors of clocks andmaps to altogether literal places: the Paris Bureau of I .ougituclc ant!the Bern Patent Office. StaIldillg atthose two exchanges, Poincareand Einstein were witnesses, spokesmen, competitors, and coordi-nators of the cross-flows of coordinated time.

()rder ofArgumellt

Because the fate of coordinated time cannot be tracked from anuclear group of railroad managers, inventors, or scientists ill a sim-ple widening circle, our story will switch scales back and forthbetween local and glohal narratives. I W<IIltto introduce Poincarein chapter 2 ("Coal, Chaos, and Convention") in a way that may hesomewhat unfamiliar. Who would guess from Science and Hypoth-esis, his best-selling book of 1902, that he had trained as a miningengineer and served as an inspector in the dangerous, hard-pressedcoal mines of eastern France? Or that for decades he had helpedrun the Bureau des Longitudes in Paris, serving as its president in1899 (and later in both 1909 and 1910)? Or that he co-edited andoften published in a major journal on electrotechnology that ran

f' ..r--EINSTEIN'S CLOCKS, POINCARE'S MAPS

abstract articles on fundamental issues of electrodynamics next topieces about undersea cables and the electrification of cities?

Understanding the transformation of timeits radical secular-ization - requires a relocation of Poincare, whose conventionaliza-tion of simultaneity is flattened into two dimensions if he is seenpurely as a mathematician-philosopher or mathematical physicist(though he was certainly both). More is needed than a simple addi-tion of a side-interest in engineering. Poincare figures here not as afree-floating monad who seized this or that "resource" from philos-ophy, mathematics, or physics to solve particular problems. Instead,throughout this book I want to situate Poincare in the midst of pow-erful series of moves that, at a few critical intersections, formedroughly consistent ways of acting within physics (or philosophy orengineering). It is not that a preformed Poincare plucked meredetails of procedure from his alma mater, Ecole Polytechnique, butinstead that he was also very much its product. As he put it, he andhis colleagues proudly bore Polytcclmiquc's "factory stamp." Chap-tcr 2 is about that stamp, under which it was as reasonable for Poin-care to assess milling accidents as to augur the stability and fate ofthe Solar System or to generate abstract mathematics. It takes usclose-in to Poincare to capture this wider link between the materialand the abstract And that bond is crucial if we are to understand insubsequent chapters the multiple ways ill which Poincare insistedon examining the concept of simultaneity under the different butintersecting lights of physics, philosophy, and technology.

But the "factory" of Poincare's Polytechnique education-alongwith the mining and mathematical years that followed- is still notyet a wide enough terrain on which to locate the secularization oftime coordination. That larger territory extended even beyondFrance, to the colliding networks of wires and rails that the GreatPowers were erecting at breakneck speed. Matching these systemsat their often-eontesteel boundaries could only be accomplished bycodes and conventions that, in the 1870s and 1880s aimed some'-, ,

Synchrony 43

1IIIIespainfully, to mesh the collision of incompatible length andlillie standards. So in chapter 3 we will pull back from the close-inILime of chapter 2.

Chapter 3, "The Electric Worldmap" is after this vastly largerI imescape of earth-covering networks- clashing empires of time. InIhose late-nineteeIlth-eentury decades, nowhere was the demandForworld-covering conventions more apparent than in the drawingof global maps. Confronting a staggering increase in the volume oftrade during these years, navigators were increasingly frustrated bymaps with differing and often unreliable longitudinal grids. So toowere colonial authorities, as they stepped up the pace of the con-quest of new lands, the exploitation of resources, and the buildingof railroad lines. All demanded precise and consistent geodesy.These various demands carne to a head in all 1884 meeting at theAmerican Stale Department, when twenty-two countries foughttheir way toward a single prime meridian-thc zero point oflollgi-tude-to he placed in Crccnwich, 1'~Jlglalld.Frustrated, indeedinfuriated by the arrogation of that global zero-arc to the hub of theBritish I':mpire, the French delegation lobbied for a decimalizedtime, dctcrmined to put a French stamp of rational cillightelllllcnt011 the new world order of clocks and maps.

Chapter 4, "Poincare's Maps," picks up at an intermediate range,at the height of this French campaign ofthe 18<)()s to rationalizetime-in which Poincare played a determinative role. Chargedwith the evaluation of the longstanding French revolutionary pro-posal to decimalize time, and, with it the clivisions of the circle,Poincare and his intcnninisterial committee encountered firsthandthe competing proposals for how to conventionalize the measure oftime. Indeed, it was precisely in this period that Poincare beganserving as a senior member of the French Bureau of Longitude, theagency charged with coordinating clocks around the world to pro-duce the most accurate of maps. Here, in Europe, Africa, Asia, andthe Americas, in the world of precision-synchronized times and geo-

44EINSTEIN'S CLOCKS, POINCARI~'S MAPS

desic maps, we can finany confront Poincare's philosophical pro-posal of 1898 to treat simultaneity as a cOllvention. If simultaneitycould only be specified by agreement on how to synchronize clocks,then a felicitous precedent would be to coordinate them exactly asdid the telegrapher-longitude finders. This move-at once a state-ment of up-to-date cartography and of the metaphysics of time - isof cxtraordinary importance. Newton's ahsolute, theological timehad no place; instead there stood a IJTocedure. l':nginecrillg com-

mon time stood where Cod's ahsolute time had heen.Nothing in Poincare's 1898 convcntionali/.ation of time directly

addressed either electrodynamics or the principle of relativity. Thatconnection carne only in December 19()(),as Poincare reexaminedearlier work of the Dutch physicist, Ilcndrik Antoon I,orcutt .. Backin 1895, I ,orentz ha(l advanced a theory of the electron that incor-porated the following extremely clever idea. III the rest [rnmc of theether, where the cquatiolls govcrning eleclric and magnetic ficlds(Maxwell's eqnatiolls) were sUpposc(llo hold good, 1 .orcntz spoke of"true time," time. Suppose some object, such as an iron hloek, weremoving in this ether rest frame (traveling throngh the ether) and t)",1"Maxwell's equations gave a detailed description of the electric and

J1Iagnetie fields ill and around the iron. 'low should the physics hedescribed from a frame traveling with the iron block? It scemed as ifthe physics would suddenly become vastly more complicated as onetried to take account of the fact that the moving frame was racingthrough the ether. Bnt Lorentz found that he could simplify the equa-tions, making them as simple as in the ether rest frame, if he rede-fined the fields and the time variahle. Because he had redefined thetime of an event so that it depcnded on where the event took place,

Lorentz called t1oc;!1 "local time" (Ortszeit), the same word used ineveryday life to describe the (longitnde-dependent) time of Leiden,Amsterdam, Of Djakarta. The crucial point was this: Lorentz's localtime was purely a mathematical fiction used to simplify an equation.

Poincare first published a time paper in January 1898 in a phi-

I

I

Synchrony 45

Iosophy journal. His goal was to show that clock coordination bymeans of electric telegraph exchange fonned the basis for a con-ventional definition of simultaneity. It was tcchnologieal and philo-sophical and had strictly llothing to do with the physics of movingbodies. By contrast, in his second move (]9{)()), Poincare dramati-cally extended Lorentz's tlo,-al 10 the physics of altogcther real (notmathematical) moving frames of reference. True, Poincare dideverything possible not to call attention to the difference betweenhis "apparent" local time and Lorentz's mathematical one.Nonetheless, the concept had moved: ill Poincare's hands, localtime lost its fictional status alld became the time that movina-framcb

observers would show on their clocks .rs they corrected for the factthat sigllal exchange would heat ;lgaillsl or run with all ether wind.

With Poincarc's ]<)()() il itcrprclntiou of local time, suddenly all

three series-physics, philosophy, and geodesy-intersected in thecoordination of clectrosynehroni/.ed clocks. Agaill responding toLorentz, Poincare made his third move with synclnoni:l.ecl clocks in190)-()(). lu 1904, Lorentz had modified his local time, [1",a], tomake the equations of electrodynamics in the fictional movingframes even more similar to the "true" ether rest frame. Poincareseized I .orcntz's result, adjnsting (inter alia) the definition of]oealtime 10 make the mathematical correspondence exact between fie-tionalmoving [r.uncs and the true resting one. But the crucial pointfor Poincare W;lSnot that he had sl igh t·lylllodified I .orcntz's theory.Rather, it was this: Poincare had demonstrated that clocks coordi-nated as they moved through the ether would give exactly Lorentz'snew local time and would do so For real observers moving in thatframe. The relativity principle held good, even while Poincare con-tinued to oppose "apparent time" to "true time." By 1906, Poincarehad placed the light-coordillation of clocks front and center forthree projects fundamcntal to modern knowledge: technology, phi-

losophy, and physics.'1 'he French polymath had begun with geodesic time, shifted reg-

i

i:,. i

EINSTEIN'S CLOCKS, POlNCARf:'s MAPS

isters to his antimetaphysioa], conventional time, and then clearedhis way to the physics of local time and relativity. 'J 'hroughout hisphysics- but also throughout his philosophy, technology, and pol-itics-Poincare saw his world as improvable through rational, intu-itive intcrvcntion; he reveled in pushing a problem into "crisis" andthen resolving it. IIis was the optimism of a progressive engineerwilling to reassemble major struts and cables of the structures hetackled, but insisting that the built world of "om fathers" bcrespected, incorporated, improved.

III chapter 5, we turn 10 "I':i1lstcin's Clocks." Not to the prophetic,world-famous, and lll~lthelllalically inclined I':instcin of 1033 or1053, but 10 Einstein the tinkerer. souping up homcbuilt instru-mcnts ill his Kralllgasse aparhucnt, Ihe I':imlein riveted by theclesig\l of ruuchincs .uicl thc analysis of patents. This was neitherthe suddenly celebrated II:insteill of posl-World War Ilkrlillllor theabstracted, hermil like elder I<inslein of Princeton, but the thor-oughlyengaged 19()5 youth of Bern. '!'llOlIgh its technological infra-structure C~lI11Claic, when Switzer\;lIlci inaugnratec\ its rail,tclegraph, and clock nclwork, syuchrouizcd tiuic there was a verypublic affair-am] Bern was ils center. l'rom Ikm electric lillieradialed outward, 10 Ihe clock indllslry of the Jura regioll, to thepublic display of mb~1I1clocks, to thc railroad, and, of course, to thepatenting of synchronized clocks.l<instein was ill the thick ofit.

Yet Einstein's palh 10 coordinated time was very different fromPoincare's. Einstcin's vision was less ameliorist. lirallling himself as

a heretic and an outsider, I<illstcin scrutinized the physics of thefathers not to venerate and improve, hut to displace. I':instein sawthe coordination of lime, and indeed his physics and his philosophymore generally, as part and parcel ofthe same critical reevaluationof the founding assumptions of the disciplines. ]':instcin did notmove methodically from one aspect of lime coordination toanother. Most elements of his approach to relativity theory werealready in place before he even touched the problem of time; for

Synchrony 47

example, by 1901 he had already dismissed the ether that Poincarehad struggled so hard to maintain. Einstein's engagement with crit-ical works at the boundary of physics and philosophy were hy thenlong-standing, and at the patent office, be ane! his fellow inspectorshad been dissecting the machinery of time for three years. So inMay 1905, when Einstein began defining simultaneity hy way ofelectroeoorclinated clocks, it was not, as it was for Poincare, a mat-ter of distinguishing "apparent" from "true" time alongside a quasi-fictional ether. For Einstein clock coordination was the turn of thekey that would at last set in motion the theory machine that lie hadstrucrcrled for a decade to assemhle. There was no cther; there were

bb

actual fields and particles, and there were but rcal tiuics given by

clocks.In the final chapter, "The Placo of Time," it is possihle to see

how the work of Einstcin and of Poincare could be bolh cxlraordi-nurily close yet far apart, l'rcciscly ill the uneasy rclalior: betweentheir eompcting uses of coordinated time, they stand not as pro-gressive against reactionary approaches to nature, but as two strik-ingly different visions of whatmade modern physics moclcm - theconsummate Polyleehnician's hopeful reforms against an outsider'srebellion against foundations. Yet despite their differences, bothwere grappling with the same extraordinary insight into clcctroco-ordinatcd time, and ill so doing botl: men stood at the crossing oftwo erreat movements. On ouc side lay the vast modern tcehnolog-

b

ical infrastructure of trains, shipping, and telegraphs that joinedunder the signs of clocks am] maps. 011 the other, a new sense ofthe mission of knowledge was eIllerging, 011ethat would define timeby pragmatism and conventionality, not by eternal truths and theo-logical sanction. Technological time, metaphysical time, and philo-sophical time crossed in Einstein's and Poincare's electricallysynchronized clocks. Time coordination stood, unequaled, at thatintersection: the modern junction of knowledge and power.

- ,.

-------- --- ----------------------------------

Chapter 2

COAL, CHAOS, AND

CONVENTION

HIE DRAMATIC success of Poincare's 1902 collec-tion of philosophical-scientific articles, Science andTfy/)othesis, his position in French intellectual life was

unmatched. Standing at thc pinnacle of mathematics, physics, phi-losophy, he was scientific rapporteur of a major scientific expeditionand had served as president of the Bureau ofT ,ollgitudc. llc cmlxxl-icd the successful Polytccluiician, garnering all early reputation illmathematics and then proceeded c1ircdly to the llilty-gritty of mill-ing cnginccring. Here is our central thcllle-inieriwillccl ahstrac-tion and concreteness-far more closely bound for Poincare alld hiscontemporaries than scholars and engineers of later times everexpected. No wonder that the fonner students of Ecole Polytcch-niquc asked him 10 use their annual address to reflect "Oil the PariPlayed by Polyteclmicians in the Scientific Work of thc XIXtll Cell-tury." As he prepared that 25 January 1903 lecture, Poincare siftedthrough the presentations of recent honorees. "I see alllong my pre-deccssors," he told his classmates and colleagues, the "dean of ourgenerals, numerous ministers, scientific engineers, the director of alarge company, those who conquercd our overseas empire andthose who organized it, and those who brought from the earth, threeyears ago, the ephemeral splendors of the [Universal Exposition onthe 1 Champ de Mars." How, Poincare asked, could a single educa-tion have produced such a combination of scientists, soldiers, andengineering entrepreneurs?'

Coal, Chaos, and Convention 49

At a time when the division of labor had penetrated science,Poincare wondered aloud what the Ecole had done to hold togetherthose disparate specializations. True, he allowed, the competitiveexams selected giftcd students with diverse aptitudes; true too thatthe traditional "nobility" of the school served as an inspiration("Those who fight for their country, like those who combat for truth .. . .") But somcthing more must be at work to produce a worldvicwthat pervaded such scattered pursuits. Perhaps it was a rubbing ofshoulders-certainly chemists, physicists, and mineralogists all ben-efitted from the high mathematical culture of their formativeschooling. Even among the most abstract of Polylecllllique matlic-maticians, moreover, "we see the constant concern with applica-tions" -not just among the obvious figurcs who had madeapplications their metier, but also ,lJllOllg the most scholarly of theschool's products, including one of the most powcrht] mathemati-cians in the history of Poly technique, Augustin Louis Cauchy.Cauchy, despite his well-known opposition 10 a socially engagedmathematics, drew slTollg1y on mechanics. Poincare tlicu invokedhis own teacher, Alfrcd Cornu, who liked to repeat that mechanicswas the cement thai held together the various parts of the Poly-tcclmiciau's soul. "There it is," he concluded, "that factory stampthat 1 was looking for; om physicists, our mathematicians arc all abit mechanicians."!

If the Poly technicians= Poincare foremost among them-emerged from their training with the "factory stamp" of mechanicsimprinted on their outlook, this already differentiated them fromscientists trained in the universities. But for Poincare that was notall. University professors fretted about the unity of science; Poly-technicians had another concern, that of joining thought withaction. It was action, Poincare insisted, that inoculatecl Poly tech-niquc's graduates against the melancholy that assailed many uni-versitv researchers over the purported failure of science. That bondbctw~en the abstract and the concrete was the most essential feature


of the "factory." Science changed; so too did the world. Poincarewas fully prepared to allow the education to evolve: "The Ecolemust transform itself bit by bit like all things human, but it must nottouch that which makes its soul, the alliance of theory with practicemust not bc broken; it must not be mutilated, for without it thcrewould only remain a hollow name."

When Poincare had come to Polytechniquc back in 1873, theproblem of balancing pure knowledge against useful applicationswas gripping France as never before. Just two years earlier, Germanyhad pounded France into a humiliating defeat, leaving Germanywith new lands, united, euphoric, building scientific institutes andmonuments to hail the victory.'! France, now minus Alsacc-Lorraine, struggled desperately to understand the roots of its cata-strophic defeat. The technical infrastructure of the Statc came in toquestion. hook after book lamented the sorry state of the country'srailroads and, more generally, its inadequate preparation for ;1 newage of fighting. But more than any particular piece of tcchnology,eri tics dissected the institutions of technical learning, wh ichappeared to need reconstruction, and fast. None of these institu-tions had greater weight than Ecole Polytechniquo, the GrandeEcole Poincare hac! just entered.

Polytcchnique, founded in 1794-,had no parallel in the UnitedStates, Britain, or Germany. Built to train an elite corps of enginccrsable to mold the military into a force of modernity by using anenlightened science, Polytechnique was to be a scientific institutionwhere mathematics, physics, and chemistry would prosper withmathematics above alL Its students chosen by a competitive exam-ination (the famous COIlCOllfS), Polytechnique produced a fraternityrigorously schooled in a mathematics-based engineering. Aftcr theirgraduation, generations of these students joined the highest levelsof the State's administrative structure, overseeing at first the newnation and, later, in the nineteenth century, an empire. Part

--_._---_._ .._._ .._.-

51Coal, Chaos, and Convention

Oxbridgc and part Sandhurst? Half MIT, half West Point? Snchcomparisons fail. The Polytechnician was far more scientific thanhis British equivalent school cd in the Classics, more mathematicalthan a rising American enginccr, and less inclined than an eliteGerman physics student toward precision laboratory work. Poly-technique was, and remains, a unique institution, possessing by the1870s a mythological status ill France.

For the first years after its founding, the revolutionary engineerand mathematician Gaspard MOllge used geometry to successfullybind the conflicting demands of practical engineering andadvanced mathematics. Projective gcometry, he believed, trainedthe mind, revealed scientific truth, and sculpted stone, wood, andfortifications. Over the course ofthe early decades of the nineteenthcentury, however, Monge's progrml1 began to falter. Mathematics,significantly propelled hy the conservative Cauchy, self-consciouslyhegan to shed its ambition of joining the world with the mind. Sci-ence ascended. applications retreated-a trend encouraged hy theconstruction of new, more specialized engineering schools.'

When Paris fell to the Prussians, the French found no shortageof institutions to blame. Pasteur, joined by a chorus around France,lent his prestigious voice to those who saw the German triumph asa failure of French science. At Polytechniquc the charges echoedloudly - it was a major center of scientific engineering and the stu-dents were already in uuiforiu. Alfred Cornu, <ol fonncr student ofthe school who had returned as a rising star alllong the physicists,articulated the school's position after the disaster, one delicately bal-ancing science and worldly engagement. lle became, so to speak,an ideal type of the new' J 'bird Republic Polytechnician, gliding eas-ily from the pure to the applied. As Poincare later remarked withadmiration, Cornu's work traversed a wide field of optics, bringingnew instruments and techniques not only to physicists but alsoto astronomers, meteorologists, and even clockmakers. Having


designed and built at Nice an extraordinarily precise astronomicalelock with a massive pendulum, Cornu traveled there every year toperfect his clock. In addition, Cornu developed a detailed mathe-matical theory of the coordination of elocks by the exchange of elec-tric signals.' Neither his joining of the pure to the applied nor hisspecific interest in electric time coordination was lost on Poincare.

Cornu's course was filled with stylized demonstrations of partic-ular laboratory phenomena. Although he did not train his studentsto do the handwork themselves, experiments were for Cornu a vitalpart of science-its alpha if not its omega. Nor was Cornu alone: heand his colleagues made sure that a young scientist emerging fromPolyteclmique in the 1870s did so with a deep respect for experi-ments (though no great familiarity with the manipulation ofdevices, complex measurements, or data analysis). Instead, studentslearned to see the great mathematical structures that embraced dataas the endpoint of scientific work. 'I 'hey learned to put little faith inthe literal truth of particular assumptions about atomism or electricfields. It is tclling that when Polytechique filled a position in chem-istry, the faculty aimcd above all to maintain the balance betweenthose who believed in atoms and those who die! not."

This was the world that Poincare entered in November 1873.Competitive, alert, engaged, Poincare watched his fellow studentslike a hawk, writing home about his rivals' grades, occasionally com-menting 011 student hazings or musing over the political machina-tions of the Jesuits. Mechanics seized his attention, and in thisall-important subject his grades rose rapidly toward nineteen ortwenty (out of a possible twenty). With pride, he wrote home that hehad found a simpler demonstration than the one his professor hadpresented in class. He wrote, too, of his progress in both technicaland freehand drawing. When, to the surprise of the workers, he anda group of Poly technique students visited a local crystal factory, Poin-care, told of his fascination with the workers' dexterity and the tech-nology of their Siemens ovens." Even as a student, Poincare


I «( )i~llizeclthe "factory stamp" of Polytechnique. But in the account'('I,orled to his mother, the teaching held none of its later glow:

It is as if we are in an immense mach ine whose movement wemust follow on pain of being passed by; we have to do what 20generations of X [Polytcchniquc] did before \1S and what 2n + 1generations of conscripts will do after us. Ilere yO\! use only twofaculties of yom intelligence: memory and elocution; understand-ing a course is something anyone can do with some work and thatis why everyone call get me to cram if they want. ... T am there-fore condemned to this choice: give up personal work or slay ill Illyplace; as this altcrnntivc lasts only two yens, the choice [ havemade is not ill doubt: because the aclv;mtage 1 will take from lilyposition is inconuncnsurahlc; but it has to he guarded .md lswilch-ing to l<nglish:1 this is the question."

On Cornu's clcarlr, Poincare spoke, quite personally, of howmuch Cornu would he mourned, as a friend, an advisor, alld as amaster leacher-and Poincare's career followed in many respects ;1

similar path. Both had been star students at Poly technique, botl:had gUile on 10 the Ij:cole des Mines, both accepted the call backIoPolytcchuiquc to teach, both served the State in engineering-administrative capacities. The lessons stamped on them were deep.Poincare, Cornu, and their contemporary Poly technicians main-tained a lifelong commitment to the link between abstract and con-crete knowledge. It was a testimony to their training that both servedon the board of the Bureau of Longitude and together along withtheir fellow Polytcchuicians, drove a myriad of technologically pro-gressive projects, from the electroteehnical journal they helped run

to the scientific commissions 011 which they served.Of course, the relation between pure science and engagcd

technology was not frozen once and for all at Poly technique-oranywhere else. It was much more like a vast and slowly undulating

·-.---~~--" ." ...~..--------------


sea, sometimes with olympian science looming high above a troughof technology; at othcr times with a triumphalist military and indus-trial tcchnology cresting over the claims of purc knowledge. For abrief moment after the great defeat of 1871, Cornu and his alliesflattened this sea into a smoother surface of roughly equivalentclaims, at least around Polytechnique. Inside this "immensemachine" where technology and mathematical physics circulatedwith equal force, Poincare became Poincare.

Coal

Before turning to clocks it is worth exploring two moments early illPoincare's career, for they tell us a great deal about who Poincarewas, how he thought, and where he stood in thc turbulent flux ofteclmologies and sciences. As a shorthand, we may think of thesetwo episodes as moments of coal and chaos, for during the firstdecade of his work-from the late 1870s to 1890 or so~Poincarewas grappling not only with a new, wildly unstable mechanics ofthe Solar System but also with the grubby, dangerous world of min-ing in late-nineteenth-century France.

Craduating in 1875, Poincare followed tradition by moving withthe other two valedictorians of his class to the Ecole des Mines.There, the three-i-Poincarc, Bonnefoy, and Petitdidier- began theirstudies ill October. III Poincare's mentor, mathematician Ossian Bon-net, tried to get Poincare's course load reduced because of his math-ematical work, but the School of Mines would hear nothing of it.So Poincare finished his mathematical thesis while lcarning the insand outs of ventilator shafts. Geological fieldwork took him, forexample, to Austria and Hungary in 1877.

Poincare's cultural circle was also expanding. His adored youngersister, Aline, introduced him to the philosopher Emile Boutroux,whom she would eventually marry. Boutroux and Poincare imme-diately began discussing philosophy. Having studied in Heidelberg

55Coal, Chaos, and ConventiO/l

l·I '( .rO;1/-

I~~ •.. ,,'\ ~"~.'...t:;

Figure 2.1 Poincare's Curre ofHaflfliness (with detail). This letter, writtenby Poincare to his mather during the sununer of 1879, includes both a haiul-drawn map of his geological travels and a geometrical curve showing the "lim-its of his joy" in "normal times," "yesterday," "in trains," and "right now"SOl/ReI':: ARCHIVES IiJ':NRI I'OINCAIU::, 1',1021.

until the Franco-Prussian War, Boutroux had made his own theGerman philosophical commitment to join thc humanities and thesciences. Productive, enthusiastic, religiously inclined, Boutrouxargued (following the Kantianism he imbibed in Hcidelberg) that

EINSTE:IN'S CLOCKS, POINCARE:'S MAPS

much in the scientific domain was more of the mind than "outthere." Through Boutroux, Poincare came to meet other philoso-phers, including the philosophically inclined mathematician JulesTannery. The group did not share Boutroux's religiosity (Tannerywas an ardent, secular Republican), but all sought a middle waybetween science as simple observation ancl science as mental ere-arion. Poincare seemed to find the view conzenial: for years he toob ' . "

argued that science needed just such a mix of induction and deduc-tion. As Poincare put it in a letter to Aline sometime around 1877,observation and induction ought be treated with "reserve." Headded, "you will say induction can only give us knowledgc of thesame nature as the observations themselves, observation cannotteach us anything about Substance ... it call only show us the phe-norncnon hy itself; and not even the phenomenon in itself; but onlythe sensations that it produces in us." Experience, Poincare told hissister, could never be sufficient to ground the full gCllerality ofknowledge. "Eh what do you want me to clo about it; let us alwaystake what belongs to us, ami as for the rest, we must rcsign ourselvesto admit that it will remain to us forever but a dead letter."!'

Anothcr of Poincare's fellow Polytcclmicians, the philosopher-scientist Auguste Calinon, hcld a similarly cautious view aboutknowledge that "did not belong to us." In 1885, Cal inon publisheda treatise on the foundations of mechanics and gcometry. He andPoincare seemed to have been on good terms; when they saw eachother in early August 1886, Calinon followed up with a copy of hisrecent Critical Study or Mechanics. It began, straightaway, with acautionary note about absolutes in space and time:

Many authors, in mathematics as in philosophy, accept the notionof absolute movement as a first principle (idee premiere). Thisopinion has been much contested; ... it is worth remarking thatfrom the point of view of rational mechanics, this question has noimportance; the movement of a point, considered in isolation, is a

Coal, C liaos, and Convention

purely metaphysical conception, because, even allowing that onecould imagine such a movement, it is impossible to certify it andto determine its geometric conditions, for cxa tuple, thc form of itstra jectory. 11

57

II, I

, I

, !

Because of the inaccessibility of the absolute, Calinon would onlyspeak of relative movement. Similarly, he suggcsted that simul-taneity too had to be accessible: two moving stellar objects at par-ticular positions would he called simultaneous only if one saw them"at the same time." For Calinon, the 11\110:111 registTation of the eventswas so important that he wantedto take into account the time ittook for the sensations to be registcrcd by the brain: "The very ideaof time is therefore inherentto the Illude hy which our brain func-tions and has no sense except for minds made like ours."" A Kan-tianism, no doubt, hut onc that was distinctly more psychological(or psychophysiological) than that which dominated the German-speaking scene. Apparently Poincare wrote back almost immedi-ately addressing the work point-by-point. Though that letter is lost,Caliuon's reply survives, from which it is clear that Poincare's veryfirst comment addressed the notion of "at the same time." It appearsthat Poincare agrecd that "it is hy our sensations alone that we judge

simultaucity or successiveness."!'Poincare's philosophical speculations about thc limits of scien-

tific knowledgc, the restricted power of observation, and the activerole that the mind must play in making science, were themes thatremained with him for the rest of his life. But none of these meta-physical musings interrupted either his mathcmatica] work (he sub-mitted his mathematics thesis in 187~) or his work on mining. InMarch 1879, Poincare received his degrce of "ordinary engineer"from the Ecole des Mines, arriving 011 3 April for his new positionat Vesoul, where his inspections hegan the next clay and continuedintensively over the following months. On 4 June 1879, he reportedthat Saint-Charles had just about exhausted its pits- "veins both

ErNST'EIN'S CLOCKS, POlNCARl~'S MAPS

poor and irregular." On 25 September at the pits of Sainte-Pauline,he focused on aeration, removal of gas, and sources of water- justthe sort of engineering tasks that Ecole des Mines had emphasized.A month later, 011 27 October, Poincare arrived at the pits of Saint-Joseph to inspect the smelting works. His last mining visit took placeon 29 ovember 1879.

But one stop on the itinerary, at Magny, was anything but rou-tine. In the evening of 31 August 1879, at 6:00 P.M., twenty-two mencleseenc\cd for their shiftwork into the coal pits About 3:45 A.M. anexplosion rocked the mine, instantly blowing out the miners' lamps.Two miners in the cage were violently shaken, two were knockedinto the sump (which, luckily, was covered with a board about fivefeet down). These fom survivors staggered to the earth's surface.Master miller [uif, who had been off duty near the pits, immediatelyled the men hack into the mine, where (hey discovered a pile ofclothes hurning without flames like a piece of smoldering punk. [uifheaded straight for them, extinguishing the material before il couldignile the wooden retaining structures, the coal, or, worsl of al],another catastrophic gas explosion. Following cries, they discoveredEugene [canroy, a sixteen-year old, who died of his wounds the nextclay. Every other miner the team found during the search wasalready dead, some of appalling burns.

Poincare entered thc mine almost immediately after the explo-sion, in the midst of the rescue operation, despite the risk of a sec-ondary detonation. As the assigned mining engineer, it was his johto sort out what had caused the disaster. Searching for that culpa-ble first spark, he turned first to the lamps. Designed by HumphreyDavy in 1815, these "safety lamps" surrounded an illuminatingflame with a closely woven wire mesh that passed light and let airin but kept the flame from escaping. A punctured lamp in amethane-filled mine is a disaster in waiting. Numbers 414 and417had belonged to Victor Felix and Emile Doucey, they were neverrecovered. Lamp 18 was totally destroyed by a cave-in - its mesh and


glass no longer anywhere to be found, the rods twisted and broken,and the top entirely detached from the base. His attention, Poincarewrote in his investigation report, was particularly drawn to lamp 476:it had no glass and two ruptures. The first tear, long and wide, seemedto have come from an interior pressure. The second, by contrast, wasrectangular and clearly came from the outside, in fact the puncturewas a dead ringer, according to all the workmen, for a strike from astandard-issue miner's pickax. That particular lamp had been signedout to Auguste Pautot, a thirty-three-year-old miner, but it was notfound next to his hody. Instead, Poincare observed, lamp 476 stillhung from a tim bcr support a few inches from the ground and in theimmediate proximity of workman Emile Pcrroz's corpse. Poincareand the rescuers found Pcrroz's OWll lamp intact, elsewhere.

Throughout his report Poincare mixed ,1factual with a more per-sonal tone, one nol yet hardened by years of accident inquiries. lierccouuucnded the chief miller for compensation in virtue of hisbravery, and concluded the medical section with the mournfuladdendum that he hoped the millers had died instantly, sparil1gthem a long agony. Poincare's conclusion listed 110tonly the victimsbut the nine women and thirty-five young children they left behind:"Even the generous efforts of the company will perhaps be insuffi-

cient to relieve so much misery.?"]':xploring the causes of the accident, Poincare's language turned

analytic, advancing hypotheses and counterhypotheses, facing themone by one against the evidence, He acknowledged, for example,the commonplace that miners upstream of an explosion in the airsupply are usually burned, while those downstream arc asphyxiated.In the Magny disaster, all the deceased suffered hums, so it was log-ical to think that the explosion hac! occurred down the airstreamfrom the last man, Doucey. Cave-ins seemed to reinforce thisdeduction and to suggest that the gas explosion occurred in the half-moon (see figure 2.2). Against this seemingly plausible notion stoodanother hypothesis that "equally well accounts for the facts." In par-


ticular, Poincare considered whether the explosion might haveoccurred near the timber peg immediately adjacent to the pointwhere lamp 476 stood:

So here we arc in the presence of two hypotheses up until this timeequally plausible: explosion in t-he half-moon, explosion at the top

of the lift. Without the Doucey lamp one cannot prove directly

that it had not caused the initial ignitioll of the gas_ But diverseconsiderations nonetheless support the idea that the primary acci-dent took place in the work spaee of Pcrroz. II,

Sincc Perroz was a coalloadcr and therefore had no pick, Poincarereasoned that it must have been Pautot who had accidentally pUllC-

turcd the lamp with his axe, and then inadvertently exchangedlamps with Perroz. Sometime after tha! switch, the punctured lamp476 had lit the atrnosphcric IIIethane iIIi["j,ili Il(1 the conflnzration. , b'· b· ,

and setting off a secondary explosion atthe point where the incom-pletely burnt gas encountered the principal now of air.

Step by step, Poincare reasoned on through the iuvcstigation,eliminating other possible sources of gas one by OIlC: Some sourceswere outside the flow of air, other veins of coal too old to bedegassing. Clinching the argument, he added, W<lSthe fact that Clny

source of gas from a distant source would have risen to the top ofthe tunnel and not, therefore, been in contact with the low-hanging lamp 476. Any slow venting of gas would have asphyxiatedPcrroz who, according to the medical personnel, had died stand-ing. No, Poincare concluded, the gas must have entered suddenly,probably from a natural gas vent just a single step from lamp 476.When the gas hit the punctured lamp, the miners were doomed. I)

Poincare worked the investigation for months. He returned to themine on 29 November 1879 to follow up on the mechanics of aer-ation, conducting tests, making measurements of flow, and deter-mining the relative air pressure at different points in the shafts. He

Coal, Chaos, and Convention

IIiI

IiI

I, I, !

I, III

submitted his report at Vesoul on the first of December 1879. Thatsame day the ministry of public instruction advised him that hewould be given a junior lectureship in the faculty of sciences atCaen. But neither mathematics nor <lny of his other pursuits evercompletely diverted Poincare from his interest in mining. At the endof 1879 he still hoped to continue his mining engineer career simul-taneously with his mathematical one. In fact, he never left the

@ 11,.,11 • ." d, ;fo"j••y>CI.,J' •.

7ill;'" -;,~~iiJr"Y"/'/.,, _,<" !"•••.,.•••...••:-. r ,,_ ••••/~ !{7)1

v.:l,J4.. I.. O~~'l ~.c<.o. 1", f ••

~--I'~-' ,_-,-~--'-<....-7t..;.... ·--;:'!-T-~--i .....;.-,.J •.•..•••../~~.:.---cr../_--l <::7•.•...-

:::-.fQ .""t"~:1.1/J"

a_...,..c.~3)AC~.-.63~~{'.--==;-_5'

Figure 2,2 Magny Explosion Mal). Poincare drew this mul) to trace the flowof air through the mineslwft at Mag ny, during his days as a mining safetyengineer. On the basis of his investigation, he concluded that the fatal explo-sion of 31 AUgtlst 1879 had been caused by a miner's inadvertent puncture ofhis Davy "safety" lamp rather than because of an explosion in the "half moon"shaft located at the top of the map. SOURCE: Roy AND DUGAS, "HENRI POINCARE"

(H)54), P. 13.

"-------


Corps des /lines: named chief engineer in 1893, Poincare becameinspector general on 16 June 1910_ Just before his death in 1912, hepublished an article titled "Les Mines" in a book he and a few col-leagues produced to join the cultural with the technological andscientific. Poincare's entry is preceded by a small picture of a Davylamp without comment, but no doubt a sign for him of the still-smoldering pits of Magny thirty-five years earlier. "One spark," Poin-care wrote later in the piece, "is enough to ignite _.. ; well, I refuseto describe the horrors that follow.':"

Chaos

EveIl while sketching und improving the machinery of mining-lamps, lifts, and pit vcntilators=-Poincare wrestled with mathcniut-ical problems that were, at the same time, physical ones. Thoseproblems converged on what had become the great challenge ofcelestial mechanics: the three-hody problem. It is easy enough toslate. The motion of a single body is given by Newton's injunctionthat a body in motion tends to stay in motion. The motion of twobodies, attracted to 011eanother by Newtonian gravity, could also besolved. With the simplifying assumption that- the planets were oulyattracted by the sun (and not by each other), it was a straightforwardexercise for Newton and his successors to calculate the precise lra-jectory of these bodies around the sun. But for a system of three ormore mutually attracting objects, such as the SUIl, the m001l, andthe earth, the situation was far more difficult. Eightecn interrelated

equations had to be satisfied to solve the problem. If space is mea-sured by three axes x, y, and z, then a full description of the motionof the orbs would require thc positions x, y, z at each moment intime for each of the three heavenly bodies (that makes nine equa-tions), along with the momentum of each ill each direction(another nine). By choosing the right coordinates, these eightecnequations could be reduced to twelve.


For many mathematicians of the mid-nineteenth century, thetrend of their discipl ine was toward an ever-marc-rigorous formula-tion - precise definitions, proofs dcsigned to annihilate the smallestshred of doubt. Such a passion for airtight logical proofs was notwhat drove the curriculum at Polytccliniquc, ,1I1dit never formedone of Poincare's abiding concerns. Nor was he after better meth-ods to solve equations, though in astronomy such studies couldincrease the accuracy of predictions about where a planet might befound. Charts of the ephemerides (as the juxtapositious ofhcavcnlyobjects were called) were very useful to a ship's navigator. Findingsuch numbers thatwere both scientifically and practically impor-taulmight have been justthe sort of thing that- ,I Polytcchniciall likePoincare wanted. But continuing ill the usual way was not anoption: he could show that the usual approximation methods forfinding t-he ephemerides gave dramatically wrong predictions ofwhere the planets would be. Never having been drawn to the purem.itltcmal iciau's fixation on rigor and now convinced of the futilityof the applied astrouoiuer's traditional death grip Oll uumcricalmethods, he uccdcd a dramatically new approach.

Poincare louuc] thll new entry into celestial mechanics thoughdiagr<lIlIs: he locuscrl OIl what he called the qualitative featues ofdiffercntial equations. J\ differential equation tells how a system ofthings-poillts, planets, or water-changes from one moment to aninfinitesimally later moment. By itself this is not much use in mak-ing predictions: knowiug where a planet will be an instant from nowwill not help a ship's navigator. For a useful longer-range prediction,the astronomer had to add up many infinitesimal changes to cal-culate, for example, where Mars would be next June. 'Io lllanymechanicians, solving such problems meant doing this adding up(integrating) and putting the final result in a simple, recognizableform. This was not Poincare's goal.

More or less from the time Poincare left the mine pits, he aimedto attack differential equations in his own way. Instead of following

I

'I

ii1

- --- --- --------------------------------------

64 EINSTEIN'S Cl.OCKS, POINCARE'S MAPS

one water droplet down a stream, so to speak, he wanted to charac-terize the flow pattern of all the drops making up the surface of thewater. He was after the general pattern of flow to extract the featuresof the system as a whole. For example, how many vortices formed-six, two, none? Such an approach would neither provide an elegantformula to yield the velocity of a particular droplet so many ccn-timetcrs downstream, nor offer a new numerical scheme to approx-imate the position of Mars next 12 April. Instead, Poincare sough I'

a pictllre that would capture the physiognomy of the equation andthe physical system it represented. Under what conditions would anasteroid or planet fly off into spa~c? Careerinto the SUIl? Of COIHSCsuch studies were abstract, mathematical; but they were, at the sametime, also concrete. Poincare wanted, above all, 10 grasp curves andtheir qualitative behavior-later could come the details of formu-las, numerical predictions, or the last clegrec of rigor.l"

By staking his reasoning to the fulncss of the visual-geometricalapproach rather than the icy cdge of algebra, Poincare was return-ing, now wit-h far greatcr sophistication, to the mathematical ambi-tions of a much older Polytechlliqlle. No! for him the great ubstractformulas of Euler, Laplace, or J ,agrange. II- was J ,agrange, after all,who so distrusted geollldry that he swore his great work 011 analyticmechanics would stand Oil algcbra alone, never would it rest ongeometrical constructions. Not <1 mechanical analogy, not a singlediagram would sully its pages.

By contrast, Poincare worked precisely in such geol1lclricalways, and mechanical analogies were near to hand. Already ill1881, when focusing differential equations that were linked to thethree-body problem, he highlighted IIis qualitative, intuitiveambition:

Could one not ask whether one of the bodies will always remainin a certain region of the heavens, or if it could just as well travelfurther and further away forever; whether the distance between two


bodies will grow or diminish in the infinite future, or if it insteadremains bracketed between certain limits forever? Could one notask a thousand questions of this kind which would all be solvedalice one understood how to construct qualitatively the trajectoriesof the three bodies?'"

Here, in the joint realm of the geomelTical-visualizable and thephysical, were concerns Poincare returned to time after time, justas he came back throughout his career to questions in the mathe-matics of differcntial equations and thc physics of the three-bodyproblem. As he put it in 1885 (abou! one of his most importantpieces of mathematics), one simply "cannot read ... parts of thismemoir without being struck by the resemblance between the var-ious questions which are treatedthere nud the great astronomicalproblem of the stability of the solar system."!' Mechanics-machines-always lay near. It W~IS the iactory stamp.

Poincare pushed ahead with his qualitative program for under-standing the behavior of differcntial equations, with success suffi-cient to catch the attention of the world's leading mathematicians.When, illlllid-1885, Nature printed an announcement for a math-cmatical competition honoring the 60th birthday of Oscar II, theKing of Sweden, Poincare was a leading contender to win. CostaMittag-Leffler, a well-known mathematician and editor of ActaMathenwtic([, had responsibility for gathering the committee ofjudgcs. Firsl he recruited Charles 1Termite, one of Poincare's Poly-technique teachers, and then llcnnitc's own professor, the formi-dable German mathematician Karl Weierstrass, whose mathematicallifc had long stood for relentless logical rigor. (Mittag-Leffler washimself on friendly terms with Poincarc.) Entries were clue 1 June1888: the very first question was on the three-body problem:22

Between the announcement of the prize and the submissiondate, the French Academy of Sciences elected Poincare to its ranks.This was a signal honor. It meant that, as of 31 January 1887, at the

~--~----------------------.-----


age of thirty-two, he was a fixture of the French scientific elite.Membership in the Academy meant he could bc (and frcqucntlywas) called to a wide range of administrative functions, from theBureau of Longitucle to intcnninistcnal commissions ranging acrosslegal, military, and scientific domains. Adjusting easily to this newpublic role, Poincare bcgan writing for a broader audience. Of thcnearly 100 nontechnical articles and books he penned for newspa-pers, journals, and scientific reviews, you call count 011 OIlC handthose written before his appointment to the Academy of Sciences.

Throughout the whole of his career, visual, intuitive methodsserved as Poincare's pole star. He had uscd uou-Euclidcan geollle-try as a way of cracking problems at lite very heginning of his work.And now, using visual (topological) techniques that he hac! honedduring a decade considering dilfcrcnfial equations, Poincareentered the prize competition under his I .atin banner, "For the stars

do not cross their prcscrilicd limits." III that adage, lI111ehwas con-veyed. Technically, Poincare was aillling to set hounds on themotions caused by the mutual attraction of tile planets, reaffirlllillgthe stability of the solar system. But bcyoud the mathematics, Poill-care's motto reflected his deep (lith ill HIe basically stable nature ofthe world around him. Despite the excellence of several nlllller-llpcontributions, Poincare won the compclitiou hands down; offcringnot only results but also a host of new methods that placed hisachievement at the pinnacle of mathematics. All was, or seemed,right with the world.

Aftcr submitting the prize essay (perhaps thinking of the role thathis own qualitative, visually oriented work had played in showingthe stability of the Solar System), Poincare stepped hack to surveythe role of logic and intuition in mathematical science and peda-gogy. Looking over older mathematical hooks, he said, contempo-rary mathematicians saw work punctuated with lapses in rigor.Many of the older concepts-point, line, surface, space-nowseemed absurdly vague, The proofs of "our fathers" looked like frail


structures unable to support their own weight. Poincare acknowl-edged that mathematicians now knew, as their fathers clid not, thatthere are crowds of bizarre functions that "seem to struggle toresemble as little as possible thc honest functions that have S0111euseful purpose." These new functions might be continuous hut theyarc constructed in such a peculiar way that one cannot even definetheir slope. Worsc yet, Poincare lamented, these strange functionsseem to he in the majority. Simple laws seem to he nothing hut par-ticular cases. There was a time when new functions were inventedto serve practical goals; now we mathematicians invent them toshow off the faulty reasoning of om fathers. If we were to follow <Istrictly logical path, we would familiarize beginners, from their startin mathematics, with this "teratological museum" of freakish new

[unctions.But this tcratologieal p<1th was not one Poincare counseled his

readers to follow-whether students or pure mathcmaticiaux. Inmathematical education, he argued, intuition should not becounted least among tlu: faculties of mind to be culhvalcd.1 low-ever important logic was, it was by way of intuition "that the math-cmatical world remains ill contact with the real worlel; and eventhough pure mathematics could clo without it, it is always ncecssaryto come back to intuition to briclge the abyss [that] separates sym-bol from reality." Practicians always needed intuition, and for everypure geometer there were a hundred ill the trenches. Even the pnremathematician, however, depended on intuition. Logie could pro-vide demonstrations and criticisms, but intuition was the kcy to cre-ating new theorems, new mathematics. Poincare was blunt: amathematician without intuition was like a writer locked ill a cellwith nothing but grammar. His view was therefore that instruction(he referred explicitly to Poly technique where he was by then teach-ing) should emphasize the intuitive and abandon these formal,unintuitive functions that only served to haunt the mathematical

legacy of our mathematical ancestors."

68 E:INSTEIN'S CLOCKS, POINCARf:'s MAPS

This plea for mathematical intuition appeared in print as Poin-care's prize paper was about to be published. But in July 1889, EdvardPhragmen, a twenty-six-year-old Swedish mathematician working asan editor of Acta under Mittag-Leffler noticed some problems withthe prize proof. He relayed thcm to Mittag-Leffler, who cheerfullytold Poincare on 16 July that, with a single exception, "one couldmake thcm disappear almost immediately.'?" Poincare soon under-stood that thc exception was Dot easily repaired; this was neither atypographical error nor a simple gap easily plugged with a few linesof more carcful mathematics." Something was deeply wrong with hiswork. Not only the prize, but his, the journal's, and the judges' rcpu-tations werc at stake; Poincare had to figurc out what was wrong.

Here was the issue. As in his studies of differential equations,Poincare had considered three bodies: a little asteroid huttlingaround the orbiting system of [upilcr and the Sun. What could theorbit of the asteroid do? One particularly simple behavior would beto return evcry time to the same spot with the same velocity: simpleperiodic motion: 'Io represent such repetitive orbits in a dramati-cally simpler way, Poincare proposed a startling idea: Don't thinkabout the trajectory itself. Instead, Poincare realized that he couldexamine the situation once each time the asteroid came around-creating a stroboscopic picture, so to speak, that has come to beknown as a "Poincare map." Properly speaking, his map plotted theasteroid's momentum and its position each time around, but we cancapture the idea by picturing the map as a vast sheet of paper, muchbigger than any plauct, spread in spaec perpendicular to the aster-oid's wandering. Every time the asteroid comes back, picture itpunching a hole F in this cosmic sheet. In a simple periodic orbit,the asteroid would punch through the sheet and then travel throughthat same hole over and over again for all eternity. That hole istermed a fixed point. More generally, Poincare's idea was to studythe patterns punctured in the two-dimensional sheet by the asteroidrather than its full orbit in space.


If the asteroid began its orbit at a different position and speed,however, it need not travel in such a simple, repetitive way. Forexample, imagine that another, identical asteroid crossed the sheetnear, but not through, the hole F. One possibility is that the punch-throughs would, orbit by orbit, drill a succession of holes throughthe sheet that approached F, and, in the fulness of eternity, reachit. Imagine a curve S drawn through successive holes. This curvedaxis S through F is called stable, if an asteroid starting anywhere onthe line (that is, whose punch-throllghs begin anywhere on thecurve) gradually tends toward an orbit that circulates through holeF every time (see map 1 ill figure 2.3). Conversely, a curve throughIi is called unstable if, in the distant past, an asteroid punching Fgradually moves away [rom Jr' 011the curved axis U (see map 2).. It was Poincare's claim in his prize papcr that if an asteroid's punch-throughs fled from a fixed point like F, they would eventually settledown toward another fixed point. Such a rcsul t would have describedan ordered, bounded world, a world fully matching Poincare's hope-fill motto of stars hemmed within their limits. Pushed by Phragmcnto study his argumcnt more closely, Poincare dissected the problemcluring the fall of 1(;(;<), amI h is confidence in planetary stability beganto crumble. Meanwhile, publication of the prize paper went forward.

On Sunclay, I December I (;(;9, Poincare confessed to Mittag-

Leffler:

I will not conceal from you the distress this discovery has causedme. In the first place, I do 110tknow if you will still think that theresults which remain, that is the existence of periodic solutions, theasymptotic solutions I, and my criticism of earlier methods]deserve the great reward you have given me.

In the second place, much reworking will become necessaryand I do not know if YOll can begin to print the memoir; I havetelegraphed Phragmen. In any case, I call do no more than con-fide my perplexity to a friend as loyal as YOll. I will write to you atlength when I can see things more clearly."

----------------------------------------------


Asteroid .-

~

/ Sun'

(~#---cll,·

c.,.e,.

(JllslahkAxis, /1

/ S2

S["hle-Axi:--, S

II

,.. ,.. Ii

'viAl'l MAl' 2 MAl',

Figllre 2. 3 Poincare'« Mal). Poincare's "stroiJoscoIJic" diagrall/s tmckillg theintermittent {nniciures ora sliee! so resell/hied a ci/T/ogra/)hic retnesentaticnithat they became universally known as "Poincare niap«,' with rei/lures C01/l-

/JlOlII)'referred to as "isloiuls" "slratt«,' and "valley»." Mal) I depict» a slab]«"axis" S along which successive [nniclure« converge towan) the fixed/JOint, 1"-

Mal) 2 sbow« an unstable axis l r with successive {iunclure« running away [nnnF, and Mal) ) portrays the cro.~sil1goj"bolh all unstable and stable axis at F.III this last case a f)ll1!c/ure Co near the curved stable axis S is [ollowei] by sub-sequent hits progressing towani I" (while remaining not far from S), and thenfleeing from F (while remaining alongside the unstable curved axis U).

Wednesday, 4 December: Mittag-Leffler wrote Poincare to reporthow "extremely perplexed" he was to hear from Phragmen of Po in-care's assessment of the situation. "It is not that I doubt that yourmemoir will be in any case regarded as a work of genius by the

-----------------

II


majority of geometers and that it will he the departure point for allfuture efforts in celestial mechanics. Don't therefore think that Iregret the prize .... But here is the worst of it. Your letter arrivedtoo late and the memoir has already been distributed." Write a let-ter to me, he continued, in which you explain that, based on yourcorrespondence with Phragmcn, you found that the expected sta-bility was not, in fact, proven for all cases, and that you will send mea corrected manuscript. Mittag-I ,effier added that a good word forPhragmen would be apt-a chair was open at the university. "It istrue that my adversaries, acquired through the SllCCCSS of the Acta,will make a scandal out of this, bill I will take it with tranquilitybecause it is llO embarrassment 10 he mistaken at the same lillie asyou, and because I am firmly persuaded tlwt you will eventuallyunravel the most hidden mysteries of this extraordinarily difficultqucstion.?"

The next day Mittag-Lcffler swung into action, reporting toPoincare that he had telegraphed Berlin and Paris to demand thatthey not distribute a single copy of the flawed journal. In Paris onlyCharles Ilcnnite and Camille Jordan had received copies; KarlWeierstrass had one in Berlin. To Jordan, for example, M iltag-Leffler wrote to say that all error had slipped in and had to befixed -could he please leave his copy to be picked up by a "domes-tiquc" who would whisk it away_ "Please don't say a word of thislamentable story to anyoue," he urged Hermite, "I'Il give you allthe details tomorrow." Tracking down the other copies one hy one,Mittag-Leffler bcgan to hope that all copies were recoverable. "Iam very glad," he confided to Poincare, "that Mr. Kronecker [allequally famous Cerman mathematician and arch enemy of Weier-strass] had not received a copy." But even Mittag-Lcfflcr's alliesbegan to brielle at the campaign. When Weierstrass replied toMittag-Leffler's sugar-coated letter, his discontent showed: "1 con-fess to you, furthermore, that J take the matter not so lightly as you,Hermite and Poincare himself." Weierstrass ieily noted that in his


country, Germany, it was axiomatic that prize essays were printedin the form in which they had been judged. Weierstrass added thatthe stability question was not peripheral to Poincare's essay; rather,as Weierstrass had indicated in a report that was to have served asan introduction to Poincare's essay, it was central. What, Weier-strass demanded, remained in Poincare's paper of its entire positive

program tx

Poincare rewrote the papcr. What remained (or rather what hecreated to plug the gap), was something altogether outside the rangeof possible motions he-or anyone else-had ever considered.Chaos, not stability, reignecl in this new universe. Here is what hap-pcned. Suppose, along with Poincare, that a line of stability and lineof instability cross at the fixed point F. (This is not hard to imagine.Consider a saddle: a marble sent clown straight from the pommelalong the direction of the horse's spine will oscillate back and forthuntil it settles in the middle of the saddle: a stable point. But a 1I1<1r-hie propelled down to the right or left will fall off, never to return:an unstable point.) Now, suppose our asteroid hcgins near but noton the stable axis; it will gradually move toward F until it gets quitenear, at which point it will fall under the sway of the unstable axisand begin to wander away from V This is depicted ill figure 2. i,map 3, as the series of puneh-throughs, Co, C I, CZ, ... C7, Cx,· ...So far, Poincare had no problem."

But suppose the stable and unstable axes cross somewhere else,for example at H, which Poincare dubbed a homoclinic point. Hwill then be, by assumption, both a point on the stable axis S (dri-ving the subsequent puneh-throughs of the asteroid toward F) anda point 011 the unstable axis U (so an asteroid beginning near F will,slowly at first and then more quickly, puncture its consequents [sue-cessive holes] in sequence away from F on U through H). Now sup-pose that an asteroid flics through H; since it must remain on S, itbeats its way, in each subsequent crash through the sheet (HJ, H2,

H3, etc.) along S toward F. But since any point on the unstable axis


I~I

always remains on U, since H is also on U, all the consequents ofHalso have to be on U. So the extended U-axis must hit every con-sequent of H that we just plotted: Hj, Hz, H3, and so on. One waythis might happen is shown in figure 2.4a.

ow consider a different asteroid, C, near J-I but on U (figure2.4b). Because H is 011 S, C (being near S) will start to move toward

Unstableaxis, U

(I

/1

(a) (b)

Figure 2.4 Chaos in Poincare's Map. When the stable and unstable axescross, ccnnolexity can follow. Indeed, it was precisely the possibility of thischaos-inducing crossi1lg that Poincare left unresolved in his first submission ofthe prize essay. As described in the text, this leads to the enormously complexextension of the unstable axis that begins in (a) and then is developed more[ull» in (b). Even the behavior of (a) is just the beginning or the complexitythat would follow as the new crossing IJoints ofS and U (at the points markedX) are taken into account. Understandably, Poincare despaired of ever beingable to draw the "latticework" that a more complete representation would haveto show.

Ir".....·1 ••• .--------- .•...-.----.------.---~


F. This is just what we saw in figure 2.4a. At the same time, sinceC starts on U, its consequents (C, C\, Cz, C3 and so on) have to stayon U as U is extended. So the series C, C1, C; moves toward F. Buteventually, as the consequents of C approach F, the subsequent C'sbegin to beat a retreat along the unstable axis U as in figure 2.3,Illap 3. Since U crosses S at H, the C's, in their retreat along U, alsoeventually cross S (here illustrated by C(,). The U-axis, after cross-ing S atH, has to zoom all the way back to C4 to hit it, and thcnthe U-axis has to head back once again toward F to intersect S atH+ Notice that because the extended U-axis to and from C(, has hitthe S-axis (at the two points labeled X) we have two new homoclinicpoints and the lllap becomes vastly more eo]11plicated yet.

As a result of all this complexity, far from settling into houndedbehavior, the unstable axis, and therefore allY asteroids on or nearit, will wander all over the Poincare map, cre;;lting a motion so extra-ordinarily complex that Poincare himself proved unable to depictit. When he eventually expanded the prize essay for pnhlicalion illhis New Methods of Celestial Mechanics, hc struggled to describe

the figures that resulted:

When we try to represent the figure formed by these two curvesand their infinitely many intersections, each corresponding to adoubly asymptotic solution, these intersections form a type of lrcl-Iis, tissue, or grid with infinitely fthe mesh. Neither of the twocurves must ever cut across itself again, but it must beml back upouitself in a very complex manner ill order to cut across all of themeshes in the grid an infinitc number of til1les.

"I shall not even try to draw it," he added, yet "nothing is more suit-able for providing us with an idea of the complex nature of the

three-body problem.'?"A hundred years after the vexed publication of this prize essay,

Poincare's exploration of chaos was all the rage, celebrated as the


,1.1\\ II 111;1 new science, a revolutionary advance over the simple101 ,.lid ions of classical science. Some late-twentieth-ecntmy physi-, 1.1:;, philosophers, and cultural theorists hailed the sciences of, 'III I pi exity (as they came to he called) as a form of "postmodernI,J IV, ics,' while powerful coin putcrs spewed Poincare mapsu unutely illustrating what their inventor had c1espclired of sceing on1);lper. Some of these maps revealed new physical phenomena; oth-"IS graced art galleries." But in 1890, Poincare proposed no revo-Ii rtion in the nature of science, Confronting a potcntially damagingscandal over the prize, he patched up the gap in his argumentationand, in exploring the new dynamics, found what he had neithersought nor dcsi rccl- a crack in the stability of the Universe.

Far from waving a radical banner, Poincare showed that,although the number of such chaotic orbits was inhni!«, the likeli-hood that ,1Il asteroid would find itself in an unstable regime wasinsignificant as measured against the likelihood that its orbit wouldbe in ,I stable one. I laving lost an absolute stability, Poincare hac! tosettle for a probabilistic one: "One could say," he wrote about twoyears after the revised paper, that "the [unstable orbits] were theexception and the [stable ones] the rule." Instead of trumpeting abreak from stability, Poincare stressed the power of the new quali-tative methods to explore classical celestial dynamics: "[T]he trueaim of celestialllleehanics is not to calculate the ephemerides,because for this purpose we could be satisfied with a short-term fore-cast, but to ascertain whether Newton's law is sufficient to explainall the phenomena:"z For Poincare, the true trial of ewtori'sphysics would come by probing its qualitative features: "From thispoint of view [of ascertaining the sufficiency of Newton's law], the

implicit relations which I have just spoken of can serve just as wellas explicit formulas.':" At stake for Poincare were the basic, under-lying relations of things, not the formulae and positions thatastronomers busied themselves calculating to evcr-higher decimal

places.

'~"''''-~-~''- ;..< f,'" -' :••... , ", _l..,._,~".,;J"", ..

EI STEI 's CLOCKS, POINCARE'S MAPS

Convention

In Poincare's attention to structures rather than things, there is astriking analogy to his use of non-Euclidean geometry. For many ofPoincare's contemporaries, the non-Euclidean geometries exploredthroughout the nineteenth century marked an arresting break.Euclidean geometry had, for centuries, practically defined propcrreasoning from sure starting points to inevitable conclusions. Sinccthe eighteenth century, philosophers reading (or, perhaps, mis-reading) Kant, hac! enshrined Euclidean geometry as knowledgebuilt into the very fabric of the mind. Some scientists and pliiloso-phcrs saw non-Euclidean geometry as a radical shift in the vcry clef-inition of knowledge, a sign of hopeful modernity that brokecompletely with intuition; others feared the dreadful loss of cer-tainty. Poincare maintained a much more pragmatic stance. On theone lumd, he insisted in 1891 that if the Euclidean axioms couldbe known before any experience, we humans could not so cusilyimagine others. On tho other hand, the axioms ofEuclideall gCOl1l-etry could not he merely experimental results. If tlicv were wewould he constantly revising thcm. Since there are n~ per/{ctlyrigid bodies that we must use to instantiate straight lines, we wouldsoon "discover" that geometry was simply false: we would find, forexample, triangles with angles that did not sum exactly to I~Odegrees. Poincare insisted that ~ur choice of geometry is guided byexperimental facts but is ultimately open to choice, subject to omneed for simplicity.

One of Poincare's more broadly directed pieces dealt with sim-plicity, convenience, and the hypotheses of geometry. What arc thehypotheses? In what sense are they true? For Poincare geometry wasnothing other than a group, that is, a set of objects along with anoperation that has certain properties. One property of the operationis that it should be reversible. The integers ( ... -3, -2, -1,0, 1,2, 3,... ) have this property under addition and subtraction; adding a


whole number can always be reversed by subtracting the same num-ber. The group should also have among its possible actions that ofidentity, thc operation that leaves a given object unchanged; here,adding zero does just that. And combining operations should leadto an element still in the group: adding 5 and adding 8 gives thesame effect as adding 13. We learn which groups are useful to us byour encounter with the world but-as Poincare often insisted in hisphilosophical writings-the idea of the group itself was a tool withwhich we were born. Not surprisingly, one particularly interestinggroup for \IS humans was the movement of rigid bodies in space.Poincare argued that we have picked ordinary Euclidean geometryfrom among many other choices because the group underlying itcorresponds, in a simple way, to the group of rigid-hody 11l0tiOIlS inspace-solid objects move in our real world. Could one have cho-sell otherwise? Of course, Poincare says: we have 01l1ychosen themos! convenient geometry. Does that mean that the other geome-lrics are false? Not at all. No more (according to Poincare) couldone promote Cartesian coordinates (measuring a point's position bythe 11s11alx and y axes) as true and derogate polar coordinates (mea-snrillg ,1point's position by its distance from the origin and the angleof that radius line) as false. Once again, Poincare emphasized thatthere are free choices in representing the world, choices fixed notby sOllldhi1Jg completely exterior, but rather fixed by the simplic-ity and convenience of our knowledgc. "I won't insist any further;because the goal of this work is not the development of these truthswhich are starting to become banal.'?'

In fact, Poincare was so committed to the role of conventionalchoice that he argued that the selection of a geometry was like thechoice between French and German: Poincare contended that onecan choose th is or that language or idiom to exprcss the samethoughts. Imagine intelligent ants who lived on the surface of a sad-dle, and defined straight lines as the shortest distance between twopoints. Ant Mathematician says: "The sum of the angles of a trian-

..•....., po

EINSTEIN'S CLOCKS, POiNCARI~'S MAPS

gle is less than two right angles." We (from our human perspective)would describe the same situation in "Euclidean" rather differently,because we would see the ants' triangles as shapes with curved sides.Human Mathematician might say: "If a curvilinear triangle has forits sides arcs of circles that, if produced, would cut orthogonally thefundamental plane, the sum of the angles of the curvilinear trian-gle will be less than two right angles." Both statements capture thesame situation but in differen! idioms. So there is IlO contradiction.Such a correspondence shows that the theorems of ant-saddlegeometry are no less consistent than our ordinary geometry; theymight even be useful: a saddlclikc "geometry being susceptible of aconcrete interpretation, ceases to be a useless logical exercise, andmay be applied." That is the punchline: Various geoll1etries arc sim-ply different ways of presenting relations amollg thillgs; which weuse depends Oil convenience." .

All through Poincare's mathematics, his philosophy-s-and as wewill see, his physics-lay this productive theme: find the groupstructure of what call be altered, and choose the most convenientrepresentation. Yet while making those free decisions never losesight of the fixed points, the iuvariunts=-tliosc bits of the worldlchunchanged by om choices.

WHERE, TlmN, WAS Poincare by 1892? The rising star of Frenchmathematics, he had made his name through work that made dra-matic use of non-Euclidcau geometry, advances in qualitativeapproaches to differential equations, and a stullning new approach

.Ito the three-body problem. In philosophy, geometry, and dynamics,he had begun to work out a vision of knowledge that had two simul-taneous goals. De-emphasizing particulars, he found the freechoice available in formulating the problem. The choice of a coor-dinate system was not given by nature but made by us for our ownconvenience. Similarly, particular approximation schemes were to

Coal, Chaos, dl1d Convention 79

be selected by us for specific purposes; even the choice of a specificgeometry had no absolute importance. Poincare's view: use l'~llclid-

ean geometry when it is useful, when it pays to employ a non-Euclidean geometry, use that. In differential eqnations or in thephysical systems they represented, there were always many ways ofchoosing variables-to describe, for instance, the flow lines of waterdown a stream. What was significant were the underlying relationsthat remained unchanged even after such changes in description:the vortices in a flow of water, the knots, saddle points, or spiral end-points of geometrical lines. Similarly, the length of a line remains

fixed when we rotate coordinates.These two aspects of Poincare's work-the variable and the

fixed _ cmcrzcd toccthcr and can oulv be understood together. r Iob b )

says, in different ways over many years: Manipulate the flexibleaspects ofkllowleclge as tools; choose the form that makes the prob-lem at hand simple. Then seize those rclatious that stand Listdespi lc the choices made. Those fixed relations stand for knowledgethat endures. Together the variant and invariant make seielltific

progress possible.For a hundred years, scholars have struggled to get at the root of

Poincare's conventionalism. Some, with good reason, have stressedthe role of geometry. As Poincare emphasized over and again, how-ever, lllathelllatical statements can be made in the language of non-Euclidean just as well as in F:uclidean geometry. Other schoLnshave scrutinizecl the works of earl ier figures in geometry - such asFelix Klein, the great German geolllcter who propagandii',ed soforcefully for different kinds of geomctry. Still others have goneback to Sophus Lie for the root of Poincare's picture of free choiceamong geometries. After all, Poincare explicitly cited Lie as a math-ematical forebear, and Lie was quite clear on the arbitrariness ofmany choices made by the mathematician. For example, Lie said

that Descartes iclentifies the variables x and y by a point on theplane. But (according to Lie) Descartes could, "with equal validity"

r

" 44 -- ------------------------,..-


have chosen to symbolize x and y hyaline, and develop geometryfrom that asssumption. Moreover, Descartes defined x and y accord-ing to a specific coordinate system- the x and y refer to their dis-tances from the x- and y-axes. There too is a certain free choice:"[PJrogress made by geomctry in the 19th century," wrote Lie, "hasbeen made possible largely because this two-fold arbitrariness ...has been clearly recognized as such." Lie was here contcnclin« that

b

mathematical progress followed froill the recognition that therewere always mallY ways to represent mathematical concepts. Choos-ing the particular representation of mathematics, choosing this orthat geometry is, l,ie argued, a matter of "advantage and convc-nicncc." It was, as one scholar has persuasively argued, "one of thegrounds of Poincare's coiunuhncnt to a view of geometry thM heldour choice of geometries t-o be ouc of open choice, grounded bycOl\venience."'" No doubt Poille~lre's emphasis Oil free choice ingeometry can be hunted hack to the CCflll;In polyruath [Icnuunn

Helmholtz, who strugglccl 10 disentangle f;lctllallllc;lllillg lrom clcf-initions in gcometry, always elllpl",sizing the central role of mobile,rigid objeels ill fixing om concepts of space. It lIlay he too tluit Poin-care's ideas on matiIelll<ltieal conventionalism should he pursuedback to thc myriad geometries of Bernhard Riemann, or for thatmatter to the more recent work of Poincare's teacher, CharleslIcrmitc. ,7

Propelling this sense of a freedom of choice was a pedagogicalconventionalism (if YOI1 will) to be found ill 1"11C stridently agnosticinsttuctionn] style oflhe Ecole Polyteclmique. That abstention from

absolute commitment to any particular theory was a prominent fea-ture of Alfred Cornu's courses, which Poincare had attended as astudent. Alternative theories each had advantages and disadvan-tages; all were constrained only by the much-emphasized experi-mental fixed points. For Poincare, the invariants of physics (whichprovided objective knowledge) were the fixed relations between

...,---------,---,=-c-,--,,,,,.-. -'-,-_ -----.,~.--------,---____,

Coal, Ch.aos, and Cunvention

experiments, relations that survived the ever-changing flux of theo-ries. Recall that the same free choice among theories had informedPoly technique's even-handed hiring-some representative scientistsfor atomism, some against. Such an abstention from absolute theo-retical commitment characterized Poincare's own courses; lectur-ing OIl electricity and optics in 1888, 1890, and 1899, for example,he gave each major theory its moment in the sun, displaying itsvirtues and vices for the students to judge. A rhyzomatic "root' of

conventionalism here too.Finally, in Poincare's exchanges with his brother-in-law's (Emile

Boutroux's) philosophical circle, Poincare would have found con-vcutiounl ism ill a philosophical register. This loose affiliation ofphilosophers and philosophically minded scholars offerecl Poincare,early 011, ~Imore reflective view of the marhcmatica] sciences. Rawempi ricism was avoided as woefully inadequate to account for thegenerality and extent of scientific knowledge. Pure idealism (recluc-ing reality 10 mcutal l ife) could not explain the concordance ofideas wi lit the world. Drawing strongly on the Kant revival under-way ill CeIlnany, Boutroux and his circle rejected both theextremes of idealism and empiricism. Taking science and lheI111 IIIani lies to be inextricably bound, these philosophers saw bolhstructured by an active role for the mind and a suspicion toward thepurely metaphysical. In his encounters with Auguste Calinou'swork on the philosophical foundations of physics, Poincare walkedthis philosophical middle line straight toward the problem of

simul taneity.Geometry, topology, pedagogy, philosophy-each of these ways

of parsing Poincare's world tells \IS something about the ways inwhich scientific "free choice" made sense to him. Intriguingly,around 1890, Poincare began regularly to call "free choice" by anew name, insisting (as he had in 1887) that the geomctriealaxiomsare neither experimental facts nor (as some Kantians would have it)

I':1

I ~Ii

II

II

82 ,",~[NSTE[N'S CLOCKS, POINCARI~'S MAPS

printed in advance on our human minds. In a curt, insistent sen-tence printed in 1891, he lay clown a new formulation of his viewof geollletric axioms: "They are conventions."

Is Euclidean geometry true? It has no meaning. We might as wellask if the metric system is true, and if the old weights and measuresarc false; if Cartesian co-ordinates arc true and polar co-ordinatesfalse. Olle geometry cannot be more true than another; il call onlybe more convenient. Now, l':ucliclean geometry is, and willremain, the most convenient."

Here the status of the axioms of geometry have been explicitlylikened to terms ill a language that can be freely chosen and (in thisquotation) also to the freedom the mathematician or physicistalways has to choose a coordinate system. The new clement is IhatPoincare depicts the choice of Euelidean or non-Euclidean axiomsnot jllsl as a choice ,11l1onggrollps, hut as a choice between Ihe arlii-hury system of meters anr] kilograms and the arbitrary system of fccland pounds.

'j() appreciate this aspect of Poincare's use of "couvcution," wemllsl recognize that his reference to weights aud mcaxurcs containsthe trace of all entire world of conventions. At the same lime, <IS wewill see, Poincare's concern with meters and seconds cannot heconsidered an external "influence," onc that determined his scien-tific and philosophical work the way a hiddcn magllcl rearrangesthe iron filings above it. "Roots" and "influenccs" arc terms too

weak and external to capture Poincare's thoroughgoing engagementwith the practice of setting planctwidc conventions.

The world of decimalized, conventionalized time and space wasanything but abstract to Poincare. He flourished in (and contributedto) the Parisian, indeed worldwide skein of wires, mcctings, andinternational treaties. Here was, after all, the consummate Poly-technician who moved as easily in the depths of a coal mine as in

Coal, Chaos, and Convention,I

the far reaches of astronomical stability. But to make visible thcmechanisms of clocks, rods, and wircs- above all, to grasp the pro-duction of the late-nineteenth-eentury conventional understandingof simultaneity- it is necessary to pull back to a wider perspective.We need to move back and forth, in and out, between the details ofwork in philosophy, mathematics, and physics and the larger-scalesocial and technological conventionalization of time and space ill

which Poincare took part.In to the precision swing of master clock pendulums, out to the

undersea telegraph cables crisscrossing the oceans. In to follow theminutac of individual train sclicdulcrs, jewelers, aud astronomers;then hack (jilt to the legal rccalihration of uational and world-covcriuz lime 1.011CS.IIlthis process of scrutiny, hisloricallight nee-

b

cssarily plays off the vcry different scales utilizcc] by tccllllological,scientific, and philosophical activity. Betwecn IH70 and 19] 0, con-veil tions of space and time scin hila led wi III a critica I opalescence.

Ii,

. i

Cliap ter 3

THE ELECTRIC WORLDMAP

Standards oiSpace and Time

ARTS, HOTEL DES AFFAIRES etrangeres, 20 May 1875,2:()() ().M. Represented by their decorated plenipotentiaries,seventeen names will he put to a treaty, their resplendent titles

marching across the pagc: "His Majesty, the Emperor of Germany,""I lis Majesty, the Emperor of Austro-I Iungary," "I lis Excellency, thePresident of the United Slates of America," "His !I:xec]]ency, thePresident of the French Republic," "His Majesty, the Emperor of AllRussia .... " We are at the solemn signing of the Convention of theMeter. After years of llegotiation, thcHigh Contracting Parties nowcalled into existence an international bureau of weights and mea-sures. The new prototypes of the meter and kilogram it was chargedwith certifying would supplant the myriad of competing nationalmeasures, establish the relation between these gauges and all others,and compare results with the standards used to map the earth.

I Icrc, in the convention, diplomacy met science. When DukeLouis Dccazcs, the French minister of foreign affairs, sent out invi-tations to other countries hack in 1869 for a diplomatic conferenceon this issue, he invited politicians, hut also leading scientists likethe German astronomer Wilhelm Forster, who was director both ofthc German Bureau of Weights and Measures and the BerlinObservatory. By March 1875 the committee had come far enoughfor Decazcs to gently retire the scientific domain, in which theassembled held only a "relative competence," in order to focus 011

"questions of a political and conventional order (ordre convention-nel)," where they had "absolute competence": their conclusions

The Electric Worldl1WIJ 8S

would form the basis for binding iutcmationallaw. Conventionsjoining scientific and legal technologies had been concludedbefore - in 1865, for example, governing telegraphy. Indeed dozensof conventions had aimed to smooth collisions between countriesin trade, post, and colonization. Now, in the vital domain of themetric system, even more than the telegraph accord, the delegatcshad produced an "international contract" as dear to scientists as it

was to industrialists and politieians: a legal document that wouldrule from the spotless precision of thc physics laboratory to the

smoke and steam of the factory. I

If Dccazcs spoke for diplomacy, [c.m Baptiste Andre Dumas,organic chemist and, since 1868, perpetual secretary of thc FrenchAcademy of Sciences, spoke for French scic nlific curliusiasm. Ashead of the special (scientific) commission on tile meter. J)111naS

had bccu rcspous ililc for the recornrnendatious that IIOW stoodbefore his colleagues. Partially summarizing, partially lobbying,Dumas stood before his fellow clelegates to advocate a pcnu.mcnlbureau in Paris vested wilh the authority to set, maintain, and dis-tribute international standards. Above all, Dumas wanted to justifythe universal meter as a standard for industry, for science, forFrance, for the world. As he saw it, anyone who had set foot in 1,()Il-don's 1851 Univcrsal I<xposition immediately recognized that"chaos" reigned between national systems. Each country's peculiarsystem of wcigh ls a ncl measures made comparison among th emimpossible without tedious ealculation. At the same time, every sub-sequent exposition had demonstrated that the reach of the metricsystem was steadily growing. jl:vcrywherc people wanted to throwout discordant measures; they yearned to smash intellectual barri-ers between peoples. For DUlllas, indeed for lIIany senior Frenchscientists, the eall for international standards would be heard by all"enlightencd mcn.t Having embraced the metric system through-out physics and chemistry laboratories, scientists now taught itwidely. Factories, builders, telegraphs, and railroads had seized the

I

:1Ii

-----------_. ----_ .... - -- ---------- --.. ~-- ....-- ....------.----- . _.-'.. .


"j 'I

meter. Now, Dumas urged, public administration should back therational meter.

Dumas: Decimals mattered. For both sides, practical and purescience, it was the decimal character of the metric system that mat-tercel. Twelve inches in a foot, three feet in a yard-neither plumbernor physicist could cherish such a hodgepodge. "As for the geodesicorigin of the metric system," that pride of the French Revolution, bynow "it is absolutely without interest for commerce, for industry andeven for science." Upon its adoption in 1799, the meter was sup-posed to be exactly one ten-millionth of a quarter of the earth's cir-cumfcrcncc. Dumas assured his listeners that modern proponents ofthc metric system made no such claim; the assembled knew pcr-fcetly wcll that the earth's size could not be measured with the pre-cision needed for an intemationa] standard. For Dumas, thc reasonfor adopting the metric system was because it divided lengths intosensible units oftcn. That was what purc scientists wanted and whatpragmatic journeymen clcnumdcd. "l o spread this new rational sys-tern a center was needed. It should be "neutral, decimal, interna-tional." It should be 9([ va sails dire, in Paris.'

Dumas reminded his audience that the metric standards hadbecome international precisely because revolutionary Francehad designed the system to make it so. I ,()]}gago, ancient Hebrewshad put their measuring prototypes in the Temple. Romans set theirstandard in the Capitol, Christians sequestered theirs in the Church(which was how Charlemagne's standard kept its original purity).For eighty years, the Archives had performed this task for France,preserving the standard meters since revolutionary times. But nowthat the high contracting parties had decided to make the meter atruly international standard, they judged the revolutionary meterneither strong enough nor sufficiently invariable to serve as the pro-totype for the world's measures.

Signing the Convention of the Meter started, rather than ended,the process of distributing the meter. Bureaucrats and scientists lob-

The Electric World11ldfJ

bied, bullied, anclnegotiated their countries toward putting thescheme into practice. Some of the great experimenters of Europeand the United States contributed to it: Armand Fizeau, who hadmeasured the "dragging" of the ether by water, as well as the Amer-ican Albert Michelson, who inventcd the interferometer, an instru-ment capable of measuring length to within a fraction of thewavelength of visible light. For fourteen years, French engineersand British metallurgists hammered and smelted their way to a

tough, durable iridium-platinum alloy.While a British firm pounded these hard, pure bars into meter

sticks with an inflexible "X" cross section, the French concentratedon producing an enormous "universal comparator" (see figure ~.1),that would, by strict procedure, allow a standard length to be repro-duced on another bar to within two !"cll-thousandths of a millime-ter. It was painstaking, nerve-wracking work. When the Britishmetal workers delivered their precious bars to the French, the oper-ator at the conservatoirc would set both the standard meter and theblank bar on the hridge of the comparator. Peering through a micro-scope (M), the operator would line up the one-meter mark on thestandard. Then the operator would activate a lever, causing a dia-mond blade to inscribe a fine line precisely at the one-meter pointOil the blank. Carving subdivisions was just as difficult. The twomicroscopes would be set, say, ten centimeters apart. The operatorswould mark that length. Sliding the bar down, they would etch asecond ten-centimeter length into the bar, and so on. 'Io preparethe ~ostandard bars that the international delcgates would takehome with them, the operators repeated this operation 13,000times. The slightest slip with the diamond point meant starting over

again with repolishing of the blank.'Finally, on Saturday, 28 September 1889, two years after Poin-

care was elected to the Academy of Sciences, eighteen representa-tives of the contracting parties gathered in Breteuil for the finalsanctioning of the meter. The president of the conference can-

EINSTEIN'S CLOCKS, POJNCAR~:'S lVL\pS

liigure ).1 Universal Coinnarator. This machine served to rule preciselengths jor /J/al ill 1lIIl·uidt IIIII co/lies oltl,« sialic/arc/meter, M. For engineers,tJ/zysieisls, politician«, and /)hi/os()flhers ·es/Jecially ill France=th« inierna-tiona] succes« olLhe sl<llldurdized unit of/ellgth served as a model [cr whatthey hO/Jec/w()lIld he the dccunalization (/1/(/ standatdization oitnne. SOImu::

(;IJII.I.;\II~II':, "'I'R;\V;\UX Illi 11111(1<;\111~,/,lmN;\,/,I()Ni\1. 1l1':Si'OIllS I<'/'MESIIRI,:S" (18<)0), P. 21.

vasscd their votes= uuannuous-c and then pronounced: "This pro-totype of the meter will from now forward represent, at the temper-ature ol l\ICJtillg ice, the metric unit of length," while "thisprototype I kilogram I will he considered from now on the unit ofmass." All st.mdarcls stood on display ill the meeting room: meterssheathed by protective tubes, kilograms nested ill triple glass belljars. According to plan, each delegale ceremoniously picked a ticketfrom an urn, the number received assigning his country a meterstick, for which he offered a sign cd receipt.

Suddenly, these carefully scripted proceedings ground to anabrupt halt. 'lhe most important act- the deposit of the meter inits underground safe-was possible only with the three keys needed

The Electric World11lcljJ

1 II open the vault. One of those keys would be in the hands of the(Ii lector of the French Archives, but he was not there. The president:;t 19gested they ask for instructions from the French minister of com-nicrce, but the delegates vigorously objected. Swiss astronomerAdolph Hirsch insisted that the conference was international, notlirench. The conference would not address an ordinary Frenchminister. Out of the question: IIirsch and his colleagues would dealwith France only through its minister of foreign affairs. Diplomacy

apparently produced the missing key.Later that attcrnoon, at 1:30 to be precise, the commission

charged with depositing the in tcmatioual prototypes gathered in thelower basement of the Breteuil Observatory. There the delegatescertified that the international prototype M would from thatmoment forward be enclosed in a case covered on the interior withvelvet, lodged within a hard cylinder of brass, screwed tight, locked,and placed ill the vault. Alongside M the standard bearers thcn pre-pared two "witnesses" for burial (meter sticks, not delegates). Thesemetallic observers would forever testify, by the very conditions oftheir bodies, to anything that might befall M. In the same cercmo-nial interment, convention delegates sanctioned the kilogram, K,elevating and renaming it as the universal standard of mass. It toofound its elernal resting place in the underground iron vault in thecompany of its witnesses. With two keys, and in full view of the del-egates, the director of the International Bureau of Weights and Mea-sures locked the case, secured the inner basement door with a thirdkey, and bolted thc exterior door with a fourth and a fifth key. At theconclusion of these solemn events, the president of the conferencehanded these latter keys in separate, scaled envelopes: one to thedirector of the International Bureau, one to the general guard of theNational Archives, and the last to the president of the InternationalCommittee. From that time on, all three basement keys would be

needed to enter the sanctum sanctorum.'This was a remarkable moment. M, the most precisely forged

EINSTEIN'S CLOCKS, POINCARI~'S MAPS

and measured object in history, the most individually specifiedhurnanrnade thing, had become, by its burial, the most universal.Here was an object manifestly in France and yet not in France, reli-giously redolent and yet stridently rational, absolutely material andyet completely abstract. In an age when "family, country, church"had hccomc "family, country, science," K and M wcrc pcrfectemblems of the Third Republic: buried in specificity, risen in uni-versality. '1'he sylll bol ic resonance of the meter was losl on no one.Back in Hl76, the Republic had even memorialized the new meterby striking a richly iconographic medal in honor of the standard,the scientists who were constructing it, and the glory of thc originalmeter chosen during Germinal of Year Ill.' 011 the occasion of thcs<lllcliollillg in I H89, French newspapers recalled with "patriotic sat-isfactiou" bow shortly after thc "disaster of IH7()" forcign scientists,even 1110scwho had previously impugned French precision, IlOW«ckllowledged its triumph."

Before lhc ink was dry on the Convention of the Meter, ddcg«leswere pLllllling new standards that would be built- 011 the Illodel ofM. Scientific-technical conventions nol only gamercd symboliccapital for the country or countries that spearheaded thell], but theyalso engenclcred real benefits for trade exports and smoothed zonesof national confrontation. Conventions were ,llso respollscS 10 thesudden confrontation of industrial products at the internationalexpositions, the commercial "chaos" to which Dumas had referred.But conventions also mediated the crossing of train lines and sched-ules, and hlamc rapidly fell on their absence when trains smashedinto one another. For much of the early nineteenth century,regional (even national) systems of communi cation, production,and exchange had been free to grow in relative isolation. In the lastthird of the nineteenth century, systems coli idcd at myriad hound-aries in the colonies, markets, and fairs. It was this friction that theconventions were designed to ease. They were patches at the raggedfronts at which telegraphic, electric, and railroad networks mct.

The Electric Worlcima/J

n.,JFiume 3.2 Burial oj-the Meter. III ilie ceremonial 18r'..j<) "sanctioning" o{llle

r»sialic/arc! meter aut! /,i/()gr({1/1 a/ Hrcleuil (near Paris) the IIWS{ (Joinsluhllg/)'

created /)/zysiw/ olijecls were buried, so they could [unction externally as uut-vetsal nteasures. Ilere M lies ill its protective metal case on the ll/J(Jer size/roril« Iril)/)' locked underground vault, while K presides over its six "witnesses,'three slal!ding to each side. SOURCE:LEBURP.i\(} j.'-'TEHNATIONALDESPO/IlS I';I'MI':'" IHI':S:

1!)7~·-/()75, 1'. jC).

Covcrllmcnts drew up conventions to calm the frantic rustlillgof incompatible maps as navigators tricd to plot routes at the bound-ary of colonial dominions. Thcy introduced conventions to Facili-tate the movement of dynamos, gcar trains, and steam cngines.Regulating these cOllfronlatiollS required hard-fought instrumentsof accommodation, and their number multiplied: conventions ofwar; conventions of peace; convcutions of electrical powcr; con-ventions of temperature, length, and weight. Conventions, as we

will see, of time.The ycars after Poincare's January 1H87 elevation into the Acad-

emy of Sciences came at the height of debate over these new stan-\

EINSTEIN'S CLOCKS, POINCARf:'s MAPS The Electric WorldmafJ

dards. Academicians took an interest down to the detailed metal-lurgy of the meter bars, and their fascination with the meter led tofurther conventions, as when one of France's eminent astronomerssubmitted a paper to the Academy in which thc meter served as a1110delfor the decimalization of money. When, just after the sanc-tioning of the meter, one challenger wrote the Academy to disputethe fidelity of the new bars to the old Archives standard, Berlinastronomer Forster laid down the law: WI 'he international commit-tee of weights and measures [finds it] unacceptable to allow thebase of the metric system to depend on uncertain and incessant eor-rcctions, IlOW that that base has been materially defined hy the inter-national prototype."? M !lOW ruled alone.

Pushed by the French at every turn (in part our of principle, inpart as a countermeasure to thc force of imperial Britain), the COH-

cept of convention widened, condensing into a siligle word a tripleresonance. Convention invoked the revolutionary Convention ofYear II that introduced the decimal system of space and time; con-vention designated the iutcrnatiouul trcaty, the cliplomutic instru-mcnt that the French, more than any other COI\ U try, pushed to theforc ill the second half of the uiuctccnth century. More generally,convention is a quantity or relation fixed by broad agreement. A con-vcntion, fixed by convention, in the tradition of the Convention.When gloved hands lowered the polished standard rueter Mintothe vaults of Paris, thc French, literally, held the keys to a universalsystem of weights and measures. Diplomacy and science, national-ism and internationalism, specificity and universality converged inthc secular sanctity of that vault.

But if France could lock space and mass in the protected lowerbasement of Breteuil, time proved more elusive. At the beginningof the 1880s, one French review lamented that clocks were extra-ordinarily recalcitrant, each one's own "personality" repelling anyattcrnpt to regularize it by making corrections based on tempera-hue. Not that French astronomers and physicists had not tried. All

over Enrope, neighborhoods, cities, regions, and countries werestruggling to standardize and unify their clocks. In Paris and Viennaduring the late 1870s, industrial steam plants injected subterraneanpipes with compressed air, then modulated that pressure to setclocks pneumatically around the city. Customers could wanderthrough pneumatic shops to select their preferred display of Vie to-

rian exactitude.At first the fifteen-second delay caused by the time it took the

pressure pulse to race under the streets of Paris seemed like noth-ing. Yet time sensitivity had sufficiently mounted by 1881 that eventhis lilly delay (causing the clocks at different points in the pipeworkto cliffer From one anothcr and from the Observatory) became visi-

]'igure 3.3 Pneumatic Unification of Time: The Control Room (circa1880). Jirom the control room at the J{ue du Telegraphe in Paris, the pipelinesIJlIl7liJecltime under the city streets to synchronize clocks ill every quarter of themetropoli». SOURCE: Cr lMmCNIJ'; C/::N(:/W .1':1ws I/e)/(/ .()(;I':S .l'NI·:r IMAI'IQII/':S, ARCHIVES DE

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94 l'~INSTEIN'S CLOCKS, POINCARE'S MAPS The Electric Worldmap

Two striking features of time coordination emerge from this lit-tle vignette. First, time awareness had become acute. Beforc thenineteenth century, clocks normally did not cven have minutehands." ow a fifteen-second discrepancy could drive cnginecrs tomodify public clocks. Second, the transmission timc-cven of apressure wave traveli ng at the speed of sound-looked to profes-sionals and the public likc a problem demanding correction. But ifthe late-nineteenth-century public wanted their seconds adjusted,astronomers hacllong grown used to far greater precision. UrbainLe Verrier, director of the Paris Observatory and co-discoverer of theplanet Neptune, had long since wanted electrical time unification.Synchronizing clocks hy pneumatic means would have beenabsurdly inaccurate in the context of late-nineteenth-century astro-nomical work. In I S7S, no doubt prompted by the Observatory'srole in the unification of the system of weights and lengths, l .c Ver-rier proposed Sl"<l1ldardizing and unifying Parisian time by electric-ity, as the astronomers had already unified the various rooms of theirOWIl observatory. Physicists Cornu and Fizeau, along with theObservatory's astronomers, all endorsed the idea. It was a perfect-Poly technique project. Le Verrier lost no time in pressing theDepartment of the Seine for support. Le Verrier and his astronomersinsisted that their goal was to extend the interior order of the obscr-vatory to the whole of the city: "I propose to the City of Paris to givethe public clocks a synchronized action and a precision superior tothat which we have habitually satisfied ourselves .... If the City ofParis agrees ... it will find here the opportunity to give a new andfertile boost to the art of eloekmaking which has made famous thenames of French artisans.'?"

Paris agreed, promptly establishing an illustrious commission toguide its clocks. Gustave Tresca would join the time standardizationdrive; it was he who was supervising the production of the standardmeter sticks and weights that would grace the basement at Breteuil.Edmond Becquerel would be there, too, as a major French physicist

Figure 3.4 Pneumatic Unification of Time: The Disf)lay Rocnn (circa1880). llere customers=both conunerciul and !Jril'(/{e·-·coulcl!Jllfcl!ilse clocksthat would register the care/idly timed burst» oFair tliat they would receivethrOl/gh the pneumatic !)ifJe.~o(l'lIris. S()IIIH:I':: (:, »u:« ;NII';( :/;:N/·:KII./·: /lI-:S II, ,Wi)( :I':S

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hIe. Astronomers caught the problcru, so did the engineers ofhridgcs and roads. SOOll the publ ie did as well. A[ first the engineerstried to slung off the discrepancy: "this small discordance, iudis-putablc in theory, has little practical importance since we arc onlydealing with clocks that display minutes, and where the miuutchands jump ill steps and do 110t permit further divisions, evenapproximately between that division of time." The elock mindcrshastened to add that thcy would offset the Observatory's clock bythe fifteen seconds the pulse took to reach the outermost reaches ofthe network. To he exact, thcy thcn mounted retarding counter-weights on each pneumatic clock based on its distance from thecenter. In this way, they reassured their readers, "practically thewhole of the discrepancy will be corrected."

95

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(he was the father of Henri Becquerel of radioactivity fame).Renowned architect Eugene Viollet-le-Duc served on the commis-sion, no doubt because of his famed restorations (coordinating grandchurch clocks presented huge architectural and structural issues).Charles Wolf, astronomer at the Paris Observatory, was a commis-sioner; he had inventeclmuch of the observatory's electric time-coordination system. The astronomers and their allies ran aclock-building competition ancl soon had a working trial system.

By the time the commission reported back to the City ill [anuary1879, Le Verrier had died. But his plan lived. A dozen synchronizedclocks would dot Paris, joined by telegraphic cable to the motherclock in the Observatory. Built precisely 011 the model of coordi-nated precision they had erected in their own Observatory, each ofthese secondary clocks had its mechanism set to run fift-een secondsfast each twenty-four hours. A controlling pulse from the Observa-tory drove an electromagnet in each public clock and that magnelslowed the pendulum, pulling the remote clock into synchronywith thc mother clock. Each secondary clock radiated lime electri-cally, resetting other public clocks in city halls, important sqllares,and churches. From now on, the report proclaimed, the pub!icwould have forty public clocks announcing the time correct to thenearest minute - indeed, to the nearest second just after it receivedthe reset signal. Still, there were spatial and legal limits past whichthe Observatory time wires would not go:

We have not included in the list of clocks to be regulated anybelonging to the railroad. It is not that we have misunderstood thcenormous interest that the public would have ill knowing thatthese clocks are in agreement among themselves and with those ofthe City. But ... it seemed to the Commission that it would beimprudent to engage the City ... itself in such a complex service,where big interests are in play, and where its responsibility in caseof accident arising from the regulation of the clocks could be

1

IThe Electric Worldmap 97

engaged in an unfortunate way. One can not doubt, however, thatthe [railroad] Companies, when thcy see at their doorstep all theclocks of the City regularly indicating the time, and all the sametime, will spontaneously put themselves ill accord with the time ofthe Observatory. 'I'hat day, the unification of time in Paris will bethe unification of time ill all of France. II

Here was an admirable vision: the Observatory would stretch itswalls until Le Verrier's system embraced the entirety of Paris. Aclock at the country's center of precision would multiply itself untilevery jeweler, every citizen, would have astronomer's time within astone's throw. By example, trains and finally all France would fol-low. 'I'hrougll this series of symbolic reflections-a temporal hall ofmirrors-Le Verrier's astronomically set pendulum would set the

lime of cvery clock ill the COUllITy.The docks never worked. lee in the sewer systems promptly cul

the wires at numerous points: the current ended up driving theclocks without the intervention of the mother clock. SOOIl publicclocks all over Paris were hawking their own peculiar times. III

embarrassment and anger, the commission attacked the chief cngi-nccr, precipitating a cascade of mutual recriminations over patentsand the patent failure of the public clocks to register anything likellic right time, Pleading that the commissioners use his latest inven-tions, the chid engineer lambasted clocks that were accurate onlyOil recciving their reset signal: "In regarding the clockfacc at anymoment, the observer must have the absolute certainty that theclock is correct to within a few seconds at the most, not to withinfive minutes."?

During 1882 and 1883, reports streamed back to the authoritiesthat the clocks of one arrondissement after another were not gettingproper electrical guidance from the Observatory. By the spring of1883 not a single public dock tied to the secondary regulators wasreceiving any current at all." French authors conceded that their

rr-------------------,·----------------------r ,"

EINSTEIN'S CLOCKS, POINCARI:;'S MAPS The I~lectric Worldmap 99

country had failed to dominate the time unification of cities. Addinginsult to injury, it was London, home of the twelve-inch foot, thatled the way toward standardizing time. 1·1

After establishing the glorious, rational meter, it was galling tothc French scientific establishment that synchronized time hadslipped out of their hands. In 1889, the Obscrvatory directorpleaded with city authorities that this temporal chaos had to stop:"The Counsel of the Observatory, has bccn disturbed mallY timesby the manner in which the distribution of time has functioned illParis. Thc results obtained up till now arc in effcct far from beingsatisfactory, so much so that give]] the numerous protests, the direc-tor of the Obscrvatory had in effect to request the erasure of anymention of 'observatory time'."" At the 1<)00 l lnivcrsa] I':xpositioll,foreigners would see this sorry state of affairs. Coukln'tthc munic-ipality and the Observatory build a system "more worthy of a citylike Paris"? Under these circumstances, it became ever clearer thatrailroads were far from likely to mimic "spontaneously" theObservatory-City system, as l ,c Verrier had dreamed.

resolved hy the advance of the SUllo It required the rapidity of com-munication by rail and telegraph to seed the idea of choosing,more or less arbitrarily, the time of one locality to be imposed 011

others, and to create in this way nonnal or national hours. This hasgivell birth to a confusion of a new kind hut of the same type asthat due to the multiplicity of .mcicnt national weights aile!mcasi trcs. 1(,

Times, Trains, and Telegraf)!Zs

In France, as in many other COUlltries, each train system used thetime of the main city served. Bit hy bit, as lines from Paris wounddeeper into the hinterland, they had chased away local times until,hy 18i)8, Paris fixed the whole country's railroad time. Clock facesill the courtyards and departure lounges indicated the exactmeanlime of Paris, while platform clocks ran behind the outside clockshy three or sometimes five minutes to give the traveling public amargin of error. So as passengers waited in train stations outside ofParis-in Brest or Nice, for example-they experienced threetimes: their city's own local time, Paris time (in the waiting room),and an olEd time ill the track area. (Train time ran in advance ofBrest hy twenty-seven lJl inutes and behind Nice by twenty.) The/{CVllC analyzed other countries' time schemes, examining eachone's solution to the time problem, Russia had unified time in Jan-uary 1888. Sweden had set its clocks one hour later than Green-

wich. Ccrmany staggered under multiple Land-based times."Nowhere else has the question of time been posed ill a more

pressing manner than in the vast network of railroads of the UnitedStates and in the English possessions of North America." Groundedill the North American railroads' April 1883 decision to synchronizeall their clocks by zones, the Americans and Canadians had chosenGreenwich as time zero, blocking out huge longitudinal swathsfrom "Intercolonial time" in the East to "Pacific time" in the West.

"Let us add, before leaving America," the French railway journalconcluded, "that the [American] charts and color maps offered to

It was not that the French railroaders did not wan! coordinatedtime. They, like the rest of Paris, were trauslixcr] hy the coming tri-umph of the Parisian standard meter as its 188<) sanctification drewnear. The industrial Ceneral Review or l\ailwads opened its 1888discussion of time hy referring clirectly to the extraordinary successof metrical reform:

The metric system, one of the most glorious crcationx of Frenchgenius, has already conquered half of the world, and its completetriumph is no longer doubted by anyone. Its authors have added anew calendar, but they have not concerned themselves with fixingthe beginning or middle of the day ... questions which seem

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the public seem to us, by their clarity and beauty of their printing,noticeably superior to that which we usually see in our countries ofancient civilization." According to the Revue, when internationalscientific delegates gathered in Washington, D.C., in October 1884,it was the railroaders who had been ablc to remind them that "anychange would be useless and inopportune." Now thc stakes wereclear: could the French -could the world- adopt a "generalizedAmerican system"? For the French railroad Revue, this was a qncs-tion that should not be left exclusively in the hands of geographcrs,gcodesists, and astronomers." No doubt with Paris standoffishastronomers ill mind, the author wrote: "It is only when the rail-roads and telegraphs have rcalizcd ltime] rd~)J'J11that one can hopeto see their example followed by other administrations and munic-ipalities. Ar«] il is only then, as in North America, thatthe reformcould be complete and could make fell its benefits."'s

French railroaders, telegraphers, and astronomers looked with amixture of aclruirution and anxiety at Britain and the United Stateswhen it came to lillie reform. America stood out for its industrialdistributiou of time, Britain for its world-dominntitu; network ofundersea cables. When Ilenri Poincare joined the Bureau of Lon-gitudc ill 1 i)<)~, he entered a world quite differellt from the vastcommercial and scientific enterprise administered hy the Britishand the Americans. Clocks ran with stulllling precision in theObservatory and appalling inaccuracy in the streets of Paris. TheFrench, especially the Poly technicians, rued this urban failure, butthey were proud of their principled, mathematical, philosophicalapproach to standardization. They had brought the Enlightenmentmeter to a triumphant victory and begun extending the universalrationality it announced into the chaotic dominion of lime.

On the other side of the Atlantic, North American time reformcould boast no leader with the scientific stature of Le Verrier. It sim-ply is not possible to reduce thc American time coordination storyto the work of an individual, an industry, or a scientist, despite many

\

The Electric Worldmap

~"I'II101

attempts. Instead, the movement toward synchronization was alwayscritically opalescent, with dozens of town councils, railroad super-visors, telegraphers, scientific-technical societies, diplomats, scien-tists and observatories all vyina to coordinate clocks in different, b

ways. That effort was so hybrid, so fluctuating in its allegiances andcoordinated grids, that astronomers sold time like businessmen andrailroaders spoke to the universal order of nature.

French savants found America's most impressive science notmathematical physics, mathematics, or pure astronomy, but ratherthe work of the ambitious Coast and Geodetic Survey. Teams of car-tographers and surveyors were busy laying out the boundaries,rivers, mountains, and natural resources of the rapidly expandingcountry. Like all their fellow map makers, the Americans struggledwith time, because time was inseparable from longitude.

Finding local time on the spot was a matter of watehillg the sky,then setting a clock by the moment when the sun passed its high-est point. Or, more precisely, it meant detcrmining the moment acertain star crossed an imaginary line running vertically up fromthe northern horizon. If the surveyors also knew what time it washack at a fixed reference point- Washington, D.C., for examplc-they could then simply reckon the time difference between localand Washington time. If the two times were the same, the survey-ors were somewhere on the same longitude line as the Capitol. Ifthe surveyors found their time to be three hOlUS earlier than Wash-ington, then they were an eighth of the way around the glohc, tothe west.

The map maker's problem was therefore always this same ques-tion of distant simultaneity: What time is it right now back inWashington or Paris or Greenwich? So explorers, surveyors, andnavigators carried clocks (chronometers) set to the time of theirport of departure. All the longitude finder had to do was to com-pare local time to the chronometer. But getting a precision clockto guard proper time in the unsteady motion of a ship's cabin or on

1.02 EINSTEIN'S CLOCKS, POINCARJi'S MAPS

a mule's back was never easy. Add the vagaries of temperature,moisture, and mechanical failings, and the provision of a stable,precise chronometer became one of the most difficult machineproblems ever attacked. For John Harrison, the extraordinaryeighteenth-cenhuy elockmaker, efforts to huild an accurate seago-ing longitudc clock consumed thc whole of his life." Giftedthough he was, Harrison did not end the search for movable time.The hunt for reliable, transportable clocks con tinned throughout

the nineteenth and twentieth centuries. Astronomers foughtlollgand hard to devise a precise way to use HIe moon's movementagainsllhe fixed stars as a giant clock readable from anywhere. Butthe moon's position was hard to fix matllelll<ltically, and in the fieldor on a ship it was difficult 10 measure just where Hlc moon was,except for those rare moments when ilactually passedin front of astar or planet.

The single measurement American surveyors 1110Stwanted W,ISthe longitudc difference hclwccu the New World and the Old. Butthe map makers simply could not conic lo a COllSCllSUS.One des-perate series of attcmpts=-only one among mally-hegan in Angllst1849, wirl: seven trausatlantic voyages in each direction, each hear-ing twelve accurate chronouictcrs. Tile hope was that their timecargo would finally show the true difference ill lime, and thereforelongitude, across the Atlantic. lu I i-l51 they stashed on hoard thirty-seven chronometers, taking advantage of five sailings from Liver-pool and two from Camhridge, Massachusetts. After haulingninety-three chronometers across the seas, the astronomers opti-mistically claimed a shore-to-shore time difference to within one-twentieth of a second."

Such vaunted precision soon rang hollow. Despite the presenceof ever-more-vigilant eloek tenders on the ships to protect the tick-ing freight, the measured time clifference from the United States toEngland was, impossibly, different from that from England to theUnited States. Something on the high seas was confounding

The Electric Worldmaf)

the clocks. Astronomers suspected that temperature was probablythe culprit, with the lower temperatures far offshore slowing theclockworks. This meant that if a lethargic clock set sail at 1:00 P.M.

from Cambridge, Massachusetts, it would arrive in Europe show-ing that Cambridge time was earlier than it really was and induceBritish map makers, relying on the clocks arriving in England, toput Cambridge, Massachusetts, to the west of its actual location.Conversely, a slow-running seagoing clock set initially ill Liverpoolwould suggest to the Americans that I.ivcrpool time was earlier thanit was, so the New World map makers would draw their maps withLiverpool to the west and therefore closer to the shores of NorthAmerica. Testing, calculating, and interpolating did little to help.Crowding the ship with more supervisors, better temperature COIll-

pensators, and superior clocks jusl spewed 0\11 additional conflict-ing data. Unable to measure the number that mattered most, thelongitude difference between North America ancl I':urope, map

makers despaired.For hundreds of years, cartographers could only dream of heing

able to send a signal of simultaneity to fix longitude. The telegraphcracked the problem. Over vast distances, <111 electric current wouldrace a signal through the wires so fast thu t the reception ancl trans-mission seemed practically instantaneous. During the summer of1848, observatory astronomers fro: n the J J arvard Observatory andthe Coast Survey tested t11is new function for the telegraph. Oneperson would tap on the key and the other would listen for a beatat the distant end. Each distant tap would leave a mark on a paperthat wound through the receiver's printing device. One evening,one of the mappers, Sears Walker, wondered aloud if they couldn'tdirectly observe and transmit their observation of a star passingthrough the north. Bonel replied: Why not make the escapement ofa clock act like a telegraph key so the ticks would be heard any-where and everywhere along the telegraph line? Then, Why not letthat clock-driven signal mark on a smoothly turning cylinder

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,.EINSTEIN'S CLOCKS, POINCARE'S MAPS

located far from the clock?" By comparing the position of marksmade by a locally set clock with the position of marks made by sig-nals sent at known times from a distant clock, surveyors could accu-

rately compare distant and local time.

distant 12:00:00--;>1 distant 12:00:01--;> 1 distant 12:00:02--;>1

local 12:00:00--;>1

For instance, here the local noon occurs about a half-second afterthe distant noon. Instead of trying to register time by stopping aclock when a star crossed a spider-thread reticle in their telescope,the astronomers could simply measure the distance between lineson their paper. From that simple measurement, the surveyors had

longitude.By the end of ]851, telegraph cables strcrcl led from Cambridge,

Massachusetts, to Bangor, Maine; from there the time signaljumpccl.jn a second transmission, from Bangor all the way to Hal-ifax, Nova Scotia. As American scientists began advertizing theirelectric time transmitters, they found a ready audience ill Europe.Bond noted: "It is a gratifying circumstance that this invention isknown and spoken of in England only as the 'American method;and the Astronomer Royal has laid the wires at Greenwich prepara-

tory to introducing it there.':"It was not just the astronomers and map makers who cared about

the rapid dispersal of simultaneity. Trains had schedules to main-tain, and by 1848-49 railroads hegan forming voluntary associationsto fix, by convention, the time on which they ran. For much of NewEngland that meant that all trains on or after 5 November 1849were to adopt the "true time at Boston as given by William Bond &Son, No. 26 Congress Street.'?' Any railroad not already in thiscommon time system soon was motivated to be so. On 12 August1853, two trains of the Providence and Worcester line slammed into

The Electric Worldmap 105

II,i(

Figure 3.) Tlu: American Method. By recording the arrival of ielegrapli ~ig-ual» Oil a tneeisefy rotutini; dWIH, the transmission of time could be nuulevastly mote accurate tliau by earlier, acoustic means. For longer stretchesiuudet the At/alltic, fiJl' ex(wl/Jle) /he si11lllltaneity men used the more-sensitiveme//lOcI invented hy I,ord Kelvin: the incoming electric time signal caused anurrot-mcuntetl /11agllellv twist. ever .wi slightly, which caused a re{lecteclliglzlbeiun In shiFt Oil a sheet o{flaIJel'. SJ)lIRCJo:: CREEN, REPORT ON TELEC]v11'1 //(; f )I';/'I';/{-

,1/lNAI'ION (IX77), OI'I'OSJ'J'Jo: P. 2:;.

each other at a blind curve. Fourteen people died, and newspapersblamed the tragedy all a conductor with an itchy finger 011 thethrottle and a slow watch at his side. With another had-watch dis-aster just a few days earlier, train lines found themselves underimmense pressure to coordinate their clocks. 'Iclegraphieal1y trans-

mitted time became a standard railroad technology."

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106 EINSTEIN'S CLOCKS, POINCARl~'S MAPS The Electric World17lC1fJ

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tem. Hailed ill the press, visible in the streets, studied in observato-ries and laboratories, the synchronized clock was anything butrarified science. Its capillary extension into train stations, neigh bor-hoods, and churches meant that synchronized time in tcrvencd inpeoples' lives the way electric power, sewage, or gas did: as a circu-lating fluid of modern urban life. Unlike other public services, timesynchronization depended directly Oil scientists. By the end of theHl70s, the Harvard College Observatory was but one site sendingtime, though for a few years its service was OIlCof the largest. Idio-syncratic developments ill Pittsburgh, Cincinnati, Creellwieh,

Paris, or Berlin set each apart.

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Figure 3.6 Traces of Time. 'JeJegrof)h keys and the traces oFclis{anlly sen!time signals recorded hy the "Americml Method" (l SS3). SOlIl(CI':: Cu. 1II':NI(Y

DAVIS 1-:1' AI.., T/,:, .l<:C:/(.,I/'II/<: I ,()M :/'/'111>1-:IN ,VI,-:x,c:<, .IN!> Ci-:N·/K\I./\~·II':/{/(;!\ (INSS), ('I.ATt,: I.

Partly pushing the observatories, partly pushed by them, trainsupervisors, telegraph operators, and watchmakers accelerated theelectrical coordination of clocks both in England and in the UnitedStates. By 1852, directed by the Astronomer Royal, British clockswere sending electrical signals over telegraph lines both to publicclocks and to railways." Soon the Americans were, too. Summingup the status of their time effort, the director of the Harvard CollegeObservatory boasted in late 1853 that the "beats of our clock can,in effect, be instantly made audible at any telegraph station withinseveral hundred miles of this Observatory.'?" During the 1860s and1870s, coordinated time reached deeper into the cities and train sys-

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Shortly after those first experiments on electrical time, HarvardObservatory hired a telegraph line to distribute to Boston the timeits nstronomcrs had determined by the measurement of the stars. By1871, the observatory director was charging for the service, hopingto install a prominent clock "so that the public can see and learn toappreciate the met hod of conuuunicating time.'?" Returns weregood: in 1875, the service netted $2,400, a yield sufficiently largethat the observatory hired a proprietor for its time business."Astronomer Leonard Waldo carne to Harvard in February 1877frolll Yale, where he had run a similar service. By then the Canta-brigians had invested over $8,000 in instruments, clocks, and tele-graph lines. Now they needed customers. Using their telegraph totrigger its noon start, Waldo planned to drop a large copper timehall down a mast on top of one of Boston's higher buildings. Hehoped that this public display, visible both to landlubbers and nav-igators, would dramatically boost the observatory's recognition. Sowould a major recruitment of railways. Jewclers and clockmakcrstoo were needed as time clients, not to speak of private individualswho clamored (or ought to, according to Waldo) for precision time.

Marl\eting Time


Waldo hoped a widening clientele would persuade big manufac-turers that time really was money, or at least was worth buying."Vires multiplied, snaking through the observatory that aspired to

be the master clock for all ew England.3\1

Hard-driven Waldo pounded out his message wherever he could.Encouraged by Western Union, he printed a pamphlet that adver-tized the time service to a hundred New England cities and tOWI1S.His time, Harvard Observatory's time, would be based all an impres-sive Frodsham clock, corrected once each day at 10:00 A.M. towithin a fraction of a seconcl. From this master clock, time wouldcourse through the region on two circuits ill addition to thc mainonc linking the observatory, the Boston Fire Department, and thecity of Boston. In the unlikely event that the Observatory clockfailed, Waldo promised his time-hungry customers that they wouldreceive a hack-up signal from clockmakers William Bond & Sons.All clay long, at two-second intervals, pulses shot out from theObservatory, skipping, for identification purposes, every minute'sfifty-eighth second, while every fifth minute the service would omitthe pulses that would normally go out on the thirty-fourth to sixti-

cth seconds. ,I

Citizens like the proprietor of the Rhode Island Card Board

Company wanted to know the time:

Will you have the goodness to inform me whether the time fur-nished at the W[ estern] U Inion] Telegraph office Boston fromyour observatory is actual Cambridge time, or Boston time. -Thatis, whether an allowance is made of thc difference in timc hctwcenthe two places before transmitting the signals-I·] Does thc littlehand that beats seconds on thc dial in Boston correspond preciselywith the beating of the standard clock at Cambridge? Are correctsignals furnished to Providence by telegraph direct from yourobservatory? -A number of Citizens of Providence and vicinityhaving fine watches are desirous of having this information."

iI

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Did cardboard manufacturing demand split-second timing? Rather,the cardboard mogul and others like him wanted exact timebecause their "fine watches" demanded it; they had come to viewthe exact coordination of their timepieces as a value not capturedby the purely pragmatic. Fostering such a modern temporal enthu-siasm was Waldo's great hope. Not only his own circulars, talks, andcorrespondence but surely also the ever-increasing role of railroadshad begun to create a sensibility that could only work to the advan-tage of Harvard's time service. Five years of selling time had done

much to foster this awareness. Waldo put it this way:

In ... time the community gCllcrally had been unconsciously cdu-cated to the desirability of a uniform standard of time. Accuratetime-pieces, in many places, were daily compared with the Obser-vatory signals, and their rates so determined were considcrcdauthoritative. So critical, indeed, had the subscribers become, thaterrors of a fraction of a second were detected and commented

upon.

Did the running of trains and the calibration of fire bells requireall accuracy that would better an error of four-tenths with one oftwo-tenths of a second? Of course not. Yet Waldo both pushed thepublic and was pushed hy them to ever greater precision. In hisown way, he participated ill the creation of a modernist time sen-sibility, one with hounds that far exceeded the practicalities of

precision."Back at his time factory, Waldo struggled to protect his regulator

clocks from variation in climate, to systematize telegraphic con-nections, and to engage a cledicated observer to determine clockerror each day. To guard the university clocks from variations oftemperature, the astronomers sealed a basement room against theelements. This "clock room" stood in the west wing of the observa-tory and was completed 2 March 1877. Some 10' x 4'2" wide, 9'10"

rr-." "

110 EINSTEIN'S CLOCKS, POINCARE:'S MAPS

high, its double walls protected the all-important clocks. Only a safedoor penetrated these thick barriers. When the door closed snuglyit scaled against fel t packing. Inside, each of the three treasuredclocks stood on marble slabs on brick piers, their faces illuminatedby tin reflectors so they could be viewed from behind small, thickglass windows (immediate human presence posed a threat to accu-racy). In observatories around the world, from Berlin to Liverpool,from Moscow to Paris, similarly obsessed astronomers shaved errors

from their mother clocks."Split-second timing was one thing; marketing it was another. At

the limit of the Boston tilne-selling regioll stood I Iartford, a city thathad vacillated between its own local time and that of New YorkCity. WIlen a I Iartford worthy, Charles 'Icske, wrote to Waldo ill[uly 18n, illdicating his interest ill converting his town to HarvardObservatory time, Waldo took notice, 'Icskc reported that he hadcorralled the l lartford Firc Department and its con nnittcc, firedepartments typically being the agelley whose noon bell signaledtime to the public. I Iartford's mayorliked the idea of purchasingCambridge limeto set hammer agaillst bcll at noon alldlllidllight.

Bllt rounding up diverse interests and divergent times was less sim-ple, as 'I eskc lamented to Waldo: "H is Iikc awakening the dead outof their sleep, to get people interested ill this matter, for we havehere ill 1Iartford all sorts of time and everybody claims that his timeis correct." 'Jeske reckoned it would cost him a (T(Joddeal of effortb . .... , ?

and a reasonable price from the observatory, to nail down the boardof alclcrmcn and the conunon council. But more than just mOlley,autonomy was at stake. "Will yon give us Cambridge time? Can yougive us Hartford Time? What is the exact difference between Cam-bridge & Hartford?" Several months later he was still hammering

away at his various opponents."Scratching out his report in November 1878, Waldo left a blank

where Hartford would be, he knew that city stood on the regionalborder between two time dominions carved by train tracks. "It is to

I, The Electric Worldmap 111

the Rail Road that we must look for the most certain support of ourscheme for a general distribution of the observatory time signals.... it is the rule that the Rail Road regulates the time of townsalong its line." Train time followed the big city centers, and theNew York to Hartford line put the latter squarely in New York'stimc radius. But the domain from New London and Providenceup to Springfield fell in Cambridge's time zone. "For some yearsto come therefore I think Hartford will be the point at which wemust cease to give Boston time." Disputed lands might lie atthe margins, but the regional conquest of simultaneity was neverin question: "local time throughout New England should be

di scouraged."'"Cambridge lost Hartford. I':vell 'Icskc's desperate recruitment of

the president of Trinity College could not move thc city council.Eventually the Hartford Fire Department threw up its hands andbought a marine chronometer to ring its noon alarm. Dejected,Teske serihhled to the observatory that "of course" this was "con-sidered good enough by those who are ignorant of the minutenessof your Time Signa!." Having failed to move his city, Teske offeredto buy l larvard time for his store (one assumes he sold timepieces);he was determined to have an "absolutely correct Time Signa!."'l wo years later, Connecticut officially set its time to the meridianof the city of New York using electrical signals from Yale Observa-

tory. From the college, time would siphon through the New Havenjunction up the railroad tracks of various railroad companies. Thesetrain lines were ill turn obliged by the law to shoot electric timeclown all their roads, to mount coordinated clocks at their stations,

and to forward time to all intersecting railroads.Railroad magnates were not amused. They had thcir own times

and resented any state intrusion. The general manager of New York& New England Railroad Co. grumbled, "The standard time of thisroad is Boston time ... hut under a ridiculous law in the state ofConnecticut we are obliged to use N.Y. time whenever we cross the

•112 EINSTEIN'S CLOCKS, POINCARE'S !\IIAPS

state line .... It is a nuisance and great inconvenience and no useto anybody as I can see.""

Throughout: sudden changes of scale. One day the HarvardObservatory would solve a navigator's problem. Another day, its staffworried about the frozen time ball they released down a high mastby remote control. On yet another, they drafted plans to wire hun-dreds of cities across the whole of New England. All around theUnited States, such regions of time coordination grew, as did fric-tion at their boundaries. A jeweler's store here, a train line there;occasionally a meridian section, a region, or a state. By the end of1877, Dearborn Observatory (south of downtown Chicago) con-trolled the clocks of half a dozen jewelers, four main railway com-

panics passing through Chicago, and the Chicago Board of Trade.If Harvard's Waldo was fanatically striving to shave lnmdrodth-of-a-second errors off his regulator, Dearborn cheerfully indicated that"no grcat pains arc taken to keep very accurate time. 'J 'he standardsignal clock is gcncrally kept within half a second of the cxacltiuic.... As long as the time furnished is within a second or so of beingexact we are satisfied, and we consider that cl ose enough for allpractical purposes."

Dearborn was right. Train operators and passengers surely didnot need clocks more accurate than human reaetion time, But dif-ferences in time culture reflected more than that. First, lIarvardObservatory's time service had its origins in longitude determina-tion. There a wide consensus existed, not just in the United States,that map making ought to be as accurate as possible. Surveyorswanted accuracy to tenths if not hundredths or even thousandths ofa second. Second, the cultivated precision mania of the I IarvardObservatory had come to resonate not only among astronomers butalso among high-end watchmakers and their gentlemanly NewEngland customers. The culture of precision ticked sooner andlouder in Boston than in Chicago."

But the greatest contrast lay not among the American observato-

/

The Electric World11lap 113

111":; but between the United States (or Britain) and France. It is sim-I,ly unimaginable to picture an Amcriean or British astronomer inI :-->79refusing to pull a time-bearing telegraph wire through thcdoor of a railroad station, as unimaginable, certainly, as it is to pie-ture an American astronomer defending the unification of timebecause it would complete the unfinished business of the Age of

Reason.

Measuring Society

In the fluetuations of sea le that marked every stage of the timecampaign, one powerful surge toward the global came in the I f)70sthrough the American Metrological Society, founded by FrederickA. P. Barnard, president of Columbia University. Calling on anillustrious assortment of scientists, he urged an intcmationalism thatgrouJlcled its cosmopolitanism on commercial exchange: "Thediversi ty of the eOllventional methods employed by different peo-ples for determining the quantities and values of material thingshave been in all times a source of infinite embarrassment to theoperations of commerce, and a serious obstacle in the way of intcl-ligellt in ter-colllllHmi cation between nations." Metrological reformon the Continent struck Barnard as a sign of hope, one that had yetto cross the shores of the l<:llglish-speaking lands. Remedying thatfailure was the goal of the society. On Tuesday, 30 December 1873,the group approved a constitution that set out to "bring [weights,measures, and moneys] into relations of simple commensurabilitywith each other." Metrologists would attack the zero of longitude,the units of force, pressure, and temperature, as well as the quan-tification of electricity, bringing their results to the attention of Con-gress, the states, boards of educations, and universities. It was, inshort, a lobby for focusing French rationalism through a eommer-eiallens and printing it on American civil society, from the school-

room to the railroad yard."


Cleveland Abbe, meteorologist and astronomer with the UnitedStates Signal Corps, found his way to the cause through frustrationwith patchwork time. In 1874, when Abbe had enlistcd amateurobservers to study aurora, his troops couldn't agree on a commontime base, confounding Abbe when he tried to combine the variousfield sightings. Appcaling to thc metrological society for help, withbureaucratic justice he was promptly madc chair of the committeeon coordinated time. With Barnard and the Canadian booster Sand-ford Fleming, Abbe became one of the most outspoken lobbyists fortime unification, producing matcrial usod before Congress in 1882and at international congresses in Venice (1881) and Rome (] 88 "3).111

Abbe's metrological society time team argued in 187<) that trulylocal times, in an astronomical sense, hadlollg vanished in favor of amishmash of railroad times. Consequently, the society urged "pub] icinstitutions, jewelers, town and city officials ... to regulate the pub-lic clocks, hells, and other time signals, hy the stauclan] adopted hythe principal railroads in or near their respective localities." One sllg-gestio]) was to strip the seventy-five various meridians down to threezones, corresponding to four, five, and six hours west of (;reellwieh.Such a partial unification, they judged, would he good. But one sin-gle time standard for the nation would be far better. Set six hours westof Greenwich, th is fully national hour would be dubbed "Railroadand 'lelegraph Time" for "these corporations exert such all influenceOil our every day life that we arc persuaded that if they once take thatstep towards unification about which they have been talking for manyyears, then everyone in the whole conununity will follow.':" Preciselyat the moment when Lc Vcrrier was urging French railroads to adoptastronomers' time "by example," Americans like Barnard and Waldowanted civil time modeled Oil train time.

Stridently modern, the metrological society resolved to lobbyboth state and national governments for changes that would extenddeep into the fabric of ordinary life. Observatories, allied with rail-roads and telegraph systems, could deliver time anywhere on the

! !1

The Electric Worlcl11la!J

continent. The metrologists insisted that railroad and telegraphtime be displayed by a coordinated clock in every puMic lmilding,every national and state capi tal, every liospi tal, prison, customhouse, mint, life-saving station, light house, navy yard, arsenal, postoffice, and postal car. "On aud after July 4th, 1880," they wantedone standard legal time for all purposes throughout the UnitedStates. 12 'Io win this battle, the metrological society knew it wouldhave to recruit railroad and telegraph officials as well as nstrnunm-ical allies, including Waldo and his counterparts at otherobservatories. As important a recruiting target as any was the thirty-three-year-old secretary of the Ccncra] 'l 'ime Convention of Rail-]"(J<1CIOfFicials and editor of Trovelers' OftlciCl/ Railway Guide for theUnited Stales and Canada, William F. Allen.

Allen was the time shuffler of all time shufflers, the bureaucratbchiud the endless lists of trains and schedules. IIwas Allen whoschcclulcd lhc local schedulers: Allen, the railroadm<ln who, morethan any other, stood responsible for organizing the myriad ironmads into a guide that allowed the traveler to make connectionsbel ween Iiucs, Ami he, at least in June 1879, equivocated before hecame to hack a plan for unification." On the one side, he was beingpressed by the scientists' continental scale of action: thcy wantedthe whole country under the rule of a single time convention. 011

the other, he .md the railroads had to accommodate ordinary peo-ple who were usee! to operating on local time. So he compromised,settling for the status quo that nailed time along the tracks to the bigcities they served. 111 [u nc 187<), Abbe dismissccl All ell's antique

a ttachrnent to calli llg it twelve o'clock when the sun happened tobe near the meridian. "The advantages of uniform time far out-weigh the first week's awkwardness of the proposed change. Abolish

old times is the watchword." I I

Time reformers popped up everywhere. One outsider, a teachernamed Charles Dowel, unsuccessfully petitioned Allen to adopt hiszone system." If Dowd was an outsider to railroading, looking in,

•116 EINSTEIN'S CLOCKS, POINCARE'S MAPS

Sandford Fleming was the consummate insider, a railroader andpromoter, looking out. The Canadian enginecr took to massiveprojects with an eye scaled to empire. Having cut railway linesthrough thc maritime provinces, put forward plans for the Pacificrailway, co-designed Toronto's Palace of Industry, set the beaver onCanada's first stamp, and later lobbied for the transpacific cable,Fleming proposed a system that would cover the world. He had notime for town council pragmatism, but instead entered with a pro-gressivist, imperial swagger, and a tincture of injured colonialpride. In 1876, he began writing articles hailing the new train andtelegraph technologies, while deriding as antique the time systemsthey shattered: "We still eling ... to the system of Chronomctryinherited from a remote antiquity, notwithstanding difficulties andinconveniences which arc constantly met in every part of theworld." Flcming imagined today's traveler heading by ship fromLondon to India. Hardly had this modern expedition left the shoresof England, and the voyager's time was wrong. Paris time displacedGreenwich time, only to fall to the times of Rome, Brindisi,Alexandria and then to new times assigned daily until the ship putsinto port in India. Maddeningly (in Fleming's view), Bombay timesplit between local and railway, with the railway time pinned toMadras. Such regressive confusion, Fleming argued, had to besimplifi ed. 4('

Fleming wanted a single, universal time convention for theearth as a whole, with each of the twenty-four zones labeled byassigning to the O-degree longitude line the name prime meridian;the letter A would stand for the 15-degree line 13the 30-derrrec, . b

line, and so on through X (34 5-degree line). "Universal," "cos-mopolitan," or "terrestrial" time was then determined by an imag-inary clock fixed in the center of the earth, with its hour handpointed permanently at the sun. When the earth rotated so thatmeridian line C crossed the hour hand's line of sight to the sun, it


11

,,' d, I II("( ; o'clock everywhere. When D crossed that imaginaryI,", II W;IS\) o'clock everywhere. Every clock in the world would

,I"I,i.I\' II,e same time simultaneously. If Big Ben said it was, . '.11 n (meaning 30 minutes and 27 seconds past C o'clock), then

" \\111 dd a clock at Times Square or downtown Tokyo, the "elec-1,1< I,·lcgraph affording the means of securing perfect synchronismIII ')ITf the earth." Here was a scale of electric time unification that

,1"';i1fcd even continental America. To accommodate local sensi-IIIIi lies, Fleming hatched watchmaking schemes. One allowed the11';("1 to rotate the whole watch face so the wearer's local noon (say,101 example, F or Q, depending on location) stood at the top.;\ uother design provided side-by-side clock faces, one for local, the

other for terrestrial time."'10 Fleming, such time coordination was vital for the larger conn-

tries like Canada, the United States, and Brazil; it was helpful forthe European nations of France, Germany, and Austria, and itwould obviously benefit Russia, with its ISO-degree longitudinalexpanse. But Fleming's Canadian vision still had its focal point onLondon: "It is of still greater importance to the Colonial Empire ofGreat Britain with its settlements and stations in nearly every merid-ian around thc entire globe, and with vast territories to be occupiedby civilized inhabitants, in both hemispheres." Railroads and tele-graph lines drove this unification. Some 400,000 miles of telegraphlines now ran over seabed and land; 95,000 miles of train tracksprawled through Europe and Asia. Railway men like Flemingexpected that the world would soon boast a million miles of rail

alongside even greater lengths of wire.

Lines of telegraph and steam communications are girdling theearth, and all countries are being drawn into one neighbour-hood- but when men of all races, in all lands are thus broughtface to face, what will they find? They will find a great many

u8 EI STEI 's CLOCKS, POI CARE'S MAPS

Figure 3.7 Fleming's Cosmopolitan Time. Having heguJl as all engineercarving railroad routes across Canada, Sandford Fleming /(lshiolled himselfas a great defender of a system of electrically based time that would link thewhole world to (/ single "c(),mlO/)()lital1" hour. In this 1H7<Jdiagram, he showedthe world itselia« a giant clock tin' which twenty-four letters would replace thetraditional reckuning hy 1, 2, or 3 o'clock. "C o'clock," he hoped, wouldbecome the universal time when all imaginary line {rom the center of the earthto the sun passed through. the longitude line conventionally labeled "c."SaURO:: FU':MING, "TIME RECt-:ONING" (1879), P. 27.

nations measuring thc day hy two sets of subdivisions, as if they hadrecently emerged from barbarism and had not yet learn cd to counthigher than twelve. They will find the hands of the various clocksin use pointing in all conceivable directions.

This chaotic condition, Fleming insisted, had to end."Fleming's first article "Terrestrial Time" failed to reach the


powerful audience he imagined. In 1879 he struck again, recy-cling his first attempt but now in even broader terms, pushingmore explicitly than before the need for a universal prime merid-ian (at Greenwich). The dustbin of history was full of failed con-tenders for this line, he noted. Cape Verde (about 5 degrees westof Senegal) had been one such putative zero meridian. GerarclMercator had fixed on the Island del Corvo in the Azores becausethe magnetic needle there pointed due north. The Spanish hadchosen Cadiz, the Russians Pulkovo (outside St. Petersburg), theItalians Naples, the British Cape Lizard (Cornwall), while Brazil-ians referred their world back to Rio. If one put the prime me rid-i;m at the grc,ltesl luunau construction, then it should cross theGreat Pyramid - or so cla imccl Jhc mystical Scottish Royal

Astronomer Piazzi Smyth.But when Fleming had finished with his ecumenical homage

to prime meridia of years past, he returned to Greenwich, fromwhich nearly three-quarters of the world's shipping set its course.Happily, lie reported, the British antunertdian (the line 180degrecs removed [rom Creenwich) ran through the Bering Strait,crossing a lilly hit of Kamchatka but otherwise spanning waterfrom pole to pole. Selting the prime meridian in the Bering Straitwould leave the world's (Creenwich-based) longitude linesuntouched and would necessitate only a minor adjustment in thelabeling of those lines. ]':xcoriating the French for their national-istic preference for Paris, Fleming laid the "universal" linethrough the observatory central to the British empire. Shippingand imperial power trumped history, mysticism, celestial mechan-ics, ancl other nations' nationalism." Fleming's proposal fell likemusic on the ears of American time reformers. Abbe informedhim in March 1880 that he was working to enlist telegraph anclrailroad companies; Barnard proudly displayed Fleming's

I· . t I 10cosmopo itan-time wa c .ies.Not everyone was sanguine about this new universalism. Barnard

1\


alerted Fleming that Piazzi Smyth was advancing contrary ideas. In1864, Smyth had decided that the Great Pyramid embodied the wis-dom of sacred Hebrew metrology, ancient knowledge that held con-temporary relevance: "seeing how our nation is agitated just now byquestions of a change in its hereditary Metrology, and is urged by apowerful political party to take a radically subversive, instead of acorrecting, improving, and reforming, step in that direction."Where French (and some British) metric reformers saw progress,rationality, and universalism, Smyth saw gestures "fatal to nationalinterests and connections." Where British units struck metric advo-cates as irrational, Smyth loved the inch and cubit as the last linksvia the Pyramids to ancient divine light. II

Barnard blasted back. Given the balance of political and culturalforce, the North American reformers judged themselves able, moreor less, to ignore Smyth's opposition. But British Astronomer RoyalGeorgc Airy could not be so breezily toppled So when Airyweighed in against Barnard in July 1881, it must have stung(Barnard immediately forwarded a copy of the letter to Fleming).Airy addressed Barnard politely but would not deign to mentionFleming by name. "It seems to me," Airy cautioned Barnard, "thatyou must begin with considering, OIl grounds of convenience andinconvenience, what: the mass of"{ieople want; and must think ofmeans of supplying that want." Whatever "the Canadian writer"might think of the traveler's travails, the issue of resetting one'swatch on long-line railroads was not a problem, claimed Airy. Letthe San Francisco-bound train from [ew York set its clocks by ew

York time; on the return trip passengers and railroad men couldsimply abide by San Francisco time. No, the practical problem wasnot on long American trips, but rather in the "limitohoptious" dis-tricts straddling lines of time change. "As to the Cosmopolitan Timewhat does a man living in Ireland or Turkey care about Cos-mopolitan Time: It is wanted by sailors, whose profession carriesthem through great ranges of longitude .... And there its utility

/


ends." Incredibly to Barnard and Fleming, Airy judged Greenwichitself a poor choice for a time center. '100 far to the east to be fairly

located within England, the observatory's sole claim to legitimacycame in being authoritative. For Airy, time should be unified onlywhere unification made sense, ,IS ill the island of England. But try-ing to establish a universal time was a futile battle for the inconve-nient goal of "hard and fast" lillie lines. "I do not imaginc that it will

ever he received.?"'vVriting to Fleming, Barnard tried to soften the blow hy referring

to Airy's excessively "opinionated" views and occasional past blun-ders, including his very public and wrongheaded intervention in thecontentious dispute between French and British claims to the dis-covery of Neptune. Barnard reported to Fleming that he had lob-hied Colonel Clarke of the Ordnance Survey in Britain with rathermore success: Clarke would support the cause of time unification.Bul it was clearly a delicate moment. All Barnard's political skillswere tested as he tried 10 get negotiators of the international Law of

atious to endorse lime reform. Barnard lost the chairmanship ofthe lillie committee to the vastly more famous William Thomson(Lord Kelvin), who would, Barnard confided, need to be "edu-eated."Worse, no one hac! bothered to notify Thomson that he wasOIl the Law of Nations time committee, much less its chair. Butwh ilc Burnard was trying to in jeet enthusiasm into Thomson, hehad to dampen Fleming's boosterism, pleading with his northernally in letter after letter to reign ill his scatter-shot polemics: "Jesteem it bad policy to evince uncertainty on the eve of battle, orto change point in face of the enemy." Time languished inCOI nmittee. 53

The apostles of unified time faced difficulty back in NorthAmerica, too. While Barnard and Fleming stumped for a unifiedinternational time with Greenwich as its center, the United StatesNaval Observatory aimed for one fixed to the nation, not the world.Naval astronomers scoffed at the idea of ordinary people gaining

~-------1-2-2------E-IN-S'~NS~'=CARi.S Mm

;-~ :

anything whatsoever from a worldwide time, and opposed thelocality of time zones, On the contrary: thcy wanted a European-style scientific time, grounded in a national observatory (theirs),uuiforrn for the entire country. Rear Admiral John Rodgers, supcr-intcudcnt of the observatory, girded for battle in June If)f)], look-ing skyward for support: "'I 'he Sun is the national clock used bymallY, and its position regulates the hour of rising, eating, working,aud of going to rest. No other clock can supersede it, as it is the 011eordained by Nature to regulate man's life." 'Iruc, he conceded, rail-roads uccclcd their own time, .mcl the federal governmellt couldmaucla!c tile printillg of W;lshingtoll time ill the schedules. But"It Ihe people who (10 not carc for scientific time arc a thousand Forouc of those who do, .u«] besides, I see llO overpoweri ng reasonwhy we, with fifty millions otpcop]c slioulcl t;lkc the scientific timeOF;1 ua lion II<nglane!1 with ollly thirty mill ions. If numbers aur]growth prevail, thcy shollld accept ours. I rhink that tile fecling ofuntional ilv is too strollg with tile masses I~)]'philosophers to Ldk it;IW;IY·"Scielltists, Rodgers concluded, "souictirucs overestimatetheir FlIllc:tiollS.";1

In the increasillgly timc-wirccl world of the carly I i)i)()s, lin rcreformers clllipaigllcd for limc unification Oll conflicting scales.Banlarcl, I"lcmillg, aucl lh oir allics puslicd for a globc-covcrillg"'I crrcxhial" time; the grcat uatioual observatories of France,Britaill, .iud th« United St;lles each advocated its own nationaltime. Railroads ami cities were the wild carcls, much dcpcudcd 011

the couvcntious thcy chose. Woulcl cities conform to train time asthey did ill Britain and much olAmcrica? And if so, by what geog-raphy of simultaneity? Or wonld trains retain their own time, as illFrance? Convenience ami convention were the watchwords, hutwhose master clock woulrl set which lesser clocks? In late I f)f)2 ,Allen endorsed a compromise proposal: set one-hour timc zonesfor the whole North American railroad system. The mctrological

The Electric Worklmap

society wclcomcd Allen's efforts, enthusiastically rcporting thatCongrcss resolved to instruct the president to call for an interna-tional convention to which the U.S. would send three delegates.New York was contemplating switching its time ball to Grccnwiehtime, thc U.S. Post Office adopted a common time, and Barnardwas lobhying President Chestcr J\. Arthur while stumping for timereform with Secretary of State Frederick T. Frclinghuyscn. Boththe American Society of Civil Fngineers and the American Asso-ciation for the Advancement of Science backed the effort. Ii On therailroad tracks, the time unification schcme rolled cvcn moreswiftly. Somc southerners briefly rchellee! with a systcm tailored totheir needs; hut their move was crushed. \(,Whcn Allen and the rail-road presidents, managcrs, passenger agents, and snpcriutendcntsmet for their Ceneral Time Convention on II April li)i)j ill St.

LOllis, Missouri, railroad sentiment seem cd to have turned towardthe change to an hour system divided along the 75th, 90th, and

l05th meridian lines.Allen weighed in hard: " ... the 'Hard Scrabble' systcm now in

use, with its fiFty diffcrcnt standards intersecting and interlacingeach other, is an abomination and a nuisance which cannot betoo SOOll rcmcdiccl." To displace such chaos Allen presented hispiece de resiutance: a map with three longitudinal time zones, eachtinted in its OWllcolor, and its enemy, a multicolored quiltwork ofthc current division of time. Enthusiasts could buy either map,though thc second one (dcpicting current chaos) couldn't bc massprinted (too complicated) and cost twiec as much. "A singlcglancc at this map is sufficient, I think, to convince cvery one ofthc absurdity of the present status of this matter." As Allen madeclear, the time zone systcm could have its zero linc anywhere.True, the temptation would be grcat to pin the zero of longitudein Washington, D.C. But such parochialism was, he contended,

unacceptable:


(

~~:==~~~~'.'• l"c,,1 "sun" lim.,. by whi<h Ih"'I'~lnsol

one- or mo,,,, r.,,]/o,,d, ",.,.,,~ or""~lodbdor(\ S!',nd",d Tim •• W/II IIdoplcdfigure, indi(J'" I"(.JI lim.,. when il wal

,J. 12.00 o'doc~ noon in W'lIhir19Ion.D. C

(- •••••• SI""",,.,d. T,m" ZOO" boundaries.,Jopt<l'd by r,,,lro,,dl Nov. 18. 1883.

_Prole,,! S!,lndolrd T,n"~zonebound.,,,,,,

L_,-",~",.",='_""'_'_"_..o. .._·_'-."__ ., ..-_~.,.,,·,., __,,cc_"".--

1~~;_J"::-~;~~'=:~--~:'~~~~~~~~;o~E2=--'~~.=,=,::::,~-,::~S~~'J::'-=-~;~~~~~;

l,'igllre 3.1) 'Trains, Times, and Zones. Time lIlzijica/ion-(/Il issue {()Tieionn-er«, astronomern, and slawlardizeTs-g(/ined IJ()wer when railway «chedulers100/, Ul) the cuune of zoned lillie to avoid/he IJroliferalio71 of Iocal times. Thisrailway mal) IJlo/s many or the difFerent local times he/rife the zone reionn ofNovembe: 1883, as well as the dividing line» thai the railways adapted «iterthai dale, SOURCI':: CARl.TON). CORl.lSS, 'l'w:ll:w(w'i'w()/'i()()NS (1')S2), 1'. 7.

We are, all of us, more or less imbued with a fecling of local pride,and if the meridian lime of the "Hub of the Universe" is the stan-dard by which the trains on our particular road arc run, we feel likeholding to it. But, my friends, what right have you to claim thatparticular meridian as bclongillg to your city. '1'he villages of CUIll

Tree and of Hard Scrabble arc 011 the same meridian and have asmuch right to give it a name as your beautiful city has .... For allordinary business transactions one standard is as good as another,so long as all agree to use it. 57 /

II

I1

The Electric WorldmalJ

Time was a convention, an agreement like any other that would,depending on the accord, unify cities, lines, zones, countries, or theworld. Inscribing that arbitrariness into the collective language wasas great a transformation as the acquisition of a regularized time

awareness.Both astronomers and railroaders viewed the new technologies of

transport and connnunicatiou as disciplining time more effectivelythan any school. As Allen put it, "Railroad trains are the great edu-cators and monitors of the people in teaching and maintaining exacttime." Train lines had altered the experience of time across Europeand North America; more than that, for an ever-growing portion ofthc population, railroad schedules had come to define time, toinstantiate synchronicity. Indeed, without the quintessentially mod-em trains and telegraphs, the temporal structure of the world would,for most people, drift from its moorings. "I venture to assert," Allenadded, "that if th is city were cut off from railroad and telegraph COIll-

unmication for all entire month, and on the first night all clocks andwatches were simultaneously and surreptitiously set half an hourFaster or slower, not one person out of a thousand would ... discoverFor himself that any change had been made.'?'

Windillg \lp the convention, Allen slipped into a revealing para-ble that was at once tongue-in-cheek and reflective of the railroad-ers' position, since in setting conventions of time they weredetermining the electric enforcement of simultaneity for the COUIl-

try as a whole:

It is on record tlia l a sural] religiolls body once adopted two reso-lutions as a declaration of its faith. The first was,Resolved, That the saints should govern the earth, Second,Resolved, That we are the saints.")

Resolved or not, some among the railroaders saw the time mas-ters as anything but saints. This opposition was not, as Allen some-

r---~---------------------"----'-----'-",-'"p.'126 EINSTEIN'S CLOCKS, POINCARE'S MAPS

times suggested, based on a reactionary attachment to the removalof God's own noonday sun, Protesters uniformly accepted the prin-ciple of a railroad-and-telegraph-determined simultaneity, Therewere, after all, already effective time zones carved out by railroadsfrom the Atlantic to the Pacific, A railroad guide in September1883, for example, showed some forty-seven lines running on NewYork time while thirty-six took time from Chicago's clocks, whilePhiladelphia's clocks govcrncd another thirty-three." Every trainlinc accepted the conventionalism of time, This fundamental fea-hue oflate-nineteenth-century time was so deeply hammered intorails and wires that it was as present to time-zone protesters as it wasto boosters, What then did the dissenters dispute? One newspaperarticle, defending a single national time, targeted the observatories,where astronomers, in charge of far-flung outposts, had grown fatfceding time to regions; local simultaneity had become "the meatUpOIl which these star-gazcrs feed." Another anti-standard timecomplaint carne from an almanac publisher: sunrise and sunsettimes would be thrown into a cocked hat by time unification." Mostprotesters simply disputed the dividing lines of conventional sin 1111-

tan city, their antizonisrn grounded in the convenience oflocal trainschedules, or regional, national, or universal time, Very few invoked"God's true time,"('Z

(With just a week before the General Time Convention was to

begin on II October 1883, Allen told a dissenting Massachusettstrain line that he now had some seventy thousand miles of roadlined up behind time reform. As mileage mounted, he treated theopposition with less solicitude." Cities too fell into place, III Boston,the trains agreed to switch to standard time if the Harvard Ohser-vatory and its dependent institutions would do so as well. When thetime convention delegates at Chicago's Grand Hotel received a cru-cial telegraphic concession from the Bostonians, it was clear thatthe reform would pass: "The city, the railroads, and the observatoryonly await affirmative vote of Convention before fixing date for

The Electric World11laf)

changing all public time in Boston," Applause echoed through theroom." Saluting the inevitable, thc Naval Observatory too agreedto the zonc system, setting aside its national-scientific aspirations."

When the vote came, railway officials canvassed not hy the 11Ilm-ber of delcgates for or against, or evcn hy the number of companiessaying yay or nay, Instead voting was by mile of track (appropriatelyenough), For the reform: 27,781 miles of track within the convcn-tion plus 51,260 miles of nonmember rails, yielding 79,041 ironmiles in favor of Creenwich-bascd time zones. A mere 1,714 trackmiles lay opposed. "Resolved, that we hereby pledge ourselves to runthe trains upon our respective roads hy the standards agreed uponand to adopt thc same when the next schedule goes into effect," 18November 1883,(,('Allen wanted a system ot branchcd electrically

coordinated clocks that would join all thc time balls and train clocksand urban clocks together, pinning the whole to Crccnwich."

As the seventy-nine thousand miles of railroads hoped, New Yorkagrccd to zone simultaneity on 19 October 1883, when MayorFrankliu l<dson signed his approval. Edson forwarded the recom-mendation to the city's aldermen wrapped in a sheaf of railwaydocumcn ls and instittttiona] endorsements. By year's end, conven-tionality talk about lime was as common in New York as Paris; cvcnan American hig-city politician could proclaim: "What is called[ocal time is only a mean which differs from astronomical time, butwhich suits the convenience of thc people in any locality becauseall agrce to use it." Since the majority of the community benefitsand difference is slight, the mayor reasoned, why not conform to thenew standard?" "Conventional and arbitrary," chimed the cityfathers, t-ime "should be accommodated to that which is most agree-able to the interests of the people whom it is designed to direct."With those words came the resolution that at noon on 18 Novem-ber 1883, not only thc railways but also New York City time wouldbe that of the seventy-fifth meridian, running several minutes westof City Hall."


'rime reformation had passed from a myriad of competingsimultaneities to a tightly coordinated fact, plucked from tele-scopes, confirmed by humming iron rails, then wired into metro-politan clocks. Barnard wrote Flcming on 22 October 1883,reporting that the railroads had finally successfully attacked time:"This settles the question forcver, for this hemisphere. In Europe,we cannot hope for a similar result in our time. Paris will probablynever consent to use Creenwich timc, but we need not concernourselves about that." Perhaps, Barnard mused, the North Ameri-can triumph of zone simultaneity "[m\ight stir up dilatory govern-mcuts to take action in regarclto the proposed Prime Meridian

Conference at Wash ington."711

Time inu: SfJ([ce

In the Paris of micl-1884, however, observatory time was not, for asingle minute, mainly abouttraiIlS and city clocks. The Paris Obser-vatory hacl never been structured as a couuucrcinl enterprise. '[ 'imc-distrihuting astronomy, at least among the Polytec[llIici<llls nnd thcirallies, did not have the slightest role (as for IlIany of their Britishcounterparts) in sanctifying empirc with natural theology. COll-vcrscly, even among Allglo-Ameriean metric boosters, the charmsof the meter tended to he charms of facilitated, international com-merce. For Fre!lch savants including Poincare, his teachers, andcolleagues, exchange advantages might well he apparent. But therewas far more to decimalization, unification, and rationalizationthan that. These were longstanding Enlightenment ideals, idealsthat joined French aspirations to restore national dignity after the"disaster" of 1870 to the establishment of the secular, progressiverationality that they held to he the hallmark modernism of the

Third Republic itself.For Poincare, progressive and technical goals were united in the

Bureau of Longitude, one of the great centers of enlightened sci-

The Electric Worlclmap

ence since the Revolution. By 1884, the Bureau's principal activitywas using observatory-based electrical time to Illap the world elec-trically. Indeed, for the whole period from the mid-1860s to the1890s, France, Britain, and the United States raced to establishsimultaneity over a sprawling network of undersea telegraph cablesto fix longitudes and redraw the globalillap. This race for symbolicmap-possession contributed to the explosive atmosphere surround-ing the prime meridian showdown slated for October 1884 ill Wash-ington, D.C. But the stakes involved in setting the electricworldmap were higher still. IJl J 898, when Poincare argued ill "TheMeasure ofTime" that simultaneity was a convention, he had beenfor over five years <I"member" (one of the handful of guiding fig-ures) at the Bureau, serving in that capacity from 4 January J 893until his death ill 1912. In September 1899, about a year and a halfafter he published "The Measure of Time," Poincare was electedpresident of that institution, a post he rose to again in both 1909 and19 J O. No figurehead, Poincare issued reports, led commissions, andoversaw longitude operations during some of his most productive

years.The Bureau of I ,ongitude? One might imagine such a calcula-

tional lnucaucracy to be of little interest when set against the higherreaches of Poincare's mathematical physics or his inquiries intonon-Euclidean geometries, the stability of the Solar System, or dar-ing philosophical accounts that put conventions ill place ofabsolute truth. But the Bureau's task is central to our story. Rightlyunderstood, the vast theory machine it ran will alter our under-stancling of a turning point in Poincare's rcconccptualization of

time.On 7 April 1884, the astronomer Herve Faye stood hefore the

Academy of Sciences in Paris to read a report hy Lieutenant Octavede Bcmardieres that raised a crucial issue. De Bcmardiercs was oneof the first of a new type of naval officer trained not only for hisocean-going career but also brought up, so to speak, by the

------ - . -

, '

"I ,-

I

EINsn:IN's CLOCKS, POINCAR~:'S MAl'S

astronomers at Montsouris. He so excelled in his astronomy that hewas soon co-a uthoring a massive 336-page report on the very unoce-anic longitudinal difference between Berlin and Paris. But to theAcademy of Sciences, de Bernardieres reported that the precisionoflongituclc determination had increased dramatically over the pre-vious years, sometimes thanks to the transport of accurate clocksand sometimes by astronomical means. In 1867 these older tech-niques fcll by the way as the first cable spanned the Atlantic Ocean,closing the longitudinal gap between England (Greenwich Obser-vatory) and the United States (Naval Observatory, \Vashington).Throughout the 1870s and J 880s, the new technology undergirdedall long-distance longitude work as telegraphs coupled to subma-rine cables crisscrossed all the world's oceans."

[n Britain, especially, factories chumcd out prodigions quanti-ties of cable. First, a thick copper conductor was insulated bycommercial "gutta" -;J newly developed mixture of gUill, gntta-pcrcha, resin, and water. Then the manufacturers wound jute yamto provide a cushion between t-he gutta-coated cable and a ring ofthick iron wires to p\.otect the copper core from hreaking. Morejute bound these iron wires together; then more wires with moreyam (at least near the dangerous roeky shore), and a final water-proof outer sheathing of the Malayan rubberlike gntta-pereha.Steam-powered ships carried the mile-long sections out to sea,where on board cable masters tied them together to span thou-sands of miles and someti mes hauled them out again when they(all too often) were split hy sea life, icebergs, volcanoes, anchors,

or sharp rocks."As de Bernardicrcs knew well, the French had long been frus-

trated by the discrepancies ill map making that resulted from longocean voyages (which rendered chronometers unreliable). TheFrench Bureau of Longitudes was directed in 1866 to fix clear sec-ondary locations around the globe. It duly launched six parties tothe various corners of the world. Their assignment was to use the

r-0", f.


position of the moon against the background of the stars to deter-mine the local longitudes of sites in North and South America,Africa, China, Japan, along with others in the Pacific and Indianocean islands. Such mapping demanded a monumental cffort, andthe French government withheld neither expense nor effort. Inprinciple, the idea was simple: if astronomers in two parts of theworld could both pinpoint the time at which the position of themoon reached its highest- point on the celestial sphere, then thoseobservations would he simultaneous. The navigator would look upon a chart what time that was back home and observe what time itwas locally. ' I 'he difference gave the longitudinal difference betweenthe two points. A difference of six hours? -90 degrees of longitude.

But moon culmiuatious were notoriously elusive. Evcn the mostskilled astronomers seemed unable to fix the moon's zenith againstthe stars without significant errors and that was a huge problem.I Icrc is why. The earth spins on its axis once per day, making thestars appear to rotate every twenty-four hours. The moon travelsmuch more slowly against the background of the stars, about onceevery thirty days. So in the time the moon crosses a given angle, thestars have moved thirty times that angle, thereby multiplying anyerror by thirty. Piloting a ship through distant shoals with that kind

of uncertainty killed sailors."Because of the difficulty of "shooting the moon," astronomer-

sllfveyors bunting their longitude reached for other, more easilymeasured, heavenly events. Navigators had been using total eclipsesfor centuries; Columbus used one to fix his longitude on his transat-lantic explorations. So when American map makers wanted to fixthe longitudinal relation between Washington and Greenwich,ohserving the moon-darkened sun seemed promising. The UnitedStates sent a steamer to Labrador on 18 July 1860, hoping to com-pare the results to that same event as viewed from Spain.

Another longstanding practice of the astronomers was to watchthe moon as it arced across the night sky until a star winked out


/

behind it. That moment of disappearance (occultation) could alsobe exploited to set simultaneity between distant points. Measure thetime of occultation locally, look on a chart (or wait for a report bypost) to find what time that same event was observed in Grecnwichor Paris, thcn subtract one from thc other. So astronomers both inthc United States and Europc watched and measured with enor-mous care as four stars of thc Pleiades dipped under and then outfrom behind the moon. An occultation of the planet VClJUStookplace on 24 April 1860; astronomers huddled in wait for it in theFredericton, New Brunswick, and Liverpool observatories. Findinglongitude W,lSpart of the job description of French, British, andAmerican astronomers, and they deployed evcry conceivablemethod to find it. But the quest to link the United States to the"well determined li:mopean observatories" remained unfulfilled.Kvcry expedition produced a new number."

Mapping offered both symbolic and practical mastery over space.In the great land grab of the mid-nineteenth century, fixing posi-tions was critical for trade, for military conquest, for laying rail-roads." When the United States plunged into civil war, the CoastSurvey became a strategic asset. Congress had long beforedemanded that the smveys cover rivers as needed by commerce ordefense. Now map makers hoped to deliver on that assignlllent,working closcly with Union admirals in North Carolina and 011 theMississippi. At first, the telcgraphie survcyors, including CeorgeDean, set about rcducing data already in hand to provide precisepositions of key southern military sites, dctermining longitude dif-ferences between them." Watching, measuring, calculating: thesurveyors plotted Rebel emplacements around Charleston andSavannah, while a small group of reconnaissance topographersjoined General Sherman on his march from Savannah to Golds-boro, Georgia. When the war ended, the surveyors began plottinga future using their wartime telegraphic surveys. They had new andbetter measurements of almost every major town from Calais,

The Electric Worlclmap 133

Maine, at the northeastern edge of the United States, clown to NewOrleans. Benjamin Gould (who headed the survey's telegraphiclongitude effort) and his team looked eastward to fill the one criti-cal gap-New York City to Washington-that remained in thequest for a complete electrical map of the United States cast of theMississippi.

The surveyors looked to the ocean. They did so ill some desper-ation, because no matter how hard the survey had tried, conver-gence on a longitude difference between Europe and the UnitedStates continued to prove infuriatingly elusive. They reviewedmoon culminations, restudied data on the occultations of stars andplanets, and pored over old ehronollleter results. But reanalyzingold data was simply not enough: "The discordance of results, whichindividually would have appeared entitled to full reliance, is thusseen to exceed four seconds; the most recent determinations, andthose which would be most relied upon, being among the most clis-corclant. No amount of labor, effort, or expense had been spared bythe Coast Survey for its chronometric expeditions, inasmuch as themost accurate possible determination of the transatlantic longitudewas specially required by law." In addition, the latest chronometerstudies differed from the best astronomical studies by an embar-rassing and irreducible time difference of three and a half seconds."No one had any idea whieh result to believe.

Only underwater electrical telegraph cables could break theimpasse. Beginning in August 1857, missions had struggled againstthe North Atlantic to lay a telegraph line. Cables broke again andagain; in June 1858, thc fleet once more launched from Plymouth,I<:ngland,with the vast cable. Just three days out at sea, a gale toreat the ships ceaselessly for nine days. Despite significant damage toone ship (and one sailor so terrified that he lost his reason), cable-laying continued. On 6 August 1858, the first signals finally passedthrough the cable, followed by a cable break and the cessation ofsubmarine cabling during the Civil War. Pulling out from Valentia

',-------------------------------_.- - ------------------

f ,,;_,_:,V'- -:, EINSTEIN'S CLOCKS, PorNeARr~'s MAPS

Island in southwestern Ireland in July 1865, the Great Eastern, amammoth ship five times larger than any other, began haulingcable toward Newfoundland. Twelve hundred miles later, both thecable and the ship's lifting gcar sank into the sea. The mission wasaborted." In 1866 another crew set out, this time aiming to run amuch-improved cable from the tiny fishing hamlet at Heart's Con-tent, Newfoundland (on the eastern side of Trinity Bay, aboutninety miles from St. John's) to Valentia. This time: success. Com-munication started on 27 July 1866, and the sl1fveyors immediatelybegan sending time signals. Gould dispatched his longitude teamin small groups to staff the dilapidated way stations up the EastCoast. 'I(J inspect the telegraph line from Calais to Newfoundland,the expedition chartered a schooner, plying from Nova Scotia'sCape Breton Island to their destination at Heart's Content, New-foundland. Every mile, repeaters (relaying the signal) neededinspection; they had to crush-train dozcns of isolated telegraphers.""

Gould himself set sail for J .ivcrpool and 1,()lldOIJ 011 12 Scptcm-ber 11)66by the Brihsh mail steamer Asicl, first to confer with theBritish cable COll1pany officers and thcu toohring his measuringinstruments h) the Irish terminus. BlIlIlping through thc Irish couu-

trysidc 011 a jury-rigged spring-cushioned cart, the astronomershauled their precarious tower of crates forty-two miles, then ferriedtheir goods to Valentia across the straits from Killarney. Conditionsat cable's end were discouraging. The British company refused theAmericans permission to pull land lines into electrical contact with

the undersea cable for fear a lightning strike would damage theirfragile leash on the New World. That meant the Americans had toset their observatory adjacent to the telegraph company building atFoilhornrnerum Bay, "remote," as the time men put it, "from anyother dwelling-house except the unattractive cabins of the peas-antry." On this rugged terrain, the time men hanged together theirmakeshift observatory, 11' x 23', bolted to six heavy stones buried inearth, protected from southwest gales by the adjacent telegraph

The Electric World111cJ!J

house, and shielded by rising ground from northwest weather. Thelarger room was their observatory; the smaller, on the eastern end,became their dwelling. Their lab was simple: a rigid mount for thetransit instrument, nooks for clock and chronograph; a spot for therelay magnet that woulcl pass the signal along toward Greenwich,the Morse register, and a recording table."

From what Gould clubbed Valentia's "peculiarly unastronomicalsky" came rain. Buckctsfull. Clouds allowed but one or two glancesof the noontime SUllo When the sun did poke through, theastronomers, ever vigilant, fixed their meridian. Finally, 011 14 Octo-ber 1866 at ~:()() ;\.M., the Americans glimpsed a few stars throughthe haze and took transit readings. J .ocals reported that for the eightweeks prior to tire surveyors' arrival it had rained at Valentia everyelay withoi Ii exception. During the seven weeks that the survcy crewlived and worked in their Irish shack by the sea, they saw four dayswithout rain and only a single clear night. "The observations were,ill general, made during the intervals of showers; and it was all eventof frequent occurrence for the observer to be disturbed by a copioi ISfall of rain while actually engagcd ill noting the transit of a star."Time sentries at the other end of tire line in Newfoundland had itworse, 'J Uegraphic Surveyor Ceorge Dean spied nothing, not a sin-gle glimpse of tire sun, moon, or stars.

I lcrc was Victorian high technology on the ragged edge ofBritain, powering their transoceanic signal with a battery composedof a percussion gllll cap with a morsel of zinc and a drop of acidu-lated water. Weather gods permitting, the Irish station would cable"COULD" in Morse code; Newfoundland would respond"DEAN ," followed by time signals - half-second pulses punctuatedby five-second intervals. At both ends of the cable, teams hoveredover instruments. After crossing the Atlantic, thc signal was too weakto drive the drum recorder, so they used the mirror galvanometer,a vastly more sensitive device invented by British physicist WilliamThomson. A delicately suspended mirror with a tiny magnet glued


to its back reflected light from a kerosene lamp. Nearby was a coilwired to the undersea cable. When a signal current coursedthrough the cable, the coil became an electromagnet, gently twist-ing the little permanent magnet with its attached mirror, whichshifted the reflected light of the kerosene lamp against a mountedsheet of white paper. Even the weakest of transoceanic time signalsbecame visible. Anticipating the signal, observers would focus thebright light of their kerosene lamp 011 the mirror. And wait, hourafter hour, in the cold, damp night, hoping that an electric currentcrossing under 4,320 miles of ocean would dance a tiny spot ofreflected light across a soggy paper sheet.

The mobile astronomers strictly followed their disciplined hard-won procedures, pried from longitude campaigns that both Gouldand Dean had run during the Civil War. Gould's team received itsfirst signal OIl 24 October IB(l); in the weeks that followed, Couldand his telegraphers eked out lour more exchanges in tiny windowsof astronomical weather. An ocean from Gould in Newfoundland., .. , ' , .,Dean's struggle to relay the signal down to Boston was much lesssuccessful. As Ihe cable snaked along the eleven hundred roughmiles from Heart's Content to Ihe entry point into the United Slatesat Calais, Maine, comnumication broke down "day after day, andweek after week." Nothing worked. Suddenly, on 11 December, asharp frost gripped the defective landline coming into Calais. Allat once ice admirably insulated the wire and the pulse shot likelightning from Heart's Content to Calais. Just before New Year'sDay 1867, the Newfoundland team steamed into Boston Harbor,having bagged the longitude differcnee between Harvard andGreenwich observatories."

With the Atlantic wired for simultaneity, the tempo of electricmap-making only increased. Immediately following the British-American collaboration, the French hauled a line from Brestthrough St. Pierre off Newfoundland to Duxbury, Massachusetts.American astronomer-surveyor Dean and his peripatetic team of

The Electric World11lop

';\Lrveyorsdeployed again, almost immediately, to begin planningwith the French naval authorities for a time check Once the Brest-Paris line was secure, the surveyors had their dream, a series of tri-angles that would serve as a double check of their longitude results.For example, the longitude differences ought to (and did) add tozero if one went from Brest to Paris to Greenwich and back to Brest:

(Brest-Paris) plus (Paris-Greenwich) plus (Greenwich-Brest) = O.B]

The French Naval Lieutenant de Bernardieres was all too awarethat his American and British counterparts were on the longitudi-nal march. In the spring of 1873, at his superiors' instigation, U.S.Naval Lieutenant Commander Francis Green had begun sendingsuboceanic time signals to map the West Indies and Central Amer-ica. Traveling the seas in the side-wheel steamer The Gettyshurg,Creon's team hrought precision to the longitude of Panama, Cuba,Jamaica, Puerto Rico, and many other islands." On his return in1877, the authorities set the lieutenant commander to work again,this time to exploit the newly laid telegraphic cables crossing theAtlantic: London to I .isbon to Recife in northeast Brazil. For thefirst time the American Navy could ply its hydrographic trade allalong the eastern coast of South America from Para to Buenos Aires.At last, the Navy boasted, it would settle the much-disputed Ioca-tions of places like Fort Villegagnon (in the Bay of Rio de Janeiro),where previous longitude men had clashed over an astonishingthirty-second time discrepancy, an eight-mile uncertainty overwhere one's ship wendelhit the eastern edge of South America.

With the help of the French, who shot their Parisian signalsdown through the wires to Lisbon, the Portugcse too joined theGreenwich-based map-making scheme." At Porto Grande off theBrazilian coast, the longitude team halted, waiting for the "sick sea-son" to subside before they dared land at Pernambuco: "A less inter-esting place than Porto Grande to pass two or three weeks could not

EINSTKIN'S Cl.OCKS, POINCARE'S MAPS

l'~-

be found," groused the Americans. "The island of St. Vincent ismerely a heap of cinders.'?" Finally, the astronomers hopped a royalmail-steamer into Pernambuco and set the machine into motion: apulse from Greenwich Observatory to Land's End, down through828 miles of undersea cable, out from the instrument room of theEastern Telegraph Company near the lighthouse at Carcavcllos,then back out from the Royal Observatory of Lisbon across theAtlantic, into the grounds of the Brazilian Naval Arsenal, up insu-lated wire over the arsenal walls, along the roof of the port captain'soffice, through the esplanade, by balconies, and down to one ofThomson's mirror galvaJlometers, where it would sway ils beam ofwhite light.

Subtlc, evanescent, and unreliable. Yet when that electricalpulse finally reached Rio ill July IHn, it was of royal significancc.Brazil's Emperor Pedro II had bccu ill the United Stales duringIH76, then launched a greal I':uropean tom, visiting 'I 'my withl lcinrich Schlicmauu, receiving COlli1111 III ion at" rhc Iloly Sepul-cher ill Jerusalem, and reveling with Qucen Victoria's daughler andher husband ill Vienna. In Paris the Academy of Sciences inductedPedro as a foreigll associate; Victor llugo received him ill cclchru-tion of Iitcraturc. Back in London, he lunched with the Queen alWindsor Castle. Civell this public life, and apparently all equallyentertaiuing private one, Pedro returned somewhat reluctantly toRio. Nothing, however, could keep His Majesty away [roru Lieu-tenant Commander Green's ramshackle observatory to witness theelectrical arrival of European time."

Today the word "observatory" may bring to mind a romanticimage: a glistening hemisphere perched on the craggy peak of amountain; the astronomer, sliding the sky slit opeIl, swivels his greatbrass telescope to view the heavens, while white-coated assistantsshuffle quietly at his side. Not for Grcen and his U.S. Naval team,who would eome to town (such as it was, say, in Porto Grande) andset up shop. Finding a location with a good view of the sky near the

The Electric Worlcl71lClIJ 139

telegraphic office was obviously key. They would then scrape ameridian (north) line onto the ground and build a cement andbrick pier. On top the astroexplorers set a small slab of marble thatthey carried with them and, on top of that, their precious brass tran-sit instrument, through which they could watch stars cross a spider'sthread that marked the meridian line. It would take two sailor-astronomers about an hour to assemble their portable wood obser-vatory (8' x 8'), with a canvas top ill case of rain. Into this tiny stationGreen crammed clocks, telegraph keys, and either a recordingdrum or a Thomson galvanometer to display the incoming signal.When the observer needed a telegrapher at his side, the room was,

one could say, cozy.Having entertained Pedro II witlithc clectromapping of Rio, the

American Navy sailcc] Oll. I<:arly ill] f)fn, Washington ordered theteam to the west coast of South America now that cables joined ittoo to the telegraphic system. This new expedition followed cablesrunning from Galveston, 'texas, Ihrollgh yellow-fever-infested VeraCruz in southeastern Mexico. With Vera Cruz on the electricworklmap, they sailed down the western coast of South America,hopillg to exploit the cable binding Salina Cruz in southeasternMexico to Valparaiso, Chile. The team faced down quarantines at

cw Orleans and Galveston, only to arrive in Peru in the midst of

the Cliilcan military occupation.Thanks to the intervention of the American minister to Peru, Mr.

S. L. Phelps, the occupying admiral of the Chilean army promised

10 assist the time hearers. From Lima, the navy men headed southon 13 October 1f)f)3, tying Valparaiso to Lima, and by carly 1884they were banging together their wooden observatory in Paita, Peru.Pounding rain drenched the desiccated town for the first time inseven years: "the soil of the place, ordinarily arid and dusty, was con-verted into a sickening and fetid mud ... the whole town ... ren-dercd almost uninhabitable.T" Furthermore, "operations in Peru,"the officers reported, "were at points occupied as military posts by


F:g:tre3:9 Portable Observatory: Bahia, Brazil. American Naval oll/cers

deler/l1l1l1ng «nnullaneitv-c cnu] there/fire low..til udina] 1'/'/-'- '.1" b( (I creuccs-c n, ore er toIIW/J more precisel» 11 A ' 1 ', " 7C rvucncas. ,ongllucle exbcdil icni» bv Frcn 'iJ Il-'I' ,II I A " ' cu, It ./.1 I,anc niencan ieam« were {iar! scientific par! inili! , 1 I. 'I ," , " ,_., I my, auc [rar! ex]: orauan,I l,e, (/.\11())WmIC(il o/J.lervatones" often 110 more than f){)rtahle wooden shuck«accoinbaniei} hy a [ew {nece« 0/ electricalle'egrdfJh eqlli/JllIelll, «nue uuumetsIIllrrors, and a slIrvevor's iclesco]«: 'l'h! 7' 7 . ", b "li I"" , ' , e) came (/1 CI cost. numerous surveyors(,Ie( of disease and accident while hyillg 10 fJill eleciricalsilllu/t({llCily to theS iore« oflhe Amencm A '1 I I \(,' ,.. ", ,\ a, ana j trica. S()l]I(CJ<:: CIU:i':N, /{I-:I'()/{I()N'I'VU:C:II,;II'I/IC

[)I,:n-:I(,\/I,"I,\I I( iN (11)77), i,'I()NTISI'Il-:CI':,

an,illvading army, and the observers had to contend with the dila-~OJ I~less, and 111 the case of the military commandant at Arica theindifference and stupidity, of officials," not to speak of customdelays, fog, and brokcn cables, Yet on 5 April 1°°4 tl A· "ff " / . . . ()O , le.· Tll CLl Cel I]

o rcers set sail for New York with their South A "',,I . it I W) mcncanongl uc es.'

In tiny, far-flung observatories, the American British ' 1F- ,I ' " , anc

renc 1 sentnes of time took their readings from the skies and

The Electric WorlclmafJ 1.[1

matched them against the pulses from their cables, Stars told each

station its local time, cables whispered to them of time somewhereelse, It was devilishly hard work, demanding precision results, strongcables, and orehcstrated teamwork. One of de Bernardicres' Frenchcollahorators pcrehcd his station near thc ruins of thc city of Cho-rill os, just south of Lima, Another waited by his telegraph in theobscrvatory of the naval school in Buenos Aires, Linking up the var-ions wires, de Bernadicres bcgan signaling electrically from Val-paraiso to Panama, All along the route, relay men strugglcd to keepthe signal moving without a break: the tiny current tickling the mir-ror; reflcctcd light flickering, As soon as he saw the light spot move,the operator would relaunch the signaL Starting on 18 January1~8:;, while the Amcricans were still reaclying crates ill Washingtonfor their expedition along the coast of Peru awl Argcntina, theFrench team sci/',ed three cxcellcnt astronomical amI electricalevenings. Just after their last measurement, the submarine cableinto Panama snapped, severing communication between theirminuscule observatory and Paris, But they had results: the longitudeof the flagpole over the stock market of Valparaiso stood 4 hours, 55minutes, and 54,11 seconds earlier than the Montsouris time room

thousands of miles to the east.It was just after this intense round of competition and collabora-

tion with the Americans that, on 7 April 1884, de Bernardiercsissued his plea to his acadcmician colleagues in Paris, His reporttold the scicntists that there were new possibilities for French sur-veying: two great oceans had just been linked across South Amer-ica by telegraph, with cablcs snaking their way at 12,000 feet acrossthe formidable Andes, As clc Bcrnarclicres put it, the Paris Bureauof Longitude should now imaginc creating an "immense gcodcsienetwork that would encompass the entire globe, fixing precisely its

form and dimensions.?"The French Navy backed the plan, lending officers, sailors, and

materiel. De Bernardieres would install himself at Santiago or

EINSTEIN'S CLOCKS, POINCARll'S MAPS

nearby Valparaiso, and others would tell time to thc north in Limaand Panama and across the continent in Buenos Aires. Just a fewmonths earlier, the American company Central and South Ameri-can Cablc had laid their undersea line from Lima to Panama.Adding to an already established line stretching from Panamathrough the Greater Antilles, North America to Europc, deBcrnardicrcs and his colleagues had a filamentary link all the wayback to Paris. Since other lines also went from Valparaiso throughBuenos Aires, lho Cape Verdc Islands aile! eventually to Europc, thewhole coustitutcd a vast circuit of SOll1C20,000 miles of gutta-pcrclia-covcrcd copper, allowing the two routcs to check oneanother.

Out of Crccu's American mission and de Bcrnardieres's FrenchOllC came an enormous, world-clasping polygon of simultaneitywith vertices ill Paris, Crccnwich, Washingtoll, Panama, Valparaiso,Bucllos Aires, Rio clc [anciro, and I .ishon. Amazingly enough, reck-oncd in two different directions, tllis irregllbr octogon carne within1 SO yards of closing. From the polygoll, spokes jutted out to Asiawhere the Americans were electrically grasping the contours ofIndia, while the French, from a hagile bamboo hut, a few pieces ofelectrical cquipuicut, some astronomical gear, and a cable-end,hcgan their electrical pinpointillg of [laiphoug.'JI

This lirclleh world net of cables and time signals shot cast, west,north, and south from Paris. Astronomers shaped much of its char-acter, and ill turn, the IOllgitude machine transformed their obscr-vatories. 'Iakc, for example, the fourth volume of the Annales duBureau des Longitudes, which in 1890 opened with an account ofthe Bordeaux Observatory. Whatever research might yield, thereport made plain, the observatory was built neither to scout newphenomena nor to place the human form in a cosmic context. No,the city of Bordeaux, like so lllany others, had built all observatoryto set ship's chronometers so thcy could determine their longitude

The Electric WorldlJwiJ 143

I~o de :)al1cro

()a(paraiso

A,z:res

Figure 3.10 Cabled Time in South America. One of the major French lon-gitude explorers, de Bemardieres raced against the Americans to ccnnblete anelectric-time-based cartograiJhic net tied bad to the Paris Ohsemltory. '1() hiscolleagues hack at the Academy o(Sciences, the Frenchman urged the creationo( the polygon sketched here: "an immense geodesic networi: that wouldencompass the entire globe." SOURCE: MAP MOlllFlIm FROM Tw: TIM I';"AIL~S, LON-

DON, OFFICE OJ" TIm TIMES, 1986.

') r--···-·-···-····-·-·-~·~-·--144 EINSTEIN'S CLOCKS, POINCARE'S MAPS

at sea." This meant that the Observatory's vcry first task was to estab-lish its own longitude, which it completed by using telegraphic timcsignals with Paris on 19 November 1881, locating itself II minutesand 26.444 seconds west of the capital-plus or minus eight-thousandths of a second.

City by city, country by country, the French Bureau ofLongituclcextended its network of longitudinal fixed points, first nationally,running telegraph wires from Paris to the distant cities of France,and then, through an array of undersea cables, to the distantcolonies. By ISBO, ninety thousand miles of lnostly British cable layon the ocean floor, a ninety-million-pound machine binding cvcryinhabited continent, cutting across to [apan, Ncw Zcaland, India,through the Wcsllndics, the East Indies, and the Aegean. Coin-pcting for colonies, for news, for shipping, for prestige, inevitablythe major powers clashed over tclegraph ic networks. For tll roughcopper circuits llowccl lime, and through time the partition of theworldmap in all age of empires,

As maps merged, a consensus emerged that a universallyacknowlcdged first meridian was needed. That origin arc would setone nation's capital at thc symbolic center of evcry glohallllap.Every clock and every longitude measurement in the world woulclrefer back to the dead center of one country's transit inxtrumcnt.

Though the immediate struggle was over a symbolic centralityrather than control of land, no one mistook its importance. IIighnoon for the diplomats and scientists was to be 1 October 1H84 illWashington, D.C., in the Diplomatic Hall of the American StateDepartment.

Battle over Neutrality

Two years prior to the meeting, in August 1882, President ChesterA. Arthur and the American Congress had approved a resolutioncalling for an international conference to be assembled in Wash-

The Electric World11111/J

ington for the purpose of setting a unique and universal primemeridiau." While American politicians came to consensus, a groupof scientific delegates gathered for an international geodesic con-ference convened in Rome in October 1883. Swiss astronomerAdolphe Hirsch reported on their deliberations, starting with theircelebration of the network of telegraphic longitude fixes that hadfinally speciFied reference points across the European continent.With many countries producing maps with their own capitals as thezero longitude point, a new question had arisen: Could all these ref-creucc points be referred back to one single and unique primemeridianline? Now, Hirsch recorded, it was time to set aside idealsof a science isolated from the world and instead to make a contri-bution that,in a far deeper way, joined science and the wider prac-rica] domain. Creat nations had an opportunity to help navigation,carlograplty, geography, meteorology, rail transport, and telegraphiceOJ mnuuicatiou. It was time, once and for all, to choose a universalprime meridian. Just because the earth was a sphere, IIirsehiusistccl, there was no natural prime meridian. That is, a prime lati-tude-thc equator-was picked out naturally by the spin of theearili. But "nature" had selected no prime meridian of longitude.I':vcll thc magnetic north pole could not be used to single out anyp.u+icular longitucie as prime, as the magnetic north wandereclabout over lime. 0, the choice of a prime meridian was necessar-ily arbitrary and therefore subject to reasons "purely practical and

couvcn tiona I[col1vcntionclle]."lIcrc was a theme the experts repeated over and over again: the

exchange of ideas, products, and peoples demanded new interna-tional institutions even while respecting the individuality of nations.Clobal conventions must prevail over local ones. Unions of post andtelegraphs now embraced the entire world. The Convention of theMcter already united the majority of civilized countries, there wereconventions of electrical standards; conventions to protect intel-lectual, artistic, and industrial property; conventions to protect COI11-

EINSTEIN'S CLOCKS, POINCARI;;'S MAPS

batants in conflict. Even their own geodesic association testified thata purely scientific goal- the establishment of the exact shape of theearth - coul d propel such coordination among nations. Hirschinsisted that it was time to find a practical solution to the unifica-tion of longitude, and the conference therefore recommended thatCreenwieh become that prime meridian, with a date change at theantimcridian on the opposite side of the earth?'

A year aftcr Rome, the delegates to the Washington Conferencejoined U.S. Secretary of State Frederick T. Frclingliuyscn at theSlate Department. With a rigorous record of the conference prc-pared and approved as it progressed, thc statcsmcu and scientistsjoined the battle ovcr thelOllgillldin,d zero point. Poincare ofcourse read these proecedings; he even cited them verbatim in hislater articles.! [c, along with lIIany others who studied the pro-ceedings, witnessed the incxtricahlc mix of politics, philosophy,astronomy, and surveying.

AFter a formal welcome hy the secretary of stale in which hepointedly renounced establishing the prime meridian in the UnitedStates, I .cwis M. Ruthcrfunl of the American delegatio]] shol Ihostarling gun by proposing, as had the ROllle Conference, 111<1tthestandard meridian pass through the center of the transit instrumentat Greenwich Observatory. French Minister Plenipotentiary andConsul-General to Canada Albert! .cfaivrc immcdiatclv cautioned,}gainst hasty action, belitlling the Renne decisions as the product ofmere "experts." l lcrc ill Washillgtoll, the loftier vantage point ofpoliticians ought to prevail: "It is, moreover, our privilege to bephilosophers and cosmopolitans, and lo contemplate the interestsof mankind not only for the present, hut for the most distantfuture."?' Only such a distanced view would allow consideration ofprinciples. Backing down, the Americans proposed that the confer-ence merely accept the idea of a single prime meridian.

Such backtracking offended the British. Captain Sir VJ.O. Evansof the Royal Navy protested that Rome had already narrowed the


question: the prime meridian should bisect a great observatory, nota mountain, a strait, or a monumental building. Science, after all,demands precision, not some vague gesture toward a natural featureof the earth. And the list of such great observatories was short: Paris,Berlin, Greenwich, and Washington." Commander Sampson ofthe United States Navy concurred, saying that the chosen observa-tory must have the requisite telegraphic time links to the wholeworld: "We may then say that, from a purely scientific point of view,any meridian may be taken as the prime meridian." IF onedemanded convenience and economy there were fewer options,and that choice narrowed considerably if the prime meridian hadto pass through ,1 thoroughly wired, governmcntally backed obser-vatory. If one recognized that allY prime meridian other than theBritish one would require altering llIaps for the 70 percent of worldshipping that used the Greenwich meridian, there was only one realchoice: Crccnwich." No doubt encouraged by the twin salvoes ofthe British and American navies, Rntlicrfnrd rejoined the siege ofParis: "The observatory of Paris stands within the heart of a largeand populous city," a city suhjeclto movement of air, tremors oftheearth. The Paris Observatory hacl to be moved. "The only thingwhich keeps it there is the remembrance of the honorable career ofthat observatory in limes past.''')S

Not so, the French astronomer and delegate Jules Janssenretorted. 'I 'he Paris Observatory remained vital because it was linkedelectrically with all the other major observatories, its abilities welldocumented by a use of telegraphic mapping altogether compara-ble to Greenwich. What mattered historically was this: FollowingPtolemy, Cardinal Richelieu had set the prime meridian Oll theisland of Ferro in the Canary Islands. Since the easternmost pointof Ferro rose from the sea some 19°55' 3 JI degrees west of Paris, reck-onings became hard to calculate. Eighteenth-century Frenchastronomers simplified longitude calculations hy decreeing thatFerro's prime meridian would be, statutorily, exactly 20 degrees west


of Paris, Since even French astronomers could not physically movethe island of Ferro 4' 57" east, Janssen admitted that this conventionmade the prime meridian Paris, disguised.

No doubt Janssen could read the politics as well as anyonc else:thc likelihood of replacing Greenwich by Paris (disguised as Ferro)as the prime meridian was nil. But Janssen was not about to fold histent. (This was an astronomer who, during the siege of Paris in1870, had taken off in violent winds in a balloon for Algeria toobserve an eclipse.) It was time to seize loftier ground than Ptole-maic (and now French) Ferro, for the conference was beginning toskid toward the crassest of decisions. "Instead of laying down thegreat principle that the meridian to he offered to the world as thestarting-point for all terrestriallongitucles should have, above allthings, an essentially geographical and impersonal character, thequestion was simply asked, which one of the meridians in useamong the different observatories has (if I Illay be allowed to usethe expression) the largest number of clients?"?"

Clients. The vcry thought offended a rational (French) sensibil-ity. [ansscn hoped thai customs and customers would not throwindustrial (British) smoke before philosophical (French) principles.There was, hc reminded the assembled, the long tradition ofFrench hydrographic engineers; there was the universally respectedalmanac, the Connaissance des Tem1J8. And 1I0t least his collcaguesought to remember that it was the French who, in revolutionarytimes, had stepped past the pied de H.oi as a unit of length in favorof the rational meter. Rational science should trump royal tradc.!'"Janssen opined: "Without doubt, on account of our long and glori-ous past, of our great publications, of our important hydrographicworks, a change of meridian would cause us heavy sacrifices. Nev-ertheless, if we are approached with offers of self-sacrifice, and thusreceive proofs of a sincere desire for thc general good, France hasgiven sufficient proofs of her love of progress to make her co-operation certain." A reasonable agreement, Janssen concluded,

The Electric WorldmalJ

cannot protect only one contracting party. III I In other words, put thelongitudinal center of the world anyplace neutral. Anyplace but

Grecnwich.Come, come, the British astronomer John Couch Adams har-

rumphed. It was Adams whose work had already been twice mobi-lized in skirmishes with the French, once over the question of whohad discovered Neptune and again when he contradicted the resultsof the great Laplace on the motion of the moon. Wc are not hel-ligerents, he now insisted, we arc all neutral, as in all matters sci-entific. We are not dividing territory as after a war but in a friendlyway represcnting friendly nations. What will provide the greatestconvenience to the world? Ancl we should provide that conveniencewithout thc lcgal fictions of a displacement from some other obscr-vatory (Paris disguiscd as Ferro), but rather calling things "by theirright names." Practical, hard-headed decision making ought to bethe order of the day: "It was quite clear that if all the Delegates herepresent were guided by merely sentimental considerations, or byconsiderations of amour pro/He, the Conference would never arriveat any conclusion." To the charge of French vanity, [ansscnanswered by accusing the British of vulgar self-indulgence:

We consider that a reform which consists in giving to a geograph-ical question one of the worst solutions possible, simply on theground of practical convenience, that is to say, the advantage toyourselves and those YOll represen t, of having nothing to changc,either in your maps, customs, or traditions-such a solution, I say,can have no future before it, and we refuse to take part in it.!"

Loyal to the practical and commercial, the Americans sided withthe British. What is neutral? demanded Cleveland Abbe. Histori-cal, geographical, scientific, or arithmetical neutrality? True, Francegave us neutral weights and measures, but those measures have anarbitrariness to them by virtue of the standard weights and measures

-----------------_._._--_ ..... _-

EINSn:IN's CLOCKS, POINCARlt'S MAPS

on which they rest. "Neutral" system of longitude is "a myth, afancy, a piece of poetry," unless YOll can tell precisely how to do it.!"

Janssen retorted: A neutral point would have two advantages,geographical and moral. Choosing the Bering Strait would removethe prime meridian from all centers of population for the statutorychange of date, it would neatly slice the globe into the Old Worldand the New. Or, if not the Bering Strait, then another remarkablephysical point; laying the zero point of time and longitude throughthe Azores would cost less than the Bering Strait because tele-graphic cables already ran near. In either the Azores or the BeringStrait, one would define the zero of longitude from existingtelegraph-connected observatories, not the center of the strait itself.(Janssen had just noted the excellent electrical connectivity of theParis Obscrvatory.) No doubt looking pointedly to Adams, Janssenurged his colleagues to bear in mind the "lively discussion" raisedby the English and French press over the discovery of Neptune(both sides had claimed astronomical priority). Dclving deeper intothe past, Janssen saw those same Continental-British tensions inseventeenth-century battles over the calculus between defenders ofNewton and those of Lcibniz: "The love of glory is one of thenoblest motives of men; we must how before it, hut we must also becareful not to permit it to produce had fruits."11l1

Outnumbered, [ansscn soldiered on: economic reasons mightfavor Greenwich, Washington, Paris, Berlin, Pulkovo, Vienna, orRome, but such choices would necessarily be artificial. "Whateverwe may do, the common prime meridian will always be a crown towhich there will be a hundred pretenders. Let us place the crownon the brow of science, and all will bow before it." Yes, one Anglo-Saxon responded, but any chosen place belongs to a country. Not atall, shot back Janssen; the equator is neutral, yet it traverses nations.England's General Straehey protested against the clistinctionbetween longitude for geography and for astronorny-> "longitude islongitude." It most certainly is not, Janssen seethed. Longitude

r.

The Electric Worldnzap

depends like any measure on context. "Is not a weighing necessaryto determine a chemical equivalent of an entirely different kind fromthat of a commercial weighing? Yet it is still a weight."!"

Cleveland Abhe, who hac] fought so hard with the AmericanMetrological Society for unified time, doubted the naturalness of"neutral." What if Russia were to rceonquer the country on this sideof the Bering Strait? What if America purchased half of Siberia?'" I'hat point I:in the midst of the Bering Strait] is not cosmopolitan."Only stars over the earth, something above human considerations,could possibly he deemed neutral. !fI(,

[ust so, interjected Sandford Fleming. Habituated to argmnenbill tenus oft he transport of goods and people, he viewed the Frenchproposal for "a neutral meridian [as] excellent in theory, but I fear_ . _entirely beyond the domain of practicability." 'I'ben, shippingmanifest ill hand, Fleming recited numbers from a compilation ofships and transport tonnagc that had been guided by the variousprime meridians: Greenwich, 72 percent of tonnage; followed byParis, 8 percent, with the rest of the world making up the remain-der. Perhaps as a sop to his l-rcuch colleagues, Fleming offercd toset the prime meridian exactly 180 degrees from Greenwich, in thelIIidst of the "uninhabi tcd" part of the Pacific.!" Such a movewould, he added, keep astronomical events practically unchanged011 the Creeliwich-basccI charts, inverting midnight and noon, 2:00A_M. for 2:00 P.M., and so Oil. As for diplomacy, flipping the longi-tudinal line across the globe from London's suburb foolecl no one,least of all the French, who knew all about proxy prime meridiansfrom their long use of Ferro. On a vote for a neutral meridian, theFrench plumped 'for: joined only by Brazil and San Domingo. Alltwenty-one other nations voted against.

Speaking for France, Lcfaivre morosely assessed the debate asvoid of astronomy, geodesy, or navigation. Reminded of tonnages inthe context of Anglo-American complacency, he allowed "the onlymerit of the Greenwich meridian ... is that there are grouped

-•••• ~1' _ • I ' , '

~ - - J _ ' • • I " ~, ,


around it, interests to be respected, I will acknowledge it willingly,by their magnitude, their energy, and their power of increasing, butentirely devoid of any claim on the impartial solicitude of science."No reason, neutrality, or impartiality-only commerce pure andsimple. Lefaivre conceded that the Empire had won by commer-cial prowess, but on no other grounds:

Well, gentlemen, if we weigh these rcasons-> [the] only ones thatat present militate for the Greenwich meridian-s- is it not evidentthat these arc material superiorities, commercial preponderanccsthat arc going to influence your choice? Science appears here onlyas the humble vassal of the powers of the day to consecrate andcrown their success. But, gentlemcll, nothing is so transitory andfugitive as powcr and riches.

All empires have fallen, and this one too shall pass. Do not enchainscience and subordinate science, And will there he reward for theabandoruuent of our French meridian? Would America and Britaindcign to take up the metric system? No. "Wc arc simply invited tosacrifice traditions clear to our navy, to national science, by cldclingto that iunuolation pecuniary sacrifices." Sir William Thomson, thesenior scientist- at the gat-hering, confirmed Janssen in all but his lowopinion: this was a "business arrangemcnt," not a scientific ques-tion. 'I 'he question was soon called for the adoption of "the merid-ian passing through the transit instrument at the Observatory ofGreenwich as the initial meridian of longitude." San Domingovoted against the sanctification of Greenwich; Brazil and Franceabstained. 'I wenty-one nations supported it.!"

Other issues racked the world longitude system, disputes that onlymade sense in a world wired for electrical time. Indeed, the wholeconference could be seen as an extended conflict over the newlywired world of electrified time distribution. United States delegate

W. F. Allen, fresh from his railroad time victory, offered the confer-

The Electric Worldma()

cnce the logical asymptote of all these developments: "It would ...be one of the possibilities of the powers of electricity that the pendu-lum of a single centrally located clock, beating seconds, could regu-late the local time-reckoning of every city 011 the face of the earth."!"

Against this ultimate time fantasy lay a universe of local customs;even the seemingly innocent question, When should the day begin?was vexed. Some favored commencing the day at the antimcridianof Rome to facilitate computation of ancient dates by thc Grcgoriancalendar. Astronomers wanted the clay's start at noon to avoid split-ting the night into two elates. Meanwhile, the Turkish delegatenoted that the Ottoman Empire recognized midnight-to-midnightclays (heme a la fr(lIlque) but also reckoned from the bisection of therising sun by the horizon iheure (/ la turquey: "Reasons of a nationaland religious character prevent \IS ... from abandoning this modeof counting our time."!"

Important as these cross-cultural synchronizations were, no oneat the conference doubted that the struggle was between Paris andGreenwich. Defeated in rcsolutiou after resolution, the Frenchheld one last hope: the decimalization of time. Their ambition fora rationale, scientific measure of time, analogous to the meter, haddeep roots in Paris. In Year II of the French Revolution, the Con-vention struggled to institute a decimal system of time keeping with"decades" of ten clays (rather than weeks), days partitioned into IC11-

hour units, and right angles split into 100, not 90 parts. A few revo-lutionary clocks still survive; one (figure '3.11) shows an equilateraltricolor triangle signifying that, under the new liberty, monthswould be divided in equal parts, with the vertices standing for daysof rest. Among scientists, few took up the new system, but Laplaceclid in his epochal Celestial Mechanics, and sectors of the govern-ment even tried to impose the system. But faced with massive pub-lic resistance, Napoleon killed time decimalization in a deal cutwith the Roman Catholic Church."!

Janssen took the floor one last time to plead for the global instau-

153

EINSTEIN'S CLOCKS, POINCARI::'S MAPS

Figure 3.l1 French Revolutionary Ciock (circa 1793). The equilateral tri-angle signiFied that, under the Ilew liberty, months would he divided into equalparts with the vertices standing j(JI' days oiresi. SOIIRCJo:: ASSOCIATION I,'RAN(,:AISI':

[)I':S AMATI':URS J)'IJORLOC 1<:1(11':A"CII':NNI':, {(I<:V(lI-: m: /";\SS()(;IAI'/( IN f!1<,\N(:,\ISI':, VOl, XX

(H)S')), P, 211,

The Electric Worldl1w/J 155

ration of this long-deferred decimal time and division of the circle.His hope-put as a resolution-was that the decimal system, \lOW

entering the mainstream of European trade and manufacturing,might finally be extended to time, Confronted with the same pub-lie opposition faced by his revolutionary forebears, Janssen reas-sured his colleagues: "It is feared that we want to destroy habits fixedfor centuries, and upset established \lsages." But no such fears werejustified. "If we failed at the time of the Revolutiou, it is because weput forward a reform which was not limited to the domain of sci-ence, but which did violence to the habits of daily life." This timeit would not mandate a change for the people of the world, but only

be imposed where it was of use.At every stage of the story ill France, [rom the rueter to time and

longitude, conventions of spaec and time wcre powerfully bound tothe legacy of the Convention. But for all the delegates, and indeedfor the larger metrological community behind them, settling onconventions of space and time was never just about precision mapsor intersecting rails. To treat the Washington clashes as a step on allinevitable march toward stanclardizcd rationality is to miss the fluc-tuating, contingent, opalescent character of synchronization. It is tomiss the constant crossing and recrossing of the pragmatic with thephilosophical, the abstract with the concrete.

After the French rout at the prime meridian, dclegates looked fora way to accommodate the French on decimalized time withoutendorsing either its Enlightenment ambitions or allY practical planfor its implementation. In the end, the conference merely expressed"the hope" that further technical studies on decimal iz ing timewould be resumed.'" It was not much for the French delegates tocarry home. To advance the cause beyond that minor, conciliatoryvote, the French needed someone with stellar scientific credentialsand engineering-administrative clout to champion this radical refor-mation of time conventions. For almost a decade the issue sim-mcrecluneasily in French technical circles. Enter Henri Poincare.

------------------ ------

Ch ap ter 4

POINCARE'S MAPS

Poincare's Maps

history of the quasi-autonomous states that had left the countrystruggling with a hodgepodge of mechanical and electrical timesystems. It was this time disunity that hrought thc aging GeneralFieldmarshal Count Helmuth Carl Bernhard von Moltke to speak,on 16 March 1891, to the Imperial German Parliament. Railroadshad been key to von Moltkc's celebrated triumph against France.For almost a half-century he had impressed upon his countrymenthe vital role of trains in the rapid deployment of military assets.Already in 1843 he had insisted, "Every new development of rail-ways is a military advantage; and for the national defence a fewmillion on the completion of our railways is far more profitablyemployed than on om new fortresses." Yon Moltke drove theseplans to completion, grounding his military strategy in the powerof new railway lines. By the fall of 1867 he claimed that with thesouth Cerman slutcs he could have 360,000 men massed in threeweeks and 430,O()() ill four.'

Such planning paid. Not only the Germans but also their Frenchadversaries recogni/,ed after the Franco-Prussian war of 1870-71that vou Mollkc's dextrous use of precision-synchronized trains haddcslroycd lhc Second I':mpire, fundamentally changing the balanceof Furopcan power. l'or the twenty years following his triumph ovcrFrance, von Molrkc's (and later Schlicffen's) Crcat Ccneral Staffoversaw a massive expansion of the military as it grew into the forceof a unified Reich. Patiently, obsessively, the gcnerals ran an end-less series of technical war games as they practiced the choreo-graphed marshaling on million soldiers using a hundred thousandtrain cars. In 1889 the military pleaded with the Reiehstag to adoptstandard time to simplify their train scheduling. The politicians

refused."Von Moltke of March 1891 was an unequaled hero in Prussia.

When he entered a public place, men stood in silence until he tookhis scat. So when the general appeared before a plenary session ofthe Parliament on the subject of time and railroads, it was a major

Time, Reason, Nation

FTER THE 1884 World Time Conference set the primemeridian in Greenwich, resistance in France hardened.Janssen returned to Paris, still fuming from the rout. Appear-

ing before the French Academy of Sciences on 9 March 1885, herecounted, blow by blow, the battles of the previous year, startingwith the political: the Americans had loaded the meeting with smallstates that were allied to the US. Happily enough, there were somevictories, hc assured his colleagues, reprinting a long speech by theFrench delegation. One aftcr the other, [ansscn recalled, the Amcr-icans and British had taken the floor to fight the French, each Anglo-phone ill his special domain of competence. "It is perhaps permittedto say, despite the authority, the talent, and the munber of scientistswho com hated the principle of the neutrality of the meridian, thatprinciple resisted these shocks without bcing disturb eel and withoutany scientific breach. The meridian proposed by France remains stillthc impartial, scientific, and definitive solution to the question. Webelieve that there was honor to our country to have defended thatcause.": On the Continent, Janssen was [Jot alone in his discontent.The Abbe Tondinc de Quarenghi campaigned in 1889-90 in thename of the Bologna Academy of Science for the prime meridian tobe moved to Jerusalem, thc Universal City "par excellence," centerof the three continents of the ancient world and the common sanc-tuary of three world religions.z

Unlike France, Germany was not troubled by the Grcenwiehprime meridian. The Germans were preoccupied with their long

From the audience rang out: "schr wahr" (vcry true). Von Moltkcwent 011 to say that while thc currcul piecemeal ruin of time mighlonly be all inconvenience for the traveler, it was an "actual difficllltyof vital importance" for the railway business and, even worse, forthe military. What, he asked, would happen ill case of troop mobi-lization? There had to be a standard, one that would t~lll along thefifteenth meridian (about fifty miles cast of the Brandenburg Gale),that would be the reference point; local times within Germanywould differ but would require all offset by a mere half-hour or soon either extreme of the empire. "Meine Herrell, unity of timemerely for the railway docs not set aside all the disadvantages whichI have briefly mentioned; that will only be possible when we reacha unity of time reckoning for thc wholc of Gcrmany, that is to say,when all local time is swept away." Empire demanded it.

Von Moltke conceded that the public might dissent. But aftersome "careful consideration," scientific men of the observatories

EINSTEIN'S CLOCKS, POINCARl~'S MAPS

event.' In his scratchy voice (hc died just over a month later), van

Moltkc intoned:

That unity of time (Einheitszeit) is indispensable for the satisfac-tory operating of railways is universally reeognizcd, and is not dis-puted. But, moine Herren, we have in Germany five different unitsof time. In north Germany, including Saxony, we reckon by Berlintime; in Bavaria, by that of Munich: in Wurtcmburg, by that ofStuttgart; ill Baden, by that of Carlsmhc, and on the Rh inc Palati-natc hy that of Ludwigshafcn. We have thus in Cermany fivczones, with all the drawbacks and disadvantages which result.These we have in om own fatherland, besides those we dread tomeet at the French and Rnssian boundaries. This is,1 lllay say, aruin which has remained slanding out of thc once splintered COll-dition of Germany, hut which, since we have become an empire,it is proper should be clone away with.

Poincare's iVlalJS

would set things right, and lend "their authority agaillst th is spirit ofopposition." "Meine Herrell, science desires much more than wedo. She is not content with a Ccrman unity of time, or with that ofmiddle Europe, but she is desirous of obtaining a world lime, bascclupon the meridian of Grecmvich, and certainly with full right [romher standpoint, and with the end she has in view." Emus and fac-tory workers could shift their clock startillg times as lhey wished. Tfa manufacturer wanted his workers to start at the crack of dawn,then let him opcn the gales at 6:29 ill March. Let the Linl1crs fol-low the sun, let the schools and courts make due with lhcir alwaysloosc schedules. Von Moltlc wanted a nationally coordiuatcd clockbased Oil Crccnwich. What rualtcrcd to the Cencral Slaff W,IS llwlthe railroads and armies should answer to a coordinated single lime,one linked to the emerging electric worldmap. Much of I':mopcfollowc(]7

Bulilot all Europeans. Perhaps the best known action against(;rcell\vich is also one of the murkiest. On Thursday 15 FebruaryI S94, a yOllng French anarchist, Martial Bourdin, bought a ticketIroiu WcshnillSter Bridge to Creellwich. According to one of twoobservatory assistants, when chatting ill the lower computing room,the pair "were suddc: dy startled by aloud explosion, the detonationof which was sharp and clear. ... I immediately remarked to Mr.Hollis, "I'hat is dynamite! Spol the time'." Trained to observe by theclock, they duly recorded the detonation at 4: 51. When a police-man arrived at the clctonatiou scene in the park below the observa-tory, he found Bourdin dying. 'I 'he anarchist had lost his hand andreceived a massive blow of explosive and bomb fragments. For ycars,doubt lingered about Bourdin's motives; anarchists suspected apolice setup; others saw ill it one morc in the long series of Frenchanarchist strikes, including onc OJ) the Chamber of Deputies illParis (December 1893) and another ill a Paris cafe just three claysbeforc Bourdin's demise. Joseph Conrad's version of the events illhis 1907 work The Secret Agent remains the canvas Oll which these

r---~-------------------------------------}', ,60 Emmm', CWCKS, PO'NC,"", Mxr-s,,-.' ~

;-.;.l

events have been seen: a dark sketch of dupes, manipulators, andcareerists from which no one emerges unsullied. In Conrad's worldthe conniving First Secretary of a Foreign Power insisted on anattack that would frighten the class enemies beyond murder: 'Thedemonstration must be against learning-science. Thc attack musthave all the shocking senselessness of gratuitolls blasphemy." It muststrike at the mysterious scientific heart of material prosperity. "Yes,'he continued with a contemptuous smile. 'The hlowing up of thefirst meridian is bound to raise a howl of cxccratiou.':"

Without a doubt the first meridian stood as a powcrful if highlycontested symbol. But even in France, where [ansscu and othersrecoiled at Britain's arrogation of world power, there were thosewho were entirely supportive of setting French time to the masterclock of the great Christopher Wren observatory.

Charles I .allernand, a member of the l-rcnch Bureau of l,ollgi-

tude and an ally of Poincare, made his support of Crccnwich timecrystal clear. Of course universal time (a single time for the wholeworld) would he an unmitigated disaster: the [apancsc man ill thestreet would surely refuse to live and work by the lime it happenedto be in Crccnwich at that moment.' I .allcmand insisted that timereform would have remained mired ill chaos if the orth Ameri-cans, "with their admirable practical sense of Business'inen, hadn'timagined an ingenious compromise, uniting, or approximately so,all the advantages of the universal ham with that of local time":time zones."

Writing in 1897, Lallcmand insisted that it was all unparalleledvictory in the domain of human reform that only ten ycars had suf-ficcd for a simple, practical system of time zones to have conqueredalmost the totality of the civilized world. All of Furopc now adheredto the system with the exception of France, Spain, and Portugal.What was needed for the French to join in this reform was so little:a delay of a mere 9 minutes and 21 seconds would set things right.Not only was the present system foolishly complicated, it meant, as

r,~

1 Poincare's Maps

Lallernand sadly noted, that on the other side of the earth, there wasan equatorial zone spanning 250 miles between the antimeridianlines of Paris and Greenwich in which the very date was ambigu-ous. Standing (or floating) in that purgatorial time zone, yon couldclass yourself as witnessing 31 December 1899 or 1 January 1900,depending on which set of maps lay beforc yoU.11

For Lallernand, such ambiguity was intolerable. Objections flewfast and furious in this campaign of articles and broadsheets. Someclaimed that the zones weren't "neutral,' following the line takenat the contentious Washington meeting. False, Lallemand declared:Not only did the new zone system follow the standard, neutraltwenty-four-hour clock, but the "vertiginous speed" of acceptancein both the new and old worlds had showed just how neutral it was.It is quite true, he conceded, that one mcridial l inc ran throughGreenwich. But that reference point was already familiar to nine-tcnths of the world's sailors. Can one really say that exchanging alongitude of zero for 9 minutes and 21 seconds would cause us tolose our French originality and scientific personality? Nonsense, hefulminated. Paris had long taken the position "20 degrees east,"using a first meridian on the island of Ferro. Even the much-vaunted neutrality of the revolutionary Convention that establishedthe meter is not exact: what began in revolutionary France as a neu-tral measure (l meter = 1110,000,000 of a quarter of the circumfer-ence of the globe) rapidly deviated from that ideal as foreign nationscopied a reference bar set ill Paris. How, then, he demanded, couldFrance possibly consider it a humiliation to modify its prime mcrid-ian? Some said it would render obsolete all French maps. No, Lalle-mand riposted, we could even overstrike the new longitude lines ina different color. He concluded that he and his countrymen wouldnot be sacrificing their national meridian for the British. Theywould merely be offsetting their clocks by 9 minutes and 21 secondsfor the benefit of telegraphy, navigation, and train travel. All "menof progress," he concluded, should back the reformation of time."

162 EINSTEIN'S CLOCKS, POINCARI<;'S MAPS Poincare's Maps

Decimalizing Time

As Lallcmand's "defection" suggested, decisions taken at the Wash-ington Conference of 1884 reverherated through the FrenchBureau of Longitude. In addition to their fateful decision aboutGreenwich, the Washington delegates had also "expressed thehope" that the definition of the astronomical and the nautical daysmight he joined, so both would start at midnight. Astronomers hadlong started their official day at noon, profiting from the absence ofanything of observational interest during the day to keep their pre-cious nights unbroken by a calendar change. Meanwhile the rest ofthe world utilized nighttimc quiet to change its clay at midnight,thereby keeping dayl ight within a single calendar day. Boosted byconcern emanating from the Canadian Institute and the Astro-nornica l Society of "l oruuto, the Minister of Public Instructionasked the French Bureau in lW)4 for its opinion.

Poincare led the charge and hegan, characteristically, by weigh-ing inconveniences. "It is evidently inconvenient lillco1ll11wde] foran astronomer 10 changc the dales ill his notebook ill the middle ofa night of observations." lie could forgcllo make the switch, leav-ing records vastly complicated. But this same "incovcnicnce" nowexists for the sailor making solar observations at sea. Indeed at everymoment the sailor currently faces precisely the same problems asthe astronomer, and worse. Where the astronomer works withoutdistraction, the mariner has a million worries; where the astronomercan always give the observations a fresh look later, the marinercould be dashed against shoals hy the slightest error. So let theastronomers write "night of 11-12" in their notebooks. What aboutthe discontinuity in time 011 the day the reform was instituted? Bet-ter to straighten out that "inconvenience" now than later, Poincare

responded.If there was a serious objection, it was this: any such reform

would necessarily scrap the many compilations of astronomical

phenomena, such as those inscribed in the British and Americanastronomical almanacs, the French Connaissance des Temps, or theGerman Berliner [ahrbuch. Were any of these volumes to alter theirtime conventions, converting among them would present a vastlygreater problem than the current confusion. Only an internationalaccord could implement this laudable effort to simplify time. Untilinternational accords prevailed, the Bureau's members concludedthat the French should wait, though all agreed that a twenty-four-hour clock would be an improvement. 11 But soon the French put

even the twenty-four hours in a day under scrutiny, following up onthe Washington Conference concession that left "hope" for time'sdecimalization. In February of 1897 the president of the Bureau ofLongitude established a commission with Henri Poincare as its see-retary to determine whether France should serap the old twenty-four-hour day and )60-degree circle in favor of a truly rationalsystem. The president bluntly asked: why had the great Conventionof 179) failed to extend the decimal system to time and the cir-cumfcrcnce of a circle, and were objections to such a novel systemstill va lid?"

Onc commissioner serving with Poincare, Bouquet de la Grye, aformer Poly technician and prominent hydrographic engineer,responded. The Convention had aimed to banish everything thatrecalled the ancient measuring customs of the ancien regime andto consecrate true French unity by deploying common measuresacross the whole of the country. With the meter, the Revolutionsucceeded. But the Convention's time reform of months and weekshad been a disastrous flop, as hacl Laplace's valiant hut doomedattempt 10 decimalize the hour. De la Grye reminded his col-leagues that few decimal clocks survived, and no one outside ofFrance took any interest in them. From this debacle, de la Gryefound clear guidance for the present: "The metric system suc-ceeded because it was the simplest and it put an end to a veritableincoherence in local measures; the decimalization of time and cir-

~---------------------- ..----------

ElNSTElN'S Cl.OCKS, POlNCARE'S MAPS

cumference failed because the whole world employed the samemeasures and the proposals sinned precisely by their lack of unity.?"Convenience ruled. Where reforms simplified lives, the publicwent along; when reforms did not help ordinary people, the

schemes fluttered softly into oblivion.Poincare duly recorded the debates that followed. President

Loewy insisted that if the Revolution's metric time had failed, it wasbecause French astronomers could not find partners for the reformin other European states. General de la Noc noted that the geo-graphical service had indeed adopted decimal angles, as had thegeodesic services in Belgium. Cornu ascribed one differencebetween the late-eighteenth-century and the late-nineteenth-century present to the loss of habituafion to the duodecimal system.The most curious feature of all was that the contemporary Britishengineers were so trained ill their primitive measures of "inches"and "feet" that they simply refused to understand the advantages ofthe decimal system. 1.css despairing of his cross-channel colleagues,the director general of the Paris-Lyon-Meditcrranean Railroadevinced some sympathy for thc Anglophones; he reported thatmany British engineers suffered undcr their present system andwould love to break out of their island's archaic conventions.Impressed by the historical French drive toward the revolutionaryten, stirred by their historic role ill rationalizing the world, thc corn-

mission voted to decimalize time.But that vote left: much undecided. The railroad representative

assured his scientific colleagues that any attempt to alter the twenty-four-hour day was doomed to failure. De la Crye held out for a uni-fication of time and geometry by dividing the circle into 240 parts.Loewy admitted that he had dreamed of a full-bore decimal world,but the burden of past maps and measures led him, mournfully, toconclude that the obstacles to such a brave new world were notpassing difficulties. He endorsed de la Crye's compromise; a circle

Poincare's Maps

divided into 240 parts would put the globe into synch with the clockas each hour of the earth's rotation would correspond to a turningof the world by an elegant 10 degrees. Poincare backed Loewy,

adding:

Were we in the presence of a tabula rasa, the best system would beone that divided the circle into 40() parts 1100 grads per quarter cir-cle, or 100 kilometers per grad] .... But we cannot break com-pletely with the past, because not only must we take account ofpublic repugnance, but scientists themselves have a tradition towh ich they remain tied."

Keep the twenty-Four-hour day, Poincare said, and divide the circlein 240 parts. Commander Cuyou rejected such compromises,insisting on division into 400 parts. The navigational demands at seaand the calculation of tides brought the mariner into a never-endingseries of painful and dilficult calculations. Why not provide an easy-to-use decimal system For the scientist or navigator while leaving thepublic to count time according to its old habits? Trainmen, CUYOlladded, were already habituated to a timekeeping system that was offby five minutes from city time and were equally at case with atwenty-four-hour clock. Why not a two-time system? Such an amal-gam was intolerable, Poincare replied. Civil time was clearly linkedto longitude. Any mixed system necessitated a conversion factor thatwas truly convenient for any llSCr.

17

Convenience, convention, continuity with the past. These termsarise again and again in Poincare's abstract philosophy. Yet herethey are written in the less-than-etherial concerns of real-world engi-neers, seagoing ships' captains, imperious railroad magnates, andcalculation-intensive astronomers. Monsieur Noblemaire, directorof the Paris-Lyon-Mediterranean Railroad, argued as follows to rein-force his intervention: Suppose you leave your train station at 8:45

I

A.M. and arrive at 3:24 P.M. How long is yom trip? One has to think.But by expressing travel problems in decimals, thc confusions of

A.M. and P.M. vanish. All that remains is subtraction:

start: 15.4U h

end: 8.7511duration: 6.65h

I lcrc was convenience that mattered to a society on thc move."Mariners, like the Commandant of the Naval School, saw only ben-efits to the transition to decimal time and longitude. Maps wouldbe easy to alter, and physicists shouldn't have a prohlem. After all,according to the good captain, physicists had adapted easily enough

to ee1ltimeters, grams, and seeonds.'<)

Deeimali:.<ing riiuc, easy? That would have been news to thephysicists. When the presidcnt of the l-rcuch Physical Society,

llcuri Beequerel, got his ha1Hls 011 the proposal in early April 1wn,he was not amused. I':vell leaving aside the expense of changing allclocks, marine chronometers, pcnclllla, an(\ watches, the physicists

saw dire eonseqnences for the electrical industries and those thatnowecl from them. l-or it had only been in 1881 that the eentimeter-gram-scc()J1(l system (CCS) had been adopted illtenwtionally andonly ill April 18% that the president of the Repnblie had deerecdthat the rational CC;S system of measure should be used ill all mat-tcrs of State. N cedlcss to say, one of the COfllerS[Olles of that newlyGltional system, the sexigesimal second (113,6()() of an hour), nowlay ill the crosshairs of this decimal revival. Not (July would the pro-posed decimal second (I /l 0,000 of an hom) uttcrly alter themechanical and electrical units of current, work, and the like, hut

all the practicalullits (amperes, volts, ohms, and watts) that arcdefined in terms of them would have to change as wcll. "What anupset in scientific practice and the entire mechanical and electri-cal industry!" All the instruments would have to be al tered. "What

1

I

III1

Poincare's MailS

.1 Illlge expenditure without any profi t, neither for science, nor forindustry!" If one weighed the advantages agaillSt the disadvantages,the physicists' balance tipped decidedly toward the status quo: keepIlle old second. For the physicists, this case was closed before it

opened."The physicists' plaintive cries did not move Poincare. Or rather,

iIJ the face oHicrce protests from the public, the navigators, and thescientists, Poincare refused to engage the debate at all, insteadproposing to resolve the problem with the technicallcgerdemain of:I reforming Polytcchuician. On 7 April 1897, Poincare brought thecommission a table he had prepared that displayed each proposedsystem, the kinds of multiplications required (ignoring factors often) to express angles, to convert time to angles for expressing lon-gitude (degrees per hour of the earth's rotation), and to convertangles froiu the old 360-dcgree system to the proposed decimalones. For example, to express an angle of a circle and a half (1.5rotations) in the lOO-divisioJl system, there's 1JOconversion factor atall: 011ce the factors of ten arc taken into account, you just have 150units. No mental aritlnnctic, the multiplier is just I. For the 4()()-division system, 1. 5 circl cs would be 600 units: to gct From 1.5 tothe6 in that 600 (the ndditional mnltiplication by 100 requiring nobrainpower), you need to multiply bv 4. The second column tellshow to switch from parts of the circle into time: if the whole circleis IOD units, you need to multiply hy 24 to gct houls-lOO units ofrotation equals a full twcuty-four-hour clay. IF the circle is 4()O units,you need to multiply by 6 to get hours. Finally, to switch back intothe old 360-clegree circle, you would (for thc 40()-Ullit circle) jnstmultiply by the factor Y, whereas a I OO-uuit circle required multi-

plication by 36.Good technocrat that he was, Poincare had scanned the table to

find the simplest conversion factors. Only the 40()-Ullit s~stemrequired no double-digit multiplication. So there it was. Poincarehad, objectively, the least "inconvenient" solution, 011ehe happily

EINSTEIN'S CLOCKS, POINCARI~'S MAPS

defended to shrieks of protest against the proposed scrapping of

evcry angle-measurement in the world."

Divide circle Factor for Factor to Factor to

into this many angles greater convert arcs convert to 360

parts than circle into time degrees

100 1 24 36

200 2 12 18

400 4 6 9

240 24 1 15

360 36 15 1

Poincare's table presenting the case for dividing the circle into 40() parts.Source: Henri Poiucarc, "Rapport sur les resolutions de la commission chargeede l'Clmlc des projcts de d6cimalisatioll dntcmps cl de la circonfcrcnce" 17 April

1W)71, Archives of the Paris Observatory.

I Icrc was an engineering-dictated armistice in a war pitting allagainst all on social, economic, and cultural grounds. Whcn thedust settled, the hostile factions had compromiscd evcn further,keeping the twenty-four-hom clock and decimalizing the hour into100 minutes with each minute split into lOO seeonds.

2ZThese half-

measures left Captain Cuyou cold. Sea captains wcrc habituatcd toreading complex tables, as hc drily noted; it mattered little to himwhether the table consulted had simple or complex formulae forconversion. Ultimately, the committee splintercd into almost asmany opinions as there were members. One camp lobbied for adivision of the cirele into 400 parts, another wanted 240 parts, anda third (physicists, sea captains, and telegraphers) preferred the tra-ditional 360 divisions with decimal subslices. Astronomer Fayebucked all these proposals, demanding a clean split of the round

into 100 parts.Amidst this deci-striie, Poincare and his allies tried to remain

above the fray, adjudicating the competing systems with equanim-

Poincare's Maps

ity. Scribe and contributor Poincare dutifully rccordcd his ownopinion, one entirely consistcnt with his views about unifying civiland astronomical time: all these "systems arc acceptable and onemust choose that one which would have the greatest chance of suc-cess before an international congress." With the president on hisside, Poincare's forces won in a voice vote: the unity of angle wouldbc the "grad," that is to say l/400 of the circumfcrence. That deci-sion, while reinforced in a later meeting, did not quiet the debate.Some of the commissioners themselves dissented: the chief engi-neer of the French hydrographic service filed a report protesting thetremendous burden that would be caused by trying to reprint the3,000 charts (not to speak of the instructions, tables, and yearbooks),issued by the service, The entire instrumcntarium of navigators,moreover, would be rendered obsolete overuight. Sailors might aswell throw their chronometers, pcndu]a, watches, theodolites, andsextants into the briny deep. Another protester coutcudcd that thedecimal commission was merely managing contradictory interestsin a way that would disappoint the public with a badly tailored com-promise, Cornu argued that there was one rational system and onlyonc: the proposed reform was neither an adventurous, rationalcharge into the future 1101' a safe retreat to the status quo. For Loewy,the radical decimalizcrs had missed the point: the new system cutout much of the irrational and complicated bits of a system that, inits historical bricolage, made no sense. For the moment one coulddo llO better than settle. Loewy and Poincare had the votes to backtheir liberal compromise of a partial reform: 12 for, 3 against.z1

Voting silenced no one in the debate over the measurement oftime, which turn blcd, later in 1897, into the pages of Cornu andPoincare's journal, L'Eclairage Electrique. Clcarly uncomfortablewith the commission's compromise, Cornu reported that "an unsta-ble and divided majority" had formulated a solution that wouldhave great difficulty in finding universal acceptance. Evcn beforethe committee had finished its work, he said, the French Navy and

--~~-- .••••• a&.2.i".i."""'··· --. III


the army's geographical service both had objected, since the formerwould gain little simplification in their usual calculations, while thclattcr would actually be stepping backward. According to Cornu,decimalizing time was harder than decimalizing space. Lengthreform had met a triple condition: it held clear benefits for a major-ity, it offcred no enormous inconvenience for those not directlyconcerned, and it fit well with gencral public enthusiasm for a unityof length. Everyone was glacl to escape from the trading confusionthat had prevailed at national, provincial, and conununc borders.Hc expected no such cclcbration of this flawed time reform."Cornu insisted that it was the day, the natural unit of time, thatshould he decimal izcd-llot the wholly artificial hour. If the daywcre the base, then a hundredth of the day would be just about aquarter of all hour, and a hundred-thousandth of a clay would equalO.ii6 old-style seconds. 'I 'hat would he a gratifying unit of timebecause it corresponded so closely 10 the typical adult heartbeat, om" 1" 11 l nninatura sma tcrupora umt.

But "interests trump logic," Cornu domly noted, and no inter-ests hacked the one logicd reform that would bring order to time.Chaos did 170/ currently reign ill the world of time, as it had in spa-tial mcasurcmcnts before the reform of the meter. In a sense, time

was already unified among countries, as length had not been beforcthe meter. Into this unreceptive atmosphere, Cornu observed, thetime commission was now dropping a hopelessly confused com-promise that sanctified the all-too-artificial number of twcnty-fourhours in the day, and then dccimalizing this useless hour. Decimaliractious of an hour were unnatural, Cornu insisted: a hundredth,thousandth, and ten-thousandth part of an hour were 36, 3.6, and0.36 seconds, respectively. This was no good; an astronomical clockcould not beat at intervals corresponding to these units of time: 3.6seconds was too long for a pendulum and 0.36 too short. Havingspent ycars building and maintaining his own astronomical clockwith a massive pendulum, Cornu charged ahcad: the whole human

Poincare's Mal)S

organism made thc second special. Not only did our pulse surgeevery second or so, but our capacity to react, by sight or sound, tookabout a tenth of a second, adding to thc value of a time unit that wasapproximately a heartbeat long. According to Cornu, the body, theexisting clocks, and the sun all militatcd against decimalizing thehour. Cornu despaired, moreover, at the commission's other com-promises, If the hour was to be maintained (which hc opposed),then the logical division of the globc ought to be in 240 parts, mak-ing each hour of rotation carry the carth through the even divisionof ten parts. Yet here, too, the commission hadmisplaycd its hand,dividing the circumference of the world into 400 parts. Since 40()parts did not dividc evenly into thc twenty-four hours, even the geo-graphers would gain Iittlc convenience as they reckoned longitude.As far as Cornu was concerned, this reform had failed to decimal-ize the on ly truly natural period of time hy refusing to seize the dayas thc basic temporal unit in our lives: "men of science should ...prepare the future not by compromises, hut hy the progressive adop-tion of [the decimalizcd day and circle] in the domain in which

they arc masters of convention.'?'Attacked in public by his friend and mentor over the COJllPro-

mise solution that he had crafted, Poincare 100 now had 10 inter-vene ill print, not least because the legitimacy of his conunissiouhad heen thrown into question. Like Cornu, he acknowledged thecompeting interests. Unlike Cornu, however, Poincare saw such dis-cord as the mandate for a rough and ready scttlement. As always hc

aimed for an engineer's progressive middle course, avoidingboth revolution and reaction. The essential point, in his eyes,was to drum out of existence such monstrosities as iih25m40s or25° 17' 14". As far as he was concerned, the important point was the

adoption of any decimal system.As Poincare kncw full well, the physicists (that is, the electricians)

had fled the room. Poincare now tried, gently, to usher them back.Surely they had exaggerated the inconvenience of the decimal sys-

rII


tem. If they'd only read the report, they would come over to his side(or so Poincare thought). So he began to cite from it. After so manyyears of struggle to establish an acceptable system of electrical units,it was understandable that the electricians could not easily abandonit now. But, he urged them, be reasonable. For all practical pur-poses, by any measurement one simply is comparing one thing toanother: one time to another time, one resistor to another resistor.In any such industrial operation there is no need to go back to theunderlying definition of a unit. The storekeeper measures elothwith a meter and has absolutely no need to remember that themeter is the forty-millionth part of the terrestrial meridian. Only theso-called absolute units would be damaged by the reform. (Anabsolute unit of electrical current, for example, was defined not inrelation to any particular materials, but by identifying an ampere asjust that amount of current which when passing through two par-allel, infinitely thin bars a meter apart would repel each other witha certain forcc.) In effcct, Poincare said: Let the English worryabout the natural thcology of absolutes; it was convenience notdivine sanction that mattered. '

Indeed, Poincare insisted that the object of the physicists' com-plaint was inconsequential. True, the old scxagesimal clocks withtheir sixty seconds and sixty minutes could only awkwardly be com-pared to the new observatory clocks that would display centihours(hundredths of hours, equal to thirty-six seconds). So what?Chronometcrs need only indicate intervals of time, indced verysmall intervals. There is simply no need to reset them to a specifictime of day. But push the thought experiment to thc limit. Imagine,Poincare continued, that the astronomers adopted the decimal sys-tem, followed by such a spectacular diffusion among the generalpublic that there was not a clock based on seconds still to be foundanywhere. How much bother might those rare physicists be subjectto who wanted to determine the absolute value of electrical resis-tance (the ohm)? They would have to multiply by 36. "And for

Poincare's Maps 173

them to avoid this operation we are daily to impose tedious calcu-lations on thousands of mariners along with millions of school-children and former schoolchildren?" Which do we do moreoften - determine the absolute value of the elcetric resistance, fixour position at sea, or add two angles, or two times? In sum, Poin-care accused the physicists of blocking progress for the astronomersand the public just because they, the physicists, would not profit. Asfar as Poincare was concerned, some progress was better than none.If units differed in astronomical treatises and elcctrical books, thatwas a small price to pay to rid the world of the absurdity of havingthree units in a single number like 8h,14111,25s.2

(,

Despite the prodigious amount of work they put into their cam-paign, Poincare's time commission stalled. Finding open forcignhostility to the idea of such time reform, thc Ministry of ForeignAffairs let the Bureau of Longitude know ill July 190() that State wasnot ready to back the effort. After a hundred years, the revolution-ary strugglc to rationalize time expired."

Although they lost the attempt to decimal izc time, many partic-ipants in Poincare's commission argued passionately over timezones and time distribution. Sarrauton, for example (never one toavoid polemics), turned his guns toward the zone system. Hc took0I1e of his scathing reviews (on thc proposed time zones) and sentit personally, on 25 April 1899, to Loewy at the Bureau of Longi-tude. It began, as so many time-pleas did, with all homage to thc railalld cable: "The surface of the globe is criss-crossed by trains riding011rails, by fast boats full of voyagers and merchandise, and on theaerial and submarine telcgraphic lines, news circulatcs with thespeed oflight. ... The surface of the planet has been, in a certainsense contracted." Time zones of synchronized elocks were theanswer, but certainly not these English time zones.

Sarrauton demanded that the wedge-shaped time coordinateddivisions of the earth be liberated from the grasping claws of theBritish Empire. His ire had been roused by a proposed "Boucle-

.--EINSTEIN'S CLOCKS, POINCAR{i:'S MAPS

noot" law that would have delaycd Paris time by 9 minutes and 21seconds: "This is immediately the time of Greenwich; the Englishmeridian, soon, 'France towed by England' and the collapse of themetric system!" Happily, as far as Sarrauton was concerned therewas an alternative-the law of Gouzy and Delaune-that woukl dothe right thing by zones, decimalization, and the long-lost primemeridian: it would divide the hour into 100 minutes, the minute intoIOO seconds, sct civil time into twenty-four timc zones, and countlongitude from the Bering straits beginning OIl 1 January IYO(). 'Thisis the achievement of the system of decimal units, France realizingonc of the most important reforms of modern times, .md in scien-hfie matters, the preponderant French influence in tlio world. Wehave arrived at a crossroads ancl thcsc two projects of law mark thetwo roads that open before us. We must choose."?' Whatever itsaclvantages for rational France, Gouzy anc] Delaune's proposal neverpassed. France adopted the Crccnwicl: meridian 011<) March 1<JI1.

In these ferocious debates over zones, decimalization, aud theprime meridian, time conventions crossed arenas tkil we lcncl tothink of as far from each other. law«, maps, scicuc«, iudustry, dailylife, and the legacy of the l-rcnch l{,evoi\1tion all collided, drawill~in leading figures from the French lcchuica], intellectual, and sci-entific establishlllcnts. At the Bureau of I,()]]gih](le, Poincare'sphilosophical hope for "conventions' and "convenience" ran smackinto the everyday realities of navigators, electricians, astronomers,and railroaders. Just before Poincare published "The Measure of'rime" in 1H9k, physical, conventional, and coordinated time hadconverged in whirling reformist dcbate that was thoroughly abstractand yet altogether concrete.

Of Time and Ma/)s

If one of the Bureau of Longitude's projects in 1897 was the estab-lishment of decimalized time, even more pressing was the orches-

Poincare's Maps

tration of one of the most difficult time-synchronized mapping pro-jects in the Bureau's illustrious history. Already in 1885, the Min-istry of the Navy had assigned the Bureau the task of determiningth~ exact positions of Dakar and Saint-Louis in "our colony" ofSenegal." Years in the making, the Scnegal report only appearedamong the Bureau's publications in 1H97 - coming into Poincare'shands just before he wrote "The Measure of Time" and took on thc

presidency of the Bureau.Mapping "om colony" was no easy task. Governor Louis Faid-

herbe had violently annexed the Wolof and Cayer regiollS of Sene-gal by IH65, enabling the colonizers, at least intermittently, to clearthe road from Saint-Louis to the Cape Verde pcuinsula. By 1k8 5,the colonia] goveIIIlllellt had a railway link under construction join-

ing Saint-I .ouis and Dakar.But lavinz iron tracks did not stop fierce anticolonial resistance.

, b

French forces, still battling in the cast and south, never completelysnpprcsscd the rebellion against them. Insurgencies were still erupt-inz on the eve of World War 1. In the heat of these oolouinl battles,

b

the Bureau's men were there to fix the position of Sellegal's twomain cities, in part to extend mapping into the interior of the colonyalongside conquering troops. But the French colonial project hadeven grander ambitions. By providing exact coordinates at Dakar,the lirelleh authorities intended to extend their cable system fromthat port clown the lcngth of the west coast of Africa to the Cape ofGood Hope. Longitude, train tracks, telegraphy, and time-synehronizatioll reinforced each other. Each showed a differen!

facet of a new global grid.By the time the Dakar-Saint-Louis expcdition set off from Bor-

deaux, the Bureau had already extended its telegraphic reach toCadiz's San Fernando Observatory (about fifty miles northwest ofGibraltar). From there, the French relied Oil British Cable's linkjoining the Cadiz and Tencrifc observatories (Tcnerife Observatoryhad just recently been cabled to Senegal). One hour each evening,

EINSTEIN'S Cl.OCKS, POINCAR(:'S MAPS

RIQUE-'1!:; 11"";;,,,,,:;;;,::,,

$>., (!f01.••"¥.,,. ...,.1•.•.•.•. j",;ti<'l '!-/ .''. ·l~iI.~; w·•.•. \..',""';;-ch 0'

'H.rl;";<'E "'I" 1 ""..u",~',,..l,. n..d~-l ,:: -·."",f::C""'j:::,f7Id

Figure 4. J Cablillg Simultaneity: Paris, Cadiz, 'l'eneri]«, and Dalcar.

Undersea =: /Jrolijeroled ill the last/Jarl of the nineteenth century, andlongdude [inder« instantly seized the ofJ/)(Jrlul1i1y of using each Ilew linl: toWire time ({C~OSS the oceans .. The French Bureau of I ,ollgilude made use ofBritIsh cuu] SfHl1llsh subuuuine cable« to get their time signal limn the obser-vaiorv at Cadiz, Stiain, over 'i'elleri(e and thence 10 /)(11, it S .' V

, , . - 1\(, .• OURel·.: IVII':N 1)1<;

SAINT·~IARTIN, AII,\S UNIVI·:J(SI';J. (lS77).

the astron.omcrs controlled the cable. For France 'ISL()1' '111 f r:• _~ - ( , c r , II c: 0 ..JOll-

~lIlental Europe, renting cable time from the British had enteredinto the. order of things. Controlling the vast majority of the world'ssubmarm.e cables, the British passed messages between France andl~S colonies everywhere but North Africa. Alone the Tcnerife-Sene~al, West African, Saigon-Haiphong, and Oboek-Perim cablescost France almost 2.5 million francs per year, paid, gallingly

II

Poincare's MafJs

enough, to their imperial competition, the British. Such depen-dence burnt slow and deep in the French establishment; the mili-tary, commercial, and journalistic sectors all chafed during the1880s and 1890s under British communications dominance. Butthe Chamber of Deputies blocked French cable proposals oneafter another: One casualty was an 1886 link from Reunion toMadagascar, Djibouti, and Tunis; another, in 1887, from theFrench West Indies to New York, and a third from Brest to Haiti,in 1892-93.'0

Just as they rclicd on the British cable-laying firm, the Frenchauthorities needed the Spanish. Ceeilion Pujazon, astronomer at SanFernando, offered his observatory as a rclay point, linking the Paris-launched signal to Senegal through 'lcnerile. TIking the steamshipOrenoqlfe of the Compagnie Transatiantiquc, the astronomersarrived, worse for the wear, in Dakar on 15 March 1895. GovernorSeignae-Lesseps immediately put his troops at their disposal. Theartillery captain commanding the Dakar garrisoJl offered laborersand indigenous masons, and housed the scientists in the military'smess halls-there being (according to the querulous chief astro-nomer) no decent hotel to be found anywhere. With horror thechief astronomer noted that passengers were sleeping in straw bed-ding like natives.

Military aid to the lllap troops did not end with food and lodg-ing. The Bureau of Longitude astronomers took up their posts inthe fort's blockhouse, looming on the point of Cape Verde to pro-teet the coal park and anchorage. Thick concrete walls designed toprotect artillerists against attack allowed the astronomers to installtheir timekeeping pendulum in the bunker's sheltered room. Thiskept the temperature of their all-important clock under control, anabsolute necessity in Dakar's ferocious heat. Establishing theirmeridian telescope outside the blockhouse, astronomers mountedthe collimator on the parapet of the gun battery. Five clayslater, on20 March, the team steamed for Saint-Louis. Welcomed by the gov-

---~.~-.- ..-.-.----- -------------.--~


ernor's aide-de-camp at "the political center of om colony," theyhammered into place a Saint-Louis station."

A gubernatorial edict prevented people from entering or leavingtheir operations building during the observations (footsteps dis-turbed the pendulum). Those few natives allowed to pass by did sowithout carts, in bare feet, on sandy soil. Observations ran from 26March until 11 April 1895; the team launch cd thcir first signals toDakar on 29 April and to San Fernando on 2 May.

Not cverything went well. The river flowed north-south, makingthe Saint-Louis meridian sighting extrcmely difficult. It was good to

NORO I/.'.'~

';.1 /,

Figure 4.2 Measuring Dalwr. The overlap olmilitar» structures and geo-gra/Jhical work was extensive-i-jar the French, the British, atul the Americans.At Dnkar, the French longitude expedition used evelY aspect ol the [ort over-looking the vital coal yards to establish the lUlldamentallongitllcie measure-ment ol the colony. SOllReI<:: ANNiI/.I<S / )11 BII/{/'AII /)/·;s t : )N( :/1'1 II lI':S, VOl.. 5 (18')7).

Poincare's Maps

be on the riverbank to avoid obstacles, but they couldn't very wellplant themselves in the middle of the river to sight due north towardthe polestar. "Marauders" began stealing anything metal left in theopen, including, almost daily, the spike used for collimating the

shooting of the stars.

The 260 kilometers of wire that link Dakar to Saint-Louis were

established in the bush-covered plains of Cayor, with primitive

means and in the midst of a population that was hostile if not in

open war with us. The wire was so often cut, the poles so often

knocked down and then re-established more or less well, that one

does not find the normal Iphysiea11 conditions of an ordinary line.

Let me add that at sunset the dew was so strong that the poles

dripped, and where 5 insulators ordinarily would suffice [back in

France], even 70 failed to give a trace of electrical wave.

Even once the signal made it along the train tracks through Sene-gal, the signals from Santa Cruz (Tenerife) to San Fernando failedbecause, during the crucial nights of observation, there were activeand official transmissions on the Spanish land lines following theelection of deputies. Then came corrections. There were the usualcorrections for temperature variations; there were correctionsthrough "personal equations," the characteristic psyehophysiologi-callags of each observer as he signaled a star crossing the meridian.There were corrections for thc behavior of the delicate mirror thatregistered the signal's arrival. In the end, after doubling the weightof one set of observations and compensating for various otherinstrumental and human errors, the team. settled on a San Fer-nando-Saint-Louis longitudinal difference of 41 minutes, 12.207seconds.' Not wanting to miss the opportunity of a rare steamboatleaving Dakar for 'Ienerite, the astronomers corralled some home-sick sailors to quickly pack their instruments for the voyage back toParis. Their report to the Bureau appeared in print in 1897.

r


By the time the Senegal report saw light of day, French-Britishrelations over their colonies were deteriorating, and telegraphiccables ran through the center of many disputes. British cable com-panies refused to employ foreigners and were clearly readingFrench messages between Paris and Dakar or Saigon even beforethe French authorities had them in hand. At the 1885 Cable Con-vention, Britain insisted on the rights of warring nations to tear uptheir opponents' lines-clearly an advantage to the country thatowned twenty-four of the thirty extant cable ships. In 1898, tensionsincreased to the brink of war. Racing to control a part of the Nile inSudan, Captain Marchand's French squadron was rcady to stake aclaim; but while the British troops remained in continuous contactwith London, the French cable inexplicably went silent Only whenthe French Governor loaded thc cannon in Dakar (whcre thcFrench Bureau of Longitude men had just been) did the cable,magically, come alive. H

Back in Paris, the longitude battle between thc French andBritish capitols would not end and could not be contained in thcdomain of the politicians. Even as the Bureau of Lonzitude con-

b

tinucd to vex itself about whether French clocks should be sct byGreenwich time, the astronomers went clock-to-clock over the mostbasic of questions: where was Paris in relation to London or rather, ., .,how far east did the Paris Observatory stand in relation to the RoyalObservatory? Back in July 1825, thc two national rivals had tried tosettle the problem by launching rockets from thc English Channel,using their explosions to synchronize clocks. Lc Verrier and SirGeorge Airy then tried again by tclegraph in 1854, settling OIl a dif-ference of 9 minutes and 20.51 seconds. Unfortunately that con-sensus collapsed in 1872 with the American Coast Survey telegraphcampaign that accompanied the laying of the transatlantic cable. Itdetermined that Paris was nearly a half-second farther away fromLonclon-9 minutes and 20.97 seconds. Half a second was far toolarge an error for anyone to tolerate in the era of hundredths, if not

Poincare's Mal)S

thousandths, of a second, so the Astronomer Royal, along with Gen-eral Perrier (director of the Geographical Service of the FrenchArmy) and Admiral Mouchez (director of the Paris Observatory)joined forces in 1888 to settle the question (so they hoped) for good.

Appointing two observers from each country, thc astronomersplanned to conduct measurements shoulder to shoulder. A French-man and an Englishman would literally stand next to each other,with onc pair in England and the other in France. They shared atelegraph line, they traveled together back and forth across La]\.IIanelle, and they coordinated their procedures down to fine cor-rections of personal errors. They even shared a single battery-runelectric light to avoid needless heat that might distort their instru-rncnts. At Montsouris, the Frcnch and English instruments stoodon piers twenty fect apart. Yet the results caused dismay:

English longitudinal difference from Paris to London:9 minutes and 20.85 seconds

Frcnch longitudinal difference from Paris to London:9 minutes and 21.06 seconds.

A fifth of a sccond. Still too much. So again, in 1892, the yearPoincare was elected a permanent member of the Bureau of Lon-gitude, after years of ncgotiation, the teams oncc morc wircd thcirtelegraphs into place. Again the astronomers securcd thcir instru-ments on thc stone piers, launchcd electrical waves, and painstak-ingly reduced data. To their immense embarrassment, the resultswere no more harmonious than they had been in 1888. The twogreatest European observatories, both of which claimed to lllap thewhole world, could not agrec on their own positions to within a fifthof a second. Once more the French found a greater expansebetween Paris and London than the British did. This telegraphictime crisis finally came to a head in 1897-98, during thc Bureau ofLongitude presidencies of Loewy and then Cornu. The Paris Obser-

EINSTEIN'S CLOCKS, PO[NCAR{;;'S MAPS

vatory, in conjunction with the International Geodetic Conference,insisted that the two observatories stabilize the European map with

a proper time exchange."Clearly, issues of conventions were not confined to the far reaches

of gcometry or philosophy, rather, they were ubiquitous. Conventionsconcerned the prime meridian, decimalized time, submarine cables,map making-even the relative location of Paris and London. Every-where onc looked from the Bureau of Longitude in 1897-98, inter-national concords ill the world of space and time seem cd urgellt.

In this light, Poincare's "Measure of Ti111e" reads as somethingquite different from a purely metaphorical tract. First, thc calcn la-tion of Paris time from a distant site (whether London, Berlin, orDakar) was not all abstract problem at the Paris Bureau des Longi-tudes in 1897: it was the most pressing issue of their map-makingmission. Second, Wt)7 marked all enormous intensification of thelong war over couvcntional decimalization, a debate that Poincareengaged directly. In short, in 1897 more than ever, ilwas the Bureauon ,oJlgitllde that W<.IS responsible for the precision simultaneity mea-surcmcnts thatwould permit the extension of an ever-more accuratemap ofthe world relative to the marble longitude pier of Monts om is.

Indeed, when Poincare proposes in "The Measure of Time" thatsimultuucity must be understood as a convention, it is crucial toattend to the literal. Synchronizing distant clocks hy the observationof astronomical events was standard practice for French, Ccnnan,British, and American surveyors. Transits of Venus, occultations ofstars by the moon, eclipses of our moon and [upitcr's moons wereall useful events to set clocks by (if only inaccurately) on distantcolonial shores. I laving been a member of the Bureau for four ye,mill 1897, Poincare knew perfectly wcll that clock coordination hyastronomical sightings had, for many reasons, long been overtakenby the telegraph as the most accurate standard of simultaneity.

Instcad-> this is the crucial point - Poincare invoked telegraphi-cally determinedlongitucle as the basis for establishing simultanc-

·--------------,-;;;:-;:;--,-~"w~.ijj'MI!J-al!llalllla.x._-_- a__ I1_ •• __ C__Jilllll.•-,

PoiI1C(//,(j'~ Maps

II\, between distant sites. He insisted, in the most celebrated lines ofII-Ieessay, that in the synchronization of clocks one had to take theIime of transmission into consideration. He immediately added thatIIlis small correction makes 1ittlc difference far practical purposes.And he remarked that the calculation of the precise time of transitFor an electrical telegraph signal was complex. From at least1892-93, Poincare had taught the theory of telegraphic transmis-sion of signals and reviewed the experimental studies that measuredthe speed of electrical transmission in wires of iron and copper.That interest did not wane. In 1904, in a series oflecturcs to theEcole Superieure de Telegraphic, he extensively analyvcd the"telegrapher's equation," COlliparing it to work by others and specif-ically referring to the physics of undersea telegraph cables."

In the practices of signaltTansmission time lies a key point to ourpuzzle. At first glance, it might seem impossible that Victorian car-tographers were t-aking account of the time of signal transmission astheir electrical pulses sped simultaneity across continents andoceans. But we need to look al what they were actually doing as theystruggled against the myriad errors that entered the procedure. lnfact, ill their error corrections, the electric mappers had long sincebeen taking precisely the transit time into account as they syuchro-nizcd clocks betwcen Paris and the far reaches of the United States,Southeast Asia, Klst and West Africa. Or, for that matter, in thcintransigent precision measurements between Paris and Crccnwich.

They did not need to wait- for relativity.Back in 1866, as we saw, the US. Coast Survey put a monu-

mental cffort into determining the longitude gap between Cam-bridge, Massachusetts, and Greenwich, England, over the firstAtlantic cable. The surveyors corrected for the usual errors in clockrates and in the measurements of star positions. But they were quiteaware that the instant a telegraph key was pushed in Calais, it didnot register in Valentia. That gap was in part due to the observers-their reactions were not instantaneous-and in part due to the

I


instruments' inertia. It took time, for example, for the magnet toswing the little mirror around sufficiently to cause a noticeabledeflection of the light beam. These difficulties, which the authorsdubbed the "personal error in noting," could largely be eliminatedby measuring these delays under controlled circumstances. Butthere was another crucial contribution to the delay between trans-mission and receipt, and that was the time it took for the signal tocross the Atlantic from Nova Scotia to Ireland. Amidst the listing ofall the other errors, there in plain print are the measured transmis-sion times: 25 October 1866,0.314 seconds; 5 November 18660.280 seconds; 6 November, 0.248 seconds." Or look back at theCoast Survey's myriad missions to Mexico, Central America, andSouth America. Or to de Bernardieres's missions, or to the vast webof links among European observatories.

Everywhere the electrical surveyors were measuring the time ittook the telegraphic signal to pass through the wires; everywhere sur-veyors were using that delay correction to establish distant simul-taneity. Here is how they reasoned. For simplicity, let's grosslyexaggerate the time the signal takes in transit, and call it 5 minutes.Suppose the eastern obscrving team sends its signal at 12:00 noon,eastern local time, to their western partners located 1124of the wayaround the globe-that is, exactly 1 hour westward (-1 ham).Because of the transmission time, the wcsterners would receive thesignal at 11:05 A.M., western local time. If they forgot to correct forthe 5-minute delay, this naive western mission would conclude thatthey were at a longitude point that was 55 minutes earlier (- 55 min-utes) from the eastern stations.

(East-to-west apparent difference) = (real longitude difference) +(transmission time)

(Here -55 minutes = -60 minutes + 5 minutcs.) Now let's imaginewhat happens for a signal traveling west to east. West sends at local

I!

1

1.JII

i.

Poincare's Maps

west noon (I :00 P.M. local time in the east). But by the time the sig-nal from the western station arrives in the east, the eastern clockwould not read 1:00 P.M., but rather 1:05. Our observers, if theywere unaware of the time it took the signal to travel, would con-clude that western local time was 65 minutes earlier than easternlocal time (-65 minutes). In other words, the actual longitude sep-aration would be shorter than our observers would believe if theyforgot to take into account the signal time. This means:

(West-to-east apparent difference) = (real longitude difference) -(transmission time)

(Here: - 65 minutes = - 60 minutes - 5 minutes.)Now, if you add the measurements (cast-to-west apparent differ-

ence) and (west-to-east apparent difference), yOllget exactly twicethe reallongitudc difference. The + and - transmission times sim-ply cancel out. And, if you subtract the (west-to-east apparent dif-ference) from the (east-to-west apparent difference) you gct twicethe transmission time: (apparent east-to-west - apparent west-to-east)= 2 times (transmission time). So,

Transmission time = 1/2 (east-to-west apparent difference - west-to-east apparent difference)

That simple tool for calculating transmission time formcd partof the procedural mantra of every long-distance surveying team inthe world: in the West Indies, in Central America, in South Amer-ica, in Asia, and in Africa. Certainly the Bureau of Longitude's peri-patetic astronomers had long been using it as they hauled theirwooden observing shacks from place to place: between Hong Kongand Haiphong or Brest and Cambridge. Telegraphic map-makerssaw, understood, and said perfectly clearly that the telegraphic sig-nal time had to be taken into accoun t to establish precise simul-

----.--.~-----


taneity and therefore longitude. For Poincare not to have known thisaround [898, we would have to assume that he ignored everyBureau of Longitude report written during the years he had servedas a member, as well as avoided hearing any discussion of theiractual procedures. We would have to suppose that when, in the"Measure of Time," he wrote "let us watch [the telegraphic lonsi-

. b b

tudc savants] at work and look for the rules by which they investi-gate simultaneity," he somehow did not understand what his ownlongitude crews (and cvery other British, American, German, andSwiss team) had been doing for the previous quarter century. Thisbegs credulity.

Back in the late 1870s - when Lieutenant de Bernardieres, Cap-tain r .e Clerc, and astronomer I ,oewy sought, quite literally, to reat-tach France to the Illap of Europe-one of their most importantlinks was to be a telegraphically fixed lonaitude cliffercnee between. b

Paris and Berlin. Time delay was an immediate COl1eeIlJ. Theauthors noted in 1882 that their signals "were affected hy smallerrors with different causes all of which must he taken into accountcarefully": errors due to the response of electromagnets, the loss of

time caused by the slllggishness of the mechanical parts, the rela-tivc separation of the pell tips, and finally the "non-instantaneity ofthe transmission of the electric flux." To determine that transmis-sion time, there was work to do ill the observatory; the astronomer-surveyors had to be certain, for example, that the currents used werealways the same. But there were also assumptions to be made, forexample, that the velocity of the electric signal was the same in bothdirections. In agreeing to the procedures for fixing time throughexchange of telegraphic signals, the language of conventionsentered up front. 10 synchronize clocks between Berlin and Paris,protocols had to be established, agreements concluded; they evenscripted in advance the greetings between stations. As in the Con-vention of the Meter, conventions of simultaneity demanded inter-national standards, detailed accords on every step of the process.

Poincare's MafJs

Now it makes sense that we find among the headings of theFrench Bureau of Longitude's Paris-Berlin report, Conveniums Rel-ative to the Exchange of Signals," When the Bureau of I .ongitudenailed Bordeaux to the map in 1890, in the list of other corrections,such as pendulum errors and personal equation errors, we finallycomc to it: "the delay S of the electrical transmission."'" For theFrench team in Senegal, it was therefore fully routine to takeaccount of the finite signal time of their electrical pulse; like somany other telegraph missions by 1897, the team simply applied theby-then usual rule to calculate the transmission time: "The differ-ence between these results [apparent Saint-I,ouis-to-Dakar andapparel It Dakar-to-Saint-I .ot tis], which is 10.320 seconds] representsdouble the time taken for the transmission of the electrical waveplus other errors." III Routinized as they were, such corrections werecritical for the highly exaeting measurements facing Poincare andhis colleagues at the Bureau. In measurement after measurement,compensating for time delay loomed large as surveyors strugglecltoeliminate the recalcitrant longitude clashes that still remainedbetween Paris and Crecnwich, or between Paris and the far-flungFrench colonies of West Africa, North Africa, and the Far KISt.

In a certain, unfairly retrospective sense, it is obvious that thelongitude finders had to take into account such a lime of transmis-sion. After all, they claimed to be recording longitudes to the thou-sandth of a second, and the transmission time for light over 0,000kilometers was about a fiftieth of a second. Electrical waves woundtheir way through equivalent lengths of copper undersea cable sev-eral times more slowly, making the correction nearly a tenth of asecond. In the late-nineteenth-century world that vaunted carto-graphic precision, this was too much - every second of time error atthe equator meant half a kilometer of cast-west confusion.

Poincare's remarks in his 1898 "The Measure of Time" abouthow to define simultaneity by telegraphic signal exchange were not,therefore, imaginary speculation about conventionality. Here was

---~


one of the three permanent Acaclemy members of the FrenchBureau of Longitude, by far the most famous, just a few monthsbefore he was elected president, reporting on standard geodesicpractice. All around him he could see simultaneity operationalizedthrough the Bureau's active network of cables, penclula, and mobileobservatories.

Poincare could also see how scientific procedure crossed intophilosophy. Somc twelve years before, his Poly technique friend,physicist-philosopher Auguste Calinon, had urged him toward anaturalized view of time and simultaneity. Poincare had respondedsympathetically. 'I 'hen, in 1897 -at precisely the moment Poincarewas most deeply immersed in the decimalization of time -Calinonpublished a new book. His thirty-paged tract, A Study of the VariousQuantities of Mathematics, laid out the vicious circle of our rea-soning about the equality of durations. A container is fillcd withwater, then emptied through a spout at its base. Does the emptyingtake equally long each time the process is repeated? 'l o answer thequestion presupposes an independent measure of lime. But Cali-non pointed out that the same question then would occur ill thisindependent measure: what would calibrate the calibrator? Poin-care clearly was struck by Calinou's formulation and quoted it in"'1'1 M f Time" "() f the ci .'lC . easl1re 0 . Ime: . ne Ol t le circumstances of this phe-110011CnOn [the time needed to empty the water from a container] isthe rotation of the earth, if this spced of rotation varies, it consti-lutes, in its reproduction of the phenomenon, a circumstance thatno longer remains the same. But to suppose this speed of rotationis constant is to suppose that one knows bow to measure time.?"

Calinon went even further than Poincare indicated. He empha-sized the historical arbitrariness of human time divisions; the sea-sons, for example, were chosen not based on any scientific ormetaphysical conception, but for simple material utility. When sci-entists entered the picture, they simply chose the "simplest andmost convenient" mechanism, which for Cali non meant that the

Poincare's 1'\1(//)5

motion of the hands of a clock were such that, by their use, the for-mulae for the movement of thc planets would be as "simple as pos-sible." Calinon concluded that there was an irreducible choice inthe measure of time, one that had to be bascd on convenience: "Inreality, measurable duration is a variable, chosen from among allthe variables present in the study of movemcnts, because it lendsitself particularly well to the expression of simple laws of move-nlent."·)2

In thc intcrsecting circles around Poly technique, Poincarecontinually faecd "choice," "convenience," and "simplicity" in themeasure of time, both throughout the technical world (railroaders,electricians, astronomcrs) and ill thc scientific philosophy of his cir-cle of Polvtcchnicians. His "Measure of Time" of january 1898 pre-cisely marks that intersection. The measure of time is a convention,one tied to the realities of scicntifie procedure. It is essential, how-ever, to also see what the papcr was not. Poincare's "Measure ofTime" W~IS HO/ all inquiry into simultaneity that took this principledcorrection of simultaneity into the heart of his physics. There is nota single word ill this article about frames of reference, clcctrody-narnics, or I .orcntz's theory of thc electron. Like his field geodesists,in early I f)98 Poincare saw electromagnctic exchange as key to pro-viding a conventional, rule-governed approach to simultaneity. Alsolike his geodcsist colleagues, he saw thc scientific consequcnce ofthc time-delay definition of simultaneity as just another correction,wcdged hctwccn the inertial hesitation of an oscillating mirror andthe psychophysiology of the ohservcrs. Unlike the geodesists, Poin-care saw a philosophically significant point in that correction. LikeCalinon, Poincare saw philosophy in thc scientist's measurement oftime. But unlike Calinon, Poincare had a clirect involvement in thecoordination of distant clocks. Only Poincare stood precisely at thatintersection; only he scized on the exchange of elcctrical signals tomake a routine physical proccss into the basis for a philosophicalredefinition of time and simultaneity. By crossing the electrical sur-

EINSTEIN'S CLOCKS, POINCAR(.:'S MAPS

vcyor's moves with those of the naturalizing philosopher, a piece ofeveryday technology suddenly functioned in both domains at once;it could serve in the clock room at Montsouris and graee the ReviewofA1etaf)hysics and Mow/s.

In Poincare's 1897 field of action, conventions of simultaneitywere everywhere: no one would even bother to claim authorship ofthe longitude finder's rule for transmission-time eorrection. Belowthc threshold of signed patents or authored scientific papers, thegeodesist's correction was part of the vast sea of anonymous knowl-edge that structured the telegraphic surveyor's everyday practice.More gcnerally, convcntious surged into thc visihle in every inter-national technical conference, ill every accord over length, elec-tricity, telegraphy, mcricliuus, and time.

Recall Poincare's words about the nature of physical laws ill the"Measure of Time": "no gelleral rule, no rigorous rule, [ruther] amultitude oflittle rules applicable to each particular case." Poincarebelieved that the redefinition of time was another longitudehunter's correction that should uotultimatcly dent the simplicity ofNewlon's epochal laws: "These rules arc 1101 imposed 011 ux, andone call amuse oneself by inventing others. Nouclhclcs« we would1101 know how to deviate frolll these rules without crreatlv compli-

b J

eating the formulation of the laws of physics, of mechanics, ofastronomy." We choose these rules, Poincare insisted ill oft-ciledwords, not because they arc true, but because they are convenient.As far as Poincare was concerned in IB9H, that meant glIardillg thelong-established laws of Newton for which a simpler alternat-ive sim-ply could not be imagined. "In other words," he concluded, "allthese rules, a1\ these definitions, arc nothing but the fruit of auunconscious opportunism." In Poincare's insistence 011 the con-ventionality of time, we hear ideas that we can now recognize ashaving echoed through the halls and wires of the Bureau of Longi-tilde and Ecole Polytcchniquc, a technical universe ill which diplo-mats, scientists, and engincers used international conventions to

Poincare's Maf)s

manage the colliding imperial networks of space, time, telegraphs,and maps. This world too was Poincare's, a way of being in sciencethat stooel a long way from Einstein's.

Mission to Ouito

Poincarc's-c-and the Bureau's=-cngagemcnt with telegraphic lon-gitude work intensified between 1R98 and 1900. Within a fewmonths of the Bureau's publication of their longitude fix of Dakarand Saint-Louis, the Bureau shifted into high gear to launchanother major expedition, this time to l'~euaclor, with Poincare asscientific secretary. Discussion of such all expedition had begunlong before, certainly as far hack as IHS9 at the Exposilion Uni-versclle. In the midst of that techno-fair, the American delegate tothe International Ccodesic Association had asked for ,1 dclcnnina-tion of the length of a mericlial arc (an arc along a line oflongitllc\e)as pa rt of ,111 efForl to determine the shape of the earth. If the earthwidened around the equator and flattened at the poles (as Newtonhad predicted two centuries earlier), then a longitudinal arc cover-ing, say, 5 degrees of astronomical latitndc near the equator shouldbe shorter than a 5-degree arc nearer to one of the poles. That theearth was oblate was long known: the question now was to deter-mine that shape with a precision fitting t-he age. The President ofEcuador approved, telling the French that they would have the fullhelp of his government. As the proposal bounced between the Mill-istry of War, the Ministry of Foreign Affairs, and the Army's Ceo-graphical Service, the cost began to rise, even as its importanceremained clear." Nor did Ecuadorian politics hold still. With hisascension to I':cuador's presidency on ') June l895, Ceneral EloyAlfaro began the secular Liberal Revolution that aspired to reformevery sector of national life. 'file bulging earth had to wait. .

On 7 Octoher 1898, the American delegate at that year's Inter-national Geodesic Association mceting at Stuttgart again pleaded

EI STEIl'S CLOCKS, POI CARE'S lAPS

for a long-overdue remeasurerncnt of the shape of the earth by wayof an expedition to Quito, Ecuador. Bouquet de la Gryc, the Frenchdelegate, reminded the assembled that, just four years previously,the Plenipotentiary Minister from Ecuador had proposed such anexpedition but that the 1895 revolution had required an "adjourn-merit" of the question. After the American delegate's politeacknowledgment, the British representative spoke less diffidently:wishes were fine, but the geodesists needed to say precisely whatcould and should he done. London demanded France's rcspollsc tothe need for mcridial action. De la Crye was "persuaded that inFrance one would look with a favorable cyc Oil the wish that wereopcll negotiations on a new measurement of the are of Peru."Having watched American surveying forces naillocatious up anddown the Americas, and wi tncssing the British near-monopoly 011

undersea cables in pursuit of their own cartographic a III hilious, theFrench understood full well that, if they hesitated, the AmericanCoasl Survey would grab the joh. Bllt if the Americans sei/.ed themap, as Poincare put it, "the honor of om country would he rav-ishcd.?" France mohilizcd.

From Paris the Minister of Publici ustruction offered lir. 20,()()()

for a reconnaissance mission to Qllito IIsillg personnel ;tSsiglled hythe Minister of War. III this up-to-elate foray, the Minister of PublicInstruction would extend the much-heralded eightecllt'h-eclltmymcnsurcmcut by 1 degree of latitude to the north and 2 degrees tothe south, with the area around each base to he given topographi-cal summaries and surveys of the horizon. Immediately, the Frenchwould send an avant-gardc expedition that would move fast, tra-versing 3,500 kilometers of some of the bighest rnountaius in theworld in only four months. Departing from Bordeaux on 26 May1899, the team worked at breakneck speed. While they were away,tensions with Britain mounted; there was the affair of the Frenchcable lines that had "inexplicably" failed during the French-English

Poincare's Maps

race to stake colonial lands on the Nile, and then the outrightBritish censorship of cables on 17 November 1899 during the BoerWar. On 8 December 1899, the French Minister of Coloniesannounced a cable bill of unprecedented size. Just a week later, theCouncil of Ministers passed a plan for an imperial network bud-geted at 100 million francs. Polemics over the cable projectappeared in publications on both right and Icft. '15 The Quito map-ping team sailed back to France in the midst of this brouhaha, arriv-ing ill Paris Oil the last day of the nineteenth century.

At their meeting on Monday, 23 July 1900, it was up to theFrench Academy of Sciences to decide whether and how to under-take the full mission. Poincare left little doubt as to the obligationshe expected his country's scientists to meet:

If our country owes itself its part ill the conquests of modern sci-cncc, I·hellall thc more reason we must 1I0t abandon a position Oilwhich our fathers hoisted, so to speak, the intellectual flag ofFrance. Our rights have been publicly recognized. Should werespond to these courteous invitatious by a declaration of impo-tence? l-raucc is as dyn.unic and richer than it was onehundredand fifty years 'lgO. Why would she leave to younger nations thetask of completing what the France of yesteryear had begun?"

The minister asked the Academy to control the operations; Poincareurgcd the august hody to go further. Shouldn't they follow thelegacy of their intrepid eighteenth-century forebears, Louis Codin,Pierre Bouguer, and Charles-Marie La Condarnine, who had sur-veyed a degree of arc in Quito beginning in April of 1735? A cen-tury and a half later, however, academicians could well ask if it wasnecessary for scientists to accompany the expedition into the Andes.Such a voyage would demand more than calculational abilities, asthe rather sedentary Poincare conceded:

..--------------------------

194 EINSTEIN'S C1.0CKS, POI CARJ:;'S MAPS

A high scientific competence, technical facility, and habits ofscrupulous regularity would be indispensable, but would not suf-fice. One must be in a state that would support great exhaustion,in territory without resources and ill every climate. One must knowhow to lead men, obtain obedience of one's collaborators andimpose that obedience on the half-civilized servants one is forcedto employ. All these intellectual, physical, and moral qualities arcfound united ill the officers of our geographical service."

What the academy could do from the safety of Paris was to main-tain scientific control hya commission charged with examining theobservation notebooks.

Poincare himself headed mission control. He made it clear inhis report of 25 July ll)O() that imposing the grid Oil this equator-ia I region would demand three bases. 'I o ensure reliability, theseshould be loeatednsing the same instruments employed ill deter-mining meridian length in France. Qnitoitself would he manucdby a most gifted (Frcuch ) astronomer, l'rancois (;onnessiat· of theLyon Observatory, with the whole operation generously funded byan anonymous clonor later revealed to he Prince Rolaud Bona-parte. With French officers operating the extreme stations, COIl-

ncssiat would make simultuucons observations at Quito, ensuringaccurate longitude fixes. As always, the telegraph was key in theestablishment of distant simultaneity: unc wire would run fromQuito to Caynquil, boosting its signal with a relay; another wouldtie Quito to the distant north station. If the relays introducedunacceptable error into the simultaneity determination, as theyoften did, Poincare was prepared to slice them from the system byhoosting thc battcry power of the initial station. At present, theteam was already working to string the telegraph network all thcway to the southern station. So the extreme ends of this far-flungmountain network would be tied back to Quito, with Quito's timebound to Gayaquil's. Cayaqnil, in turn, would coordinate its

--._-..----- - ----·------::-iifiI- ·---IiiiIi~~.-~."__--•. - _

Poincare's MalJS 195

\\

Mt:RIOIE.~LJE OUITO ••••.••!d",lI"

Figure 4.3 Quito Meridian. Poincare reported regularly on the Quito expe-dition. In this picture, the multui!« triangulations (ire shown; these were usedto measure the length of a iongitiulinal arc in order to give greater precision tothe shape of the earth. This network of latitude and longitude measurementswas then linked by cable to the world telegrapli net-and would be calibratedto the French prime meridian. SOllRO:: Por eARl;;, O/';{JVHK, COMl'l.kl'l':\ VOl.. 5, P. 575.

-,

-" "--""----.,..,..",~-------------------


clocks through undersea cables tied to the general world networkvia North America."

The academy approved Poincare's report as did the InternationalGeodesic Association in October 1900, with the American delegatecongratulating the French and reminding them that the UnitedStates would like to be asked first if any additional help were needed.Not likely. On 9 December 1900, Captains Maurain (of the engi-neers) and Lallemand (of the artillery) left for Fcuador as the avant-garde of what they expected would be a four-year mission to Quito."')

On Monday, 28 April 1902, Poincare reported to the Academi-cians in Paris: Members of the advanced team had spent monthsbuying pack animals and sctting up their convoys. By the time theystarted up into the mountains, the French expeditionary force had120 mules and were accompanied by forty Indian porters and sixEcuadorian officers. The vital measuring stick, consisting of lwo dif-ferent metals with diffcrent respollSCS to heat, had to be carried Oil

a man's hack. At night the humidity so distorted the micrometerthreads that they used for sighting that observations became almostimpossible between six and nine in the moming. Theil, at 11:00A.M., howling winds blasted dust through cvery crevice in the camp-site, wrccking instruments and torturing the explorers. Wild tern-perature changcs plunged through the camp so quickly that thcteam wondered if their measuring devices wendel ever settle into areliable state of equilibrium. Amidst all this, the French decidedthey would prefer to use their personal equations rather than switchpositions of the observers, which would have left Indians, alone, incharge of the base camp. Lallemand took two men on a side mis-sion to the far north in the hopes of extending thc network intoColombia, but they were promptly stymied by political turbulence.In a somewhat optimistic aside, Poincare conveyed the expeditionleaders' hope that, before 1904, they would have established tele-graphic simultaneity to all the far north stations short of Colombia. S(I

A year later, Poincare was back before the Academy, once again

Poincare's Maps 197

having drafted a report on the hard-driving expedition. It was Mon-day, 6 April 1903, and the commissioners noted with regret that theprevious year's progress had been held up 011 almost every front.First the summits were almost constantly lost in fog, making sight-ings impossible. Lieutenant Perrier had spent three months at hisassigned post in Mirador, 12,000 feet above sea level, almost con-stantly blanketed in clouds. Incessant rain pounded on his site, thevisible horizon limited to the camp itself. Furious winds shookeverything in the barracks. In one period of fifteen days, he was ableto make but one of his twenty-one measurements and caught not asingle glimpse of the signal he awaited from Yura Cruz. The valleysseparating them flowcd with a rushing river of clouds from the East.After months of isolation, Perrier's perseverance was rewarded withcalmer, clearer weather. In all intense burst of activity, the lieu-tenant completed his mission. SI

Other brigades faced similar problems and, by Poincare's reck-Oiling, gavc the same proof of their quality. At 'l acuuga, CaptainMaurain could only observe intermittently, seizing UpOll occasionalclearing. A violent cast wind accompanied by snow squalls made hiswork exceedingly painful. Gusts tore roof braces from the observa-tion station, ripping up tents right and left. At Cahuito stationLacombe found himself stranded for days in the fog and snow,unable to execute a single observation. And Lallemancl, whodirected the reconnaissance brigade and signal construction acrossexcccdi ngly tough terrain, fell into a crevasse in Cotopaxi. Othersoldiers recovered him, but for three weeks he was laid low. Amidstthese battles with the elements, the team speculated that the fero-cious weather might be linked to the volcanic activity following acatastrophic eruption on Martinique. S2

But not all the misfortunes of the longitude men could be laid atthe feet of nature. Both indigenous whites and Indians tore into thegeodesists' painfully established reference points. Apparently sur-veying rods signaled more than lat-long positions. For locals, these


markers promised buried wealth. In their search for gold, not onlydid the treasure hunters remove rods, they dug up everythingremotely near them. So the French -after their months in theoxygen-deprived, snow-driven peaks - had to resignal, reineasure,and re-mark the sites, sometimes two or even three times. Enlistingthe Church, the French enjoined local bishops and cures to staveoff the inhabitants, but neither science nor God deterred the dig-gcrs. Over the course of 1904, the French fou nd their stationsdestroyed some eighteen times, forcing the rcmcasurcmcnt of ~60pairs of points in horrendous high-mountain conditions. 'I 'he fol-lowing year, to their dismay, the simultaneity team realized, whilefi'eezillg in the craggy heights, that their native informants' reportson visihili ty had been, as they put it, "not exact." The geographersfinally understood that their informants had never voluntarily goneanywhere near such heights. On those few occasions that the localshad actually ventured to high altitudes, "visibility" meant being ableto see enough 10 climb and descend. Unlike the forces of simul-tancity, the native people had neither a need nor a desire to see farenough to flash latitude ancllongitude. Meanwhile Lallcmand C011-

tracrcd yellow fever, his colleagues sent him hack to France.Poincare delivered this cncoiuium for the mission: "The long

clays of wai ting in snow anel fog did not lead 10 all instant of dis-couragcment and the zeal, the constancy, and the devotion of theseofficcrs and of all the personnel ought never be denied. There arcgrounds for congratulating these valiant pioneers of Science fortheir courage and the results they obtained.'?' Map coordinates inhand, after eight years of effort to fix time and space, Poincarereported in 1907 that the expedition had returned to France.

Etherial Time

In following the Quito expedition all the way back to Paris, we havegotten ahead of ourselves. For during the entire span of the longitude

,

IfII!

Poincare's Maps 199

expedition - from planning in 1899 to it<;concI usion in 1907 - Poin-care pressed the technology of simultaneity in two other, very differ-ent domains: philosophy and physics. This was no accident. From thetime he completed his report on the Quito mission's objectives (25July 1900), Poincare was fully immersed in the details of telegraphicsimultaneity, down to the battery power of the telegraph lines. He hadmade the case to his colleagues that mapping Quito was of doubleimportance-as a defense of French honor ("hoisting the intellectualflag of France") and as a technical-scientific problem (determiningthe shape of the earth, mapping the world). But that was not all.

No longer thinking purely mathematically, Poincare nowreflected on the ph ilosophical, conventional basis of physics moregencrally. Just a few days after urging the Quito project on his fellowAcademicians, he delivered a paper at a major philosophy confer-ence (2 August 19(0),1+ where he asked ,I fuudamcntal questionabout what- he considered the most central science: could the basicideas of mechanics itselfbe altered? Among his French compatriots,Poincare argued, mechanics had long been treated as beyond thereach of experience, as a deductive science that would inevitablylead to conclusions n-Ol11 assumed first principles. By contrast, Britishmechanics was at root not a theoretical but an experimental science.If there was going to be allY real progress in mechanics, this cross-channel clash would have to he sorted out analytically. What part ofthis most exalted science was experimental? What part mathemati-cal? Anel-as he put it-what part conventional?

In respollse, Poincare laid out for the philosophers his judgmentof what we knew about the starting points of this most fundamen-tal of sciences, drawing from the full range of his work on the foun-dations of geomctry, geodesy, physics, ancl philosophy. In his words:

1. There is no absolute space, and we only conceive of relativemotion; and yet in most cases mechanical facts are enunciated asif there is an absolute space to which they can be referred.

-------------------_.---------_. __ .. -


Z. There is no absolute time. When we say that two periods areequal, the statement has no meaning, and can only acquire ameaning by a convention.

3. Not only have we no direct intuition of the equality of twoperiods, but we have not even direct intuition of thc simultaneityof two events occurring in two diffcrcnt places. I have explainedthis ill an article entitled "Mcsurc du Temps."

4. Finally, is not Euclidean geometry in itself only a kind ofconvention of 1<1nguage?

For Poincare, mechanics could bc alternately enunciated llsinga non-Euclidean geometry. It might be less convenient thanmechanics articulated using ordinary Euclidean geometry, but itwould he altogether as lcgitilnate. Absolute lime, absolute space,absolute simultaneity, and even absolute (Ellclidean) gcometrywere not imlJosed Oil mechanics. Such absolutes "\JO more existedbefore mechanics than the French language can he logically saidto have existed before the truths which are expressed in Frcnch.?"

These four sUlllmary statements captured a great deal of Poin-care's approach. 'I'he first reemphasized his philosophical-physicalobjection to absolute space. 'I'hc second and third recapped his1898 "Measure of Time," and the fourth linked the discussion to hisolder work 011 the conventionality of geometry. "Are the laws ofacceleration and of the composition of forces only arbitrary COll-

ventions? Conventions, yes; arbitrary, no-they would be so if welost sight of the cxpcrimcuts which led the founders of the scienceto adopt them, and which, imperfect as they were, were sufficientto justify their adoption. It is well from time to time to let our atten-tion dwell on thc experimental origin of thcse conventions." Exper-iments, for Poincare, were the raw materials of physics out of whichtheory aimed to produce the greatest number of predictions withthc highest probability. That is, experiments could serve as the"basis" for mechanics by suggesting, as it were, the principles and

Poi Ilea re's t\r1aps 2.01

rough behavior of the world that we want embodied in the con-ventions (definitions) of concepts such as force, mass, and acceler-ation. But that is not to say that experiments can simply invalidatestarting principles; at worst, in his view, experiments would revealthat a fundamental law was only approximately true, "and we knowthat already.'?" Poincare summarized his reflections on the role oftheory when he spoke to the physicists (also in 1900). As so often,he invoked the machine-based factory, framing experiments as the"raw materials" and theory as the organizing guide: "The problemis, so to speak, to increase the output of the scientific machine."?

Even in mathematics, machines and mechanornorphic struc-tures were vital for Poincare. Back in 1889, Poincare had laid intothc logieist purveyors of "teratological" functions. He came back tothe theme ill August 1900, this time while addressing the mathe-maticians gathercd for their international congress in Paris. Againhe pitted the logicists against the intuitionists. While he judged bothimportant for the development of mathematics, there was no doubtOJl which side he stood. One mathematician (a logician, in Poin-care's division) could cover pagcs and pages of print in order todemonstrate unequivocally that an angle could be divided into anynumber of equal parts. By contrast, Poincare called his audience'sattention to the Cottingcn mathematician Felix Klein: "He is study-ing one of the most abstract questions of the theory of functions: todetermine whether 011 a given [abstract mathematical] Riemannsurface there always exists a function admitting of given singulari-tics I roughly: points where the function becomes infinite]. Whatdoes the celebrated German geometer do? He replaces his Rie-mann surface with a metallic surface whose electric conductivityvaries according to certain laws. Hc connects two of its points withthe two poles of a battery. The current, says he, must pass, and thedistribution of this current 011 the surface will define a functionwhose singularities will be precisely those called for." Now Kleinknew perfectly well that this reasoning was not rigorous, but (says

-_ .•, .. - ::,-';.'


Poincare) "he finds in it, if not a rigorous demonstration, at least akind of moral certainty. A logician would have rejected with horrorsuch a conception." More precisely, the logician would never havebeen able to formulate the intuitionist's thought. IX But formulate

such machine thoughts Poincare certainly did: in pure mathemat-ics, in geodcsy, in philosophy. In the midst of it all, he pressed aheadwith studies of electricity and magnetism, bringing his ideas aboutelectromagnetic eloek coordination into the heartland of physicsitself.

On 10 December 1900, just two days after Poincare had sentLallemand and Maurain on their Quito telegraphic longitude mis-siOI1from the Care Saint-Nazairc, Poincare stood at the lectern inthe University of Leiden, outlining his ideas on space, time, andether. lIe and other luminaries had gathered to honor H. A.J .orcntz. Lorentz was for Poincare (and, I should add, for Einstein)a singular figure among physicists. In many ways, it was Lorentzwho had helped exemplify the new professional category, "theoret-ical physicist." For many physicists, especially those outside Britain,it was Lorentz who had put Maxwell's theory of electricity and mag-nctism into a comprehensible form. Instead of following the Britishtradition of reducing all matter to etherial flows, vortices, stresses,and strains, Lorentz had a starker doctrine: there were two kinds ofthings in the world, electric and magnetic fields (states of the ether)on the one hand; and material, charged particles moving throughthe ether, on the other. Fields could act on particles, particles couldcreate fields. But Lorentz had done still more, as he struggled toexplain the seeming failure of experimentalists to reveal the motionof objects-including the earth-through the vast ether that wassupposed to pervade the Universe.

For some time Poincare had, like all other up-to-date physicists,been thoroughly familiar with Lorentz's theory. He had also beenrespectfully critical of it when he lectured on it at the Sorbonne in1899, believing it to be the best available theory. Even with Lorentz

Poincare's Maps

seated in the Leiclen audience in 1900, Poincare said, it disturbedhim that Lorentz's account violated the principle of action and reac-tion. A cannon retreats immediately when it shoots a cannonball,but the ether and atoms had the odd property (according toLorentz) that an atom would act on the ether but that the materialreceiver of the atom's action would only react later. What happenedin the meantime? The ether seemed too insubstantial to carrymomentum. Poincare told Lorentz and the assembled that he couldmitigate this objection. "But I disdain that excuse because I've gotone a hundred times better, Good theories are flexible .... Illf a the-ory reveals to us certain true relations, it can dress itself ill a thou-sand diverse forms, it will resist all assaults and that which is itsessence will not change." Lorentz had created one of those flexibletheories, one of the truly good ones: "1 will not apologize" for criti-cizing the theory, he said. Instead, he only regrctted that he had solittle to add to I .orcntz's old ideas.") Despite the disclaimer, Poin-care wen t on to transform the physical significance of Lorentz's

theory.At the root of Lorentz's old ideas had been a theoretical account

of a seemingly intractable difficulty in ether physics. Was the ethersimply dragged along by transparent matter? If ether was hauledalong by the earth's atmosphere, that could explain why experi-ments never seemed to reveal earthly motion through the ether.Unfortunately, a mid-nineteenth-century experiment by theFrench physicist Annaud-Hippolytc Fizeau seemed to rule thatout. By shining light through water flowing at different speeds, hecould demonstrate that if the ether was dragged, it was only verypartially. But if the ether was not dragged by matter (and so wasfixed once and for all in the Universe), then we ought to be able todetect our motion through it. This is just what the American exper-imenter, Albert Michelson, set out to uncover by using an extraor-dinarily precise optical "interferometer" that he had invented (see

figure 4.4).

EINSfEIN'S CLOCKS, POINCARE'S MAPS

II,II

Figure 4.4 Hunting the Ether. With a remarkable series of experiments,Alberl Michelson sought to measure the earth's motion through the elusiveether. In the IRRIdevice shown here, he launched a beam of light from a thatwas stJIi! by a Izalfsilvered mirror at b: one-half of the ray reflected ofT cl andinto the eyepiece c. The other half of the ray penetrated the mirror at b,ref7ected from c, and was then bounced from b to the eyepiece c. At the eye-tJiece the two rays interfered with each other, showing the observer a cliatac-teristic [iuilern of light and dark. Ifone wave was delayed-by so little as a oart

of 0 wavelength ollight - this [iattern would visibly shi/i. So if the earth reallywas /7ying Ihrough the ether, then the "ether wind" would affect the relativetime it took /tn the two beams to make their round-tripe (the relative pha«: ofthe two waves would shift). Consequently, Michelson [ully expected that if herotated the a/)f)owtllS, he would see a change ill the interference patterns ofthe two rays. 13111 no matter how he twisted his staggeringly sensitive instru-ment, the datl: and light pattems did not budge. 'It) Lorentz and Poincare, thismeant that the interferometer arms-like all matter-were contracted by theirrush through the ether in just such a way CIS to hide the effect of the ether. To

Einstein it WClS one more suggestive piece of evidence that the very idea or theether was "sufJerfluous." SOllRCI';: MICHELSON, "Tiu: REJ.AI'!Vj'; MOTION Clio'Tl1Io: EARTII

AND L\!~IlNII"EROUS ETHER," ;\rvW/{/CN'I )OIJ/{N,\/.(WSC/I';N(;fo;, 3RIl Simms, VOl.. XXII, NO. 12fl

(AUGUST 1881), P. 124.

Indeed, Michelson thought he had the ether cornered. For ifthere truly was an ether wind, thcn thc round-trip time for a lightbeam should change, depending on whether the light was beingsent across or into the wind. But rotating the apparatus showed not

Poincare's Maps

the slightest twitch of the interference clark spot; to an extraordinary.legree of accuracy, it seemed that no motion through the ethercould bc detected by optical means. Though Michelson saw hisefforts to find thc cthcr as a dismal failure, other physicists, includ-

ing Lorentz, were moved to theorize.Taking Michelson's null result into account, in 1892 Lorentz

:\SSUIl1edthc existence of a static ether, and introduced the startlingnotion that any object moving through the ether contracted in itsdirection of travel. Bizarre as this "Lorentz contraction" sounded,the gambit worked, in the scnse that a judicious choice of this con-traction factor exactly compensated for the cffect of the putativeether wind. Lorentz's contraction explained why high-precisionexperimcnts - even thc extraordinary Michelson interferometer-would bc powerless to uncover the effects of the etherial breeze on

optical phcnomena.Remarkablv, Lorentz's contraction hypothesis was not enough.

ln thc course of demonstrating that all optical phenomena couldbe described ill approximately the same way, he introduced ill 1895a second innovation, a fictional "local time.'?" Lorentz's idea wasthat there was onc true physical time, ttme' True time was the appro-priate time to use for objects at rest in the ether. For any object mov-ing in the ether, it proved useful for Lorentz to introduce thisfictional time (a mathematical artifice) in terms of which the lawsof electricity and magnctism for that object would artificially resem-ble the laws for an objcct sitting still in thc ether. This helpful quan-

tity (tloeal) depended on the spced (v) of the object plowing throughthe ether, thc speed of light (c), and the location of the object (x);

Iloeal was just ttllle minus vxlc'. Why did Lorentz choose this locallime? Only because it gavc a sharp, if purely formal, result: locallime allowed a real object moving in the ether to be redescribed as:I fictional object at rest in the cther. Local time for Lorentz' was but

:I mathematical convenience.Poincare had viewed Lorentz's theory and its assumptions about

-


length contraction and "local time" with reserve. Even in his Sor-bonne course of 1899, he did not connect local time to histechnological-philosophical definition of simultaneity, in fact heremarked that corrections clue to Lorentz's "local time" were sosmall for the earth moving through the ether (the correction wasonly three-billionths of a second for two clocks separated by a kilo-meter) that he would simply ignore the correction." Mcauwliile,Poiucare's immersion in telegraphic longihlde determination inten-sificd. Not only was he ill the thick of planning for the Quito expe-dition during 1899-1900, he was, in 1899, also president of theBureau of LOllgitnde. If he had somehow stood back from thcdetails of the simultaneity procedures before, HOW lie was fullyellgagecl.

On n [unc 1899, for example, Poincare wrote to the RoyalAstronomer about the confounding discrepancy between tIleFrench and British measurements of the Paris-Crccnwich longitu-dinal difference. Could the British hcgin ;1 new effort iunncdiatcly?William Christie responded") Allgust pleading for more time, hutprolllising he would prepare detailed, published analyses of theirprocedures and instruments, noting that "it is desirable too that theFrench results for the longitude Paris-Crccuwich should also hepublished ill detail." Christie copied other letters to Poincare aboutthe problem, letters Christie had penned to Poincare's Bureau col-leagues. 'IC) Loewy, Christie had speculated that the error sourcemight he a discrepancy between leveling the star-sighting instru-ment based Oil a plum line and on a spirit level. Apparently the

French Army had implied that the fault might lie with Britishclocks; no, Christie replied, not possible. Instead he suggested thatboth Grcenwieh and Paris repeat the Paris-Greenwich procedure,only now between two piers inside Greenwich and again insideMontsouris. Presumably that would isolate any error accrued dur-ing the signal transmission under the English Channel. Poincarereplied immediately (9 August 1899) that he looked forward to

Poincare's Maps

receiving the British publications as soon as possible and that hehoped that they would contain the detailed calculations and themethods by which the data were reduced; in return, the Frenchwould open their hooks as both sides urgently tried to cut theembarrassing longitude discrepancy between Paris and Crecnwich."

In the midst of these longitudinal measurements and trou-bleshooting, Poincare came face-to-face with Lorentz at the Decem-ber 1900 meeting. Preparing for the event, Poincare reinterpreted,in a strikingly new fashion, Lorentz's "local time." First (though hedid not cite it) Poincare introduced his 1898 "Measure of Time"assertion that simultaneity could be given between clocks synchro-nized by thc exehangc of electromagnetic signals. That was theargllment he had produced at the intersection of longitude andmetaphysics. Now he went further, moving the teehnologieal-philosophical idea of electrically coordinated clocks into physicsitself, fOrilling a triple intersection. For the first time he pursued hisclock synchronization method for clocks moving through the ether.Poincare's sudden understanding: when executed while movingthrough the ether, the telegrapher's procedure for synchronizingclocks gave Lorentz's fictional local time, tl()cal'

"local time," Poincare insisted, WllS just the "time" clods showedin a moving reference frame wlieu they were coordinated by sendingem electromagnetic signal from one to the others. No mathematicalfiction, this was what moving observers would actually see:

Isuppose that observers placed in different points set their watchesby means of optical signals; that they try to correct these sign<llsbythe transmission time, but that, ignoring their translatory motionand consequently helieving that the signab travel <It the samespeed in both directions, they limit themselves to crossing theobservations, by sending one signal from A to 13, then another from13to A. .I'hc local time t' is the time indicated by watches set in this111<111n er.("

..-..-..=-====~-----------

208 EINSTEIN'S CLOCKS, POINCARJi;'S MAPS

Here is the electrical simultaneity procedure that we know twice:from Poincare longitude-finder and from Poincare-philosopher.Poincare-physicist inserts the procedure into a moving frame of

reference.Here, more precisely, is Poincare's argumcnt. Consider a mov-

ing frame containing clocks A and B that is moving to the rightthrough the ether at a constant speed v. Because of this motion, thelight signal from A to B (say) encounters a headwind as it beats intothe ether wind; the signal speed is the speed of light c, minus thewind speed, v (like an airplane encountering a headwind as it flicsfrom Europe to the United States). The return light signal from Bto A boosts its speed by an ether tailwind: its speed is therefore lighl

speed /Jius ether wind speed, (c + v).

I~·;=-~~i·~-I~~-~~;(~Cit;-:-=:; --?\3 IIIII I<:thcr (at rest) IIIII

L A ~ (light velocity: c + v) ~ B ~ v = velociiv of frame --?

Because speeds differ in the two directions, a naive one-way clockcoordination conducted by moving physicists would go wrong. Forexample, ifB scts hcr clock using a signal from A, she is using a sig-nal that is "really" going at c + v (relative to the ether). B gets thesignal too soon relative to a "correct" signal that would travel at c.The further away B is from A, the biggcr thc time discrepancybetween the moment she gcts the tailwiud-boostcd sigllal and themoment she would have received it were it sent al the stately speedof c. So B needs to set her clock back a bit-less if sheis close to A,

more if she is farther away. Poincare observed that the offset cor-rection to account for the too-speedy signal (~vxlc2) yielded just thcfictional "local time" correction of Lorentz's "local time."?' Poin-care's message: Clocks moving in the ether must bc coordinated bythe launch of electromagnetic signals, as beforc. But coordination

Poincare's Maps

in a moving frame demands an offset of the clocks to compensate

for the effect of the ether wind.Lorentz acknowledged the force of Poincare's criticisms in a let-

ter he posted on 20 January 1901-not a word, however, about Poin-care's interpretation of "local time." On other matters Lorentzreadily ceded: there was a problem with the principle of reaction,and as far as Lorentz could tell that might forever be the case ifphysicists wanted to account for the experiments; if the ether wasabsolutely rigid and immovable, then one could not coherently talkabout forces acting OIl it. So ether, as Lorentz had long argued,could exert force on electrons, but electrons coulc1not exert forceon the cther. Nor could one part of the ether act on another-anyattempt to speak this way was, in effect, invoking "mathematical fic-tions." No doubt such fictions were useful for calculating the waysin which the ether eventually acted to move electrons. But theywere fictions nonetheless. Alternatively, Lorentz speculated, itmight be possible to say that the ether was infinitely massive, inwhich case electrons could act on it without putting it into motion:

"But that way out seems to me pretty artificial."Lorentz had produced an extraordinary theory, one that had

utterly transformed physics hy dividing the world between a vastunmovcable ether and material electrons. Immensely successful,the theory accounted for a myriad of experiments from spectrallines to the explanation of simple optics like reflection. But asLorentz struggled to extend the theory, he fonnd himself reachingfor a variety of tools that he readily allowed were artificial. Lorentzsupposed that matter contracts as it plunges through the ether, thatthe principle of action and reaction is violated, and that the theory

needed the mathematical fiction of "local time."Poincare approached Lorentz's theory differently. As always when

treating theories, Poincare's procedure was to isolate the buildingblocks of the theory and then to manipulate the theory's most use-

.1.1

.-- ..-...-------~-"'!.'"""..'fjif!t~·"'f>l~c..""'..•.••••••••

210 EINSTEIN'S CLOCKS, POINCARI::'S MAPS

ful parts in order to advance. Here, at Leiden in 1900, he joinedLorentz's local time with his own conventional interpretation ofsimultaneity-the longitude finder's and philosopher's convention.Wi thout fanfare, he showed how Lorentz's local time could bephysically interpreted - the telegrapher's convention now set in anetherial wind.

one of Poincare's alterations of the theory sullied his assess-ment of Lorentz. On the contrary, ill [anuary 1902, Poincare nom-inated Lorentz for the Nobel Prize, explaining to the Swedishauthorities how Lorentz had seized the failure of previous physi-cists to find the ether or explain their failure to do so. Poincare: "Itwas evident that there must have been a general reason; Mr.Lorentz discovered that reason and put it ill a striking form by hisingenious invention of 'reduced time'." 'lwo phenomena that

occurred ill different places could appear to he simultaneous evenwhen they were not. Everything happened as if the clock ill oneof the places was running behind the other, and as if no conceiv-able experience could allow the discovery ofth is discordance. AsPoincare saw it, the failure of experimentalists to observe themovement of the earth through the ether was jllst one such futileattempt."

Continuing his elogc to the obc] committee, Poincareacknowledged that people often judgc theories such as Lorentz's asfragile. The sight of the ruins of past theorizing may make anyoneinto a skeptic, he allowed. But if Lorentz's theories were 10 join oth-ers in the vast cemetery of defeated accounts of the world, no onecould justifiably claim that Lorentz had randomly predicted truefacts ((aits vraili). "No, it is not by chance, it is because [Lorentz'stheoryJ revealed to us relations unknown until then between factsthat apparently were strangers one to the other, and that these rela-tions are real; and that they would be so even if electrons didn'texist. It is that sort of truth that one can hope to find in a theory, andthese truths will survive beyond the theory. It is because we believe

Poincare's Maps 211

that the work of Lorentz contains many such truths that we propose

that he be rewarded for them.'""

A Triple Conjunction

By the end of 1902, Poincare had spent a full decade facing theproblem of time coordination from three very different perspectives.As one of the exalted Bureau of Longitude's Academy memberssince January 1893, Poincare had helped lead the institution in itsquest to cover the world with synchronized time. When the issue ofconventionally restructuring time into a decimal system arose inearnest during the mid-I 890s, it was Poincare who had directed theeffort to evaluate the alternatives, culminating in the 1897 report.Then back to philosophy: in 1898 he proclaimed to a primarily

philosophical audience that simultaneity was nothing other than aconvention, a convention that would define simultaneity preciselyas his Bureau had done with their telegraphic coordination ofclocks. From the Revue de Metaphysique et de Morale, it was but afew months before Poincare was back, deeper than ever, in expedi-tionary longitlldinism. From 1899 forward he had been the liaisonbetween the Academy and the complex and dangerous longihldemission to Quito while the mission struggled to bind time and geog-raphy through telegraphically flashed simultaneity. That summerof 1900 he issued his strongest-yet philosophical statement of theconventionality of simultaneity, a statement that appeared in one ofthe most widely cited sections of Science and Hypothesis. Then areturn to physics. In December 1900, Poincare "reviewed"Lorentz's theory, turning Lorentz's mathematical fiction "localtime" into a telegraphcr's procedure, where observers movingthrough the ether synchronized clocks by exchanging signals.

This was not merely a matter of "generalizing" from the physicsto the philosophy or "applying" abstract notions from mathematicsor philosophy to physics. Instead, Poincare was working out a new

."-;. ~">",,,-,,~---.•.._._-..•• _-----'!II

I.. '1.

212 F:INSTEIN'S CLOCKS, POINCARI~'S MAPS

concept of time, showing how it fit into the rules of three differentgames: geodesy, philosophy, and physics. Just because the statementof synchronization and simultaneity functioned within all three ofPoincare's worlds, it took on a singular importance.

All through Poincare's work lay a Third Republic progressivism, asense that all aspects of the world could be improved through anengaged reason, a rational, machinic modernism. His faith carriedthe optimism of an abstract engineering, an undying belicfthat it waswithin the reach of reason to get at any aspect of the map, whether ofthe geographical worlel or that of science. All things being equal,Poincare would just as soon resolve a problem the way he handledthc decimalization disputc-by setting the various positions againstone another and cooly picking out the simplest (most convenient)relations alllong terms. Relaiion« were what was real to Poincare (therelations captured by Newton or Lorentz or by mathematics), not theparticular objects of our senses, "It may be said ... that the ether isno less real than allY external hody; to say I-his body exists is to saythere is between the color of this body, its taste, its smell, an intimatebond, solid and persistent; to say the ether exists is to say there is anatural kinship between ;lll the optical phenomena, ami neither ofthe two propositions has less value than the other."?' Objective real-ity was nothing other than the commonly held relationships amongthe phenomena of thc world. There was no otherworldly plane of exis-tence for Poincare. The importance of scientific knowledge lay in thepersistence of particular true relations, not in a back-of-the-curtainreality of Platonic forms or ungraspable noumena.

Poincare generally shied away from overt political reference ormoral absolutes. Still, once or twice, a different tenor breaks theneutral, moderated tone of his commentaries. We know, he told theGeneral Association of Stuclents in May 1903 in a Parisian restau-rant, that there arc twin fields on which action has to be taken:toward scientific truth and toward moral truth. "It seems that thereis an antinomy between our two dearest aspirations, we want to be

,J

Poincare's MafJs 213

sincere and serve the truth; we want to be strong and capable of act-ing ... _From here the violence of the passions raised by a recentaffair. On hath sides, most were driven by noble intentions." Allud-ing to the Dreyfus Affair then wracking the country, Poincare's ano-dyne summary muted his own torn responses - his powerfuldevotion to the French army and his equally urgent allegiance tostandards of demonstration. On 4 September 1899, in the midst ofAlfred Dreyfus's second trial, Poincare had intervened by proxy. Hisletter slammed the scientific basis of the charge that it was Dreyfuswho had written an incriminating torn sheet of paper (the famousbordereau) promising French state secrets to a German militaryattache: "It is impossible," Poincare concluded, that anyone "witha solid scientific education" could give credence to the nonsensicaluse of statistics presented by the prosecution. Despite that starkjudgmeut, the court reconvicted Dreyfus, though thc President ofthe Republic issued a pardon." (Poincare defended Dreyfus againa few years later on technical grounds, though stronger oncs.)Return now to Poincare's 1903 address to the assembled students.Action had to join thought, he insisted.

The day when France has no more soldiers, but only thinkers, Wil-helm II will be the master of Europe. Do you think then thatWilhelm II would have the same aspirations as you? Do YOLl counton him using his power to defend yom ideal? Or do YOllput yourconfidence in the people, and hope that they will commune ill thesame ideal? That's what OIlC hoped in 1869. Do not imagine thatwhat the Germans call right or liberty is the same thing that wecall by the same names .... To forget our country is to betray theideal and the truth. Without the soldiers of Year II, what wouldhave remained of the Revolution?"

Poincare added that every generation wonders about the fate of itswork, none more than his. "Cruelly hit at the moment they arrived


at manhood, my contemporaries set to work to repair the disaster [ofthe Franco-Prussian War] .... Years passed and deliverance did notcome. And so we ask ourselves, have you inheritcd this dream, with-out which all our sacrifices would be in vain? Maybe ... that whichfor us appeared as an intolerable injustice, ... a bleeding wound is,for you, just a bad historical memory, like the distant disasters ofAgineourt or Pavia.'?"

Crises and recuperation were always in view for Poincare: in pol-itics, but also in philosophy and in science. Ifhis generation's polit-ical ideal was to "repair the disaster" of 1H71, there were neareropportunities where the scientific machine could fe-arrange, repair,improve. In April 1904 he had a sccond opportunity to repair thcdamage caused by the Dreyfus crisis. Asked hy the court to addressthe status of the famous bordereau, Poincare, with two scientist-colleagues at the Observatory, scrutinized the cvidcucc. Theyrcmcasured the handwriting by using precision astronomicnl instru-mcnts and recalculated evcry last bit of the prosecution's proba-bilistic reasoning designcd to show the statistical near-certainty thatthc bordereau was Dreyfus's. Poincare's conclusion: the handwrit-ing analysis was nothing hut the illegitimate application ofhacllyreasoned probability on all incorrectly reconstituted document."Backed by Poincare's IOO-page report of 2 August 1904, the inter-vcntion succeeded. Poincare crushed, for example, the prosecu-tion's claim that Dreyfus had written the word "interet" on thebordereau. Alphonse Bertillon, the prosecution's star handwritingexpert, had contended that the word could only have been writtenusing the grid of a military map -a scale that famously set the diarn-eter of a "sou" equal to a kilometer. Along with his mathematiciancolleagues, Poincare created an enormous enlargement of that sin-gle word, mapping it, as it were. Their conclusion: Bertillon'sclaims about the curvature, length, axis, and hcight of the letterswere as arbitrary (changing for each letter) as his spurious micro-caligraphic analysis of the circumflex accent. There was no "geo-

Poincare's Maps 215metrical particularity" to this word. Nothing at all implied it waswritten by someone working at a staff officer's desk using militarycartography." Impressed, the court exculpated Dreyfus. Onceagain, Poincare had mapped a technical fix to a profound crisis.This time it had taken more than a chart of coefficients (Poincare'sploy to resolve the crisis of decimalization). But in a sense, the spiritwas the same: reasoning through machines and calculations, hehelped e1efuse a crisis.

Crises arose elsewhere. In September 1904, just a few weekslater, the International Congress of Arts and Science gathered at St.Louis, Missouri, for an international exposition to celebrateprogress. Delivered ill the midst of a World's Fair built to model theworld (here Paris, there London, Turin, New York), Poincare'sspeech 011 the hilurc of physics appropriately aimed to encapsulatethe whole field and to identify its weak points. Time coordinationfeaturcd promincutly, set within a larger frame of progressive con-tinuity: "[Yjcs, there are indications of a serious crisis [in physics],"Poi ncarc conceded early 011 ill his talk, but "let us not be too e1is-turbcd. We arc assured that the patient will not die of this sicknessancl we call even hope that tbe crisis will be beneficial, for past his-tory seems to gllaralll"ce it");

By Poincare's lights, mathematical physics had received its firstideal form ill Newlon's law of gravity. Every bocly in the Universe,every graill of sand, every star was attracted to every other body bya force inversely proportional to the square of their separation. Thissimple law, varied and applied to different kinds of forces, formedthe first phase of the history of physics. Out of that peaceable king-dom a crisis cmerged when Newton's picture proved inadequate tothe complex industrial processes physicists confronted in the nine-teenth century. New principles were needed, principles that couldcharacterize the whole of a process without specifying, as Newtonmight have had it, every last detail of the machine. Such new prin-ciples included the stipulation that the mass of a system always


stayed the same or that the energy of a system remained constantover time. One great triumph was Maxwell's theory, whichembraced all of optics and electricity, describing the whole as statesof a great, world-pervading ether.

Did this nineteenth-century, second phase of physics far exceedNewton's dreams? Of course. Did it show the futility of the firstphase? Poincare advised his World's Fair audience, "Not in the least.Do you think that this second phase could have existed without thefirst?" N cwton's idea of central forces had led to the principles ofthe second period (Poincare's own). "It is the mathematical physicsof our fathers that familiarized us little by little with these variousprinciples, which has habituated us to recognize them under thedifferent clothing with which they disguise themselves.'?" Our fore-hears compared the principles with experience, learned how tomodify their expression to adapt them to the givens of experience,enlarged the principles, and consolidated them. Fvcntually wecarne to see these principles, including the conservation of cnergy,as cxpcruncntal truths. Bit by bit the older conception of centralforce came to seem superfluous, even hypothetical. The frame ofNewtonian physics shook.

Poincare's staging of this new "crisis" was, characteristically forhim, a preamble to recuperation. Echoing the meliorist position hehad taken for fifteen years, he insisted that shedding past beliefs didnot demand rupture: "The frames are not broken, because they areelastic; hut they have been enlarged; our fathers, who establishedthem, have not worked in vain; and we recognize in the science oftoday the general traits of the sketch that they traced.'?' For Poin-care, physics in 1904 nonetheless stood at the threshold of a newphase in its epochal history. Radium, "that great revolutionary," haddestabilized accepted truths of physics, precipitating crisis. Everyprinciple of nineteenth century physics tottered.

One hope had been that meaning could be given to the ether bymeasuring how fast the earth was sailing through it. Poincare

Poincare's Maps

lamented that all such attempts, even Michelson's most accurateones, had ended in failure, driving theorists to the limit of theiringenuity. "[I]fLorentz has managed to succeed, it is only by accu-mulating hypotheses." Of all those Lorentzian "hypotheses," onestood out for Poincare above all others:

[Lorentz's] most ingenious idea was that ofloca! time. Let us imag-ine two observers who want to set their watches by optical signals;they exchange their signals, but as they know that the transmissionis not instantaneous, they take care to cross them. When the sta-tion H receives the signal of station A, its clock must not mark thesame time as station A at the moment of the emission of the signal,but rather that time augmcnted hy a constant representing theduration of the signal.

At first, Poincare considered the two clock-mindcrs at 1\ and B to heat rest-their two observing stations were fixed with respect to theether. But then, as he had since 1900, Poincare proceeded to askwhat happened when the observers are in a frame of reference 1lI0V-ing through the ethcr. In that case "the duration of the transmissionwill not be the same in the two directions, because station A, forexample, moves towards any optical perturbation sent by 13, whilethe station 13 retreats from a perturbation by A. Their watches set illthis manner will not mark therefore true time, they will mark whatone can call1acal time, in such a way that one of them will be off-set with respect to the other. '1'hat is of little importance, becausewe don't have any way to perceive it." True and local time c1iffer.

But nothing, Poincare insisted, would allow A to realize that hisclock will be set back relative to B's, because B's will be offset byprecisely the same amount. "All the phenomena that will be pro-duced at A for example, will be set back in time, but they will all beset back by the same amount, and the observer will not be able toperceive it because his watch will be set back; thus, as the {Jrinciple

... _._ _ - -..--.---~-...,....,.,,,.....,,--------


of relativity would have it, there is no means of knowing if he is at

rest or in absolute movernent.?"Yet coordinated clocks were not enough by themselves to rescue

all of classical, principle-based physics. According to Poincare, thechallenges of radioactivity hovered like storm clouds over the disci-pline. Energy conservation: challenged by the spontaneous emis-sion of energetic radioactive particles. Mass conservation: in troublebecause fast charged particles acted as if their mass depended ontheir velocity. Action-reaction: threatened because, according to theLorentz theory, a lamp projecting a beam of light recoiled beforethe light beam arrived somewhere else where it caused the absorberto recoil. Fvcn the relativity principle appeared threatened, forwhich the physicist-physicians had called in the antidotes of "localtime" and length contraction. What to do? Surely, trust the experi-menters. Yct for Poincare the chain of responsibility ended with thctheorists: theorists had produced this mess; they should resolve it.And any theoretical rescue of principled physics could not takeplace by abandoning the "physics of our fathers." Instead, progressdemanded rcworking the past: "let us take the theory of Lorentz,turn it in every direction; modify it little by little, and perhaps every-

thing will work out." Poincare hoped that the organism of physicswould reveal its constant identity even as it changed, like an animalshedding its shell for a new one. 10 abandon a principle such as theprinciple of relativity wonld be, he insisted, to sacrifice "a precious

ann" in the battle at hand."Poincare and Lorentz did "turn the theory in every direction,"

altering it as best they could. In May 1904, Lorentz modified his oldassumption about length contraction and his fictional "local time"in such a way that, when the shortened length and local time wereinserted into the equations of physics, the equations were no longerapproximately the same in any frame of reference moving inertiallythrough the ether, but instead identical." That striking vindicationof Poincare's understanding of the relativity principle- as he called

Poincare's Maps

II was enough to set the French polymath to work. On 5 JuneI' J() S, he summarized his res nits to the French Academy of Sci-

(II<'CS. For the first time, he had a theory adequate to account for1,(.1 h optical experiments and the new fast electron experiments,I" .th, as he had long hoped, inside the "clastic frame" of Lorentz'sI,ltysies. Published fully in 19()6 as "On the Dynamics of theI<ketron," the paper finishecl Poincare's longstanding project byIliishing the clock synchronization scheme one last step: The-vnchronization of clocks led to Lorentz's improved local time,Irom which it followed that the equations of physics took on the

:;;lIne form in all frames of reference.Just a few months later, in the winter semester of 1906-07, Poin-

(';ne spelled out for his students precisely how Lorentz's improved"local" time fit with the I .orcntz contraction to make it fully impos-sible to detect motion of the earth with respect to the ether." Againill 1908 he insisted that the apparent time of transmission is pro-portional to the a/JfXLTellt distance: "it is impossible to escape theimpression that thc principle of relativity is a general law of Nature,Ihat one could never by any imaginable means, have evidence of;lI1ything but the relative speeds of objects" -motion with respect10 the ether would never he found." Here was a monument to Poin-care's decades-long attempt to improve the machinery of physicswhile keeping the "clastic Frame" of the old-a "new mechanics"that guardcd the ether whilc challenging old ideas of space, time,simultaneity. It was the modernism of an abstract machine.

However beautiful the theory in its embodiment of the relativityprinciple, Poincare hacllong made it clear that principles rose fromexperiment, acknowledging that those roots meant that experimentscould spell trouble for principles. The relativity principle was noexception. Indeed, at the very beginning of his "On the Dynamicsof the Electron," Poincare warned that the entire theory could becndangered by new data." Lorentz too smelled trouble from thelaboratory. In a letter to Poincare of 8 March 1906, Lorentz took

j:..:

220 EINSTEIN'S CLOCKS, POINCARf:'s MAPS

pleasure in the coincidence of their results. But that concordancemeant that both of them faced a similar peril: "Unfortunately, myhypothesis of the flattening of electrons is in contradiction with theresults of new experiments by Mr. [Walter] Kaufmann and I believeI am obliged to abandon it; I am therefore at the end of my Latinand it seems to me impossible to establish a theory that demands acomplete absence of the influence of translation on electromag-nctic and optical phenomcna.?"

By the timc Poincare and Lorentz put these worries Oil paper,both saw the essentials ofthcir physics in mortal danger-their huntfor an explanation of the microphysics of the electron, their longstrugglc to instantiate the relativity principle, and their never-endingquest to specify thc status of the ether. In the early years after 1905,sonic physicists assimilated the new theory to an older ambition tofind an clcctrical explanation for all physics. Others seized themathematics, ignoring the rclonnatiou of time. But in the end, thcgrcatest th rear did not emerge from thc magnets, lubes, and photo-graphic plates of Kaufmanu's study of how fast electrons weredeflected hy electric and magnetic fields or work at any other labo-ratory. Though the "true relations" of his physics survived, in thelong term Poincare's vision of the time and space of modernphysics-one that prized the ether as all incliminable frameworkfor intuitive mathematized understanding, one that sharply splittrue from apparent time-lost its place in the canonical presenta-tion of physics. An unknown twenty-six-year-old physicist at theBern patent office was to offer a different path to understanding, onethat threw aside electron structure, the ether, and the distinctionbetween "apparent" and "true time." Instead he wired a coordinatedclock into the theory not as an aiel to the physical interpretation oflocal time but as the capstone of the relativistic arch.

Cliaoter 5

EINSTEIN'S CLOCKS

Materializing Time

N JUNE OF }905, the contrast between Einstein and Poincarecould not have been greater. Poincare was an Academician inParis, fifty-one ycars old and at the height of his powers. He had

been a professor at France's most illustrious institutions, run inter-ministerial commissions, and published a shelf of books-volumeson celestial mechanics, electricity and magnetism, wireless tclegra-phy, a11(1 thermodynamics. With over 200 technical articles to hisname, he had altered whole fields of science. His bcst-selling vol-ume of philosophical essays had brought his abstract reflections onthe mcauing of science to a huge audience, including Einstcin.Einstein, at-twenty-six, was by contrast an unknown patent officer,living in a walk-up flat in a modest section of Bern.

Unlike l'rancc or Britain, Switzerland was not a colonial power.Unlike the United States or Russia, it had no vast longitudinalspread, l10r did it have even a hccta rc of unsettlcdland to be colo-nizcd hy railways, telegraphs, and time links. In fact, Switzcrlandwas late to adopt the telegraph and, relative to other Europeancountries, late ill the construction of a rail network. But when railsand telegraphs did come to this mountainous country in the latterpart of the nineteenth century, the movement to synchronize clocksquickly gained momentum-not surprising in a nation in whiehthe production of precise timepieces was, by century's end, anurgent matter both of national pride and economic significance 1

The clock-world famous Matthaus Hipp found welcome inSwitzerland. Blacklisted in his native Wi.irttcmberg for his republi-

.;'~:-- ._--=-----

...._.i!!£!...1CX!Wi

222 EINSTEIN'S CI.OCKS, POINCARE'S MAPS

can and democratic advocacy around 1848, his trade was in timemachines of every sort. He developed electrically maintained pen-

club so regular that they far surpassed mechanical ones: a heavypendulum swung freely except when it needed an electromagneticboost. Alongside such elcctrical timepieces, Hipp perfected record-ing clocks that radically altered experimental psychology. Collaho-rating wi tll physicist-s and astronomers, he tracked the transmissionspeeds of nerves, telegraphs, and light, thereby inventing, altering,ami producing new ways to use electricity and clocks to materializelillie. Though he worked closely with scion fists (especially SwissastronOlller Adolphc Hirsch), I Iipp was more artisan-entrepreneurthan llwtite1llaticiall-sav<1nt. Founder of telegraph and electrical,Ipp;rratm factories in Bern and later NellehiHel and Zurich, Hipptook his compauy from the estahlishment of the first network ofpublic clcctri« docks ill Ccncva (I ?-i(1) to ever greater prominence.In loW) l lipp's firm became A_ De Poyer and A. Favarger ct Cic;from tllell to l<)()f) the concern extended the range of their motherclocks beyond the dominion of observatories .md railways to steepleclocks and even to the wake-up clocks inside hotels." With themarch of time into every street, engilleers needed methods toextend indefinitely the number of units that could be branchedtogether. Alloocl of patents followed, perfeding relays and signal

am pI ifiers.If you wanted to display time on a major building, you needed

more than one clock before time unification. The' Iowcr of the Island

in Ccncva boasted three around I ~~O: a hig cloeHaee in the centershowed middle Ccncva time (about 10: 11); the face on the leftshowed Paris time for the Paris-based "Paris-Lyon-Mediterranean"line (9:58); and the right-hand clock boasted Bern time, a hand-some five minutes in advance of Gcneva (10: 18). Clock synchro-nization in Switzerland was public and eminently visible. So, too,

was the chaos of uncoordinated time.Bern inaugurated its own urban time network in 1890; improve-

Eillstei1l's Clocks 22"3

Figure ). I Three Clocks: Tower of the Island ofCellevCI (circa 18IW). HeF)((:

time uuitication, a [ine clock tower like this O/le IJlIblicly regislereel the multi-plicily oitinu». SO!lI(CJo:: CI';I'<TIU': n']cONO(;RIII'IIIE CI':I'<I':VOISI':, RVC NI,XII-i 14'»+

mcnls, expansions, and new networks sprouted throughout Switzer-land. Not only was accurate, coordinated time important for l<mo-pean passenger railroads and the Prussian mil itar)" it was equallycrucial for the dispersed Swiss clockmakingiudustry, which des-perately needed the means for consistent calibration.' But time wasalways practical and more than practical, material-economic neces-sity and cultural imaginary. Professor Wilhelm Forster of the BerlinObservatory, which set the Berlin master clock by the heavens,sniffed that any urban clock that did not gnarantee time to the near-est minute was a machine "downright contemptuous of people."

Einstein's patent-office window on this elcctrochronomctricworld opened a crucial moment in the synchronization of Swiss

·1!

J':INS'J'EIN'S Cl.OCKS, POINCARJ.:'S MAPS

Figllre 5.2 One Clock: Tower of the Island of Celleva (affer IHH6). A/iertune IIl1iJ/wtioll, the scuue tower S/IOWII ill figure 5.1 needed but II stllgle dock:tune 11I1.i/ic<ll.i()1I was visib!« t()T <Ill to see. SOl 11\0:: CIWI'I(]': ll'ICON()(;I(AI'IIII':

CI': 1':VOISI':,INt: I,Xll> 'i")'

lime. For despite Celleral von Molrkc's resolluding support for apan-Cennall time unihcatiou and the undamped enthllsiasm of theNorth American advocates of one-world time, Albert l-avargcr, oneof Hipp's chief engineers and the man who effectively succeededHipp at the helm of his company, was not at all satisfied with therate of progress. He intended to say so, very p1lblicly, at the 1900Exposition Universclle in Paris. Here, the International Congresson Chronometry met to discuss the status, inter alia, of clock-

coordination efforts.' At the outset of his speech to thc congress,Favarger asked how it could be that the clistribution of electrical

Ei11S te i11' S Cloc ks

time was running so distressingly far behind the related technolo-gies of telegraphy and telephony? First, he suggested, there weretechnical difficulties; remotely coordinated clocks could rely on noobliging friend ("ami complaisant") to oversee and correct the leastdifficulty, whereas the steam engine, dynamo, or telegraph allseemed to run with constant human companionship. Second, therewas a technician gap-the besttechnical people were staffing powerand communication devices, not time machines. Finally, helamented, rlic public was not funding time distribution as it should.Such lagging boosterism baffled Favarger: "Could it be possible thatwe have not experienced the imperious, absolute, I would say col-lective need of time exactly uuiformly, and regularly distributed?... Here's a question that borders Oil impertinence when addressedto a late 19th century public, laden with business and alwaysrushed, a public that has made its own the famous adage: Time is

money."As far as Favarger was concerned, the sorry state of timc distrib-

ution was out of all proportion with the exigencies of modern life.He insisted that humans needed exactitude and universality correctto the nearest second. No old-fashioned mechanical, hydraulic, orpneumatic system would do. Elcctrici Iy was the key to the future, afuture that would only come about properly if humankind brokewith its past of mechanical clocks: a technical era riven by anarchy,incoherence, and routinization. In place of the pneumatic chaos ofParis or Vienna, the new world of elcctrocoordinatcd clocks wouldbe based on a rational and methodical approach. As he put it,

You don't have to run long errands through Paris to notice numcr-ous clocks, both public and private, that disagree-which one isthe biggest liar? In fact if even just one is lying one suspects the sin-cerity of them all. 'J 'he public will only gain security when everysingle clock indicates unanimity at the same time at the sameinstant."


How could it be otherwise? In terms reminiscent of time strug-glcs in the United States SOIl1eyears earlier, Favarger reminded theassembled exposition attendees that the speed of trains roaringthrough Europe was mounting to 100, 150, even 200 kilometers perhour, Those running the trains and directing their movements, notto speak of the passcngcrs cntrusting thcir lives to such spceding car-riages, had to have correct till1es. At 55 meters pcr second, every tickcounted, and the prevalent hut obsolete mechanical systems ofcoordination wcrc bound to be inferior. Only the electric, auto-matic system was truly appropriate: "The nonautomatic system, themost primitive yct the most widespread, is the clirect cause of thetime anarchy that we must cseape."~

'I'imc anarchy. No cloubt"hlvarger's reference recalled in his lis-teners the anarchism that had taken a powerful hold among theJura watchmakers (or for that matter it might have remindedParisian listeners ofFrench anarchist Martial Bourdin's detonationoutside Crccnwich Observa tory). Peter Kropotkin had hroadly pub-licizcd the clockmakcrs' ana rchism just a year before in his 1Wm-99Memoirs of a Revolutionist:

The equalitarian relations wl nch I found in the [ura Mountains,

the indcpcnclcucc of thought and expression which l saw devol-opillg ill the workers, .uul their unlimited devotion to the causeappealed even more sl rot 19ly to Illy feelings; and when I c.nucaway frcnn the mountains, aftcr a week's stay with the watchmak-ers, my views UPOllsocialiC>1l1were settled. I was all anarchist."

Favarger was, however, lllOrc concerned about an anarchism sig-nalcd by a broader cIisinteg ration of personal and societal regular-ity. Not for him the older P rieu marie system- those steam-driven,rigidly framed branched piPes that had pulsed compressed-air timeto fixed public clocks and private timepieces in Vicnna and Paris.Only electrical distribution of simultaneity could provide the

Einstein's Clocks

"indefinite expansion of the time unification zorie."!" Favarger's

unwavcring support for distant simultaneity issued from manysources, from the practicalities of train scheduling and the entre-preneurial ambitions of his company to a sense of what time wouldmean for the inner life of the modern citizen. Time synchroniza-tion was all at once political, profitable, and pragmatic.

Should we escape this dreaded anarcho-clockism, Favargerassured h is listeners, we could fill a great lacuna in our knowledgeof the world. For even as the Paris-based International Bureau ofWeights and Measures had begun to conquer the first two funda-mental quantities-space and mass-Favarger insisted that thefinal frontier, time, remained unexplored," And the way to con-quer time was to create an ever-widening electrical network,bound to an observatory-linked mother clock that would driverelays multiplyiug its signals and send automatic clock resets intohotels, strcetcorners, and steeples across the continents. Affiliatedwith Favarger was a company determined to synchronize Bern'sown network. When, on I August UNO, Bern sel the hands of itscoordinated clocks in motion, the press hailed the "Revolution inClocks."!'

I'~vcn today, from many places in Bcrn you call clearly see thefaces of several grand public clocks. In that August of 1890, whenthey all began running in step, the order of coordinated time waswritten UpOJl the architecture of this city of arcades and churches.Swiss clockmakcrs p\lblicly joined the worldwide project of eleetric

simultaneity.

II

Theory-Machines

During the 1890s Einstein was not yet concerned about clocks atall; but as a young man of sixteen, in 1895, he was very much con-cerned with the nature of electromagnetic radiation. That summerEinstein put on paper his reflections of how the state of the ether

228 EINSTEIN'S CLOCKS, POINCAHE'S MAPS

would alter in the presence of a magnetic field; for example, howits parts would distend in response to a passing wave. Even his untu-tored imagination was uncomfortable with the "customary eOI1-ceptiou" of radiation as a wave in static, substantial ether. Suppose,he later recalled th inking, that one could catch up to a light waveand ride it, so to speak, as classical physics might imply. Then onewould see the electromagnetic wave unfold before him, the fieldundulatingin space but frozen in time. But nothing like such afrozen wave had ever been observed." Somcthing was wrong with

this way of thinking, hut 11:instein did not know what.After a first unsuccessful application, Einstein began his training

at SwitJ'.eriallCl's (ami 011e of Europe's) great technicallllliversities:the I<:ic1gell()ssisehe '( cchnischc flochsehule (ETfI), founded illIf) 55. Cerra inly the 1<:'1'11 of I f)9() was a very differellt place fromthe I<cole Polytechniqne that Poillcarc had entered ill the carly] f)70s. 'It) be sure, both stressed engilleerillg. But Feo1c Polytcch-niquc's hllle hadlollg rested 011its schooling the elite ill a conccn-tratcd mix of pure mathematics and scientific training, a foundationOil which its gradllates would then build at places like the Schoolof Mines. I'()I' thc l'rcuch ever since Napoleon, the ambitiou hadbeen to cclucato an elite ill hierh lnathelllatics that would he (in due

b

time) able to meet the dClllands of the practical world they wonk]control. I"olllldecl ill the mid-nineteenth century ill a Swit/.erlaml

short OIl natura 1 reSOllrces and long on desire to catch lip with therapid indllstrialization of France, Britain, and Cennany, KIn wasvery different. 1':'1'11wanted an immediate link between theory andpraxis. There was never a l1lo111e1l1when the demands of road, rail-road, water, cledrica I, and bridge construction were lost to sight oreven pili ill the backgrOll!l(l.l1 'Like mechanics. At [':eole Polytcch-nique, Poincare celebrated the subject as the "factory stamp" for allstudents, from those strivinz to become abstract mathematicians to

b

those whose ambitions would take them into administrative or mil-itary service. Mathematics was the queen of the university, struc-

.i

Einstein's Clocks

turing the teaching of mechanics so that its abstractions were onlygradually specified to the point where it met application. By con-trast, in Zurich, it was a mining engineer with little interest inabstract mathematics who had set the tone of the mechanics courseback in 1855. Built more along German pcdagogical lines thanalong French ones, the Swiss insisted that the abstract should notwait for an eventual union with the applied in a next stage of edu-cation. Swiss industrialists needed help building everything fromtelegraphs and trains to water works and bridges. From the start(and throughout its history) the applied and abstract entered ETHtogether.

So, while Poincare and his contemporaries learned about exper-imentation by watching demonstrations at the front of theamphitheater, I<instcin spent a grcat deal of time lcarnillg hands-onin the well-appointed physics lahoratory at 1':'1 '11. Formal treatmentsof the principles of devices were typical of the work at Poly tech-niquc; when COrJlU wanted to study synchronized clocks, he wrotedown an elegant theory of the physics that underlay them. Instead,when Einstcin's physics teacher Heinrich l-ricdrich Webcr taught,he spoke about the precise heat-conducting ahility of granite, sand-stone, and glass. 'I'licnuodynamics at 1<:'1'11 oscillated back and forthbetween the basic equations and detailed numerical calculationsanellaboratory arrangements of glass, pUIlIpS, and thcnnomctcrs, asEinstein carefully recorded in his notebooks." Indeed, differencesbetween the two institutions reflected their views about what theo-ries said about the world. In Poincare's Ecole Polytechuiquc, hewould have found a proud agnosticism towa re! atoms (or manyother hypothetical physical objects). At ETH, Weber and his col-leagues had no time for such fancy dancing, llO interest in explor-ing, for its own sake, the myriad ways one could account.for acollection of phenomena. After introducing "heat" without concernlor its "true nature," Weber argued that the connections amongphysical quantities led directly to a mechanical picture in which

___-----~i~-..-I!I!.--I!I!--!!II. !!!III_____ _!!!I!!__ !!!i!!!!!_~.!!!!!-. ~--- ..... -- .... --- _.-

i

J

2,0 EINSTEIN'S CLOCKS, POINCARE'S Mi\PS

heat was nothing more than molecular motion. Then he calculatednumbers of molecules and fixcd their properties. No metaphysicalrealism, just a matter-of-fact engineer's assessment that atoms let thework proceed. If>

ln the summer of 1899, Einstein still was agonizing over theether, moving bodies, and electrodynamics. '10 his beloved MilevaMarie, he recalled that hack in Aarau (in secondary school), he hadthought up a way to measure, and perhaps to explain, how lighttraveled in transparent bodies when these transparent bodies weredragged through the ether." Now he conveyed to her his sense thatnaive, material ether theories, ones that proposed bits of ether hereand there llloving this way aud that, would simply have to go. Nodoubt he had absorbed some of this austere attitude toward theorythrough the emphasis OIl measurement at E'I'H. Still, the schoolclearly frustrated Eins\"cin by not offering more about the relativelynew Maxwellian theories of electricity and magnctism. So 11ebegantcachiug himself, and one clearly important source was the work ofHeinrich I Jerk Hertz had stripped Maxwell's complicated theoryof electricity and magllctism clown to its bare-boned equations and,to general astonisluucnt, demonstrated experimentally the existenceor electric (radio) waves ill the ether. Throughout his short life,lIcrtz paid extraordinary attention to thc different ways of Iormu-tiling theories of electricity and magnetism, douhling out loud thatthe "name" electricity or the "name" magnetism corresponded toallYthing substantial in its own right. Finstein then turned Hertz'scritical sword against the still-vibrant ether:

I returned the Helmholtz volume and am !lOW rereading Hertz'spropagation of electric force with great care because I didn't under-stand Ilclmholtz's treatise Oil the principle of least action inelectrodynamics. I'm convinced more and more that the electro-dynamics of moving bodies as it is presented today doesn't corre-spond to reality, and that it will he possible to present it in a

-r q is. b .t ..il..·,.i2nCaSC .., '·'waatt} &.

Einstein's Clocks

:,impler way. The introduction of the name "ether" into theories111" electricity has led to the conception of a medium whose motion(·;111 be described, without, Ibelieve, being able to ascribe physicalmeaning to it."

IO:kctricity, magnetism, and currents, Einstein concluded, shouldI j(' definable not as alterations of a material ether but as the motionIII "true" electrical masses with physical reality through empty..pace. A motionless, noruuatcrial conception of the ether mightwork better than a material one, and (following Lorentz's widely11;1 iled theory) many leading physicists had just such a conceptionill mind.

Faeed with the inability of experimentalists to either clrag the.ther or detect motion through it, Einstein sometime around -1901disposed even of this static insubstantiality. ]I:ther, that centerpieceof nineteenth-century physical theories, was gOllc. For l':illstein itwas neither the ultimate constituent of electrical particles nor theall-pervasive medium necessary for light to propagate. l':ven beforeI':instein had set foot through the patent office door, crucial piecesof the puzzle were in place; he may well have already beguJl invok-ing the relativity principle." Certainly he was reconsidering themeaning of Maxwell's equations while latching onto a realistic pic-ture of moving electrical charges. He had dismissed the ether. Still,none of these considerations directly bore on time.

From 1900 through 1902, Einsteill struggled at the margins ofinstitutionalized science. Despite having received his mathematics-teaching diploma from ETH in July 1900, he found himself unahleto secure a university joh. He took up tutoring and began pushing,outside university walls, into two domains of theoretical physics. Onthe one hand, he explored the nature of thermodynamics (the sci-ence of heat) along with its foundation and extension through sta-tistical mechanics (the theory that heat was nothing hut the motionof particles). On the other hand, he strove, not yet in print, to grasp

EINSTEIN'S CLOCKS, POiNCARf:'s MAPS

the nature oflight and its interaction with matter. Above all else, hewanted to know how electrodynamics would look for moving

bodies.l<:illstein's relentless optimism and self-confidence, combined

with a biting disregard for complacent scientific authority, shows ina myriad ofletters. In May 1901, he confided to Mileva that "Unfor-tunately, no one hcre at thc 'Icchnikum [the ETH] is up to date inmodern physics & Ihave already tapped all of thcm without sue-cess. Would I too become so lazy intellectually ifl were ever doingwell? I don't think so, but the danger seems to be great indeed."?'Or the next month, having written up a custom-made critique ofPaul Drudc (a leading figurc in the theory of electrical conduction),I<:inslein told Milcva: "What do you think is lying on the table illfront of me? ;\ long letter addressed to Drude with two objectionsto his electron theory. lIc will hardly have anything sensible torefute me with, because the things arc vcry simple. I am terriblycurious whether and what he is going to reply. Of course, J also lethi 111know that r don't have a joh, that goes without saying." If Ein-stein wouldn't hl1dge an inch 011physics, he had no more intentionof al\"cring his personal life to suit the disapproving glances of hisnearest and dearest, When friends apparently criticized his personalcomportment, he rejected their judgment out of hanel: "imagincthe Wintelcrs railed against me ... & said that I have been leading

a life of debauchery in Zurich."2]From early in his time at Polytcchniquc, Poincare had formed

lifelong bonds with his teachers. He admired his elders, filially nam-ing many of his own mathematical creations alter them. Einstein,by contrast, appears to have been absolutely undeterred by thehead-shaking of his old teachers, his incessant job rejections, or, forthat matter, his mother's stinging disapproval of Milcva Marie. Sowhen Druele dismissed Einstein's objections in July 1901, theyounger scientist simply relegated him to the throng of clay-footed

authority:

Einstein's Clocks

There is no exaggeration in what yOl1said about the German pro-fessors. I have got to know another sad specimen of this kind -oneof the foremost physicists of Germany. 'Io two pertinent objectionswhich I raised against one of his theories and which demonstratea direct defect in his conclusions, he responds by pointing out thatanother (infallible) colleague of his shares his opinion. I'll soonmake it hot for the man with a masterly publication. Authoritygone to one's head is the greatest enemy of truth."

Einstein might "make it hot"; but these authorities were not aboutto respond to his thermo-pressure with a shower of job offers. Oneafter another, rejections arrived, including one for the position ofsenior teacher, Mechanical Technical Department in the CantonalTechnikum at Burgdorf." When his friend thc mathematician Mar-cel Grossmann landed a position at the Cantonal School in Frauen-feld, Einstein congratulated him heartily, adding that the securityand good work it afforded would certainly hc welcome. Einstein,too, had tried applying. "1 did it only so that} wouldn't have to tellmyself tha t :Iwas 100 faint-hearted to apply: for I was strongly con-vinced that J have no prospects of getting this or another similarpost.'?'

Theil came a genuinc prospect of employment. The SwissPatent Offiee in Bem had placed an advertisemcnt for all opening.Einstein wrote directly: "I, the undersigned, take the liberty ofapplying for the position of Engineer Class II at the Federal Officefor Intellectual Property, which was advertised in the Bunclesblatt[Federal Cazctte] of 11 December 1901."21 Assuring the patentoffice that he had studied physics and electrical engineering at theSchool for Specialist Teachers of Mathematics and Physics at E'T'H,he promised that all the documents were ready and waiting. On 19December 1901, he rejoiced to Mileva: "But now listen & let mekiss you and bug you with joy! [Friedrich] Haller Jhead of thepatent office] has written me a frienclly letter in his own hand, in

_---~~-=---:c-=~~.---~-~-~


which he requested that I apply for a newly created position in thepatent office! Now there is no longer any doubt about it. [FonnerETH classmate, Marcell Grossmann has already congratulated me.T am dedicating my doctoral thesis to him, to somehow express mygratitude."2(; Job in hand, or almost so, he and Mileva could marry.

Evcn his attitude toward his old thesis evaluator, Kleiner, bright-ened. On 17 December he had told Mileva that he'd "descendupon ... that bore Kleiner." Einstein wanted permission to workduring Christmas vacation. '"J o think of all the obstacles that theseold philistines put in the way of a person who is not of their ilk, it'srcally ghastly! This sort instinctively considers evcry intelligentyoung person as a danger to his frail dignity, this is how it seems tome by now. But if he has the gall to reject my doctoral thesis, thenl'Il publish his rejection ill cold print together with the thesis & hewill have made a fool of hi illSelf But ifhe accepts it, then we'll seewhat ;\ position the fille Mr. Drudc will take ... a fine bunch, all ofthem. )f Diogelles were to live today, he would look with his lanternfor all honest persoJl ill vaill."'-;

Two days later, Diogcncs's little lantern cast humanity in awarmer light: "'I oclay I spent the whole afternoon with Kleiner inZurich and otherwise talked with him about all kinds of physicalproblems, llc is not quite as stupid as I thought, and moreover,he is a good guy." True, Kleiner had not yet read his thesis, butEillStein was not worried. [1is attention had already shifted else-where: "[Kleiner] advised me to publish my ideas about thc elec-tromagnetic theory of light ill moving bodies together with theexperimental method. l Ic thollght that the experimental methodproposed by me is the simplest and most appropriate one con-ccivablc.'?"

Encouraged, no doubt, by this unexpected support, Einstein dugdeeper into the theories of the ether and motion within it. Heresolved to study Lorentz and Drude Oll the electrodynamics ofmoving bodies (it is perhaps a measure of his disconnection from

Einstein's Clocks

the mainstream that he had not already done so) and borrowed aphysics volume from his friend Michele Besso. Poincare endlesslystressed ill his lectures of 1899 how valuable older physicsapproaches were. Maxwell, Hertz, Lorentz, and many others wereall worth studying in detail because even when parts misfired, eachcaptured "true relations" among physical quantities. That form ofpatience was not for Einstein. One ether-theory text impressed himonly by its obsolescence, as he told Mileva late in 1901: "Michelegave me a book on the theory of the ether, written in 1885. Onewould think it came from antiquity, its views are so obsolete. Itmakes one see how fast knowledge develops nowadays.'?" Not longbefore, he had told her that he and Besso had been pondering

I " I 1 f· .. f lIt 'niltoget icr t IC (ClI1liIOIl or a )SO utc res.In the early weeks of 1902, Einstein moved his modest collection

of houschold items from Schaffhausen (where he had a temporarypost ill a private school) to Bern, and began once again to search for

tutorial students 011 5 February 1902:

Private lessons inMA'l'III<MATICS AND PHYSICS

for students and pupilsgiven 1II0stthoroughly by;\I,BlmT 1<;INs'n:IN, holder of the feel.Polyt, 'I eachcr's diplomaC:VRI<CIITIC[(I<ITSC;\SSI': )2, 1" l'I,()OR

Trial lessons free."

A few clays latcr his prospects looked good. The young tutor's noticenetted two students, Einstein was planning on writing to the greatexpert on statistical mechanics, Ludwig Boltzmann, and his studiesoutside of a narrow band of physics were proceeding apace: "I havealmost finished reading IErnst] Mach's book with tremendous inter-

est, and will this evening.">!


Maurice Solovine, who had come from Romania to study at theUniversity of Bern, was one new student, along with another friendof Einstein's, Conrad Habicht, who was pursuing his doctorate inmathematics. Together the three founded their "AkademieOlympia," all informal club for discussing philosophy or whateverelse aroused their curiosity. Solovine: "We would read a page or ahalf a page-sometimes only a sentence-and the discussion wouldcontinue for several days when the problem was important. I oftenmet Einsteill <11110011 as he left his desk and renewed the discussionof the previous cvening: 'You said ... , but don't YOllthink ... l' Or:'I'd like to add to what I said yesterday ... .''','

Mach was Oil the agcnda. Mach the philosopher-physicist-psychologist stood for a relentlessly critical attitude toward thatwhich could not bc made accessible to the senses. Though Einsteinnever subscribed entirely to what he considered Mach's overem-phasis on the sensory, j':instein did Pill! from Mach's writingsa crit-ical club to he wielded against idle metaphysical chatter such as the1IOtiOllSof "absolute time" and "absolute spaee."'1 In ]':instein'sfavoritc work of Mach's (The Science of Meclzollics, I RS3) he wouldhave found a polemic against Newton's absolute time and spacethat hegan by citillg the master: "Absolute, true, and mathematicaltime, of itself, .mrl hy its own nature, flows uniformly on, withoutregarclto aIlything external. ... Relative, apparent, and commontime is S0111C sensible and external measure of absolute time." Suchthollgh l's disclosed, according to Mach, not the Newton of hard-boiled facts, but the Newton of medieval philosophy. For Mach,time was not something primitive against which phenomena weremeasured. Quite the opposite: time itself derived from the motionof things-the earth as it spins, the pendulum as it swings. Toattempt to get behind the phenomena to the absolute was futile.Mach's condemnation was clear: "This absolute time can be mea-sured by comparison with no motion; it has therefore neither a prae-

Einstein's Clocks 237

tical nor a scientific value; and no one is justified in saying that heknows aught about it. It is an idle metaphysical eonccption."'\

Over thc following years, Einstein often emphasized how impor-tant this time analysis of Mach was for him. For example, in a 1916article memorializing Mach, Einstcin insisted: "These quotations[from The Science of Meclwnics[ show that Mach clearly recog-nized the weak points of classical mechanics, and thus came closeto demanding a gcneral theory of relativity-ane! this almost half acentury ago! It is not improbable that Mach would have hit on rel-ativity theory if in his time ... physicists had been stirred hy thequestion of the meaning of the constancy of the speed of light. III

the absence of this stimulation, which flows from Maxwell-Loreutzian electrodYliamics, even Mach's critical urgc did not suf-fice to raise a Fccling for the need of a definition of simultaneity forspatially distant events." As it had for Poincare, simultaneity for

Einstcin crosscd electrodynamics will: philosophy."Up for discussion by the Olympia Academy was also Karl Pear-

son, the Victorian mathematician-physicist known for his coutri-butious 10 statistics, philosophy, ,l1ld biology. But intriguinglyPearson, drawing Oll Mach as well as the Corman philosophical tra-dition, also put the naive reading of "absolute time" under the crit-ical microscopc. Einstein and his academicians would have foundin Pearson's 1892 Caanunar of Science another sharply criticalassessment of the relation of all observable clocks to Newton'sabsolute time: "[T'[hc hours on the Crccnwich astronomical clock,and ultimately on all ordinary watches and clocks regulatcd by it,

will correspond to the earth turning through equal angles on itsaxis." So all clock time is ultimately astronomical timc. But manyfactors could alter the great earth-clock in its rotation -tides, forexample. "Absolute, true, mathematical time," as Newton called it,is something we use to describe our sense impressions (a "frame,"as Pearson put it). "But in the world of sense-impression itself

Z&iiluuL~.--~.........-.-,~-"",.,'--u.--.~="

I'~INSTEIN'S CLOCKS, POINCARE'S MAPS

[absolute intervals of time] have no existence." Watching stars erossthe spider Jines of our transit instruments from one midnight to thenext on two different occasions, we notice that the average personregisters roughly the same sequence of sense impressions. Fine, saysPearson. Assign those two midnight-to-midnight intervals the desig-nation "equal." But we should not fool ourselves; this has nothing todo with absolute time: 'The blank divisions at the top of and bottomof om conceptual lime-log arc 110justification for rhapsodies on thepast or future eternities of time, for rhapsodies which, confusing con-ccption and perception, claim for these eternities a real meaning inthe world of phenomena, in the fick] of sense impression."?

Along with Mach and Pearson, Richard Avcnarius's Critique ofPure }<xIJerie17.ce found ils wav to the Olympians' rcadinz list: it 100~ '. ' , b' ]' , "

took a skeptical altitude towardthat which lay outside the grasp ofexperience. Other works 011 the discussion roster included JohnSlttarl Mill's I ,()gic, which cantioncd against "the prevailing hypoth-csis of a lumi ni lcrous ether"; Dcclcki nd's sharp analysis of lhc mun-bcr couccpl; and David Hunte's disillanilillg of iuduction in theTreatise 011 I I 1I11I0 II Nature." Bill of all these works that framed thebasic notions of science againsl ,1 critical background of thattowhich Ihe 111\1l1anmind bad access, Solovine singled oul one hookfor special commentary, a volume that had just appeared in Ger-man in 1<)()4: " ... Poincare's Science (/W[ IIY/JoLhesis, whichengrossed lIS and held us spellbound for wceks."") l-rom it I':insieinand his Olympians could find strong hacking for Mach's and Pear-son's views. Poincare also alludes to his crucial article, "The Mea-sure ofTirne."

It Illay he that Einstein and his academy raced off to find "TheMeasure of Time" in its original form (publishcc] ill a French phi-losophy journal). That seems unlikely. But there's an intriguingtwist. Unlike the English or French versions, the German publish-ers of Science and IJyjJothesis translated and included a gooe!-si/,eclexcerpt from the conclusion to "Measure of Time" as a footnote. So

Einstein's Clock»

in 1904, in plain German, the Olympia Academy would have hadbefore them Poincare's explicit denial of any "direct intuition"about simultaneity, his insistence that rules defining simultaneitywere chosen for convenience not truth, and his final pronounec-ment: "An these rules and definitions arc only the fruit of an uncon-scious opportunism." In fact, the French-to-German translatorswent further, providing references to Ihe long line of philosophers,physicists, and mathematicians who had blasted absolute time infavor of relative time, with Locke and d'Alcmbcrt leading the wayand with one of the creators of non-Eucliclean geometry, r .oha-schewski, there 10 report that time was just "motion c1esignecllomeasure other motions." Pcudulum clock, spring clock, spinningearth: Poincare's German translators insisted that we had om choiceof which motion 10 use as the unit of lillie that wou lr] define thetime "r of physics. But that choice h;lclllolhing whatsoever to dowith absolute lime. Instead, the choice nudcrscorcd yet again Poin-care's argument for "opportuuism" in the physical dcfinitiou of

simultaneity ;111<1duration."While il would he a mistake to assume that the finer details of

any single philosopher's thought leapt whole into Einst-cin's work,therc is no doubt at all that he emerged from these early Bcrn yearswith a powerful sense of the distinction between that which wasaccessible to our experience and that which was, so to speak, inac-cessibly hidden behind the curtain of the perceptible. Such <lTI

emphasis on the kuowablc, especially as kuowablc through thatwhich e,1I1be grasped of the natural world throllgh the senses, waskey to the doctrine of positivism laid out hy Auguste Comte andpursued by his Illany followers. As Einsl'cin told philosopher MoritzSchlick in 1917: "Your representations that the theory of rcljutivity]sllggests itself ill positivism, yet without requiring it, arc ... veryright. In this also YOll saw correctly that this line of thought had agreat influence on my efforts, and more specifically, E. Mach, andeven more so Humc, whose Treatise of HUI1WIl Nature I had stud-

~•••_._.i'- ..-._.i ••• £I&li••e••;g.JJ•.JFC':'~~ ··-~~~"'·!t.. -


ied avidly and with admiration shortly before discovering the the-ory of relativity. It is very possible that without these philosophicalstudies I would not have arrived at the solution."?'

Philosophy mattered. Far from ungrounded ill a cultural Zeit-geist, Einstein's advocacy for a procedural notion of simultaneityand against metaphysical, absolute time fit directly into this seriesof moves to shore up the basis of physical knowledge by Mach, Pear-son, Mill, and Poincare. One by one I;:illstein and his little eirclcsought out their hooks for discussion.

Einstein's first important physics papers (1902-04) targetcd ther-modynamics and the undcrlying account of heat as the product ofmolecular motion (statistical mechanics). Somewhcre among hisexplorations of philosophy, his immersion in thermodynamics atKIT!, and his independent post-E'l'll research, Einstein hegan toforge an approach 10 physics that emphasized principles andeschewed dctailcd moclcl buildillg. I"amously, thermodynamicscould he formulated with two easily stated and yet grand claimsabout isolated systems: the amount of encrgy always remains thesame, and entropy (the disorder of a system) never decreases. Thesimplicity and scope of this theory remained for I':instein an idealof science throughout his career. III Poincare's Science and Ilyf)O"I-esis he would have found a powerful exposition of the view thatphysics was concerned wi th the analysis of such principles.

And yet the terms "conventions" and "principles" did not res-onate the same way for l':instcin (and indeed for many Cermanphysicists at the time) as they did for Poincare. III French, the triplemeaning of the French word convention (legal accord, scientificagreement, Convention of Ycar II) was vividly present for Poincareand his circle around the Convention du Metre or the proposed con-vention for decimalized time. Moving the text into Ccnnan meantbreaking that particular chain of associations. Indeed, the Germantranslators of Science and Hypothesis split their rendition of con-vention, sometimes offering a German noun that included a legal

Einstein's Clocks

accord (Obereinlwmmen), sometimes a socially conventional agree-ment (kol1ventiol1elle Festsetzung).42 More importantly, we wouldlook in vain in Einstein's works for a Poincare-like insistence thatprinciples were definitions, surviving purely because of their "con-venience." For Einstein principles supported physics and perhapsmore than science, especially in later years. In a different contextEinstein reflected:

My interest in science was always essentially limited to the studyof principles, which best explains my conduct in its entirety. ThatI have published so little is attributable to the same circumstance,for the burning desire to grasp principles has caused me to spendmost of my time OIl fruitless endeavors. "11

Principled physics was important to Ei nstcin. So was the criticalphilosophical reflection that parcel physics concepts to their basicelements. But there was more. Throughout his Bern years, Ein-stein's work and thought was saturated by the materialized princi-ples of machines. From the outset, Einstein regarded tlic patentoffice not as a burden interfering with his "real" work, but insteadas a productive pleasure. In mid-February 1902 he recounted howhe had come upon a former ETII student who was now working atthe patent office. "I Ic finds that it's very boring there-certain pco-ple finel evcrything l)()ring- I am sure that I will find it nice andthat I will be grateful to Haller as long as I live." Or as Einstein latertestified, "Working on the final formulation of technological patentswas a veritable blessing for me. It enforced many-sided thinking andalso provided important stimuli to physical thought."?'

What about time? By 1902 Lorentz had long since been experi-menting with fictional mathematical variations in the way the timevariable t would be defined for an object moving in the ether. WithPoincare's and other physicists' further articulation, the notion of afixed ether had gained ground. As we know, Poincare had (first


ignoring the ether altogether and then for systems explicitly mov-ing through it), interpreted simultaneity through light-signal-coordinated clocks. Though his use of the ether changcd, Poincarenever wavered from his conviction that the ether was enormouslyvaluable as a tool for thinking, a condition for thc application ofproductive intuition. He never equated "apparent time" (time mea-sured in a moving frame) with "true time" (time measured at restill the ether)."

Poincare, Lorentz, and Abraham were determined to begin theirtheorizing with all analysis of dynamics, the forces that heldtogether, flattened, and joincd electrons as they ploughed throl1ghthe ether. Forces contracted the anus of Michelson and Morley'sinterferometcr; forces kept all the negative charge in an electronfrom hlowing that charged particle to smi tlicrccns. Out of such CO/l-

structive, built-lip theories of matter they wanted to deduce kine-matics-the behavior of ordinary matter in the absence of externalforces.

I':insteill's goal Was altogether different: time would not beginwith dynamic». III mid-l<)()5, he advanced a new account of time

and space tlwt would start the physics of moving bodies with silll-plc physical principles the way thermodynamics hCg:1I1with theconservation of ellergy and a forhidden decrease of entropy. Lorentzwas willing to posit all artificial notion of time (tloc;.!) because of itsutility ill calculating solutions to his equations. Poincare saw thephysical cOllsequences of "local time" for frames of reference illconstant mohon. Bcfore Vinstein, however, neither Poincare norLorentz seized the coordination of clocks as the crucial step thatwould reconcile S0111C of the grcat principles of physics. Neitherexpected that rcconceiving time would lip-end their conception ofthe ether, electrons, and moving bodies. Neither expected that theLorentz contraction itself could be viewed as merely consequent toa redefinition of time. For his part, before May 1905 Einsteinacknowledged only the basic features of Lorentz's 1895 physics, and

".;~

Einstein's Clocks

not a single piece of work on electrodynamics from Poincare.Instead, Einstein was reading philosophical texts about the founda-tions of science (including Poincare's), publishing on the molecular-statistical theory of heat, and exploring the electrodynamics ofmoving bodies. Before stepping into the patent office, he left notthe slightest clue that he had any interest in clocks, time, orsimultaneity.

Patent Truths

So things stood for Einstein when he arrived at the Bern patentoffice in June 1902.'(, This site represented (and not just for Ein-stein) not only a job but also a site of training-a rigorous school forthinking machines. Heading the patent office during Eimtein'stenure was Friedrich Haller, a stern taskmaster to his underlings,who directed the young inspector to be critical at eyery stage of hisevaluation of proposals: "When you pick up all application, thinkthat anything the inventor says is wrong." Above all, he was warned,avoid casy credulity: the temptation will be to fall in with "theinventor's way of thinking, and that will prejudice YOIl.You have toremain critically vigilant.",7 To Einstein, already amply inclined to

treat what he considered arbitrary authority as obsolete, thick-headed, and lazy, the injunction to indulge his skepticism to the fullmust have been gratifying. His inclination to test complacentassumptions in the use of gears and wires echoed a similarly icono-clastic attitude in less tangible realms of physics. For in the elec-

trodynamics of moving bodies, Einstein had chosen a problem thathad challenged him on and off for some seven years and was, withincreasing force, preoccupying the leading physicists of the clay.

Einstein's work in electrodynamics in 1902 did not include aninquiry into the nature of time. But he was literally surrounded byburgeoning fascination with electrocoordinated simultaneity. Everyday Einstein stepped out of his house, turned left, and made his way


to the patent office-a walk that brought him to a workplace which,he told one friend, "I enjoy ... very much, because it is uncom-monly diversified and there is much thinking to bc done.?" Everyday he had to walk past the great clock towers presiding over Bern,their time coordinated. Every day he passed the myriad of electricstreet clocks recently, and proudly, branched to the central tele-graph office. Strolling from his street, the Kramgasse, to the patentoffice, Einstein had to walk under one of the most famous clocks ofthe city. (See figures 5.3 and 5.4.)

Friedrich I Iallcr was in many ways as milch Einstein's teacher atthe patent offiec as Weber or Kleiner had been at ETII. Under his

Figure 5.3 Coordinated Clocl: Tower: Kramgasse. As he stepped 0111 of hisKra1l1gasseapartment and turned lei! toward the Bern Patent Office, Einsteinviewed one of the great (and by 1905, coordinated) cloc/::.sof the city. SOURCI·::

BORGI·:RIlIBJ.lOTHI·:K BERN, NEe. 10379.

Einstein's Cloci:s 245

Figure 5.4 Bern's j':lectrical Clock Neiworl: (circaI9()~). Coordinated,electrical clocks were a /JIllIter ol/JracticlI I i IIl/JOrl atu! cultural tnide. By 19()5,they were <l {mnuineut piece of the modern urban Icnulsccu)« throughout thecity of Berll. SOURCI·:: illmN C)'(Y MAP I'ROM rrn: I [i\RV/\RIl MAP COI.I.I':C:TION; CJ.OCK

LOCATIONS SHOWN I'SINe DATA FROM IVh·:sslml.l,C/FI(:/II\J,ISS/C (1<)<)5)·

aegis, the patent office truly was a school for novel technology, a sitethat aimed to train a quite specific and disciplined taking-apart oftechnological proposals. Early on 1lallcr reproached Einstein: "Asa physicist you understand uothing about drawings. You have got tolearn to grasp technical drawings and specifications before 1 callmake you pcnnancur.?" In September 1903 Einstein apparentlyhad sufficiently conquered the visual language of the patent world;he received notice that his appoiutmcul had been made pcnna-nent. Still, Haller was not yet ready to promote him, commentingin an evaluation that Einstein "should wait until he has fuily mas-tered machine technology; judging by his course of studies, he is aphysicist." That mastery carne as Einstein plunged himself into the

EINSTEIN'S CLOCKS, POI CARE'S MAPS

critical evaluation of the parade of patents that came before him.Soon he could report to Mileva that he was "getting along withHaller better than ever before .... When a patent agent protestedagainst my finding, even citing a German patent office decision insupport of his complaint, [Haller] took my side on all points.'?" Afterthree-and-a-half years at the patent bench, Einstein persuaded theauthorities that, physics notwithstanding, he had learned a new wayof looking through diagrams and specifications to the core of inno-vative technology. In April 1906, Haller promoted him to technicalexpert, second class, judging that Einstein "belongs among the mostesteemed experts at the officc'" where, increasingly, patents onelectric time swelled the number of applications.

'I'imc tech nologics SpUll off patents in every sector of the net-work: patents on low-voltage gcnerators, patents on electromag-netic receivers with their escapements and armatures, patents oncontact interrupters. Fairly typical of the kind of clcctrochrono-metric work hlossoming in the decade after 1900 was ColonelDavid Perret's novel receiver that would detect and use a direct-current chronometric signal to drive an oscillating armature. It wasissued Swiss patent number 303S1 01l 12 March 1<,l04. Favargcr'sown receiver did the opposite: it took an alternating current fromthe mother clock and turned it into the unidirectional motion of atoothed wheel. The request for this patent-later used widely-wasstamped "received" on 25 November 1902 and was issued on 2May I<,l05 after a long, but not entirely unusual, evaluation period.There were patents that specified systems for clocks to aetivateremotely placed alarms, while other submissions targeted the dis-tant electromagnetic regulation of pcndula. There were proposalsfor time to travel over telephone lincs-even systems that sent timeby wireless. Other patents advanced schemes to monitor railroaddepartures and arrivals or to display the time in different timezones. Yet others specified how remotely run electrical clockscould be protected from atmospheric electricity or how electro-

Einstein's Clocks

magnetic time signals could be silently received. A cascade of coor-

dinated time.Some of these patents systemically addressed the problem of dis-

tributing simultaneity. Perret's patent 27555 came in at 5:30 1'.1\:1. on

"j i"I I,I" , I > I I .•~( ') ()! I Ii"" ) J I (oJ" 1

,II

.• .• "' I~~(~I't'!:~'i~.:~·-i~:·: ,~..tJIi0:·'·, ~'.:l

,

Figure 5.5 Patenting Coordinated Time. Patents on the electnnnagneticcoordination of lime surged around 1905. Here are but a few: Swiss Patent3370() (upper left) show» a mechanism for the electric resetting of distant clocks(12 May 19(5). Swiss Patent 29832 (from 1903) in the upper right illustratesa proposal {(Jr the electrical transmission of time. The distant clocks that wereto be control/ed are visible at the bottom of the wiring scheme. Swiss Patent37912 (1906), de(Jicted at the bottom of the figure, is one of the earliestap(JT(wed applications devoted entirely to the radio transmission of time. Suchschemes date almost to the first days of radio and were widely discussed in1905. SOURCI';; ")3700 (JAMES BESANyON AND JACOB STEIGER); z98v (COI.ONEI. Dxvio

P,:RRKr); A Il 379'2 (MAX RI·;rmOliFI·:R A n FilA Z '10IlAWI'TI.).

I EINS'n:IN's CLOCKS, POINCARf.:'S MAPS

7 November 1902 (issued in 19(3), offering "An Electric Installa-tion for the' J ransmission of Time"; Perret floated a similar proposalill 1904. Mister L. Agostinelli, applying from 'Ierni (patent 29073,issued 1<)04) proposed all "Installation with Central Clock for Incli-eating the Time Simultaneously in Several Places Separated fromOne Another, and with Bells for Calling Automatically at Prede-tcrmiucd Times." There were patent applications by huge electri-cal couibincs like Siemens ("Motherdock Relay," number 299S0,issued 1<)04) and patent's by smaller hilt still important Swiss firmslike Magneta (patent 2<))25, submitted 11 November 1903, issuedI()()4), which 11lcllllifactnred the remotely set clocks gracing the Fed-eral Parli~llllelJl' BlIildillg ill Hem, A Bulgarian took out a patent inearly I()04 for a mother clock and its electrical secondaries. Appli-cations stacked lip ill Bern by the dozens." From New York, Stock-[roh n, Sweden, 1.ondon, and Paris, inventors launch cd their timil1gdrc.nus toward the patent office, hilt iI was the Swiss clockmaking

iucluslry Ihat dOlllill;ilcd the hade,I)millg the time thnt J':instcill served <ISa patent inspector, inter-

est ill electrically coutrollcd clock systems heightened, From lW)Oto 19()() !l1C1'ewere three or four electric time applications each year(with the exception of two ill Io()() amI six in 10(1), As electric timelrauxmisxiou grew alongside the telegraph system, coordinatedclocks heg;!11 playing all ever-increasing role in both public and pri-vate sites, The umuhcrs: I t)0l, eight patents; 1902, tcn; 1903, six,;11HI then ill 1904 (the peak year fWIIl IS8<) to 1910) fourteenpatents 011electric clocks overcame the hurdles of the patent office.Numerous others, lost to history, no doubt withered under Ein-

stein's and his colleagues' critical ga;r,c."All these Swiss ehronomctric inventions-along with a great

lllallY others related to them- had to pass through the patent officein Bern and no doubt many of them crossed l-':instein's desk." WhcnEinstcin began work there as a technical expert, third class, he waschiefly charged with the evaluation of electromagnetic and electro-


mechanical patents. \; At his wooden podium, alongside twelve orso other technical experts, Einstein dissected each submission to

extract its underlying principles?'Einstein's expertise on electromechanical devices came in part

from the family business. His father Hermann and uncle Jakob Ein-stein had built thcir enterprise out of Jakob's patents on sensitiveelectrical clocklike devices for measuring electrical usage, One ofEinstein and Co.'s electrical meters featured prominently in the 1891Frankfurt Electrotechnical Exhibit, a few pages away from a mecha-nism (typical of the period) for mounting a backup mother clock toensure the continued operation of a system of electrical clocks. Soclose were the electricalmeasuring systems and electric clockworktechnologies that at least one of the Jakoh Einstein-SebastianKornprohst patents explicitly signaled its applicability to clockworkmechanisms. Conversely, numerous patent applicants proffereddevices that applied as much to electricity-measuring systems as to

electric clocks."During I':instein's patent years (June 1902 until October 19(9)

machines of every sort surrounded him. Sadly, only a few of Ein-stein's expert opinions survive, rescued from automatic bureaucraticdestruction only because the patent process had driven negotiationsinto court. In one, from 1907, Einstein took aim at a proposal for adynamo put forward by one of the most powerful electrical compa-nies in the world, thc Allgemeine Elektrizitats Gesellsehaft (A1<:G):"1. The patent claim is incorrectly, imprecisely, and unclcarly pre-pared. 2, We can go into the specific deficiencies of the descriptiononly after the subject matter of the patent has been made clear bya properly prepared claim.":" Description, depiction, claim: thesewere the building blocks of any patent; to demand their rigorousexecution formed the curriculum of Einstein's schooling under

Ifaller.A second extant opinion by Einstein concerned a patent infringe-

ment suit between a German firm, Ansch utz-Kaempte, and an


J. Einstein & Cie.Elektrotechnische Fabrik

MUnchen.

AUfif'iihrtlllg

eleklrischerKraflUber-Iragungs-anlagen

jcdcr GriiH;';e.

eleklrischerBeleuchlungs-

anlagenill jcdcin LTtu-

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Fabrikation

-.) ynu.nJ.o -Mu.s c hill. enfilr-

Belenchtung, Kraftilbertragung nnd Elektrolyse,Bogenlampen, Elekta-izit.atszahl.er-n,

Mess- und Regulirapparaten.

Figure ).6 Jalwh Einstein 6 Co. 1';illsleil1's uncle aiul [ather ran cui elec-troteclinica! com/klllY ilutt /JT()(/lIcecl, utter alia, /Jrecis;on electrical ineasunng

eqllilJ177ent that shnred niuch tech1lology wiili tlut! of electric clocks. SOI!RCI'::

()I'I"I/'I/':I.I ,1-:ZI-:ITIIN(; 1)I-:I{ IN'J'I-:/{N/,I'j( JN/II.I-:N 1':1YKI'J{( )'/'I'X ;IINIS( :II/':N AIISS'J'I-:I.I ,IINI ., Jr'RAN KFlIl('I'

AM MAIN (1f)9'), 1',949,

American company, Spcrry. Competition to build workahle gyro-scopic compasses ill the early 1910s was ferocious. Metal boats,newly electrified, were terrible sites for magnetic compasses. But inthe race to outfit the world's ships and airplanes, Anschutz-Kaempfesuspected thc Americans of having stolen their invention. HermannAnschutz-Kaempte (thc firm's founder) called Einstein, who madeshort shrift of the Americans' claim that an 1885 patent actually laybehind all their "new inventions." Noting that the 1885 patentdescribed a gyroscope that could not move freely in all three dimen-sions, Einstein skewered the Americans' claim by pointing out that

Einstein's Clocks

the older machine could not possibly work accurately in the pitch.iud roll of a craft at sea. Anschutz-Kacmpfe won. Einstein becamesuch an expert on gyrocompasscs that he was able to con tributedecisively in 1926 to one of Anschutz-Kacmpfe's major patents, forwhich he received royalties until the distributing finn was liqui-dated in 1938. Significantly, in 1915 the gyrocompass served explic-itly as a model for Einstein's theory of thc magnctic atom. Thiscross-talk between machines and theory so riveted his attention thatI~insteill temporarily put aside his work on general relativity to do aseries of collaborative experiments - exceedingly delicate ones-showing thatthe iron atom indeed functioned like a submicroscopicgyroscope.") Patenl tcchnology and theoretical undcrstanding werecloser than they might have appeared.

A few ycars later, l<inslein made it clear that he treated the veryproccsscs of writi1lg and rcading as if he were attacking a patent,even when he was trcating matters far removed from dynamos orgyrocomp'lsscs. In July 1917 his long-time friend, the anatomist andphysiologistllcimich Zallggcr, wrote EillStcin to solicit his judg-ment of ,I tcxl Za1lggcr was asscmbling on mcdiciuc, law, andcausality. 1':illStein replied that he liked the "concrete cases," "[bjutI did nollikc some of the abstract parts; they often seem to me to beunnecessarily opaque (general) and ill the proccss arc not wordedclearly and pointedly enough (not every word is placed clearly and

consciously). Neverthcless, Iunderstood evcrything; it may well bepossible that my perpetual ride on my own hobbyhorse and thc con-ventions at the Paten t Offiec have driven Illy standards to cxaggcr-ated heights in this regard.'?"

Einstein's fascination with machines and the conventions of thepatent office spilled from his workday into the rest of his lifc. Inincessant corrcsponding about machines with his friends, ConradHabicht (of the Olympia Academy) and Conrad's brother Paul (anapprentice machine technician), Einstcin bandied about ideas forrelays, vacuum pumps, electrometers, voltmeters, alternating cur-

'I:t,'j:~' . I

'. J.;, -c ,(t~

.r, ~--------------------------------------

ErNSTEI 's CLOCKS, POINCARE'S MAPS

rent recorders, and circuit breakers. Paul, in particular, cooked upone scheme after another, sometimes writing Einstein every twodays. On one occasion, having dropped Einstein a detailed letterabout a proposed flying machine (a helicopterlike contraption),Paul directly requested advice: "Should I take out a patent imme-diately? Or publish without a patent or start negotiations without apatent?"?'

Einstein, too, sought patents. One of his many ideas was for asensitive electrometer that would measure exccedingly small volt-age differences. The little machine (Maschinchen) fascinated himill all its aspects, from matters of theory to the nitty-gritty of fahrica-lion." He wrote to one of his collaborators about the gasoline theywould need to clean cbonite (vulcanized rubber) parts, and thearrangement required to ensure that the wires would dip properlyinto 1I1ercury beads on the chouitc disk. "I already know from Illyexperiments," he added, "lha! the thing can he clone with tIre mer-cury contacts. It- is only sometimes tinrc-consumiug to put the appa-ratus ill working order, and the mercury spurts out as soon as oneturns a hit too ClsL"("

Concerns about instruments, along with experiments on real andimagincd machines, held Einstein's rapt attention Writing 10 hisfriends he would switch, without missing a beat, from the rarified-theoretical to thc practical-technological. In one letter of 1907, in

the midst of telling ConradlIabieht about an article that he waswriting 011 the relativity principle and some current work Oil the per-ihclion of mercury, \l:instein in the vcry next sentence was hack tothe Maschillchen. Just about a year later, he told his friend and col-la borator Jakob LlI1h that "Ill order to test [the Maschinchen] forvoltlagcs] under 1/10 volt, I built ,111 electrometer and a voltage bat-tery. You wouldn't be able to suppress a smile if you saw the mag-nificent thing that I attached togcther myself"?' These efforts on theMaschinchen and his later work on the gyrocompass and Einstein-de Haas effect, are but a few examples ofEinstcin's particular inter-

Fi1Zstein's Clocks

est in sensitive electromechanical devices that would bridge worldsof electricity and mechanics. Electromagnetic clock coordinationproposals were right up his aIIey -- they offered ways to transformsmall electrical currents into high-precision rotary movements.

Time coordination patents continued to pour into the office. On25 April 1905 at 6: 15 P.M., for example, the office recorded thearrival of a patent application for an electromagnetically controlledpendulum that would take a signal and bring a distant pendulumclock into accord." All such inventions required documentation,including a model, specific drawings, and properly prepareddescriptions and claims. Evaluating them was painstaking and oftenlasted for months.

Sometime in the middle of May 1905 (and wc note that Einsteinmoved outside Bern's zone of unified time on May l Sth ), he andhis closest friend, Michele Besso, had cornered the electromagnet-ism problem from every anglc. "Then," Einstcin recalled, "sud-denly l understood where the key to th is problem lay." lie skippedhis greeti ngs the next day when he met Besso: "'Thank YOll. I'vecompletely solved the problem.' An analysis of the concept of timewas my solution. Time cannot he absolutely defined, and there isan inseparable relation between time and signal velocity."?' Point-

ing IlP at a Bern clock tower -one of the famous Bern synchronizedclocks --and then to the onc and only clock tower in nearby Muri(the traditional aristocratic annex of Bern not yet linked to Bern'sNorrualulu), Einstein laid out for his friend his synchronization ofclocks."

Within a fcw clays Einstein sent off a letter to Conrad Habicht,imploring him to send a copy of his dissertation and promising lournew papers in return. "The fourth paper is only a rough draft at thispoint, and is an electrodynamics of moving bodies which employsa modification of the theory of space and time: the purely kinematicpart of this paper [heginning with the new definition of time syn-chronization] will surely interest you.'?" Ten years of thought about

, '. _._ ' .C'O,"" '-.--

,---;,,~----

EINSTEIN'S CLOCKS, POINCAR~'S MAPS

Figure 5.7 Bcru-Muri Mal). Michele Hesso recalled tliat when /';illstein excit-edly !()Id him oJhis realization that lime lwei t() he de/lned hy sigllal excliane«,he (J()illied I() one clocl: tower ill ole! Bern olld 10 another (the ollly (me)JIl theuearb» tOWIIo(Muri. Sillce il is the oul» van/age /Joint [ion: wliicl: h()th mightliav« been visible, Besso (/J/(II<il1sleil7nuts! have been stal/ding OIl (he hill sh()wllI() {he northeast ()FdoWl7tolVI7Hem. SOURCI':: M()Illl-"II':IlI,'I(()~l S~()RI'I()N-VlmIAC.

tile physics of moving bodies, light, ether, and philosophy hac! cul-ruinated in Illis little paper.

Obviously time synchronization by the exchange of clcctromag-netic sigllals was not all of special relativity, hilt it W,lSthe crowningstep ill I':instein's development of the theory. Coordinating clocks

did 1101, as it had for Poincare, enter I<inslcin's reasoning as the phys-ical interpretation of Lorentz's fictional "local time." Far from it.11:inslcill heg,lll his argumellt by defilling the position of a point rcl-ativc to rigicl measuring rods (a connuouplncc), hut now supple-mented with his new definition of simultaneity: "If we want todescribe the motion of a material point, we give the values of itscoordinates as a function of time. However, we should keep in mindthat for such a mathematical description to have physical meaning,

E:instein's Clocks 255

Figure 5.8 Muri Clochiower (circa 1900). When Einstei7l gestured towardMuri'« only clock tower (/S he expluined t« Besso his 17ew lime-coordinationscheme, this is the structure to which he /Jointed. SOlIRCI':: CI-:~1l':IN[)I':SCIIRI':IBI':REI

MURI IlI':1 Bl-:R:'-I.

we first have to clarify what is to be understood by 'time'." With IlOframe of ether at rest Oil the basis of which to pick out the one truetime, the clock systems of every inertial reference frame were cquiv-alent ill the sense that the time of one frame was just as "true" asany other.

In this contcxt.Tvinstcin's paper, completed by the end of JUIlC

1905, can he read in a very different fashion from our current stan-dard interpretation. Instead of a wholly abstracted "Einsteinphilosopher-scientist" -lost in theory while absentmindedlymerely earning his keep in the patent office-we can recognizehim also as "Einstein patent officer-scientist," refracting the under-lying metaphysics of his relativity theory through some of the mostsymbolized mechanisms of modernity, The train arrives in the sta-t ion at 7 :00 P.M. as before, but now, after our long voyage throughI ime and space, we can see it was not just Einstein who was wor-lied about what this means in terms of distant simultaneity. No,(Ictermining train arrival times by lIsing electromagnetically COOI-

l<INSTEIN'S CLOCKS, POINCARE'S MAPS

dinated clocks was IJrecisely the practical, tcehnological issue thathad been racking North America and Europe for thc last thirtyyears. Patents were racing through the system, improving the clec-trical pendula, altering the receivers, introducing new relays, andexpanding system capacity. Time coordination ill thc CentralEurope of 1902-05 was not merely an arcane thought experiment;rather, it critically concerned the clock industry, the military, andthe railroads as well as a symhol of the interconnected. sped-upworld of modernity. Here was thinking through machines.

I<:instein brought into his world of principled physics the power-ful and high ly visible new technology embodied all around h im: theconventiollalized simultaneity tliat synchrolli/,edtrain lines ,md settime zones. A trace of that existing time-coordination system is thereto see ill the ]<)()5 article itself. Reconsider the coordination scheme

with which I<instein hegins the papcr: An ohscrver is equipped witha clock at tIll' center of the coordinate system. 'I'lwt master clockbolted to sp,lec position (0,0,0) detcrJllincs simultaneity when clcc-

troJllagnetic signals from distant points arrive there at the same localtime, But now this standard, centered systcin 110 IOllger appears asall abstract straw man, 'I 'his branchiJlg, radial clock-coordinationstructurc-visihle ill wires, generators, and clocks, displayed illpatent aftcr patent and book after hook on tilllekceping-wcls pie-dsel)' thai or the Furo/Jean system or the lIlother cloc/.: along with itssecondat» and tertiary clelJencleniii, (See figures 5.9-5, II .) I':instciuhad brought 10 that cstablished systcm the critical ga/,e of a physicist-patent officer: keep the idea that time had to be defincd through ,I

realizahle signal-exchange, invoke the absolute speed oflight, andcancel the system's dependency on any specific, privileged spatial

origin or rest frame for the ether.With a certain caution, we might attempt to track Vinstein's pre-

cise train of thought even further into this mid-May 1<)05 crossingpoint of the technology and physics of simultancity. One possihilityis this: sensitized to the importance of procedurally based concepts,

Einstein's Clocks

0°...... .-0

.0

···0

LE'~ende@l HOTlo9,,·,,"ire r';~lallte

~ Horloge.mere r091';e

© HoTio9"·""ro r091';e.1 r~~I,,"le

- fils prin cj paux de ~roupe

------ Fn~5econda;re~ d'cl1lbrallchernent

o COIn~)'eur!) ele clr-o - c1]r01l01l1eiri<:Juc.s

Figure 5.9 Favarger'« Time Network. Taking over from Hipp, Favarger ledthe Swiss COml)(17ZY (after 1889, A. Peyer, A. Favarger 6 Cie.) to a leading /)Osi-iion in the world of electro coordinated clocks, not only in production but alsoill invention and patenting. Here Favatget depicted a prototvpical networi:of secondary timepieces linked to a master clock. SOURCE: i.';IVARCER, "1<:U:<:'I'RIC-

1"['1::In' SI':S ApPLICATIONS" (1~H4-S5), p, 320; REPRINTED IN FWARGER, L'I:;U:C:'IHfCfI·(; (1924),

P. 394-

time coordination and its precise, patent applications, and hisOlympia Academy critical-philosophical discussions, Einsteincould have been fully primed to take up and transform any men-tion of clock coordination in the context of electrodynamics of mov-

ing bodies. Perhaps at some stage Einstein had actually readPoincare's 1900 article in which the French savant gave his firstphysical interpretation of Lorentz's (approximate) "local time" asclock eoordination by signal exchange in the ether. It is certain that

9

1': [NSTE IN'S CLOCKS, POI NCi\RE'S MAPS Einstein's Clocks

UNiFicATioN ElECTRiaUE DE l'HEURE DANS UNE GRANDE viu,r

.e.'~~~ ,: ,,(~~

" 'I 'I ,l1."11 : , ':1, '09

1" :''i1il!tl{);' I'I!I ·f", II J

ST~lIon C(Rlr;ole""ONlne

!J I' ,'I:.J..'", .'j ~I : 9.!ll:~~ 'IJ I -o~' ••..•~.'..,... il-

! i I ~hll1 ·,f,"1 ,-.::::':~!'.....; : 'j:iH'ir~lf~'I: i" '" ': =-===_. i.'

t,:.I!~I~l·ii.j ", '

~i~Cll1!I i ~mll;lj I:i~:-~, '.. --- I '.'

J • ".1

,1: ,r,~/-'"jI:tttrjfll 1[1 :1 :,' :', :;;~::i:;:iii:"i}:~';:';:""" "..,I -'n ' ' 'Ii ::: '"

Figure 1./0 Time Tclegra/>h Network J\/lo/her IJlIwdig/lwtic represeIlL(/~i()llofdi:;lrihllied electrical t! uie. SOI/RU;: 1,,\IlISI.I\I/S 1"II-:IlI.I.;l(,' )1/,;/'/.;/1'1'/,;/'/';( :HAI'/I/';N IINIl

1>1/'; 1,.,.t<:KIWS( :IWN {111l(I';N 1'( ),"1 l'lvli-,TIS( :II/'N S'lilNI )/'IINI--T,.. (VII'; NA, IX,)O), 1'1'. XX-,}),).

I

Figure 5.11 Electric Unihcation. Favarger wanted to wire the interior oj"

building«, hut more ambitiouslv the entirety or I/lajor urban centers, as thisschematic made clear. s( HII(;I';: I'AVARCI.:R, ',";;1.1'" TI(/( :/1'1:; (1<)"4), 1'1'. 427-2}), I'I.ATI'; 4-

so 111cti II tc he fore 17 May 1,)()(), I';illsteill did read Poincare's 190()

paper-on that clay I';imtein sulnniltcc] a paper of his own thatexplicitly usccl the contents of Poincare's article (though not localtime)." Could it he tlwtl';illSteill had studied or at least seen Poin-care's papcr between December 19()O aud May 1905? Morc specif-ically: had Einstcin read and clisuusscd Poincare's 1900 ether-basedreasoning, while, at SOl11elevel of awareness, he retained the seniorFrench scientist's provision of a clock-synchroni/,ation account ofLorentz's local time? l';instein did uol read French easily. But henecd not have read Poincare directly: he could have encounteredrelated ideas (in Cerman) in Fmil Cohn's November 1904 article'''I' 1 I '1'1 I . f M . S tcr "illowarc t ie ~ ectroc ynanllcs 0 ovmg, ys ems.

Student of a Strasbourg cxperimentalist renowned for his workon the speed of sound, Cohn was a successful theorist who had

begun his career in the laboratory, measuring magnetism. I':vellas he turned decisively from bench to blackboard, Cohn relent-lessly insisted on the measurable consequences of his work. By theturn of the century Cohn stood as a theorist- of repute, joinillgfellow luminaries t-o deliver a paper at the December 1900Lorentzfest. There it SCCll1Slikely that hc would have heard Poin-care's lecture; at the very least he would have had good reason tosee the printed version of Poincare's talk in the published pro-ceedings that contained his own paper. But for om purposes, theintriguing piece of the story is this: in 1904, Cohn, like Poincare,explicitly introduced clock coordination into his physical defini-Iion of local time, and he did so with a fonner experimentalist'ssuspicion of purely hypothetical quantities. In this respect he was

....-.---~~~~~-----------


rather more like Einstein than Poincare. Unlike Poincare, Cohnrejected the ether, prcferring "the vacuum," and taking local timeas given by light-signal coordinated clocks valid for optics if not

mechanics.Again, the unanswerably detailed question: When did Einstein

see Cohn's procedural local time? And again, there is little cer-tainty. Only this: sometime before 25 September 1907, Einsteinhad Cohn's article in hand (that day he wrote the editor of a jour-nal reporting just this, misspelling Cohn's name "Kahn"). On 4December 1907, the publisher recorded the arrival of Einstein'sreview papcr OIl relativity that contained this somewhat crypticfootnote-compliment: "The pertinent studies ofE. Cohn also enterinto consideration, hut I cliclnot make use of them here."" Again,Einstein would have hall to dismiss the vast bulk of Cohn's partic-ular approach to electrodynamics while extracting the idea of clockcoordination as relevant to the definition of simultaneity. (Yetanother physicist, Max Ahraham, had also begllll exploring signal-exchanged simultaneity in his 1905 text on electrodynamics,thouah not early ell<Hluh for It;insteill to have seen it before sub-b bmittillg llis article."] The limits of reconstruction arc evident, andwould be even if it were written in stone that Einstein had seen oneof these papers. But the larger gO<lllllllSt stay in view: to understandall we can of the philosophical, technical, and physics conditionsthat put lvinsrcin in a position to seize clock coordination as theprincipled starting point of relativity. Of course, we can even sketchpossibilities for the seed around which the idea condensed, whileavoiding all overwrought attempt to spcci fy exactly what the pre-cipitating seed might have been: a half-remembered line from Poin-care or Cohn encountered in the library, a particular patentapplication at work, a synchronized Bernese street clock, or a philo-sophical text batted around thc Olympia Academy. Our position isnot so different from that of the meteorologists who can provide anexcellent account of how a thunderstorm formed by studying the

Einstein's Clocks z(n

powerful updraft of an unstable column of moist air: but it is notgiven to know around which bits of dust the initial raindrops

preci pi tated.Who saw what when? What was deleted, absorbed, provoked by

each comment and paragraph? Doling out credit and priority, play-ing prize committee to the long-deceased is to employ an uncertainhistory against a futile goal. More important, more intcrcsting isthis: in the years before May 1905, simultaneity talk was growingdenser among physicists as thcy grappled with the electrodvnumicsof moving bodies. Simultaneity procedures lay thicker in philo-sophical texts, in the cityscape of Bern, along train tracks through-out Switzerland and beyond, ill undersea telegraph cables, and illthe application in-pile at the Bern patent office. In the miclst of thisextraordinary material andliterary intensification of wired simul-taneity, physicists, engineers, philosophers, and paten! officersdebated how to make simultaneity visible. Einstein did not conjurethese various flows of simultaneity out of nothing; he snapped ajunction into the circuit enabling the currents to cross. Simultanc-ity had long been in play at many different scales, but Einsteinshowed how the same flashed sign,1l of simultaneity illuminated allof them, from the microphysical across regional tru inx andtelegraphs to overarehing philosophical claims about time and the

Universe.Back in 1900 Poincare liacl launchcd his interpretation of time

as signal exchange in the midst of his r .eidcu speech, attribllting it,almost as an aside, to Lorentz .. Einstein made signal-simultaneitycentral at every opportunity, from the moment in May 1905 whenhe stood with Besso gesturing over the hills at the clocks of Muriand Bern. In a wide-ranging review of the relativity theory at the endof 1907, Einstein reiterated the pivotal role that time must play. Byhis lights, Lorentz's old theory of 1895 had shown, at least approxi-mately, that electrodynamic phenomena would not reveal themotion of the earth with respect to an ether. Michelson and Mor-

EINSTEIN'S CLOCKS, POINCARE'S MAPS Einstein's Clocks

ley's experiment made clear that even Lorentz's approximate equiv-alence was not good enough - motion through the ether could notbe detected at even higher levels of accuracy. "Surprisingly," Ein-stein added, "it turned out that a sufficiently sharpened conceptionof time was all that was needed to overcome the difficulty."Lorentz's 1904 (improved) "local time" was enough to address theproblem. Or rather, it solved the problem if, as Einstein had done,"'local time' was redefined as 'time' in genera!." Einstein's view wasthat this "'tillle' in general" was precisely the time given by thesignal-exehange procedure. With that understanding of time, thebasic equations of Lorentz followed. So with this dramatic redcfin-ition, J .orcntz's theory of 1904 could be set on the right track, withonc further, not-so-small exception: "Only the eonception of aluminiferous ether as the carrier of the electric and magnetic forcesdocs not fit into the theory described here." More precisely, Einsteinclismissed the idea that electric and magnetic fields were "states ofsonic substance," as the ether advocates would have it. For Einsteinelectric and magnetic fields were "independently existing things,"as freestall(lillg as a hloek of lead. Electromagnetic fields, like ordi-llary ponderable matter, could carry inertia. Fields did not dependOIl the state of all undetectable ether for which Einstein had not thesl ightcst IISC.

'lhcrc were lllany choices open to a physicist wanting to under-stand this post-I 90 5 controversy about the electrodynamics of mov-ing bodies. Certainly T .orentz and Poincare loomecllargc; Einstein'sreputation was growing. But there were dozens of ideas vying forattention: the relativity principle, the status of the ether, theabsolute speed oflight, the changing mass of the electron, the pos-sihility of explaining all mass hy electrodynamics. From this swirl,only around 1909 did Einstein's articulation of time rise haltingly,contentiously, but then powerfully. (Even then there were somephysicists, such as Ebenezer Cunningham in Cambridge, England,who reael Einstein's relativity very differently; he was certainly not

the only physicist who while enthusiastic about the new theory didnot take coordinated clocks to he the main event in the great dramaof relativi ty.yl

Clocks First

C()ttingen mathematician and mathematical physicist HermannMinkowski trained his spotlight early and directly on Einstein'sclocks. Long before 1905, Minkowski had built his career by apply-ing geometry where no one else had thought to apply it-to theapparently unvisualizablc field of the theory of numbers. (It shouldbe said that the younger Einstein resolutely ignored Minkowski,even when he was enrolled in the great mathematician's ET'Hcoursc.) When Minkowski saw the work of Lorentz, Poincare, andEinstein, he again looked to geometry. Now Minkowski singled outEinstein's attack 011 classical time as the key to the puzzle, the keythat, in combination with his own formnlation of a four-dimensional geometry of "spacetime," opened up a new under-stancling of physics. Calling thc new physics "radical," he even morestrongly dubbed it "mightily revolutionary" in his private drafts. Inhis much stuclicd lecturc, "Space and Time," Minkowski made itclear that it was Einstein who had liberated the multitude of physi-cal times from a fictional existence: "time, as a concept unequivo-cally determined by phenomena, was deposed from its high seat."Minkowski asserted plainly that it was Einstein who had shown thatthere was no coherent meaning of "time" by itself, only "times,"

plural and dependent on reference frame.In pursuing his four-dimensional world, Minkowski drew on

Poincare who, back in 1906, had also considered a four-dimensional spacetime. Poincare had remarked that amidst all thechanges of time and space from one reference frame to another,there was one quantity that remained unchanged. An analogy: Sup-pose you mark the location of an observatory and nail the map to a

ii

EINSTEIN'S Cl.OCKS, POI CARE'S MAPS

board with a single nail driven through the position of your house.Rotate the map 45 degrees clockwise and you change the horizon-tal distance from your house to the observatory while you simulta-neously alter the vertical distance between house and observatory.But obviously rotating the map in this way does nothing to changethe actual distance between home and observatory. That is, if thehorizontal separation is A, the vcrtieal separation, B, and thc clis-tancc C, then rota: ing the map will ehangc A (if the Illap is turnedso that the house and observatory <Healigned vertically, for exam-ple, there is no horizontal separation). Similarly a rotation willchange H, thc vertical separation. But rotating the map cannotchange thehouse-to-observatory distance, C. Minkowski showedthai the relativistic transformations of space and time could be rig-orously considered a distance-preserving rotation in the four-dimensional space made lip of ordinary space and time. Just asdistance ill 1':ucliclc<1ngeometry remained the same (despite arota-tion}, so ill relativity there was a new distance that remaineduntouched by the transformations of space and time separately.[Spacetime distance squared] was always equal to I time differcncesquared] minus [space difference squared].

lu a powerful speech in Colognc on 21 September 1908,Minkowski took IIp the mathematics of Poincare, but reorderedtheir iutcrprctatiou ill words that instantly seized the imaginationof the lllallY physicists: "Henceforth space by itself and time byitself, arc cloomcd to fade away into mere shadows, and only a kindof union of the two will preservc independence." For Minkowskircality lay 110t in what we could grasp with om ordinary senses(space by itsclf, time by itsclf), but in the distances of this four-dimensional fusion of space and time. Invoking a sh'iking imageryof projections and objects in four-dimensional spacetime,Minkowski would have call cd to mind among his Gymnasium-educated audience Plato's cave scene in the Republic. There Platodescribed how a prisoner, constrained to view but the shadows of

Einstein's Clocks

objects dancing on the walls, would find it painful to learn to peerdirectly at the full three-dimensional objects behind the prisoner'shead, much less at the light that lit them. Minkowski insisted thatin the old physics of "space" and "time," scientists had been simi-larly misled by appearance. III spcaking of space and time sepa-rately, physicists were, like Plato's prisoners, contemplating nothingmore than shadows projected onto three dimensions. The full andhigher reality of a four-dimensional "absolute world" would revealitself only through the liberation of thought, and specificallythrough the insights mathematicians could provide."

At first Einstein resisted Minkowski's formulation, seeing ill itneedless mathematical complexity. But as he ventured deeper intothc theory of gravitation, the notion of spacetime proved ever moreessential. Meanwhile, all around him, physicists took lip Minkowski'sidiom as their road into relativity, a path many fouml more acccssi-hlc than Einstein's own." A few rejected Minkowski's view that real-ity lay in four dimensions and that physics itself should hecompletely reformulated so it described this higher-dimensionalworld. Among those dubious about a four-dimcnsional physics fig-ured, ironically, Poincare himself, who already ill early 1907 hadpreemptively dismissed the utility of such a project:

It seems in fact that it would be possible to translate our physicsinto the language of geometry of four dimensions; to attempt thistranslation would be to take great pains for little profit. ... [I]tseems that the translation would always be less simple than thetext, and that it would always have the air of a translation, that thelanguage of three dimensions seems the better fitted to our descrip-tion of the world although this description can be rigorously madein another idiom."

As he had done so often, Poincare pointed out new lands, identifiedthe passes to them, and then chose to make his own stand on terra

266 f:INSTEIN'S CLOCKS, POINCARE'S MAPS Einstein's Clocks

cognita. Once Einstein began his pursuit of four-dimensional space-time set in uon-Euclidcan geometry, he never let go.

And again and again, Einstein came back to the problem of time-keeping. In 1910, for example, he once more insisted that timecould not bc grasped without clocks. "What is a clock?" he asked."By a clock we understand allY thing characterized hy a phenome-nail passing periodically through identical phases so that we mustassume, by virtue of the principle of sufficicnt reason, that all thathappens ill a given period is identical with all that happens in anarbitrary period.'?" If there is no reason to think otherwise we shouldassume the LJ uivcrsc to he constant. If the clock is a mechanismthat drives liauds around in circles, then the uniform motion ofthosc hands will mark time; if the clock were nothing but an atom,then time would be murkccl by its oscillations. By itself Einstein'sremark about the significance of "clock" extended the series ofphilosophical investigations of time by Mach, Pearson, or Poincarehimself ill "The Measure ofTimc." Now, however, a clock need Hothe a macroscopic object at all: it could even he all atom. At themotucnt I':i)lsl'cill pcnucd these words, he was writing for a scien-tific publication, hut it is not hard to see how these considerationscame to count almost immediately as philosophy. Certainly b:in-stcii i's time concept was read that way by the new breed of scientificphilosophers that included Moritz Schlick and Rudolf Carnap ofthe Vienna Circle, or their Berlin ally, l lans Reichenbach.

On 16 [anuary 1911, Einstein appeared before the Natur-[orschende Gesellschaft in Zmieh. Once again, the increasinglywell-known yOllng scientist outlined his reasoning, from the estab-lishment of the Lorentz theory to the st,lrting assumptions of rela-tivity and the procedure for coordinating clocks. Clearly delightingin his example, Einstein explained how "the thing at its funniest"emerged if one j maginecl a clock - better still, a living clock, anorganism-launched into near light-speed round-trip travcl. Onreturn, thc being would have scarcely grown older, while those

remaining at home would have aged through generations. Thoughpreviously skeptical, Einstein even tipped his hat toward Minkowski,whose "highly interesting mathematical elaboration" had revealeda method that made relativity theory's "application substantially eas-ier." It was praise that came too late for Minkowski to appreciate; hehad died suddenly in 1909. But Einstein now, like Minkowski,began celehrating the appeal of reprcsenting "physical events ... ina four-dimensional space" and physical relations as "geometrical

theorems."?'Kleiner, Einstein's old thesis examiner and sometime supporter,

then took the floor to laud his former, and formerly difficult,

student:

As far ,IS the principle of relativity is concerned, it is heing calledrevolutionary. This is being clone cspcciully with regard to thosepostulates thai arc uniquely Einsteinian innovatious ill our physi-cal picture. This concerns most of all the fonnulation of the COII-

ccpt of lillie. Until now we were accustomed 10 view time assomething 1·1.;11 always flows, under all circumstances in the samedirection as something that exists independently of om thoughts.We have become .iccuslomccl to imagine that somewhere in theworld Ihere exists a clock that categorizes time. At least onethonght it pcnnissiblc to inlagillc the thing in such a way.. - . Itturns out that thcnolion of lillie as something absolute in the oldsense cannot he maintained, hilt that, instead, that which we des-ignate as lime depends on the states of motion."

I,'II,'IIi

!I

III!:1!By contrast, for Kleiner the relativity concept itself was hardly "rev-

olutionary"; it was a "clarification," perhaps, but not something"fundamentally new." If the good professor Kleiner mourned any-thing in Einstein's physics, it was the loss of the ether. True, he eon-ceded, the concept had grown more and more incomprehensible.But without it wouldn't there be "propagation in a medium which


is not a medium"? Worse yet, didn't the abandonment of the etherleave us with formulae that lacked any "mental image"? In reply,Einstein allowed that the ether might, in the age of Maxwell, havehad "real value for intuitive representation." But the value of theether concept vanished when physicists gave up trying to pictureether as a mechanical entity with mechanical properties. After thedemise of the truly intuitive ether, the notion had become for Ein-stein nothing but a burdensome fiction.

That January clay, just about every speaker directly or indirectlybrought up Minkowski's "Space and Time" speech, which elearlyhad paved the way for a wider acceptance of Einstein's theory. Ein-stein's exchanges with one member of the audience (a 1904 gradu-ate of the University of Zurich) threw the status of the theory intorelief:

Dr. [Rudolf! Lamme]: Is the world picture resultillg from the con-ccptions of the relativity principle an inevitable one, or arc theassumptions arbitrary and expedient but not necessary?

Prof. Einstein: The principle of relativity is a principle that nar-rows the possibilities; it is not a model, just as the second law ofthermodynamics is not a model.

Dr. Lammel: The question is whether the principle is inevitableand necessary or merely expedient.

Prof. Einstein: The principle is logically not lleeessary: it wouldbe necessary only if it would be made such by experience. Butit is made only probable by experience.

For Poincare, too, principles were made probable by experience,hut principles were precisely what was expedient; they could beheld against the grain of experience only at the cost of immenseinconvenience. "Principles," Poincare had famously written in Sci-ence and Hypothesis, "are conventions and definitions in disguise."For Einstein, principles were more than definitions, they were pil-

E instei )1'S Clocks

[ars, supports of the structure of knowledge. And this despite the cir-cumstance that our knowledge of principles could never be certain;our hold on them was necessarily provisional, only probable, ncver

forced by logic or expericnce.For Ernst Meissner, then a Privatdo:r.ent at ETH in physics and

mathematics, Einstein's work on time presented a model for a vastand critical reassessment of every concept of physics. Each oncwould have to be intcrrogated to idcntify those that remain invari-

ani when one switches frames of reference:

Meissner: The discussion has shown what is the first thing to bedone. All physical concepts will have to be revised.

Einstein: The main th ing now is to set up the most exact experi-ments possible in order to test the foundation. 111 the meantime,all this brooding is not going to take us far. ()llly those cousc-quenccs can be of interest that lead to results that are, in

principle, accessible to obscrvaliou.Meissner: You have brooded over this, and discovered the mag-

nificcul ln nc concept. You found that it is not iudcpcudcut,This must be investigated for other concepts as well. YOIIhaveshown tliatmass depends on the encrgy content, and YOllhavemade the concept of mass more precise. You did not carry outany physical investigations in the laboratory-you were brood-

ing iustcac]."

Ah yes, EiIlstein replied. But think of the fille predicament ill which

that brooding about time has put us.Einstein's revision of time sei:r.ed the attention of some of his

most illustrious contemporaries. Max von Laue declared in his1911 text on the relativity principle that it was the "grounclbreakingwork" of Einstein that had, with the single stroke of his radical cri-tique of time, solved the puzzle of Lorentz's real but undetectableether." Max Planck, the dean of German physics (who had intro-

,:t!il''''

EINSTEIN'S CLOCKS, POINCARr.;'S MAPS

duced the quantum discontinuity into physics), went further. Speak-ing in 1909 at Columbia University in New York, he told the assem-bled: "It need scarcely be emphasized that this new view of theconcept of time makes the most serious demands upon the capac-ity of abstraction and the imaginative power of the physicist. Itsurpasses in boldness everything achieved so far in speculative invcs-tigatioJ]s of nature, and even in philosophical theories of knowl-edge: non-Euclidean geometry is child's play in comparison.'?"Planck's words lofted J':instein's reputation, hroadcasting Einstein'sown sense that time was the pivot point of his work. The relativityof simultaneity, Eillstein remarked soon afterward, "signifies a fun-(hncntal eklllge in om concept of time. IItl is the most important,a11(1also the most controversial theorem of the new theory ofrclativity.?"

J':1llil Colin, who had been thinking about light-coordinatcdclocks at-least as early as 1004, returned to the question ill 101") illa brief, popular hook (The Physico/ !\s/Jed of Space ani! Time) toconhout simultaneity ill a \!Joroughly I<insteilliall way (he referredto the "I ,orentz-FinsteinRelativity Principle," 110mention of Poill-care). Inell1dillg a photograph of a wire and wood mode] of clockcoordination, Collll drew dozens of clocks and rulers to emphasizeal each step of his arglll1lellt that the j':illsteiniall kinematics wasphysical, procedural, and altogether visualizablc in terms of coor-dinatcd public clocks: 'The synchronization of a Strasbourg and aKchl clock (that have been previously checked to run at similarrates) can and ought to he set ill this way: Strasbourg sends at timeo alight signal to Kchl, which is reflected; it gets hack to Strashourgat time 2. The clock ill Kchl then is correctly set if, at the moment-that the signal arrives there, its clock shows time 1 (and if not itshould be corrected to do so)." Einskin liked Cohn's presentationand said so in print."

Not for a moment did Einstein himself stop "brooding" abouttime; in 1913 he too published a new and strikingly simple argu-

Einstein's Cloe/,s 27\

ment for the relativity of time. Imagine, hc said, that two parallelmirrors make lip a "clock" where each tick is defined by the traver-sal of a burst oflight from one mirror to the other (figure 5.12a).Now suppose that this light clock is moving to the right (fignre5.12h). 'Io the stationary observer, the up-and-down motion of theflash oflight appears to make a sawtooth pattern, milch the way theball of a running basketball player would follow such a trajectory asseen hy the spectators. Here's the point: the inclined trajectory ofthe moving clock (as seen by the stationary observer) is obviouslylonger than the perpendicular trajectory of the rest observer's ownclock. But hy .issm nption the speed of light is the same ill everyframe of reference. so the ~lJlglil1g trajectory of light travels ,.11 c.(This is no/true for the basketball case, since the spectators wOllldsee the incline motion of the hall to he faster than the simple up-and-down motion seen by the playcr.) Siuc« light has further totravel alollg the incline than it docs alollg the pcrpcudicujnr. it takeslonger (D is greater than II). It follows that one tick for the movingobserver (wh icli appcars to the stat-ionary observer as fol1o\villg anincline) is rcgistered as taking more than one click for the station-

ary one (which goes straight up and down).'"So as far <IS the stationary frame is concerned, evcrything tlwt

takes place in the moving frame runs slowly. Ilowcvcr Einstein pre-seutcd his theory, the core lesson was t-he same: Absolute time wasfinished. In its place he offered <I simple, praetiC<ll proeeclnrc: Syn-chronizc clocks hy the exehangc oflighL l<verything else in the the-ory followed [rom it alongside the fundamcutal assumptions of

relativity and the absolute speed of light.

Radio Eiffel

When ccnter-issued electromagnetic signals arrived .tt distantpoints, whether ill the next room or a hundred kilometers distant,it was not only Einstein and Poincare who defined them as simul-


(a) (b)Mirror

17

Mirror

Figure '>.12 EiJ1steiJ1',~ Light Clocl: (1913). (a) ln ilu« SilllfJles/oral! expla-IW[iOI1Sof the dilaiu»: of lime, Einstein imagined two /J(/follelll7irrors with afJlllse of light reflectillg between them, each traversal ccmstitulins; a "lid." Ira clock like this [lew hy (Ill observer "at rest," the observer at rest woulel see thepul»: ftJIlowillg a sawtooth pattern. (b) /';ocll a11g1ed traversed would/i)l/ow aIOllger (diago/1al) f)(fth ilun, ill the straight ub-und-down {iai]: o( a similarclocl: ill the rest [rame. Since light travels at. the S({lIIe sf)eed ill every [tame o(reference, l<il1steill concluded thai a tick i11 the mirror [nnue woulel he inca-»un«! as tahllg IO/1ger tho II a tiel: ill the restl/mlle. There/lne, the rest observe:must conclude, lime rum slow ill the movillg [rain« o(re(erellce.

t.mcous. Not at all. On the basis of the exchange of electrical sig-nals, railroad planners schcdulccltrains, generals roused troops,operators telegraphed business deals, and geodesists drew maps.Indeed, precisely during Einstein's early patent office years, prepa-rations were being made to send time coordination signals by radiowaves-the American Navy began experimenting with low-poweredtime signals from New Jersey in September 1<)03, with the ordercoming down to broadcast from Cape Cod (Massachusetts) andNorfolk (Virginia) in August 1904. Nor was radio time just a matterfor the Americans. ']'here was an intense burst of activity surround-ing radio coordination systems in 1904 both in Switzerland and illFrance as workers tested, developed, and began deploying newradio time systems. 'The clirector of the French journal La Naturehimself took up h is pen to record new developments in the distrib-

Einstein's Clocks

ution of time by wireless. Reporting on experiments conducted atthe Paris Observatory, he noted that with the aid of a chronograph,distant synchronization now appeared possible to within two- orthree-hundredths of a second. Wireless technologies promised todistribute time everywhere in Paris and its suburbs, supplanting notonly the antique steam system but also the cumbersome land linesof telegraphically cornuumicatcd electric time. Radio time hadadvanced science through more precise determinations of longi-tude; now radio would free time from the physical burden of wire.At last, simultaneity could be broadcast to ships at sea and even into"the ordinary household.'?" Patents SOOI1 began arriving in Einstein's

office with schemes for radio time synchronization."Wireless time was all the rage ill those first years of the twentieth

century, and France pushed the new technology harel. Poincareplayed a pivotal role through his popular and technical publicationson radio, but even more powerfully behind the scenes. As he hadso many times before, Poincare crossed hack and forth betweenabstract considerations of the status of electromagnetislll and thepractical exigencies of putting radio technology to immediate use.That continuing engagement with the theory and practice of corn-munication no doubt facilitated his 1<)()2 professorial appointmentat the Ecole Professioncllc Superieure des Postcs et Telegraphes.When, that same year, he contributed all article on wireless teleg-

raphy to the yearbook of the Bureau of Longitude, he began byreviewing Hertz's famous 1888 experiments that first demonstratedthe existence of radio waves. But Poincare immediately plungedhimself into practical matters, asking: How could the new "Hertz-ian light" supplant optical telegraphy by reaching farther and dif-fracting around the curvature of the earth? How could radiopenetrate fog that would block visible light? Could new kinds ofantennae direct and concentrate radio waves? Poincare was as will-ing to attack the details of nickel-silver coatings as he was to reflecton uses of radio to avoid ship collisions in bad weather.

274 EINSTEIN'S CLOCKS, POINCAR{:'S MAPS

Figure 5.13 \Vire/ess Time. III J<)(H-Uc; niuueroux grou(JS were expetinient-

int!,with the wireless transnussian oitinie. The /vncricau Navy was one of thefirst, hut others were /JlIr,willg the same goal. III this figure FOI11u wiclely cir-culatei! [ournal ill France, the transmitter, receiver, and operator were allshown. SOllltt:I<: illt:Olll{]lAN, "1),S'J'IUBliTiON" (,,)o.j.). 1'. 12<).

As we have SCCll, the French had radio worries of a geopoliticalsort aftcr the stillging demonstration of British cable: monitorinr. and

b

cutting capacities during the late 189()s. These were concerns thatPoincare vcry much shared with other members of the Frenchadministrativc elite. Onc French diplomat warned the French

Colonial Union that, as long as Britain maintained its telegraph


cable monopoly, the French simply could put no faith in the con-fidentiality of their State messages. Using a lantern slide, he pro-jected for his concerned listeners a dramatically colored world mapwhere they could see the desperate situation for themselves. Drawnin blue were the handful of short French cables binding NorthAfrica and France and a single long line to the United States."Look, !lOW,at the immense development of the red lines: theyextend everywhere and encircle the entire world in a veritable spi-der's web. These red lines mark the network of the English tele-graphic companies"? Given the instabilities marked by anticolonialuprisings and conflicts threatening the peace between France andBritain, the situation was dire. In this charged atmosphere it is nosurprise that for Poincare security was a key feature of the new wire-less: "Optical and Hertzian telegraphy have a common advantageover ordinary telegraphy: in times of war, the enemy cannot inter-rupt communication." But while the enemy would have to be in theproper position to intercept a light signal, broadcast signals couldbe captured much more widely, even interfered with by the couu-terbroaclcasting of noise. "We remember that Edison threatened hisEuropean competitors, that he would disturb their experiments ifthey wanted to experiment in America." Back and forth Poincareoscillated between the pure and the practical, like the spark in aradiotransmitter: primary and secondary circuits were his subjects,but so was the security of French diplomatic communication."

III a search for ever-higher sites on which to post antennae, boost-ers of the nascent French radio service had already begun to eye theEiffel Tower, the fate of which remained very much undecided in1903. Eleuthere Mascart wrote Poincare from the Bureau of Mete-oralogy with a plea for help in getting the Minister of War to savethe tower (and therefore the station) from being dismantled. Thegreat tower was, he argued, a military asset, not only for' opticaltelegraphy but also for the nascent wireless experiments that hadalready begun, Surely Poincare would have the ear of the Minister


of War - would he try to save the tower on grounds of nationaldefense? Meanwhile, Gustave-Auguste Ferrie, Poly technician, engi-ncer, and army captain, joined forces with Gustave Eiffel; in 1904they succeeded in getting Eiffel's tower designated a station of theFrench radio service. Clinching their success was the army's much-publicized triumph with radio when, in 1907, Ferrie trundled radioequipment into battle on horse-drawn carts so that French forcesfighting Moroccan rebels could communicate with their comman-ders in France."

Given his position in the Bureau of Longitude, in the scientificconununity, and by then more broadly within the French intellec-tual elite, Poincare's radio-time ambitions for the tower carriedweight. I,argely at his behest, in May 1908 the Bureau urgcd theestablishment of a radio time signal frorn the Eiffel Tower thatcould be used to determine longitude anywhere the signal could bereceived. Backing from the army came easily. In tlie winter of 1908,the French govemment launched all intcrmiuistcrial commissionto control the new radio technology, appointing Poincare at itshead. The Minister of War concurred, releasing the funds. Wirelesssimultaneity had become a military, as well as a civilian, priority."

With Poincare presiding, thc seventh meeting of the commissionassembled on 8 March 1909. The director ofthe Paris Observatorywas there; so was (the newly promoted) Major Ferric, as well asengineers from various ministries including the Navy. Explainingthe situation to the assembled, Ferrie divided time signals into twoclasses. A first, rough signal, accurate to about a half-second, couldbe used by navigators at sea. Such navigation pulses could be initi-ated by using signals sent by wire from the observatory. Then therewere the "special" signals for high-accuracy geodesy. These wouldneed to be crafted more carefully to achieve a precision of one-hundredth of a second."

If you were a radio operator in one of the colonies straining foryour precise longitudinal relation to Paris, here's what you would

Einstein's Clocks

do once you had tuned in Paris. Eiffel Tower station would broad-cast a signal once every 1.01 seconds; you would listen for thebroadcast pulses beginning before midnight, Paris time. At the sametime, you would set your local clock beating a short, crisp tone onceevery second on the second (local time). By convention you knewthat the pips would begin from the Eiffel Tower at midnight Paristime, and so occur at a Paris time of 12:00:00.00, 12:00:01.01,12:00:02.02, and so on. By counting the number of Eiffel Towerpips before thc Eiffcl and local beeps coincided, you could syn-chronize the clocks. For example, if your local whole-second tonefirst coincided with the Eiffel tones on the tenth Eiffel [one, thcnyou would know that at the Eiffel tower it was midnight plus tenpips (12:00: 10.10 seconds). You know the local time of the coinci-dental beat simply by checking your own clock. So you would sub-tract Eiffcl Tower time (12:00:1 0.10 seconds) from your local timeto get the longitude difference between your radio station and thatgreat symbol of Parisian modernity. By March 1909, Poincare'scommission had a plan for sending precision time signals by

wireless.The next month, Poincare traveled to Cottingen to deliver a

series of lectures on pure and applied mathematics. For the first fiveof these presentations, Poincare presented his technical work inGerman. But at the last mecting he explained to the assembled thatthis time, without the crutch of equations, he would return to hisnative tongue. The subject was the "new mechanics." Lookingaround, he told those gathered that the seemingly imperishablemonument of Newtonian mechanics was, if not yet quite flattened,powerfully shaken. "It has been submitted to the attacks of the greatdestroyers: you have one among you, M. Max Abraham, another isthe Duteh physicist M. Lorentz. I want to speak to you ... of theruins of that ancient edifice and the new builcling that one wants toraise in their place." Poincare then asked, "What role does the prin-ciple of relativity play in the new mechanics?" He continued, "We

EINSTEIN'S CLOCKS, POINCARJ::'S MAPS

are first led to talk about apparent time, a very ingenious inventionof the physicist Lorentz." Picture, he urged his audience, "rneticu-lous observers such as hardly exist. They demand a elock setting ofan extraordinary exactitude; to be [accurate to] not one second, buta billionth of a sccond. How could they do it? From Paris to Berlin,A sends a telegraphic signal, with a wireless if you want, to he alto-gether modern. 13 notes the moment of reception, and that wouldhe, for the two chronometers, the [zero] point of time. But the sig-nal takes a certain time to go from Paris to Berlin, it can only gowith the speed of light; B's watch will therefore be slow; 13 is toointcl] igellt 10 not have real ized this; he will take care of this draw-back." Observers A and B solve the problem the way any twoBureau of Longituclc telegraphers wOllld- by crossing signals. Asends a time signal to B, and B to ;\,.,'11 It is just the way the bureau

has been doil1g business for deeacles-sending signals back andforth by cable between Paris and Brazil, Senegal, Algeria, America.Or, for that matter, as Poincare would SOOI1help make possible, hyway of wireless between the "altogether modem" Eiffcl 'Iower andBerlin.

At 2:iO P.M. 011 Saturday, 26 [uuc 1909, Poincare and his COIll-mission gathered at the I':iffcl 'Iowcr to inspect the experimental sta-tion. Ship's Captain Colin described and explained the apparatus,sUl1lming up the latest work in radio-telegraphic inventions andpointing out and distrihllting a report from thc American Navy onits recent radio synchronization of their ships' clocks. 'I'hcu camehis sUlllmary of the ever-accelerating range of the tower itself: overthe last days Colin's lTOOpShad successfully received signals in Ville-juif, 8 kilometers from the tower; in Mchun, 48 kilometers away; onup through a rnid-Iunc triumph when engineers captured a trans-mission 166 kilometers from the Champ de Mars. Even greaterrange seemed possible. Shipboard experiments had been success-fully in operation since 9 June. "The commission, immediately onending the explanations of Monsieur Colin, set the apparatus in


operation." Ammeter, wavemeter, and receiver at the ready, Poiu-care's commission elatedly witnessed a flawless (pure and stable)broadcast of time. Poincare pressed the Chamber of Deputies forcommercia! radiotelephone services and for immediate funding tomake the E iffd Tower into the grea test time synchronizer ill theworld. Approval came on 17 July 1909.')i

Exactly one week later, on 24 July, Poincare put the finishingtouches on his opening speech for the French Association for theAdvancement of Science in Lille. In early August, when he enteredthe town's Grand Theatre to deliver that address (modified from theone he had given in Cottingen) and receive the Grande Medailled'Or, he found the city's elite gathered to hear him speak on thenew physics. Again he underlined the importance of the relativityprinciple, the centrality of Lorentz's "ingenious" local time, and thenecessity of telegraphic time coordination making use of the "alto-aether modern" wireless. Poincare then introduced, as he hadb

before, "another hypothesis" (that is, one beyond the hypothesis ofthe principle of relativity and the hypothesis of "apparent time").This third supposition was Lorentz's contraction: an idea "more sur-prising, milch marc difficult to accept, which disturbs greatly omcurrent habits." An object in motion through the ether underwenta contraction along its line of motion. As ,I result of its orbit aroundthe sun, the earth's sphere would be compressed in the direction ofits motion hy about 1/200,000,000 of its diameter. Nonetheless,Poincare emphasized, that ill the moving observer's frame of refer-ence, the slowing of "local time" and the shortening of "apparentlength" so precisely compensated for each other that there wouldhe no way for the moving observer to discover that he was, in fact,

moving."Poincare's is a description of the world that resembles Einstein's

in what the moving observer sees, yet cliffers in how that circum-stance is explained. Here, in August 1909, Poincare maintained his(ever-less physical) ether, whereas Einstein polemicized at every

-- ------- -_. --..c= __~ .. -"'~""";:=.~~_~_:;:;;;;~_."~~o=,.~-=---;:=-="-"",,;;;;,_-;::;:::_~._,,, .. _. , .. _"_._

----------------


turn against what he considered an antiquated and redundantentity. Poincare introduced the Lorentz contraction as a separatehypothesis, Einstein derived it from his definition of time. Poincareguarded Lorentz's venerable "local time" and "apparent lengths"though his and Lorentz's uses of the terms were not identical: Poin-care treated apparent lengths and times as observable, Lorentz con-tinned to treat them as fictiona1. For Einstein there was simply "atime for a particular frame of reference," the time of one frame was

"t -" u I" I . fas rue or rea ashe tune 0 another. No fictions. No ether.Nothing to he "explained" about the inability of an observer todetect his or her constant motion. No daylight between "true" and"apparent." As for what could be seen: for years Poincare had beenas clear as l<instein-for any constantly moving observer all thephenomena are "well ill accord with the principle of relativity."?'

From 1908 to 1910, Poincare's engagement with electromagneticsimultaneity crossed and recrossed between relativity and the still-new radio tcchnology. Aftcr rccovering from a surge of Seine floodwaters into their radio headquarters, the French Army's time teamat the l<:iffel Tower hegan broadcasting simultaueity on 23 May1910, its distinctive tones available to be plucked out of the ether(so to speak) from Canada to Senegal% At first the signals followedParis time; only the next year, on 9 March 1911, did France agrceto reset its (and Algeria's) clocks by the 9 minutes and 21 secondsthat riveted them to Greenwich. Charles Lallemaud, who hadfought alongside Poincare in the various time and longitude cam-paigns (Quito, decimal time, time zones), saw the opportunity toput time unification into practice. Clocks, radios, and map making

at last converged.Even before the Eiffel 'Iower station opened for business, the

French longitude men had begun radio-correcting their maps, start-ing with Montsouris, Brest, and Bizerte, drawing up plans for useby military telegraphy and planning radio time-coordination to mapFrench colonies. Soon they formed a collaboration with their Arner-

Einstein's Clocks

ican counterparts to exchange signals between the Eiffel Tower andthe Arlington, Virginia, transmitter with sufficient precision to cor-rect for the signal's transoceanic time-of-flight. It was a full-dressrealization of the light-signal synchronization that Poincare had

.itten first into his metaphysics of simultaneity and then into hisphysics of local time. Popular journals took notice: "Although radiosignals travel through space at approximately the velocity of light,there is a slight hut appreciable loss of time ... in starting such asignal on its journey ... and in receiving it at the other end." Whenthe Americans formulated experimental protocols in 1912, they dis-covered that the French had already solved the problem, using thecoincidence method Poincare's commission had advanced severalyears earlier. "Here,' one American reporter wrote, "was a beauti-ful solution.'?" Wircless had made world-synchronization possible:in all directions, over vast distances, with an esscntially limitless pre-cision. Lallcmand and his longitudc allies hoped to coordinate Pariswith other transmitters supplied with time signals by an aristocraticconsortium of observatories that would "avoid all appearances of anational time." Ministers, observatory directors, and longitudeauthorities agreed: the French ideal would achieve a rational, coor-dinated, international systcm with France clearly, if unautocrati-cally, at the helm.'!" Once again, the triumph would be of aconvention in all its senses, building on the long series of interna-tional conferences and agrecments establishing the meter, ohm,prime meridian, and the abortive attempt to create rational univer-

sality from the decimalized second.While French scientists wired the Eiffel Tower to align clock

hands across Europe, the British kcpt silent, refusing to build a timetransmitter of their own. According to one historian of Creenwich,the Imperial telegraphers and astronomers saw the French andother foreign radio-time services as useful in times of peace (theBritish quickly installed receivers at Greenwich). In war, they reck-oned, no one would broadcast time. iii I Such a calculated, pragmatic

2~l2 EINSTEIN'S CLOCKS, POINCARE'S MAPS

stance was certainly consistent with the way the British built andcontrolled their international cable network. For his part, Poincarehad hardly been alone in his patriotic concerns about radio secrecy.I-Ie had emphasized the point in his very first article on radio tech-nology in 1902, and throughout the interrninisterial meetings heoversaw, the delicacy of "secret correspondence" was a subjectreturned to often as the commission prepared for the 1912 interna-tional conferences OJ1 time and radiotelegraphy. Repeatedly theFrench ministerial representatives warned that German and Britishradio transmitters had outflanked and outclassed the French in colo-nial Africa.!" Powering \1p the 1<iffel'lbwer as the beacon of worldtime (and zero point of conununication with the French Empirc)was therefore an effort at once practical and symbolic, military andcivilian, nationalist and iutcruationalist. Fourteenth-century villagershad mounted clocks on hell towers to reign over all who could hearthem, Poincare rang the I':iffcl'[()wer radio-clock through the etherto echo French scicn tific authori ty across the world.

But whether by telegraph line or by wireless, centered systemswere the tcmporal-physica] glory of Europe's Great Powers. It wasthe unified Genllall empire that von Moltkc wanted, made corpo-ral through the grand Prinulre Noimaluhr at the Schlesischer Bahn-110fin Berlin or the baroque and elegant liotloge-mere of Neuchatcl.lt was [':iHel's engineered modernity tumcd high-tech radio time-post; it was Britain's cable network sliding its copper tentacles fromCrccnwich around its cross-continental colonies. It was the Amer-ican Navy's powerful radio transmitter directing ships on the highseas and fixing the positions of the Americas' land stations, at theheight of big-stick diplomacy.

The widening gyre of technological, symbolic, and abstractphysics spiraled outward. Telegraphers, geodesists, and astronomersunderstood the Poincare-Einstein clock coordination by means ofquite literal, everyday wired (and wireless) clock coordination. Atthe Ecole Superieure des Postes et Telegraphes, where Poincare

I'; inst ei 11's Clocks

POSTE DlsmIHUTLUI( 1lF. SI(;N/'.UX IIOI{i\IRES 1l1\II.L1E I.EROY

Figure S.H J':iffel Station Schematic. Mililury rculic: saved the j';i!Te!'ji)].ver,although Poincare's eIF)r!.';to use it as a V(/S{ antenna in a time-transmissionsystem eventuallv produced a [acilit» availab!« to both civilians and the armedforces. This figure deoics» the mosier cloc/.: (ill the Paris O/JServ(f/()I}) and itslini» to the 'jiJ1.ver'sradio trausmitter. SOllRCI':: I,. 1,lmO) , "I :111':lll(l':" (N.ll.), PI'. 14-15.

had taught since 1902, the telegraphic and wireless networks werenever only metaphorical. 'I 'hey were the company business. On 19November 1921, physicist 1-C<)]1 Bloch explained the meaning oftime in a major lecture on relativity theory, using a technology thathis audience of students and faculty knew likc the backs of their

hands:

What do we call time on the surface ofthe earth? 'l akc a clock thatgives astronomical time - the mother pendulum of the Observa-tory of Paris-and transmit that time by wireless to distant sites. III

EINSTEIN'S CLOCKS, POiNCARf:'s MAPS

Figure 5.15 ";ilfel Radio Time (circa l<JOEl).The /';iflel '11)]verradio ntatuniwas located ill these lIIl/Jre/)ossessinf', sliack» ell the ji)()! olthe structure. SClIIRCI<:

/lOIILANClm A:'W ]'lm]([I::, 1 ,1'f'1';U:;CI{,I/'1 III,; S,INS 1,'1/,/<'1' I FS ()NI JI';S 1<1FCIW<j1 ws (1<)O()), [',42<).

what docs this trauxuiixsiou consist? It consists of llOtillg at the two

slutions that uccc] synchronizaliou, the passage of a COlIlll10Il lumi-

nons or hcrtziau signal.11I1

By tho time of Bloch's lecture, clock coordination hy exchange ofclcctromagnctie W,lVCS was a fJrClctical routine. For a full decadePost and Telegraphs, the Bureau of Longitudc, and the FrenchArmy had been routinely corrccting for signal time in their myriadof long-distance synchronizations. 1111 Einstein and Poincare's timecoordination was horn in a world of machines and it clearly wasreceived that way, not just in France. In Germany it was the

Einstein's Clods

cxperimenter-turned-theorist Cohn who had seized light-signal syn-chronization shortly after Poincare and lost little time after Ein-stein's 1905 paper in using pictures of clocks and models topublicize the new simultaneity. In Cambridge, England, it was theexpcrimentcrs (not the more mathematical theorists) who firstseized on the procedures of clock coordination. For American the-oretical physicist John Wheeler, the identification of theory withmechanisms and devices tracked across the whole of his career,from early radio and explosives through his apprenticeship to engi-neers and engineering physicists during World War II. When heand I,:dwin Taylor wrote their widely used text Sbacetime Physics in196), they too invoked a universal machine and displayed it at the

beginning oftheir hook (see figure 5.16).Machines tied clocks and maps ever closer together. At the

beginning of World War II, MIT scientists used improvements inliming to develop the Long Range Aid to Navigation (1,0RAN) sys-tcm that guided Allied ships across the Pacific. Postwar projects bythe American Navy and Air Force tumbled out one after thc otherunder such names as "Transit" and "Project 621B." As the ColdWar intensified, the American military demanded ever more prc-cise locating systems to aim intercontinental ballistic missiles fromshifting platforms and to guide soldiers through the unmarked JUIl-

glcs of south cast Asia.During the 1960s, American defense planners turned satellites

into radio stations that would beam timed signals to earth. Moreaccurate and stable timepieces drove these orbiting transmitters,pinging time at first from quartz crystals and later from the cesiumoscillations of space-based atomic clocks. By the time the $10 bil-lion Global Positioning Satellite (GPS) system was up and func-tioning in the 1990s, its twenty-four satellite-based clocks tickedwith a precision about which Poincare only fantasized in his Cot-tingcn or Lille lectures of 1909: 50 billionths of a second per dayproviding a resolution 011 the earth's surface of fifty feet. In a certain

------~

Einstein's Clocks

satellites would be needed to fix the receiver's position in three-dimensional space, but since the mobile ground receiver wouldnormally not have the correct time, a fourth satellite (to set thetime) was required.

In a trading zone of engineering-philosophy-physics, relativityhad become a technology, one that swiftly displaced traditionalsurveying tools. In fact, by processing the data after the fact andusing GPS measurements of a known position to pinpoint tran-

"'igllre ').16 Lattice ofS/llIce and Time. lo«! ill II/(III.Y discussiollS or tela-I il'il)' arc I ltc ntach! nelil« procedures fly wit ich lillie a lid space coordi nates WCfC

10 he II/(f/J/Jed. These are enuneutlv visible ill t/lis jilllcijiti ntaclune dejJided ill

lh« relutivit» Ic:xlhoof.; hy /';dll'ill '/(Iyfof cnu! Johll Wheeler. SOlIt(CI'::' I;\YI,()I( ,INIl

\\'111':1':1.1-:1\.Sf:\( ;)';fHlld'fll'SI<;S (H/'('), 1'. Il).

sense, the system resembled Eiffcl 'Iowcr time: CPS also used ~Ikind of coincidence method to synchronize clocks, But HOW the

saldl ires broadcast a slri1lg of pseudo-random numbers (thaI is 10

say r.mdoiu ellollgh for these purposes) -six thousand billion dig-its, The receiver thcu matched this string ,Igainsl its own, idcnticul,iutcrually stored set. By determining the offsct between the Iwoseries, the logic circuits of the receiver could determine the timedifference, and knowing the speed of light, the receiver's distanceto the sate II itc. If the receiver was already synchronized, only three

• 24 satellites • Repeating ground tracks (23 hours, 56 minutes)• 550 inclination • 5 satellites always in view

Figure).17 Global Positioning System. Not unlike Poincare's time-transmitting Eiffel ']()wer, the late-twentieth-century GPS satellites providedprecision timing (and therefore positioning) for both civilian and militaryusers, Built into this orbiting machine were software and hardware adjustmentsrequired by Einstein's theories of relativity, The result is a planet-encompassing,$10 billion theory-machine. SOURCE; RAND CORPORATION, RAND MR614-A.2 .

. --_ .. - - .._-=. ~~~--~~--.;,e~ _

nIII!I,


sient errors in the system, early twenty-first-century surveyorscould use the GPS to determine a second, unknown locationwithin millimeters. So accurate had the system become that even"fixed" parts of the earth's landmass revealed themselves to be inmotion, an unending shuffle of continents drifting over the sur-face of the planet on backs of tectonic plates. In place of "absolutecontinents," earth scientists demanded a new universal coordinatesystcm, one unattached to any particular surface feature butinstead rotating, in the imaginative eye of science, in silent coor-dination with the interior of the planet. GPS was soon landing air-planes, guiding missiles, tracking elephants, and advising drivers

ill family cars.For all these purposes relativistic time coordination was deep in

the machine. According to relativity, satellites that were orhiting theearth at 12,500 miles per hour rail their clocks slow (relative to theearth) by 7 millionths of a second per day. Even genera] rclativi ty(Einstein's theory of gravity) had to be programllled into the system.I'~leven thousand miles in space, where the satellites orbited, geIl-cral relativity predicted that the weaker gravitatioual field wouldleave the satellite clocks running fast (relative to the earth's surface)by 45 millionths of a second per day.11I1'l()gcther, these two corrcc-

tions add up to a staggering correction of "38millionths (that is,38,O()Obillionths) of a second per day in a GPS system that had tobe accurate to within 50 bill ionths of a second each clay. Before thefi rst cesium atomic clock launch in June 1977, some CPS engi-neers were sufficiently dubious about these enormous relativisticeffects to insist that the satellite's atomic clock broadcast its time"raw." Its relativity-correction mechanism idled onboard. Downcame the signal, running fast over the first twenty-four hours almostprecisely by the predicted "38,000 billionths of a second. After twentydays of such gains, ground control commanded the frequency syn-thesizer to activate, correcting the broadcast time signal. 111(,Without

that relativistic correction, it would have taken less than two min-

Einstein's Clods

utes for the GPS system to exceed its allowable error. After a singleday, satellites would have been raining erroneous positions, skewedby some six miles, onto the earth. Cars, bombs, planes, and shipswould have veered wildly off course. Relativity-or rather relativi-ties (special and general)-had joined an apparatus laying an invis-ible grid over the planet. Theory had become machine.

Imitating historic precedents, symbolic and physical protestsagainst globalized, instrumentalized time were not far behind. Inthis case one group of protesters explicitly wanted to object con-cretely to the use ofGPS in precision weapons, counterinsurgencywarfare, police actions, and nuelear war planning. In the predawnhours of 10 May 1992, two activists from Santa Cruz, California,disguised themselves as Rockwell International workers and brokeinto the clean room at Seal Beach, California, where the companywas readying NAVSTl\R GPS satellites for the air force. Slammingan axe into one completed satellite sixty times, they caused nearly$"3million worth of damage. As they approached a second satellite,Rockwell security personnel seized them at gunpoint and turnedthem over to the police. Dubbing themselves the Harriet Tub-mall-Sarah Connor Brigade (linking the heroine of the under-ground railroad to the heroine of "Terminator 2: Judgment Day"),the two militants pleaded guilty and served about two years in jail.!"In 1996, the FBI reported that the Una bomber, known for hiseighteen-year bombing campaign against scientific figures, mod-eled himself on another temporal anarchist in Joseph Conrad'sSecret Agent, which he had read a dozen times. ins Around the axis

of global time, fictional, scientific, and high-tech time machines(and their opponents) crossed and recrossed.

Beating overhead in church spires, observatories, and satellites,synchronized clocks have never stood far from the political orcler-not in the 1890s, not in the 1990s. Poincare's and Einstein's uni-versal time machines linked technology, philosophy, politics, andphysics. Or perhaps we should put it differently: these synchroniz-


ing time machines never functioned entirely in the arcane abstractor in the mutely material. The coordination of time is inevitablyabstract-concrete.

TURN-OF-THE-CENTURY Europe and North America were criss-crossed with lines of coordination: webs of train tracks, telegraphlincs, metcorological networks, and longitude surveys all under thewatchful, increasingly universal clock system. In this context, theclock coordination system introduced by Poincare and Einstein wasa world machine: a vast, at first only imagined, network of synchro-nized clocks that by the turn of the next century liad metamor-phosccl from networks of submarine cables hauled by schooners toa microwave grid broadcast from satellites. 'I'hcrc is a sense in whichl<:instein's special thcory of relativity has always been a machine, allimaginative one to be sure, but one suspended ill a constantly evolv-ing real skein of wires and pulses that synchronized time by theexchange of cleetromagnetie signals.

Such a technological reading of this most theoretical develop-ment suggests one final observation. It has long struck scholars thatthe stylc of Einstein's "On the Electrodynamics of Moving Bodies"docs not even look like an ordinary physics paper. There arc essen-tially no footnotes to other authors, very fcw equations, no mentionof new experimental results, and a lot of banter about simple phys-ical processes that secm far removed from the frontiers of science. Ill'!

By contrast, pick up a typical issue of the Annalen der Physik and avery differcnt form appears in nearly every article, characterized bythe standard point of departure: an experimental problem or a cal-culational corrcction. Typical physics articles were and are filledwith references to other papers; Einstein's article does not fit thismold. It could be that Einstein's youthful arrogance had simplytaken over, perhaps he had dispensed with the niceties of footnotes,altered the form of the usual introduction, and redesigned the typ-

Einstein's Clocks

ical conclusion as an idiosyncratic matter of individual taste. Cer-tainly self-confidence is what Albert Einstein lacked least.

But read Einstein's contribution through the eyes of the patentworld and suddenly the paper looks far less idiosyncratic, at least instyle. Patents are precisely characterized by their refusal to lodgethemselves among other patents by means of footnotes. If you aimto demonstrate the utter originality of your new machine (and uponoriginality hinges the patent), you can hardly do worse than showerthe inspector with a storm of footnotes to prior work. In the fifty orso Swiss electric clock patents granted in the years around 1905, forexample (thcy arc typical), there is not a single footnote either toanother patent or to a scientific or technical article.!'" This com-parison does not prove, of course, why Einstein did not cite othersin that first paper. But it may help make sense of why a youngpatent officer in a hurry may not have felt impelled to situate hiswork ill the matrix of papers by a Lorentz, a Poincare, an Abraham,or a Cohn. Aftcr three years of evaluating hundreds of patents underHaller's rigorous demands for analysis and presentation, the speci-ficities of patent work had become, for Einstein, a way oflife, a formof work, and (as he suggested to Zangger) a precise and austere styleof writing. III

Along the same lines, Einstein's relatively accessible framing ofthe problem of space and time would have come as second natureto a patent examiner. According to Swiss patent law (and not onlySwiss law), thc description of the invention was to be "representablethrough a model, thc unity of the invention defended, the conse-quences of the patent must be unambiguously laid out and lucidlyordered, so the whole is easily understood by properly certified tech-nicians as well as by specialists."!" In all his theoretical papers writ-ten around 1905, Einstein ended with a series of assertions aboutwhat the experimental consequences would he. In the case of therelativity paper, he concluded with the sharp, numbered paragraphsoccasionally used in physics papers but standard in the "claims" see-

·,,,~~~~~~------------------

EINSTEIN'S Cl.OCKS, POINCARE'S MAPS

tion required by Swiss statute to appear at the end of every patent.' "Striki ngly, from 1905 Einstein began describi ng (and occasionallydrawing) devices, not only for his little electrostatic Maschinchenbut also as key components of his theoretical arguments.

Would General Field Marshal vou Moltke have appreciated theirony? Sixteen-year-old Einstein, a young man who had abandonedhis German citizenship chafing at thc "herd mentality" of the mil-itarist Prussiau state, had at age twenty-six, completed the aged offi-cer's project i \l a certain sense.'!' Time had ever more completelybecome identified with timekeeping, and /';inheib;zeit a means tothe tcchnopolitical cstablislnncnt of procedural, distant simultane-ity across the globe. I<imlcin's clock synchronization system, like its

. .

more mundunc predecessors, red need time 10 procedural syn-chronicity, tying clocks logclher hy electromagnetic signals. Indeed,1':illSlciJl's schell ic For clock unity wentmuch farther, extendingbeyond cil y, country, empire, continent, indeed bcvond the world,I'DHIe infinilc, 1l0Wpsellcio-Carlesiall universe as a whole.

l lcrc the irony inverts. l'or while 1<:i1ls1·eill'sclock coordinationprocedure buill 011 decades of intcusc cffort-s toward clcctromag-netic lillie uuific.uiou, he hatl removed the crucial clement of vonMnll kc's visiuu. There was, in 1':illSfein's infinite, imagincd clockmachine, no natioual or regi()II,d Primate Ncmnaluhr, no horloge-mere, 110 master clock. Ilis was a coordinated system of infinitespatiotcmporal extent, and ils infinity was without center-noSchlcsisclier B;lhllhofliuked upward through the Berlin Ohscrva-fury to the heavens and dOWII alollg the rails 10 the edges of empire.By inf nitcly extending a time unity that had originally been eon-ccivcd according to the imperatives of German natioual unity, Ein-stein had both completed and subvertcel the project. He hadopened the "zone of unification," but in the process not onlyremoved Berlin as the Zeitzentium but also designed a machinethatupended the very category of metaphysical centrality.

Absolute time was dead. With time coordination now definecl

Einstein's Clocks

only by the exchange of electromagnetic signals, Einstein could fin-ish his description of the electromagnetic theory of moving bodieswithout spatial or temporal reference to any specially picked-out restframe, whether in the ether or on earth. 0 center remained, noteven the vestigial centrality of the special ether rest frame that Poin-care had retained. Einstein had eonstructecl his abstract relativitymachine out of a material world of synchronized clocks.

Chapter 6

THE PLACE OF TIME

Without Mechanics

y DECEMBER 1907, Patent Officer Einstein was no longeran obscure bureaucrat. Minkowski wrote to request a rela-tivity reprint, congratulating the young scientist on his

success. Wilhelm Wicn debated him on the possibility of faster-than-light signaling. Max Planck and Max Laue joined the youngphysicist in conversation; one of the best experimentalists in Ger-many, Johannes Stark, commissioned an article from him on thcrelativity principle. No longer could Einstein breezily omit the workot hix contemporaries, his cngagelllcnt in the circle of physicists wasnow active, and his footnotes reflected it. Theorists Emil Cohn and11.A. Lorentz joined Einstein's reference list in his 1907 review ofrelativity, as did experimentalists Alfred Buchercr, Walter Kauf-mann, Alber! Michelson, and Edward Will iams Morley. I EinsteinCVC]} addressed Lorentz's "local time" directly, as hc had not in1905. But Poincare's name was nowhere among the thirty-two foot-notes. Einstcin continued to pass over the older scientist in utter andunbroken silence.'

Einstein hegan by assuming that there was no measurable dif-ference between physical processes observed when they were at restand those same physical processes were they conducted in a con-stantly moving boxcar. He took as his starting point what Poincare,Lorentz, and other leading physicists had, earlier in the game, beenworking painstakingly to {JTOve. Poincare and others had asked howelectrons flattened as they moved through an all-pervasive ether,how the electron could remain stahle despite its distortion, how the

The Place of Time

ether reacted as electrified bodies and light passed through it. Butin Einstein's paper, all that the French polymath had done van-ished. Not just the bits on the ether ancl electron structure: absentas well was any reference to Poincare's simplification and correc-tion of the transformations in Lorentz's theory, Poincare's powerfulmathematical advances (inclucling the introduction of the four-dimensional spacetime), Poincare's articulation of a principledphysics, and perhaps most dramatically, Poincare's interpretation ofLorentz's "local time" as a convention of clock coordination exe-cuted hy the exchange of light signals. Not a trace.

From Paris, Poincare echoed back Einstein's silence, Einsteinwas no doubt a young unknown to him in 1905; there is really noneed to explain the absence of any reference to Einstein in Poin-care's 190(j treatise, "On the Dynamics of the Electron." But later,although he and Einstein separately published often on questionsof time, space, and the relativity principle, Poincare's silence con-tinued for seven more years. With Einstein's name on everyone'slips- including Lorentz's, Minkowski's, Laue's, and Planck's-thissurely is not happenstance. To Einstein, Poincare must haveseemed beside the point: another older physicist who in 1905 wasunable to grasp the import of Einstein's banishment of the ether orhis placement of time, without making the true/apparent distinc-tion, at the starting point of the theory. To Poincare, Einstein musthave seemed derivative, perhaps a provider of heuristic argumentsto derive the Lorentz transformations, but one who failed even toaddress fundamental issues of physics: the ether and the structureof the electron,

Yet just as Einstein was in no deep sense derivative, Poincarecould not be dismissed as a mere conservative, On the contraryPoincare proudly hailed the electrodynamics of moving bodies as anew mechanics when he spoke at Cottingen in 1909; even in St.Louis in 1904 he had heralded dramatic changes throughoutphysics. At the same time, Poincare's 1909 presentation at Lille con-

EINS'D:IN'S CLOCKS, POiNCARI~'S MAPS

veyed a certain wistfulness as hc invoked a classical physics whosemarble columns had begun to crack: "If some part of scienceappears solidly established, it would certainly be Newtonianmechanics; we lean Oil it with confidence, and it does not seem thatit could ever be weakened, But scientific theories are like empires,and if Bossuet was here, he would no doubt find eloquent accentsin which to denounce their fragility.'" [acqucs-Bcnigne Bossuet,teacher of the Dauphin, son ofI .ouis XIV, had written for the royalcharge his 1681 Discourse on Universal History. Long central withinthe canon of French litcrature, Bossuct's History occupied a fea-tured place in a 1912 volume that Poincare assembled with col-leagues from the Academic Francaisc. Aimed at educating thepublic in matters both scientific aud litcrary, the volume excerptedjust that part of Bossud's message that cautioned a prideful human-. "S 1Ity: ,0 you see pass iciorc your eyes, as if in an instant, I say notkings and cmperors hul those grand empires that had madc thewhole universe tremhle? Wlicu you see the Assyrians, ancient andmodern, the Meeks, the Persians, the Creeks and the Romansappear before you OJ rc after the other and fall, onc 011 top of theother, so to speak, this terrifying fracas makes you feel that there isnothing solid amollg men and that inconstancy and agitation arcthe propcr fatc of things liuman." For Poincare, scientific theorieswere like Bossuct's grand empires, For decades he had mined the

confrontation alllong empires of time, crossing the conventions thatmoderated the collision with a new philosophy and physics. Yet ashe peered over the two great structures to which he had devoted somuch of his life - the Newtonian empire and the French one-Poincare now saw them through the eyes of a man who had regis-tered the fragility of both.

Einstein and Poincare finally met - for the first and last timc-at the Solvay Confercnce held in Brussels late in 1911. They weretwo scientists infinitely close and yet infinitely distant. Both hadbeen fascinated sinec youth by the problem of the electrodynamics

The Place o(Time

of moving bodies. Both had productively built their theories at thecrossroads of technology, philosophy, and physics. Both understoodthc immense power of Lorentz's work and both underscored thegroup structure of Lorentz's transformations. Both seized upon theprinciple of relativity as a constitutive foundation of physics. Per-haps most dramatically, both insisted that time in moving frameshad to be interpreted by way of clocks synchronized by light-signalexchange. But the distance between the two scientists was as dra-matic as their proximity, Poincare viewed his contributions as a formof world repair, an adjustment, a turning, a rewriting of Lorentzianphysics into a new mechanics that he viewed with exhilaration andtrepidation. For the young Einstein, repair held little appeal. Tear-ing down the old was a bracing pleasure. While Poincare main-tained the ether as crucial ill his 1909 Lillc address, Einstein begana talk of his own at almost exactly the same time with a specific ref-crcucc to a physicist (not Poincare) who had assessed the ether'sexistence to "border Oil certainty." Then Ei nstei u knocked the

author's assertion into the trash.'For many reasons it is not surprising that the encounter between

the fifty-seven year old and the thirty-two year old did not go well.Maurice de Broglie: "I remember one day at Brussels, while Ein-stein was explaining his ideas, Poincare asked him, 'what mechan-ics arc you using in your reasoning?' l<instein answered: 'Nomechanics' which appeared to surprise his interlocutor." "Surprise"is perhaps an understatement. For Poincare, whose conception ofphysics came clown to mechanics, be it old or new, "no mechanics"was an impossiblc response. Abstract mechanics, after all, was whatPoincare had held up to his fellow Polytecbnicians as constitutingthe very essence, the "factory stamp" of that unique training for the

world of Third Republic France.Einstein spoke to his Solvay audience about light quanta and

quantum discontinuities, following which the extraordinarily dis-tinguished audience began to debate. Lorentz was there; so was


Poincare. Einstein initiated the discussion by reminding his listen-ers that the theory of quanta in its present form really wasn't a the-ory at all "in the ordinary sense of the word," but a useful tool.Einstein surely did not see his comments as a detailed mathemati-cal description of the type Poincare would dignify with the term"mechanics." (Einstein had called his account of light quanta a"heuristic" when he had first published it six years earlier.) Rather,Einstein hoped to offer a starting point for a later, more coherenttreatment. In the meantime, he had willingly sacrificed the con-tinuous, causal relations that differential equations captured. Butthat coolness toward the foundation of an intuitive, mathematicallydescribable mechanics was for Poincare no small matter. Summa-rizing the conference from his vantage point, Poincare spoke with-out minced words. Onc hears in his remarks a deeply troubledassessment of where the new physics, and the new physicists, wereIleadillg:

Wlurtt]«: Hew research seems to throw ill to question is 1I0tonly thefundamental principles of mechanics, it is something thatappeared to us till now inseparable Irom the very concept of a nat-mal law. Could we still express these laws ill the form of differen-tial equations?

Besides, what struck me ill the discussions that we just heard, isseeing the same theory sometimes relying on the old mechanicsand sometimes on new hypotheses that negate them, aile must notforget that there isn't a proposition that ouc can't easily prove inso-far as one inserts into the demonstration two contradictorypremises.'

Here is the pent-up frustration of a master of the "old mechanics,"the consternation of someone who had used differential equationsto explore, extend, test, and (against his own intent) upend the sta-bility and visualizability of Newtonian physics. It is the voice of a

The Place of Time

savant who has pushed toward a "new mechanics" ill every way heknew. Similarly, Poincare had significantly advanced the Lorentztheory, "turning it in every direction" as he had said so often. In theprocess, bit by bit, he had grappled for years with changed notionsof mass, length, and most dramatically, time itself. More than any-

one, he insisted both in his mathematics and in his philosophy thatone could switch, according to circumstance, from Euclidian tonon-Euclidean language. Shortly after Solvay, Poincare evenadvanced understanding of the new and unsettling quantum

discontinu ity.In Poincare we face anyone but a change-abhoring conservative.

But he contended that there were better and worse ways of handlinginnovation. The new physics, Poincare was saying, had lost its wayby abandoning, ill its frantic race ahead, the consistent and princi-pled base of any-of all-mechanics. The "honest functions" andthe differcntial equations that vouchsafed causality and intuitionhad been lost. This was not a dispute over which law best fit thephenomena. It was a gulf that, for Poincare, left Einstein and hissupporters Oil the wrong side of "the very concept of natural law."Borrowing Poincare's own earlier phrase, Einstein's quantumphysics seemed less well suited for science than for a teratological

111USeUll1.Einstein's reaction to the Solvay encounter with Poincare was

swift and unflattering. 1\ few weeks after Solvay, he confided hisviews to a friend: "I I. A. Lorentz is a marvel of intelligence and tact.

He is a living work of art! In my opinion he was the most intelligentamong the theoreticians present. Poincare was simply negative ingeneral, and, all his acumen notwithstanding, he showecllittle graspof the situation." There was certainly no meeting of minds betweenthem over the relativity theory. Their split over the quantum

widened the chasm.Yet Poincare returned to Paris from Solvay in 1911 deeply

impressed by Einstein. That November, Einstein, having only


recently moved to Prague, was a candidate for a position at his almamater, the Swiss Federal Institute of Technology. Setting aside anydisquiet at Einstein's disturbing radicality, Poincare intervened inhis favor, assuring physicist Pierre Weiss that Einstein was "one ofthe most original minds I have known." Youth mattered little· the,senior scientist judged Einstein to have "already taken a very hon-orahle rank among the leading scholars of his time. What we mustabove all admire in him, is the facility with which he has adaptedto new conceptions and from which he knows how to draw thc con-sequences. He does not remain attached to classical principles, and,in the presence of a problem of physics, is prompt to envision allthe possibilities. This translates immediately in his mind into theprediction of new phenomena, susceptible of being one clayveri-fied by experiment. I do not want to say that all these predictionswill remain impervious to the judgment of experiment when thatjudgment becomes possible. As he searches in all directions one,must, Oil the contrary, expect that the majority of the paths in whichhe embarks will he dead ends; but one must, at the same time, hopethat one of the directions that he has indicated will be the rizht one:b ,

and that suffices. It is just so that onc must proceed. The rolc ofmathematical physics is to pose questions properly, it is only cxper-imcnt that can resolve them." 'I 'his was ,] letter of the highest praise."The future will show more anelmore the value of Mr. l<:iustein"Poincare concluded, "and the university that finds a way to sceu:cthis yOllng master is assured of drawing from it great honor."

Beyond this statesmanly letter, it is impossible to say preciselywhat effect Poincare's one meeting with Einstein had on the seniorphysicist. Poincare's health was deteriorating, and he may at thistime of enormous productivity also have hac! intimations of his ownmortality. It may also be that Poincare's later reflections upon Ein-stein's jarring new vision of physics a t Solvay prompted the mathe-matician to think further 011the value of the provisional, heuristic,result-oriented efforts that Einstein hac! employed to such effect.

---. -------------

The Place of Time

[ust a few weeks after recommending Einstein to Weiss, on 11Ikcember 1911, Poincare wrote to the founding editor of Circolomntemaiicc of Palermo. Still working on the three-body problemwith which he had launched his career decades earlier, Poincarereported to his correspondent that for two long years he had becnstruggling with the problem without much progress. He now hac! topause, at least temporarily. "It would be fine if I could be sure ofbeing able to take it up again; at my age, I cannot vouch for that,and the results obtained, liable to put researchers on a new andunexplored track, seem to me too full of promises, despite the dis-appointmcnts that they have caused me, for me to resign myself tosacrificing them." At fifty-seven, Poincare was hardly old, but just afew years before, he had needed major prostate surgery. Would theeditor be willing to publish an incomplete work, one that wouldstate the problem and report partial results? (lIe would.) "Whatembarrasses me is that I will be obliged to put in a lot of figures, pre-cisely because I could 110tarrive at a general rule, but I only accu-mulated particular solutions." As Poincare had so often insisted,visual-geomclrical intuition could go where skeletal algebra could

not yet trcad.Poincare judged these particular solutions to his lifelong prob-

lem "useful." They were more than that; the paper contributedfoundational ideas to the cstablishmcnt of topology, a new branchof mathematics. Soon a young American mathematician, GeorgcD. Birkhoff, proved the crucial conjecture that lay at the core ofPoincare's exploration."

Perhaps tacit echoes of Einstein may be audible in the lastspeech Poincare gave on relativity, though the presentation nevermentioned Einstein's name. On 4 May 1912, Poincare spoke on"Space and' rime" to an audience at thc University of London. Inforceful terms, he once again repeated: "The properties of time aretherefore merely those of our clocks just as the properties of spaceare merely those of the measuring instruments."" Over the past


years, the ether had grown ever thinner in Poincare's writings, as itsrole in the theory dwindled. Now, however, the all-pervasive sub-stance simply evaporated into silence. No rejection-but no men-tion of it, either. In his peroration, Poincare let the old mechanical"principle of relativity" fall away, replaced by the "principle of rela-tivity according to Lorentz." Events simultaneous according toclocks coordinated in one frame of reference would not be simul-taneous if measured by clocks coordinated in another.

Does this mean that Poincare had abandoned the ether orbecome a thoroughgoing Einsteinian? No. Having begun his pre-sentation by asking if his earlier conclusions about space and timenow needed to be revised in light of recent developments, hereplied: "Certainly not; we had adopted a convention because itseemed convenient and we had said nothing could constrain us toabandon it." But conventions arc not God-given.

Today some physicists want to adopt a new convention. It is notthat they are constrained to cia so; they consider this new conven-tion more convenient, that is all. And those who arc not of thisopinion can legitimately retain the old one in order not to disturbtheir old habits. Ibelieve, just between lIS, that this is what theyshall do for a long time to come. 12

Poincare's time to come was short. His medical difficulties camemore frequently and more severely. Nonetheless, when asked toaccept the presidency of The French League of Moral Educationand deliver its founding address on 26 June 1912, Poincare charac-teristically accepted. For him, scientific prestige was inextricablyassociated with civic leadership and responsibility. In the midst ofbattles between anticlerical and clerical movements, in the face ofan escalating conflict with the Germans in North Africa, even as thewalls of Paris were plastered with partisan appeals, Poincare soughtprinciples that would undergird a unifying French morality. Against

..~-----~---

The Place of Time

those ready to manipulate hatreds, Poincare saw discipline as theonly defense. Discipline-morality-was all that secured mankindagainst "an abyss of sufferings." "Mankind is ... like an army atwar," an army that must prepare for battle in peacetime, not at the

last, too-late moment of engagement with the enemy. Hatred couldpropel collisions among men, collisions that risked changing theirfaith. "What will happen if the new ideas which they adopt arethose which their former teachers conveyed to them as the verynegation of morality? Can this mental habit be lost in one day? ...Too old to acquire a new education, they shall lose the fruits of theold!?" In morality, in physics, in mathematics, Poincare wanted tobuild dramatic new structures, but he wanted to do so using the oldbricks; he would employ, not discard, the legacy of an illustriouspast.

Poincare underwent surgery again on 9 July 1912, and for a fewdays friends and family hoped for a recovery. It never came; Poin-care died, following an embolism, on 17 July 1912. Dozens ofeloges appeared across the world. Perhaps the most fitting 1ll011l1-

ment was the most anonymous: later that year the Eiffel Towerbegan radiating its precision time signal. Those pulses bathed theworld in an expanding sphere of Hertzian light, fixing simultaneity(and longitude) into Africa and across the Atlantic to North Amer-ica on the basis of techniques that Poincare had introduced into

geodesy, epistemology, and physics.

Two Modernisms

Reflecting back on Henri Poincare in 1954, Prince Louis deBroglie, the physicist who had shown that particles could act likewaves, lamented that the great mathematician had just missed beingthe first to develop the theory of relativity in all its generality, "thusgaining for France the glory of that discovery." "It is impossible tobe closer to the thought of Einstein," de Broglie judged. "And yet

s.

. ~;

EI STEIN'S CLOCKS, POI CAR~:'S MAPS

Poincare did not take the decisive step; he left to Einstein the gloryof grasping all the consequences of the principle of relativity and,in particular, of establishing, by a profound criticism of the measureoflengths and durations, the true physical character of the relationthat the principle of relativity has between space and time. Why didPoincare not come to thc end of his thought? It is no doubt the turn,a little too critical, of his spirit, due perhaps to his education as puremathematician ... ." For dc Broglie, it was Poincare's training as a

mathematician that hadlcd him to see science as no more than theinformed and expeditious choice, on the has is of convenience, ofone theory from among all logically equivalent ones. According tode Broglie, Poincare failed to tread the better path Jaid down by thephysicist's intuition.' By dc Broglie's lights, Poincare was too iuucha mathematician, too indifferent to the real world to have fOrJJHI-

latd relativity as Einstcin did.My view? De Broglie's diagnosis is far too Il<lITOW. ] would argue

that Poincare did come to the "end of his thol1ght," to an image ofknowledge- including his view of mathcmalica] knowledge-thatcarried with it a ninctccnth-ccutury optimism, a 'I'hird RcpuhlicPoly technician's eng'lged, hopeful vision of a calculable, improv-able, rational world. If anything, Poincare paid too much attentionto the real world: when he jlldgcd ill lSt)S-t)t) that the corrections

to Newtonian time were ill principle necessary but too small to mat-ter, it W~IS beG1I1Se at thatmoment he was asscssing the light-sigllal"relativistic" errors against the real-world "ordinary" longitude-timing errors. Yet: to call Poincare's approach "conservative" or"reactionary" is to miss the point; Poincare's sight-linc aimeddirectly toward the ideals of a rcvolutionaryEnlightcnment that, hycentury's end (Poincare's time), had grown into institutionalizedFrench empire. All om great constructions eventually crack, Poin-care says 011 many occasions. But our response to these fissures,these crises, should not be the mysticism or the melancholy of theintellectual elites, but instead a redoubled effort to repair those

The Place of Time

breaks by the systematic application of reasoned action. A, Poincaresaw it, the scientist-engineer could apply analytical reason as read-ily to the understanding of a coal-mine accident as to planetarymotion, as easily to the mapping of the world as to the reconstruc-tion of Lorentz's theory of moving electrons .

For Poincare, the trunk of the tree of knowledge was preciselythis engaged mechanics, an intuitively groundcdmathematicalunderstanding of nature that, at myriad points, shot branches intoexperiment and technology. Searching in a thousand ways, Poin-care aimed for an understanding of the world that could on the onehand speak to students trying to comprehend their place in aninjured France and on the other hand to scientists, cartographers,and politicians struggling to wire together an empire that wouldbind Paris to Dakar, I Iaiphong, and Montreal. He wanted a

mechanics of forces and cnergy, but one sufficient to undergirdanalysis of celestial mechanics, the shape ofthe earth, or thc bchav-ior of telegraph wires. As hc reminded h is fellow anciens f)olytech-niciens in 1903, the rcquirccl mixture was one of theory awl action.In Poincare's case that meant at one time responding to British tele-graphic hegemony by fostering French radio signaling, at anotherby dismantling the unscientific indictment against Dreyfus withastronomical instruments and the calculus of probabilities.

His was a world where truth and the ultimate reality of thingsmeant far less than the establishment of communicable, stable,durable relations-the kind of reliable relations that made actionpossible. As Poincare put it, "science is only a classification and ...a classification can not be true, merely convenient. But it is true thatit is convenient, it is true that it is so not only for me, but for allmen; it is true that it will remain convenient for our descendants; itis true finally that this can not be by chance. In sum, the sole objec-live reality consists in the relations of things."" A world of scientificrationality without metaphysical profundity: objective relations, notnictaphysical objects.

----.----.---~~.

EI STEI 's CLOCKS, POINCARE'S MAPS

For Poincare, joining the abstract and concrete in this flat worlelof relations meant being able to negotiate harel-fought conventionsin the human world. Sorti ng and negotiating the needs anddemands of railroad magnates, astronomers, physicists, and naviga-tors lay front and center in the decimalization of time. And as aleading figure at the Bureau of Longitude, Poincare grasped timethrough the detailed, material procedures of engineering protocols:organizing, analyzing, reporting on the expeditions of the military-scientific colleagues he so admired as they hammered togetherobservatory shacks in the high Aneles or 011 the coastal stations ofScncgal. 'I 'imc, for Poincare, resided ill our world, OUT convenience,our exchange of optica I and electrical telegraph signals. The meta-physical worlel behind appcarances was nothing. As he wrote ill"The Measure of Time," "We ... choose these rules [of simultaneity]not because they arc true but because they are the most convenient."

For Poincare the choice of how to measure simultaneity madetime richer, 110t poorer. It meant he could work the time conceptback and forth among the protocols oflongitude or decimalization,the abstractions of a science-inflected philosophy, and the princi-ples of a new physics. "Let us watch [scientists (!)(/vcmls)] at workand look for the rules by which they investigate simultaneity," Poin-care mgceJ.i" This is precisely what Poincare did as he struggled to

synthesize the work ofhis circle of philosophers, physicists, and car-tographers. Time-as-procedure stood ill all three series:

Simultaneity is a convention, nothing more than the coordinationof clocks by a crossed exchange of electromagnetic signals taking intoaccount the transit time of the signal.

This move has provided the central drama of this book, chargingits historical moment with a critical opalescence. What was it? Inone sense it was a conventional, regulated procedure, a practical,ever-more-precise method for the day-to-day establishment of simu]-

The Place of Time

I.llIcity for the sake offixing longitude, a theory machine. As a tech-Ili!':!1 convention, it occurred again and again in the pages of thc. \ 1/1 ials of the Bureau of Longitude. At the same time, for PoincareII was a philosophical exploration of questions of time and sirnul-I :1 IIcity, a statement that he could present as his prime example of.1 conventional stance toward scientific laws and principles. Simul-t.meity was no more than electromagnetic coordination groundedIII principled agreement. In this philosophical register, the utter-.mce appeared appropriately and dramatically in the Review ofMetaphysics and Morals, fitting perfectly into the longer conversa-Iion Poincare had been conducting with a circle of French philoso-phers, many of whom had emerged from Poly technique. Finally,he ginning in 1900, Poincare presented this simple simultaneitystatement to an audience of physicists as an interpretation ofLorentz's "local time" as if Lorentz had implicitly and all along heldsuch a view. When Poincare turned to theorizing about the elec-tron, the simultaneity procedure could grace the published pro-ceedings of a physics conference dedicated to Lorentz or theProceedings of the Academy of Sciences.

Is clock coordination "really" a technological, a metaphysical, ora physical intervention? All three. We may as well ask if the Placede I'Etoile is truly in the Avenue des Champs Elysees, the AvenueKleber, or the Avenue Foell. In fact, as in a great metropolitan inter-section, the enormous interest of the simultaneity question lies pre-cisely in its position at the center of a vibrant crossing of greatintellectual avenues.

Repeated ceaselessly from East Africa to the Far East, the proce-dure of electromagnetic clock coordination was at once thoroughlytechnological and altogether theoretical. It was brass tubes withfragile, suspended mirrors, and it was global control of "universaltime." It was vast lengths of copper cable protected by heavy gutta-percha insulation, lying a mile under the ocean and served by brasstelegraph keys inside crude observatory shacks; it was also the phan-

EINSTEIN'S CLOCKS, POJNCARI~'S MAPS

tasmagorical reach of empire. Surveyors and astronomers poredover personal equations, calculating and correcting measurementsthrough simultaneity on their way to the map, the final, prized prod-uct of their longitude work. But clock coordination was also theassembly of synchronized clocks strung together like beads along acoutiueut-spanning chain through Europe, Russia, and NorthAmerica. This fusion of technology and science drew together(Ihollgh oftcn in ;J [l-out struggle) Swiss horlogier«, American trainschcdulcrs, British astronomers, and members of the German Gen-eral SLiff. Alone extreme, time synchronization represents tech-

nology conditioning humdrum daily procedure at every two-bitwhistle-stop. ;\s such it is a substantial pari of the thick social his-lory of the Ncw II:llgland or Brandenhurg countryside. At the otherextreme, il.,lallds for Ihe symbolic reach of modernity thai hadmayors, pllysicisls, and philosophers, prououncing Oil the convcn-lioll<llily of time while pods paycd hOlllagc to Ihe annih ilatiou of .

.'ijl;iCC by speed. In Ih is regisler, clock coordiualiou was rarified his-lory, pursued ,I t the pinuac]c of II:llropean ph ilosophy and mathc-lllatie;d physics.

11()rPoincare, the modern leclmology of lillie was not external tohis scientific life-Hol a "context" that from some mythical "out-side" shaped, influenced, or distorted thought. Poincare was in andof Ihis compound world, a product of and professor in the FcolcPolytcchniquc where the material and the abstract shaped oneanother at every moment. I Ic proudly bore the "factory stamp."Poincare's work on time was of a historical era and of a place; oneaspect is 110t all accidcutal influence 011 another. To externalizeEcolc Polytcchniquc or the Bureau of Longi tilde as entities outsidePoincare's true sclf is to break linkages among technical and cul-tural actions that he and his late-nineteenth-century contemporariessaw as joined. Not only had Poincare held the presidency of theBureau 011 three separate occasions, but he also served as one of itselite Academy members for twenty years, published regularly in its

l~,.,,~~~~~. ,"'-r ""

'"'''':.0"",, '

The Place of Time

journal, and played leading roles in its most active committees onthe measurement of time. Nor is it "external" to Einstein's physicsthat he trained at ETH, an institution committed hy its velY char-ter to joining theory and praxis, or that he capped that instructionwith a seven-year apprenticeship at the Bern patent office, as a qual-ity control officer in the production-machine of modern elee-trotechnology. No, these are not influences moving Einstein andPoincare from the outside. They were rather fields of action thatconveyed the high value of machines grasped through reasoll-pro-duction sites for technology (through science) and science (throughtechnology).

Circa 1900, to speak of the transmission-corrected synchroniza-tion of clocks was both central and ordinary. Transmission correc-tion of time was a working tool for the longitude finder and routinefor city engineers in Paris and Vienna, who knew about time delayall too well through their frustrating attempts to pump exact timethrough pneumatic tubes under their cities. By 1898, the transmis-sion delay of a time pulse was a standard problem for thc squadronsof engineers, cartographers, physicists, and astronomers who werecreating simultaneity eVCIYday of the week.

So in january 1898, when Poincare published his argument fortime-as-convention, he was spcaking the technology of clocks aswell as thc language of philosophy. The same utterances now couldbe heard in different registers. "Simultaneity is a convention," or"synchronizing clocks demands transmission-corrected electricalcoordination" -Are these philosophical observations or do they"really" belong to brass and copper tcchnology? Is the Place dcl'Etoile really ill the Avenue Kleber or the Avenue Foch?

In December 1900, Poincare cleared a third avenue through thePlace de la Simultaneite, when he began using clock synchroniza-tion- first approximately and later, exactly - to assign meaning toLorentz's local time. At that point three fields were fully engaged:telegraphic longitude, philosophical conventionalism, electrody-


namic relativity. It is our loss that we have dessicated this remark-able moment, split it into fragments, and scattered them over thedisconnected academic departments of philosophy, physics, andmetrology. Poincare struggled to hold that modern and moderniz-ing world together-to fix it, uphold it, defend it.

Young Einstein also stood in thc midst of this trading zone of phi-losophy, technology, and physics. But he was never out to repair anduphold any empire-neithcr the French, nor the Prussian, nor theNewtonian. Delightedly mocking senior physicists, teachers, par-ents, elders, and authority figures of all kinds, happily calling him-self a "heretic," proud of his dissenting approach to physics, Einsteinshed the nineteenth century's ether with an outsider's iconoclasticpleasure. Not: for him was the increasingly desperate hunt for a sta-ble basis of thc Solar System, or for ,1 bedrock foundationalism thatwould ground all of physics ill mechanics or electrodynamics.Instead,Einsl'cin was contcut= morc than coutcnt=-to find theory-devices that worked. Heuristics, temporary hut effective means ofgoing forward with the theory, were machines. So was his lightclock, or the myriad of machinelike thought experiments that hepropos cd for th inking tbrough the inertia of energy, E = 11lC

l. And

so, most importantly for our purposes, was his time machine, thatinfinite array of clocks connected and coordinated hy the well-rcgulated exchange of light signals.

As important as time coordination was for Poincare as a prag-malic, conventional aid to thc building of a new mechanics, it wasmore crucial for Einstein. For Einstein it was procedurally definedtime that served as the starting point from which the Lorentz con-traction would he derived. Like a classical arch, for Einstein timesynchronization held the principled column of relativity in stableunion with the princi pled column of the absolute speed oflight.

Did Einstein really discover relativity? Did Poincare alreaclyhaveit? These old questions have grown as tedious as they are fruitless.No doubt originally propelled by the offensive and widespread

The Place of Time

Nazi-era assaults on Einstein's place in physics, the struggle over"who discovered relativity" continued for decades: Who found thetheory? What is its essence? Is the core of relativity really the dis-missal of the ether or is it the mathematical formula for transform-,ing space and time? Is it an unshakcable commitment to therelativity principle or is it the applicability of the principle to allphysical interactions or is the theory rightly identified with thederivation of time and space transformations from the synchro-nization of elocks? Or is relativity really no more than correct pre-dictions of what can be observed in experiments? Above all,relativity-and thc relativity of time in particular-became syn-onymous with modern physics and modernity more generally.From our perspective, assigning a graded checklist to Einstein andPoincare counts as the least interesting part of the story of time andsimultaneity.

Far more important is to situate Poincare and Einstein at the twonodal points of turn-of-the-century time coordination, grasping thccharacteristic ways in which each navigated the flows of technol-ogy, physics, and philosophy, and understanding how each strug-gled to rip simultaneity from the metaphysical firmament and bringit to earth as a procedurally defined quantity. Time standardizationwas the order of the day, for each scientist a natural extension of thestandardization of length. It annou need itself on the faces of pub-lic clocks, railroad schedules, and inside regulated schoolrooms andfactory floors. In the Paris Observatory of the 1890s, Wolf was wind-ing electromagnets to keep astronomical docks in step and super-vising the distribution of dozens more throughout the streets ofParis. Cornu was aeljusting the giant pend ulum on his regulatorclock, joining mechanics and electromagnetism to formulate arigorous analysis of electrosynchronizatioll. Teams of itinerantobservers worked incessant time-exchanges with Senegal, Quito,Boston, Berlin, and Greenwich. Anglo-Saxon astronomers hawkedtime to railroads, while French stargazers hoped the glorious pre-

, IIIuII

""""'.' ..."~~~-----------

EI STEIN'S CLOCKS, POINCARE'S MAPS

cis ion of the observatory would be imitated through the whole ofthe eountry- reflections of a mother clock cast from mirror to mir-ror until the light of temporal rationality spilled through every streetin the republic.

Creating this standardized, procedural time was a monumentalproject that utilized creosote-soaked poles and undersea cables. Itrequired a technology of metal and rubber, but also reams of paper,bearing, contesting, and sanctifying local ordinances, national laws,and iutcrnational conventions. As a result, convcn tional, turn-of-the-century time synchronization never inhabited a place isolatedfrom industrial policy, scientific lobhying, or political advocacy. Itwould case matters if we could attribute the late-nineteenth-centurypush toward standards to a single drive-whee]: if we could say thatit all came clown ultimately to railtond magnntes or decisively to sci-enlists or exclusively to philosophers. But thc restructuring of timewas not that simple.

Tillie was complex because, long heforc the uinctccuth century,clocks and simnltaneity were already more than gears, pcndula, andpointers. III the eighteenth century, for example, the precisionchronometers of the long-suffcring British clockmakcr John Harri-SOli appeared in ,I larger print world about I'IIC longitude problem

as wcll as in diaries and satires about timekeeping and mappiJlg.From Hie start, Harrison's precision docks assumcr] a "planetary"signifieancc_17 l<'orging hack earlier than the eigh tccnth century stillclocs not shake timepieces loose from thc cultures in which theywere built. Sand clocks and church docks carried much besides the

assignment of time; they conveyed clifferent, overlapping authori-ties of God, of the feudal lord, of the lllemory of mortality. Theresimply is no getting hehind the cultural to some primordialmoment in which time was nothing but sand, shadow, or a mechan-ical pointer.

What cmerged in the late nineteenth century was not merelythe issue of a particular invention-coordinated clocks certainly

The Place of Time

existed before then. Instead, Europe and North America experi-enced a dramatic, global alteration in the place and density of clcc-trodistributed time. Linked clocks of the late nineteenth centurycovered the world. Circles of such wide-spanning technologiespulled each other along. Trains dragged telegraph lines, telegraphsmade maps, maps guidecl rail-laying. All three (trains, telegraphs,maps) contributed to a growing sense that long-distance simul-taneity made the question, What time is it now somewhere else? atonce practical and evocative. When we read Einstein's and Poin-care's many discussions of the new ideas of time and space cast illthe lexicon of automobiles, telegraphs, trains, and cannons, we areseeing the conditions under which these questions becamecommonplace.

We can think of simultaneity as the intersection of arcs, whereeach arc stands for a long seqllence of "moves" within a field. ,EiI,ethe physics we have followed. Clearly there is no single, unchangedmeaning of simultaneity from the carly 11)90s through] 905. l.ocaltime (Ortszeit) hegan in a geographical sense, became I .orcntz's fic-tionally off~ct local time, turned into Poincare's light-signal observ-able offset local time, shiftecl to Poincare's off~cl and dilated"apparent" time, only to take a new form in Einstein's relat-ivistic

time. These shifts ill the mcanings of time did not take place all atonce and did 110tplay out purely in the domain of physics. Instead,they arc better understood as a series of moves ill an evolving gamc.Consistent with the use of "move" in the everyday sense of a game,a "move" ill this more technical sense was sometimes a statement(or convention), sometimes a physical procedure. Remarkably,therc was enough sense of continuity for Poincare and Lorentz tosee their work as building step by step, even though the aims of thegame they were playing were also evolving. (If in 1894 Lorentz'sgoal was to solve an equation by making a moving object in an elec-tric and magnctic field look as if it were at rest in the ether, his goal[and Poincare's] in 1904-05 was to produce laws of physics that led

",,,,,.,,,"*'----------


to the same measurable results in any constantly moving frame ofreference. )

One arc of simultaneity, then, was that of physics-the series ofmoves transforming the electrodynamics of moving bodies. ButPoincare was playing his light-signal synchrony move in at least twoother arcs as well: telegraphic longitude determination and late-nineteenth-century French philosophy. From the time of the Amer-ican Civil War forward, telegraphic longitude became the modernmethod for determining simultaneity for longitude. Pushed by theCoast Survey, Europeans rapidly took up the American method,deploying it over land and under sea. By 1899, under Poincare'spresidency, the Bureau of Longitudc had become a global node forsending, receiving, processing, and defining simultaneity. Time atthe end of tile nineteenth century was written in devices all throughthe Bureau: methods for distributing time to cities, theories of howto improve clcctrosynchronization, debates over the decimalizationof timc.Klcctric longitudc was important for the French to fix theircolonies 011the worldmap aud articulate their internal geographies.But it was also crucial to counter the insult to European geodesypresented by the longstanding battle over thc right longitudinal dif-ference between Paris and Londou. Poincare in the lead, theBureau enlisted the Eiffcl Tower ill wireless time transmission.Inscribed in report after report from the Bureau, the exchange oftelegraphic signals using transmission times became ordinary workin thc fixing of time and plucc far from Paris. Philosophy too had itsare, its series of statements about the measure of time. No doubtPoincare could see philosophy through the work of the Boutrouxcircle, even 1110reproximately through the physics-philosophy of hisfellow Polytcehnicians Auguste Calinon and Jules Andrade, who intheir own ways were dissecting time.

The intersection of these three registers of time measurement donot necessitate Poincare's revision of simultaneity. But probing thetriple intersection of concerns at sites like Poly technique and the

The Place of Time

Bureau of Longihlde does offer a recognition of why Poincare thenand there would seize the measurement of time as an essential ques-tion tied to conventions, physics, and longitude" Of why abstracttime could be graspecl and reconceived through machines.

Eac h of the three arcs - of physics, philosophy, and technol-ogy-carried with it a sense of the new. The "new mechanics"advertised its rupture with old notions of mass, space, and time, theelectric world-spanning telegraph cables was a celebrated triumphand tool of "civilizing" empire" Poincare linked his conventional-ism about time and simultaneity with his philosophical conven-tionalism about the principles of physics and the fabric ofmathematics. But conventions for Poincare could also refer to theplethora of Frcnch-based international conventions about the mea-sure and distribution of the precise hour. Time stood un-still at this

quintessentially modern triple intersection.Throughout his work, Poincare treated his subjects with a math-

ematical engineer's modernism: that is, with a deep-seated faith illthe human ability to grasp and improve the world technically, tomap it, so to speak, <Illthe way down. [ust after Poincare's death, hisnephew, Pierre Boutroux, struggled in a letter to Mittag-Leffler tocapture the animating goal of his uncle's life work. Intriguingly, heturned 110t to mathematics or physics, but rather to geography forhis guiding thread. Boutroux recounted how all his life Poincarehad avidly followed stories of exploration and travel; both inside andoutside science, all his work was characterized by a drive "to fill the

white spaces on the map of the world.nlX

It was Poincare's abiding faith that the blank spaces on theworldmap could be filled. Gaps on the surface ofknowlec1ge couldbe completed in the causal map Poincare drew of the Magny min-ing disaster, tracking the catastrophe all the way back to the pickaxdent in the latticework of mining lantern 476. He would track thoselacuna more globally through the Poincare Map, which heexploited to chart the unvisualizable behavior of chaotic planetary

Iii

,Ij;i

EINSTEIN'S CLOCKS, POINCARf':'S MAPS

orbits as successions of points meandered over the plane. To fill inblanks on the geographical worldmap, he worked with the Bureauof Longitudc to plot telegraphic maps of Saint-Louis, Dakar, andQuito, work that also had implications for theoretical attempts heand a long tradition of physicists had made to account for the shapeof the earth. Other white spaces might be replaced by studies of theether, by investigating the structure of the electron, by insistenceon intuitive mathcmatical functions, intuitive formulations oflogic, and the productive intuitions afforded by the ether.

Poincare's was a hopeful modernism of relations graspable by us,without Cod, without Platonic forms, and (though he was fasci-nated by Kant's emphasis OJl structures through which experiencebecomes possible) without Kantian things-in-thelllsclves. Insteadof attending to objects, Poincare was forever after relations, for itwas the relation of things that would survive even when the objectsthat they tied togcther had Iadccl behind the mists of history. Truth?Civcn the complexities of conventions, definitions, and principlesthat went into the Jawsof physics, he preferrcd the objectivity thatcame with shared, durable concepts of simplicity, and conve-nience. True relations, not truth by itself. Visible surfaces, notobscure depths. Poincare pursued this reformulated Enlighten-ment vision even if it meant driving radically new concepts ofspace, time, and physical stability into the vast blank spaces ofknowledge.

Fiustcin's modernism too can be found at a triple intersection: amove ill the physics of moving bodies, a move in the philosophicalattack on absolute time and space, and a move in the wider tech-nology of clock synchronization. Einstein's Iocus was more insis-tently physical than Poincare's, more attendant to particularmaterial machines rather than to the engineering of abstract ones.It is impossible to imagine Poincare spinning an ebonite wheel ina homcbuilt contraption; it is equally hard to picture Einstein coor-dinating a massive team effort to engineer the cabling of precision

The Place of ~"i111e

electric time from Quito to Gayaqllil. While maintaining a morehands-on engagement with the materiality of objects, Einstein alsoheld a more metaphysical conception of the relation of theories tophenomena, one that led him in many different contexts to demanda sharp correspondence between clements of the theory and ele-ments of the world. Poincare never gave up his assignment of localtime to the status of "apparent" in contrast to "true." Because he sawno parallel distinction in the phenomena themselves, Einsteinwouldn't touch such a theoretical dichotomy. Time and space inone inertial frame were as "true" (or "relative") for Einstein as inany other: clocks were clocks, rulers were rulers. Where Poincarekept the ether as a means-for-thinking, an intuitive basis on whichdifferential equations could be imagined, Einstein mocked theether as a remnant idlc gcar from an obsolete mechanism. Anel hethrew it aside with the same relish that he mustered for patent appli-cations with superfluous elements. When Einstein handled thclight quantum heuristically, without reference to the wave equa-tions understood within the ether, it left Poincare fearing that theyoung phyxicis! and his supporters had jettisoned the vcry condi-tions thatmade possible real understanding of the physical world.In his terms, Poincare was right: Einstein was perfectly willing touse iutcllcctual devices as stop-gaps-heuristics that tied elementsof theory to clements of the phenomena, even if that meant violatingintuition (ill Poincare's particular sense).

Poincare struggled to map the world through differential cqua-tious, chosen for convenience in the largest sense, all the way totertiary rivulets feecling secondary streams. Did the ether and"apparent time" aiel intuition while preserving the "true relations"of observed phenomena? Then for Poincare that was satisfactory,even if it meant a certain redundancy. By contrast, Einstein wantedto orient timc and space within a theory that matched the phe-nomena, not just in prediction but in austerity. If the phenomenawere symmetric (for example, if there were no way to distinguish

EI STEI 's CLOCKS, POI CARE'S MAPS

the moving magnet/still coil from still magnet/moving coil), thenthe theory should formally encapsulate that symmetry. Later, in thequantum debate, Einstein expressed the complementary concern:that there were predictable features of the physical world to whichno element of the theory corresponded.

For Poincare space and time were pinned to the rigorous surfaceof objective relations built to meet our human need for a franklypsychological, objective, and simple convenience. His was a relent-less Third Republic secularism. By contrast, Einstein did not thinkthat theory had fulfilled its task by successfully and convenientlycapturing true relations among phenomena. He aimed for a depthbetween phenomena and the theory that underlay them. Like Poin-care, Einstein bclicvcd that laws must be simple, not for our COI1-

vcnicnce but because (as Einstein put it) "nature is the realizationof the simplest conceivable mathematical ideas." The form of thetheory therefore hacl to exhibit ill its detailed form the reality of thephenomena: "In a certain sense," Einstein later insisted, "1 hold ittrue that pure thought call grasp reality, as the ancients dreamed.""EillSt·eillbelieved that a proper theory would match the phenom-ena in austerity. In that depth lay a contemplative theology. Not thereligiosity of a personal, vengeful, or judgmental Cod, but a mostlyhidden Cod of an underlying natural order: "The scientist is pos-sessed hy thc sense of universal causation. The future to him iscvery whit as necessary and determined as the past. ... His religiousfceling takes the form of a rapturous amazement at the harmony ofnatural law which reveals an intelligence of such superiority.'?"Sometimes it was given to the physicist to advance by the provi-sional application of heuristic devices; these could ticle the theoryover until further development was possible. Such a provisional useof formal principles played a role in thermodynamics, in quantumtheory, and in relativity." But Einstein insisted over and over that,insofar as they could, scientists fashioned theories that seized somebit of the underlying, simple, and harmonious natural order. Since

The Place of Ti711e

Einstein believed that the phenomena did not distinguish true fromapparent time, neither, he insisted, should the theory.

Neither Poincare nor Einstein falls into a naive realism or anti-realism. True, throughout his career, Poincare underscored the free-dom of choice present in describing the world: in geometry, inphysics, in technology. But it would thoroughly misrepresent hisposition to lump his conventionalism with an anything-goes anti-realism. Both in practical and abstract matters he took every oppor-tunity to emphasize the central role of objective, "true relations," ofa simplicity that was 110tlip for grabs. Einstein, by contrast, is fre-quently pigeonholed as straightforwardly realist; there is, after all,the Einstein who comfortably asked if a theory was "the true Jacob."Nonetheless, he cautioJlcd that there ,HC different ways to charac-terize "reality" and tl1<1t the fecund part of theory lay not in theevents that were classifiable with spacetime coordinates, nor evenwith the di rectly perceptible. Instead, it lay in the links betweenthem, and thcse links wcre not fixed once and for alL22 Both scien-tists recognized the power of principles and conventions ill shapingthe reach of theory and the possibility of measurement. Both werefully prepared to reject concepts even if those received conceptsseemed to carry alollg history, intuitiveness, and self-evidence.Deeply embedded in a changing clectrotechnical world that morethan at any time prcvioi lsly recognized the importance of choice inmeasurement, standardi;t,ation, and theory construction, Einsteinand Poincare separately cracked simultaneity from its metaphysicalpedestal and replaced it by a convention given through machines.

Reading back from Einstein it is all too easy to cast Poincare as areactionary, striving tow.3rd (but failing to reach) Einstein's theoryof relativity. Such a retrospective view would bury Poincare'sreworking of the physics of space and time into a "new mechanics."It would he as if Picas·so were to be jettisonecl as antimodernbecause he was not 1110.clemin the sense of Pollock, or to do thesame to Proust because his was not the modernism of late Joyce.

I,


Reading forward to both Poincare and Einstein, we can see each

breaking with the past in different ways.Here were two great modernisms of physics, two ferociously

ambitious attempts to grasp the world in its totality. Poincare's mod-ernism advanced by establishing objective, simple, convenient, andtrue relations down to the smallest white space. Einstein's movedforward by chiseling out a theory that aspired to capture the phe-nomena, not just ill predictions, hilt in its underlying structures,One was constructive, building up to a complexity that would cap-turc the structural relations of the world. The other was more criti-cal, more willillg 10 set aside complexity ill order to grasp, austerely,those principles thaI reflected the governing natura] order. Thesetwin visions of a new and modern relativistic physics had much incouuunn. Yet i':illsl"cin and Poincare remained in ambivalent aclmi-ration of each other, no more able to engage each other's altcruatcmodcmity than Freud could read N ictzschc. 'Ioo close and too farto speak, their skew interpretations of relativity never crossed, evenas the two scientists radically altered "lime" ill ways that shookkJl()wledge in physics, philosophy, and technology.

l-rorn a biographical point of view, it is of course remarkable thatEinstein and Poincare were able to participate ill such variegatedtechnical and philosophical activities as if they were chess grandmasters, playing simultaneous championship gallles and finding asingle succcsshil mov« that checkmated them all. Yet chess providesonly a weak analogy. These "games" of physics, philosophy, andtechnology were of vastly different coustruction, the consequencesof the simultaneity move euormous in each domain. Philosophersof the Vienna Circle, no less than leading physicists in the 1920s,and engineers of the Global Positioning System of the 1980s alllooked to Poincare-Einstein simultaneity as a model for the con-

struction of future scientific concepts.In the end, however, the opalescent history of time coordination

The Place of Time

is falsely presented by reducing it to biography. Cropping the pic-ture to portrait size renders invisible the vast, disputed, standardizedconventions of measurable time and space that coursed throughEurope and the United States. This is not because Einstein's orPoincare's imaginations were too limited but instead because "themeasure of time" fluctuated across so many scales. Time coordina-tion had become a modern problem through the conventionalityand regulation of time flowing through observatories, cables, trainnetworks, and cities. A better analogy is this: Isobars and isothermstransformed and in part made possible predictive meteorology. Sim-ilarly, the electric world array of clocks made distant synchroniza-tion into a quintessentially modern problem resolvable by amachinelike proccdnrc-i-eveu if that machine turned out to heboth infinite and theoretical.

Times and places where the technical, philosophical, and sci-entific arc all centrally impl icatecl are rare, milch less frequent eventhan the kind of physics developments traditionally described as"revolutions." III the nineteenth century entropy and energy Jl]ayoffer similarly scale-shifting histories: think of the fateful intersec-tion of steell)] engines, thenuodynamics, ami quasi-theological dis-cussions about the inexorable "heat-death" of the Universe. 'Io finda more recent mixture of abstraction and concreteness of this kind,we can look to the mid-twentieth-century explosion of "infonnationsciences": cybernetics, computer science, cognitive science. Hereconverged the dense histories of wartime feedback devices that tum-bled out of weapons production, alongside the more arcane trajec-tories of in formation theory anclmoclels of the human mincl. Time,

thermodynamics, computation: each defined an age symbolicallyand materially. Each represented a moment of critical opalescencewhen it became impossible to think abstractly without invokingmachines or to think materially without grasping for world-spanningconcepts.


Looking Up, Looking Down

Times changed. Einstein left the Bern patent office on 15 October1909 for the University of Zurich; on 1 April 1911, he began histenure at the Karl-Ferdinand University in Prague and, in the springof 1914, joined the University of Berlin. There he both completedhis gcneral theory of relativity and became a leading spokesmanaga inst the war. After the fighting had ended, Favarger, that avatarof Swiss chronometric unity whom we met earlier, published his550-page third cdi tion of his technical treatise on electrical time-keeping, framiJlg its detailed electromechanical content, onceagain, in broadly cultural terms. The Great War, he argued, hadcontributnd powerful technological developments, but it had alsodestroyed a great part of the human wealth that sustained peace hadcreated. What remained was by contrast "a heap of ruins, miseriesalld suffering."21 Humanity needed work to overcome this disaster,and work invariably involved time.

'I'inic, Favargcr rhapsodized, "cannot be defined ill substance;it-is, metaphysically speaking, as mysterious as matter and space."(1':vell stolid Swiss clockmakcrs apparently were driven to meta-physics hy timc.) All the activities of man, conscious or uncon-SCiOIlS,sleeping, eat-ing, meditating, or playing take place in time.Without order, without specified plaus, we risk falling into theanarchy Favarger had warned against since long before GavriloPrincipe shot Archduke Fcrdinund. Now, after the Great War, therisk loomccllargcr that people could fall into "physical, intcllec-tual and moral misery," His remedy? the precise measurement anddetermination of t-ime with the rigor of an astronomical observa-tory. Bllt to functiOIl as an antidote, measured time could notremain in thc astronomers' redoubt; time rigor must be distributedelectrically to anyonc who wanted or needed it: "we must, in aword, popularize it, we must democratize time" in order for peo-ple to live and prosper. We must make every man "maitre du

The Place of Time 323

temps, master not only of the hour but also of the minute, the sec-ond, and even in special cases the tenth, the hundredth, the thou-sandth, the millionth of a second.'?" Distributed, coordinatedprecision time was more than money for Favarger, it was each per-son's access to orderliness, interior and exterior-to frcedom fromtime anarchy.

Throughout the late nineteenth and early twentieth een turies,coordinated elocks were never just gears and magnets. Certainlytime was more than merely technical for Poincare and Einstein. Itwas also much more than wires and escapements for New Englandvillage elders, time-zone campaigners, Prussian generals, Frenchmetrologists, British astronomers, and Canadian promoters. In theopalescent history of time coordination, clocks trapped nerve trans-missions and reaction times, structured workplaces and guidedastronomy. But the two great· seale-changing domains of materialtime centered on the railroad and the map. The Bureau of Longi-tude that Poincare had helped supervise stood as one of the greattime centers of the world for the construction of maps. And theSwiss Patent Office, where Einstein had stood guard as a patentsentinel, was the great Swiss inspection point for the country'stechnologies concocted to synchronize time in railways and cities.

My hope in exploring clock coordination has been to set Poin-care's and Einstein's place within a universe of actions that crossedmechanisms and metaphysics, that made abstract concreteness or,if you will, concrete abstractions. More generally, perhaps we canbegin to look at science in a way that avoids two equally problem-atic positions on the relation of things to thoughts. On one side,there is a long tradition of what could be described as a reductivematerialism, the view that demotes ideas, symbols, and values tosurface ripples on a deeper current of objects. Through thoseempiricist glasses of the 1920s through the 1950s, theoreticalphysics and its philosophy often seemed a provisional addition, notthe bulwark of science. Einstein (on this view) appeared as having

I

I!lf

~:

Ii

I'

I


taken the last, inexorable step ill an inductive process thai graduallydrove out the ether and the absolutes of space and time. Earth'smotion through the ether could not be detected to an accuracy bet-ter than the ratio of earth's velocity to the speed of light (vie, thatis, about one part in ten thousand). Later such measurementsimproved, showing no evidence of motion to a much higher accu-racy (second order ill vie, or about one part in a hundred million),and therefore, so the argument went, Einstein concluded that theether was "superfluous.'?' No doubt there is much to he said for thisexperiment-grounded Einstein. His fascination with the derailedconduct of experiments and his gyrocompass work at thePhysikalisch-Tcchnischc Rcichsanstalt reveal a theorist with a clearSCllSCof laboratory procedure and the operation of machines. Onthe empiricist view, things structured thoughts.

On the nip side was the antipositivist movement popular in thel%()s and 1<)70s.Thollgilts structured things. Anlipositivists aimedto reverse the older generation's cpistcmic order; they saw pro-gramllles, paradigms, and conceptual schemes as coming first, andthey held these to have completely reshaped experilllents andinstrumcuts. I':imtein OIl the antipositivist screen appC<lred as thephilosophical iunovator who dispensed with the materia] world alto-gclher in a sustained drive for symmetry, principles, and ()pcrationaldefinitions. There is much truth here too-reading hi:slory withantipositivist glasses exposes those moments when Jt:inst-cin waschary of experimental results, dubious, for example, of supposedlaboratory refutations of special relativity and of astronom ical obscr-vations t-hatclaimed to threaten the general theory.

Granting both ways of reading history their due, I do not meanto split the difference. Instead, attending to moments 'of criticalopalescence offers a way out of this endless oscillatiom betweenthinking of history as ultimately about ideas or fundarncntmllv aboutmaterial objects. Clocks, maps, telegraphs, steam engi ucs, com-puters all raise questions that refuse a sterile either/or cliclhotomy of

The Place of Time

things versus thoughts." In each instance, problems of physics, phi-losophy, and technology cross. Staring through the metaphoricalwe can find the literal; through the literal we can see the meta-phorical.

When Einstein came to the Bern patent office in 1902, heentered an institution in which the triumph of the electrical overthe mechanical was already symbolically wired to dreams of moder-nity. Here clock coordination was a practical problem (trains,troops, and telegraphs) demanding workable, patentable solutionsin exactly his area of grcatest professional concern: precisionelectromechanical instrumentation. The patent office was anythingbut the lonely deep-sea lightboat that the no longer young Einsteinhad longed for as he spoke to the Albert Hall audience in the clarkdays of October 1<))3. Reviewing one patent drawing after anotherin the Bern office, li:illstein had a grandstand scat for the greatmarch of modern tcehnologies. And as coordinated clocks wereparaded by, they were not traveling alone. The network of electri-cal chrono-eoordinalioJl provided political, cultural, and technicalunity all at once. EiJlstein seized on this new, conventional, world-spanning simultaneity machine and installed it at the principledbeginning of his new physics. In a certain sense he completed thegrand time coordination project of the nineteenth century bydesigning a new, vastly more general time machine valid every-where and for all imaginable constantly moving frames of referencewithin the Universe. Bill by eliminating the master clock andredefining conventionally defined time to a starting (Joint, Einsteincame to be seen by both physicists and the public as havingchanged their world.

Poincare, at the end of his life, co-authored a book cntitled WhatBooks Say, What Things Say. This quirky volume combined theendeavors of the two great academics to which he belonged: the lit-erary Academic Francaisc and thc scientific Academic des Sciences.From the literary side carne articles on the heros of culture, inelucl-

326 EINSTEIN'S CLOCKS, POINCAR~~'S MAPS

ing Hugo, Voltaire, and Bossuet. Poincare himself contributedchapters on stars, gravity, and heat, hut also on coal mining, batter-ies, and dynamos. I.iving as easily among philosophers as amongmathematicians and engineers, Poincare's scholarship, includinghis work on simultaneity, stood central to all these cultures.

Einstein's stance toward thc great academics of science was dif-fcrent. Just after World War I, Arthur Eddingtoll, the British astro-physicist, took advantage of a total eclipse to measure the deflectionof starlight by the gravitational pull of the sun (or as Einstein wouldhave it, by the sun's bending of spacetime). Thrust into front-pagefame by the resulting confirmation of his gener,lI theory of relativ-ity, Einstein overnight became a world fig\lre. Facing the limelightin his increasingly public role, his relativity work aftcr 19] 9 movedtoward the abstract unification of physical forces and away from themachine culture of the patent office. A fcw days after his 19Bspeech ill Royal Albcrl I lall, EillSlein lcfl for the United States,where he embraced a venera led if monastic existence at the Insti-tutc for Advanced Siudy ill Princcton. l lalf seer, half mascot, hespoke ill oracular ten us OIl everything from the mcaniug of Cod tothe future of nuclear warfare. In April 1951, two years before hisdeath, Einstein wrote from Princeton to Maurice Solovinc of thelaughtcr and insight of their so-unacademic academy dnring Ein-stein's Bern ycars, when parents, physics, and philosophy stoocl sidehy side:

'I() the immortal Olympia academy,

In yom short active existence you took a childish delight ill all thatwas clear and rcasouablc. Your members created you to amusethemselves at the expense of yom big sisters who were older andpuffed up with pride. I learned fully to appreciate just how far [themembers had through you] hit upon the true through carefulobservations lasting for IllallY long years.

The Place of Time

We three members, all of us at least remained steadfast. Thoughsomewhat decrepit, we still follow the solitary path of our life byyom pure and inspiring light; for you did not grow old and shape-less along with your members like a plant that goes to seed. 'fa yO\lI swear fidelity and devotion until my last learned brcnthl Fromaile who hereafter will be only a corresponding member, A.Eu

As each struggled with time, philosophy, and relativity at the turnof the century, Poincare inhabited the Parisian academies of artsand sciences, Einstein the Olympia (11011-) Academy. On 15 March1955, Michele Besso died. It was with Besso that Einstein had soproductively spoken in the weeks and months before he came uponthe coordination of clocks as the key to finishing his work on spe-cial relativity. Einstein wrote to Besso's Lllnily on the twenty-first,closing his letter with a final reference to those conversations, andto the perspectival nature of time that emerged from relativity: cc .••

it was the Parent Office that reunited us Iafter Zurichl· Our con-versations on the way home had an incomparable charm; it was ifthe all-too-human did not exist at all. ... Now he has also takenleave of this strange world a little before me. This means nothing.For us devout physicists, the division between past, present, and

future is only an illusion, if a stubborn one.'?"Long aftcrEinstcin's own last learned breath, the struggle con-

tinned among many competing interpretations of the regulatedcoordination of clocks. Synchronized time remained hypersymbol-ized. Einheitszeit never emerged from contestation among imper-ial empire, democracy, world citizenship, and .mtianarchism. Whatall these symbols helel in common was a sense that each clock sig-nified the individual so that clock coordination came to stand in,for a logic of linkage among people and peoples that was alwaysflickering between the literal and the metaphorical. Preciselybecause it was abstract-concrete (or concretely abstract), the project

----~~..--.-- ..-.


of time coordination for towns, regions, countries, and eventuallythe globe became one of the defining structures of modernity. Thesynchrony of clocks remains an inextricable mix of social history,cultural history, and intellectual history; technics, philosophy,physics.

Over the last thirty years it has become a commonplace to pitbottom-up against top-down explanations. Neither will do inaccounting for time. A medieval saying aimed at capturing the linksbetween alchemy and astronomy put it this way: In looking clown,we see up; in looking lip, we see down. That vision of knowledgeserves us well. For in looking down (to the electromagneticallyregulated clock networks), wc see up: to images of empire, meta-physics, and civil society. In looking up (to the philosophy of l<ilJ-stein and Poincare's procedural concepts of tin ic, space, andsimultaneity) we see down: 10 the wires, gcars, and pulses passingthrough the Bern patent office and the Paris Bureau of Longitude.Wc find metaphysics ill machines, and machines ill metaphysics.Modernity, just in time.

L

NOTES

CHAPTER 1

l. Einsteill, "Autobiographical Notes" [1949], 31. On the universal "tick-lock"see Eillstein, "The Prilleipal Ideas of the Theory of Relativity" [after December1916], Colledecl Po/)ers, vol. 7, 1-7, on 5. On Newtonian time and space:Ryuasicwicz, "Newton's Scholium" (1995).

2. We call IlOWread I<:illstein'swork through the extraordinary sellolarship ofseveral generations of historians. 'I 'II is literature is so vast that I call refer only a fewsources here-they serve as entry points into the wider literature: Forboth superbeditorial comments and mcliculous reproduction of documents, Stachel ct ul., cds.,Collected Pu/)ers (19R7-); I'<)\"secondary literature, 1[olton, Thematic Origins ofSci·eniiiic Thoughl (197~); Miller, "I':illsteill's Special 'I'hcory 01' Relativity" (1981);Miller, Frontiers (19R()); Darrigol, j':lectroclynllmics (2IlOO); Pais, Suhtle is the Lord(1982); Warwick, "Role of t·he;l'it/.geralcl-l .orcntz Conlructiou llypothcsis" (l991);idem, "C:llllbridge Mathematics and Cnvcndis]: Physics" (part I, 1992; part II,1993); I'<lty, Einstein /Jhilosophe (1991); M. [ausscu, J\ C011lfJlIriso/l betweenLorentz's /<ther Theory and Special Relativity in the /,ight of the I':X/Jerimellts o{Trouion and Noble, ullpublished doctoral dissertation, University of Pillsbnrgh,1995; and l'iilsing, Albert Einstein (1997). For collections of essays by leading schol-ars, see "Eiustciu ill Context,' Science ill Context (j (199)), ami Calison, Cordill,and Kaiser, Science and Society (2001). For all extensive hihliography of other his-torical works Oil special relativity: Cassidy, "Unclcrstanding" (200]).

3. The scholarship on Poincare, also vast, is 1IOW coming into its OW1I with thework of the Nancy-based project of the Archives Ilcnri Poincare, which is pub-lishing the scientific correspondence. See, for example, Nabouuaud, cd., PlJill-

care-Mittag-Letfler (1999); published articles arc mostly in Oeuvres (l9~4-53). Anoverview of current work on Poincare's technical work lllay be found in the litera-ture of note 2 above (especially works by Darrigol and Miller) along with referencescited there, as well as the volume by Paty on the links between Poincare's physicsand philosophy; see also the excellent volume, Greffc, Heinzmann, and Lorenz,cds., Hemi Poincare, Science and Philosophy (1996). Rollet's excellent dissertation

~.,...-~-- ..-.--- ..---.----'----'.-- ...-.. '--'''.'- .... '''- .._-" ..

3'0. )

surveys Poincare's role as a popularizer and philosopher- it also contains a fine

bibliography; see Henri Poincare, "Des Matlicmatiques ii la Philosophic. l;:tlldes

du parcours intcllcctucl, social ct politiquc d'uu rnatheruaticicn au debut du sie-clc," unpublished doctoral dissertation, University of Nalley 2, 1999.

4. Calison, "Minkowski's Space-Time" (1979).

5. l';illstein, "J':JektrodynJmik bewegtcr Kerper" (1905), R9'3; I have used a

(slightly modified) version of the translation given in Miller, Einstein's Special The-(J/Y ofHe/ativily (19~ I), 392-93.

6. Ibid.

7. See the sources in note 2 above; OJI the ether, Cantor and Hodge, cds., COIZ-

ception» of/·:ther (l9R I).~. 1'(lr I lciscubcrg Oil his discussions with 1':illStein about the critique of absolute

time, Physics and lleyol1d (J971), (1'3;other quantum theorists (Max Born aIHI Pas-

cual [ordun) also modeled their new physics onlvinstcin's simultaneity convention,

Cassidy, iincertaint» (J992), 19K; Philipp I'rand reported the "good joke" remarkin l':illsieill (1953), 21h.

9. Schlick, "Mc.miur; alid Verification" (19fl7), n I; see also 47.

10. Qllille, "I .ccturcs OIl Caru.rp," 64.

11. I';inslcill, i':illsteill olll'eoce (1%0), 2>K-19, Oil nfl.

12. 1':instcill,AlIto/JiograiJhical Notes 11949], 11.

11. Barlhes, Mythologies (1972),7)-77.

14. Poincare, "Mathematical Crcaliru." 119]):/, jK7-I)K.

I S. Poincare, Sciel1ce and i i)'IJOlhesis (1952), 7K.

I (I. Qllok:d ill Seclig, cd., Llelle Zeit-dlll/0e Zeit (195(1),71; huns. in Calapricc,

The QlIotah/e Einstei): (19%), IR2.

17. Remotely xc! clocks were disellssed by, ,lIllong others, Charles Wheatstone andWilliau: Cook, the Scottish clockmukcr, Alexander Bain, and the American inventor

Salllllcl I,'. B. Morse. hlr Wheatstone, Cooke, and Morse, clock coordination came

out of their work 0)) Idegraphy. See Wclch, Time Measurement (l972), 71-72.

IR. l-or prc-l <)00 disc-ussions of the extensive work on clock coordinatiou, see, for

example, the series of articles hy hlvarger, "L'Klcctricitc ct sex applications ;Ila

chronometric" (Sept. IRK4-Jlllle 1I)fl5), esp. 151-5R, and "Lcs Horloges clcctriqucs"(1917); Alii broil 11 , l landbuch. der Aslr01wmischell lnstrumentenlamde (I K99), esp.

vol. I, 1g)-il7. Oil the expansion of the Bern network, see the Ccscllschaft fur clck-

trischc Uhrcn ill Bern, [ahreshericliie, I fl90-191 (), Stadtarchiv Bern.

19. Bernstein, Natlllwi.~sellsclwftliche Vol!,shiicher (lK97), 62-64, 100-104. Iwould like to thank Jlirgen Rcnn for helpful discussions about Bemstein.

20. Poincare, "Measure of Time" 119131, 2B-34.21. Ibid., zss22. Poincare, "La Mesurc du temps" (1970), 54. Slightly modified.

NOTES TO PAGES 48-57

CHAPTER 2

I. Poincare, "Les Polytechnicicns" (I <)]()), 266-67.

2. Ibid., 268, 272-73.

3. Ibicl., 274-75, 278-79.

4. Cahan, All Institute far all Empire (19R9), esp. ch. 1.

5. Monge's polestar, descriptive geometry, plummeted in curricular importance

from 153 hours (in 1800) to <)2 hours (ill 1842). Meanwhile, amllysis, the rigorous

study of mathematical functions, climbed to the top from its secondary role. BcI-haste, Dahan, Dalmcdico, and Picon, La formation palytechnicienlle (1994),20-21; Shinn, Savoir scientiiique et pouvoir social (1980). On Monge's projective

geometry, see Dastou, "Physicalist Tradition" (1986). On pedagogy in physics more

generally, see the Warwick articles cited above and Olesko, Physics as a Calling(1991), and David Kaiser, Mahng Theory: Producing Physics and Physicists ill Post-war America, unpuhlishcd doctoral dissertation, Harvard University, 2000.

6. Poincare 011 Cornu, "Cornu" (1910), esp. 106, 120-21, originally published

in April 1<)02 (cf. Laurent Rolld, Iienri Poincare. Des Mathematiqlles (1/([ Philoso-phie. Etude du parcour« intellectuel, social et politique d'un matllf!l17alicicn all debutdu siecle, unpublished doctoral dissertation, University of Nancy 2, 1999,40<));

Cornu, "1,,1 Synchrouisation cicctromagnctiquc" (IK94).

7. Picon opposes this distant- respect for experiment to 'Jerry Shinn's character-ization of the curriculum as more frankly hostile to experilllcllt. Bclhoste, Dahan,

Dahnedico, and Picon, La [ormation polyteclinicienne (1994), J70-71; Shinn,

"Progress and Paradoxes" (l9R9).

R. See Poincare to his mother, e.g., C76/A74, C97/AU I, C 112/AI 50,

C 114/1\152, CII6!J\J6Z. ill Cottesoondauce de Henri Poincare (unpubl. Archives-

Centre (l'I::lndcs ct de Recherche Henri Poincare, 20()J), all from the academic

year I ~71-74.9. C79/A<)2, ill Corres{)undallce de Henri Poincare (unpubl. Archives-Centre

d'F:tllc!es ct de Recherche Ilcnri Poincare, 20()]).10. Roy and Dllgas, "Henri Poincare" (1954), 8.I I. See Nyc, "Boutroux Circle" (1979). Quotation frol1l Archives-Centre

d'I::tuc!es ct de Recherche Henri Poincare microfilm '3, n.d. (probably 1877) ill

Laurent Roller, rJellri Poincare. Des Mathematiques a la Phi/()sophie. I::tude du par-cours intelleciuel, social et I)olitique d'un matliematicien au debut du siecle, unpub-

lished doctoral dissertation, University of Nancy 2, 1999, 78-79, Oil 79; also cf. 104.

For the limits of science debate, see Keith Anderton, The Limits of Science: A

Social, Political and Moral Agenda for Epistemology, unpublished doctoral disscr-

tation, Harvard University, 1993.

12. Calinon, "I::tude Critique" (1885), 87.

332 OTES TO PAGES 57-75

13. Ihid., 88-89; letter Cali non to Poincare, 15 August 1886, in Coireuxnulancede Henri Poincare (unpubl. Archivcs-Centre d'I~:t11(lcs ct de Recherche Henri

Poincare, 20(1).

14. Calinon to Poincare, 15 Angust 1886, in Correstxmdance de Henri Poincare(unpubl. Archivcs-c Ccntrc d'I::tlldes et dc Recherche Henri Poincare, ZOOI).

15. Roy and Dugas, "Henri Poincare" (1954), 20.

16.1hid., 11).

17. Ibid , 17-18.

IR. Ibid., n; on Cacn appointment sec Gray and Walter, Henri Poincme(1997), l.

19. On Poincare's emphasis on curves see Cray, "Poincare" (l9<)Z); Cilain, "La

thcoric qualitative de Poincare" (FNl); Coroff, Introduction, in Poincare, NewMethods (llJl)~), 19. Two fine articles on Poincare ami chaos arc Cray, "Poincare

in the Archives" (19<)7), and (more technical] Andersson, "Poincare's Discovery of

Llourocliui« Poillls" (llJ94).

20. Corol], Introduction, in I)oillcare, New Methods (llJ9~), 19, from Poincare,

"Mcinoirc surlcs courbcs" Ililllli, ~7()-77.I<lllphasisaddcd.

ZI. Poincarl', "Sur les courhcs dcfiuics par Ics equations c1ifferenlidlcs" 11;)1)5],

l)(); cited ;llld lranslaled in Barrow-{ .rccu, "Poincare" (1l)97), 14.

22. ItJrrow-Crecll, "Poincare" (llJl)7), SI-5l).

n. Poincare, "I ,a I.ogiqnc cl l'iuluiliou" [11)1)l)1, I ~2.

Z4. Millag-I.erner 10 Poincare, I () [uly Will), letter il9, ill f.<I C01TesfJolI.c/allceentre ('oil/can! el Mil/<lg-f .e/iler (I ()l)()).

Z5. "I h.ul Ihol\ghl 11,;11(1/lII,ese .isvmplol ic curves, havillg ruovccl away [rom a

closed curve rcprcscul iru; a periodic solution, woulcl then asymplurically approach

lire same curve." Poillcare 10 M ill;lg-1 .erner, I Decem her Ill;)'), leiter 90, ill f.<I Cor-res/)(mc/<fllce entre l'oincat« elMilI<fg-f .eflleT (1')99).

Z(l. Poincare to Mittag-I.effler, I December 11);)<),letter ')0, in 1.(/ Corres(Joll-

dance entre Poincare ct MiUag-f .efller (1,)9lJ).

27. Millag-I .cfflcr 10 i'oillcare, ;111(1Hilaehed notes, 4 December jilll9, leiter 92,

ill I.a C()rres/)()ll(lanGe entre Pouicar« et Miltag-f .e/lZer (llJl)9).

ZI). WeierslTass 10 Millag-1.eftler, il March 11)<)0,note to letter lJZ, in La Corres-fJonc/<lllce entre Poincare et Mitfag-I.ef17er (J 99lJ).

Z9. I'or an accessible discussion of chaotic phenomena, see I':kelaml, Mathe-matics (198!)), and Diucu and J lolmcs, Celestial Encounter» (1<)96), from which

the following figures arc drawn; more technical discussions ill Barrow-Green,

"Poincare" (1997); auc] Corolf, Introduction, in Poincare, New Methods (19lJ3).

30. Poincare, New Methuds (1993), part 3, section 397, 1059.

31. 011 the postmoclcru interpretation of chaos, see, for example, Hayles, Chaosand Order (1991); Wise and Brock, "The Culture of Quantum Chaos" (1998); for

physics and the connection of chaotic physics and art, see Eric J. Heller,

www.ericjhcllcrgallcry.corn (accessed [une Il), ZOOZ).

32. Poincare, "Sur le probleme des trois corps" II il901, 490; Poincare, Preface

to the French Edition [lSlJZ], in idem, New Methods (1993), xxiv.

33. Poincare, Preface to thc Frcnch 1':dition II ;)<)Z], in idem, New Methods(1993), xxiv.

34. Poincare, "Sur les hypotheses fondamcntalcs" [1887], 91.

~ 5. Poincare, "Nou-Eucl idcau Geometries" [1891], in idem, Science and

HYf)othesis (J 9(2),50,41-43.~6. Cicdymin, Science and Conventioll (198Z), ZI-Z3, on Z3.

~7. On Riemann, for example, ef. A. Cruenbaum, "Carnap's Views" (1963);

and his Geometry and Chronometry (1968). On Helmholtz as a source for Poincare,

Gerhard Llcinzmann, "Foundations of Ccornetry," Science ill Context 14 (ZOOI),

457-70. On reading sources of Poincare's mathematical conventionalism from

more COlitemporary sources stleh as Jordan or Hcnuite, see Gray and Walter, Intro-ductiou, in llenri Poincare (l9lJ7), 20.

3il. Poincare, "Non-Enclidean Ceollictries" Ilil9].!. in idem, Science andHY/Jothesis (19()Z), 011 SO, emphasis added.

C II APT)': R 3

I. Due Louis Deeazes, in Documents c1ifJ[omatiqlles (1875), see 36. For all

excellent introduction to the joint moral and technical history of standardization,

see Wise, cd., Precision (1995), and further references in the rich essays by Simon

Schaffer, M. Norton Wise, G fa ham Cooday, Ken Alder, Andrew Warwick, Fred-

cric I Iolmcs, and Kathryn Olesko. On the original mission to fix the meter see

Alder, Measure (Z()02).Z. J.B.A. DUln;]s, ill f)oCll1llen/s dif)lolllatiques (J 875), Ill-30, esp. IZ6-27.

3. Cuillaumc, "'I ravaux dl t Hurcau Inkru;llional des Poids et Mcsurcs" (I ;)90).

4. Comptcs rcndus des sec111ces de la premiere conference gencrale des poicls

ct rucsurcs, Poincare, "Rapport" (lill)7). After II,e burial ofM, metrological work

moved toward the adoption of a different sort of procedure, one in which the wave-

length of light became the standard oflengtll-;Ind so replacing that particular bar

with a certain number of cesium wavelengths. This amalgamation of metrologists

and spectroscopists, astrophysicists, and optical physicists is tracked by Iwo fine

pieces: Charlotte Bigg, Behind the Lines. SfJectroSCI)fJic Enterprises in Early Twen-tietli Century EurofJe, ullpublished doctoral dissertation, csp. Part II, University of

Cambridge, 200Z; ami Staley, "Traveling Light" (ZOOZ).

5. "Le Nouvel etalon dunlCtrc" (1876).

6. Le Temps, Z8 Scptcmbc T 1889, I.

333

334 NOTES TO PAGES 92-107

7. See, for example, in Comptes rendus de I'Academie de« Sciences: Violle, "Sur

I'alliage c111kiJograml11c" (1889); Larce, "Sur l'extcnsion du systeme metr ique"

(1889); Bosscha, "f:tlldes relatives iJ la comparaison du metre international" (1891);Foerster, "Rcmarqu-, sur Ie prototype" (UN1), 414.

8. "Extra it du Rapport du Chef du Service 'Icchniquc," Pouts ct Chaussccs, 5

March 1881. Archives de la Ville de Paris, VONe 219.9. Dol iru-van ROSSlllll, History of the Hour (1996), 272.lO. "Consci] de l'Ohservatoire de Paris, Prcsidcncc de M. l .o Verrier" [1875];

I.e Verrier to M. le Prcfet lJanuary?, 1875?), both Archives de la Ville de Paris,

VONe Z19.II. "Projcr d'UnifieatiOll dc l'hcure dans Paris. Rapport de la Commission dcs

horlogcs," 22 January 1879. Archives de la Ville de Paris, VO C 219.IZ. Trcsca, "Sur lc rcglagc clcctriquc de I'hcurc" (188()); 11IgcnicIIf en Chef,

Adjoint aux 'I ravaux de Paris, "Quelques Observations en Rcpollse'llI Rapport <111

25 Novcmbrc, 1880." Archives de la Ville de Paris, VONC ~184, (J.

13. See, for exalllple, C. Collin to M. Williot, 23 September 1882; G. Collin

to M. Chretien, J 0 April 188'3; hoth Archives de ]a Ville de I'aris, VONC 219.14. Hregllet, "r:l1l1ifie.ltion de I'hcurc" (1880); on time coordination ill l'aris,

see also David Anhin, "hiding Star," forthcoming.15. lVI. I'~lye to M. lc Dircctcur, Direction des 'lravaux de I'aris, ](i [auuary

188<1.Archives de b Ville de Paris, VO C 219.I(). orellillg, "[,'(Jnificatioll" (1888), 19j.17. Ihid., 198,200-201, and 202.18. Ihid., 21]]9. Sohel, T.o/lgill/de (19l)5), and Bennett, "Mr. 1 lnrrisou" (2()02).20. C. P. BOllel to A. n. Bache, Supt uses. 28 Feb. 1854. I l.uvart] University

Archives, Harvard College Observatory, Cambridge, MA. Chrouomctric lxpcdi-

Iion, letters, reports, miscellany; Box I: Reports.

21. W. C. Bond, "Report of the Director" (4 December 1850).22. W. C. Bond, "Rcport of the Director" (4 December 1851), clvi-c1vii; C. 1'.

Bond to A. n. B,IChc, Supt. USCS. 22 Oct. 1851. Both clOClI1l1ellts ill }Iarvard Uni-

vcrsity Archives, Harvard College Observatory, Camhridge, MA. Chronometric

I':xpeditioll, letters, reports, miscellany; Box 1: Reports.

23. Stephens, "Partners ill Time" (I <187), 378.24. Stephens, '''Reliahle 'I'imc'" (1989),17; who cites, 011 19, Shaw, Railroad

Accidents (1978), )1-33.25. Bartky, Selling Tinze (200(), M.

26. "Report of the Director" (J 853), clxxi.

27. The litcrature 01\ individual observatories is simply immense, and there is

no better survey of their various roles in time coordination than Bartky, Selling Time

(2000), which concentrates on the American case.

Z8. Jones and Boyd, "The First Four Directorships" (1971), on 160; agreemcnt

with Boston & Providence Railroad, Boston & Lowell, Eastern Railroad Company,

Boston and Maine Co., etc. Harvard University Archives, Harvard College Obscr-

vatory, Cambridge, MA. Observatory Time Service, 1877-92. Box 1, folder 7.Z9. "Historical Account" (1877), 22-23.30. Pickering, in idem, Annual Report of the Director (1877), 10--11.31. Report from Leonard Waldo, assistant to Prof. Edward C. Pickering, Direc-

tor of the Observatory Harvard College, 20 November 1877, Appendix C in Pick-

ering, Al1nllal Report (1877), 28-36.32. George H. Clark, Proprietor, Rhode Island Card Board to Director of Carn-

bridge Observatory, 16 May 1877. Harvard University Archives, Harvard Collegc

Observatory, Cambridge, MA. Correspondence re: Time Signals. Folder 2.33. Waldo, "Appendix e" (1877), 28-29.34. Ibid., 33-34.35. Charles 'Jeske to Leonard Waldo, 12 July, 8 August, 15 August, and 1 J

November 1878. Harvard University Archives, Harvard College Observatory, Calll-

bridge, MA. Correspondence re: Time Signals. Folder J.36. Leonard Waldo, handwritten report to Director for year cnding I Nov 1878.

Harvard Uuiversity Archives, Harvard College Observatory, Cambridge, MA.

Observatory Time Service, 1877-9Z. Box I, folder 8.37. Charles Teske to Leonard Waldo, [illegible day] December 1878 and 15

April I 87<J. I larvard University Archives, Harvard College Observatory, Cambridge,MA. Correspondence re: Time Signals. Folder 1; "Law of Connecticut, approved

March 9,1881," Statutes of Conn., 1881, Ch. XXI. Harvard University Archives,

Harvard College Observatory, Camhridge, MA. Observatory Time Service,

1877-92. Box I, folder 6; S. lVI. Seldon (Gen. Mgr. New York & New England RR

Co.) to W. F. Allen, 23 March 1883, William F. Allen Papers, New York Public

Library Archives, Ncw York City, NY. Incoming Correspondence: Box 3, book I.

38. 'l'. R. Welles to L. Waldo, 5 December 1877. Harvard University Archives,

Harvard Collcge Observatory, Cambridge, MA Correspondence re: Time Signals.

Folder 2.

39. Proceedings of the American Metrological Society (1878), 37.40. Bartky, "Adoption of Standard Time" (1989), 34-39.41. "Report of Committee on Standard Time" (May 1879), 27.42. Ibid.

43. W. F. Allen to Cleveland Abbe, 13 June 1879. William F. Allen Papers, New

York Public Library Archives, New York City, NY. Outgoing Correspondence: Box

3, book VII, I; the two Time Conventions merged in 1886 becoming American

....------- -----.-.-------~~~--

335

I"

:1

I

NOTES TO PAGES 115-123 NOTES TO PAGES 124-128 337

Railway Association, later Association of American Railroads. Sce Bartky, "Inven-

tioi. of Railroad Time" (1983), 13.44. Clcvclam! Abbe to W. F. Allen. 14 June, J879. William F. Allcn Papers,

Nc\v York Public T .ibrary Archives, New York City, NY. Incoming CorrespollClcnce:Box 3, hook I.

45. Charles Dowel had in mind a system not far from what was adopted. Butwhen ill J87lJ he asked Allen if he, Dowel, could prepare an article explainiug hisidca for "National Time" in Allen's Railway Cui de, Allen demurred, saying thatthere silllply was no space for the intervention. Charles V Dowel to W. F. Allen, 3DOctober 1879. William II. Allen Papers, New York Public I .ibrary Archives, NewYork City, NY. Iucomn u; Corresp0\l(!cncc: Box 3, book I; W. II. Allen to Dowel, 9December 1879. William l. Allen ])apers, New York Public I .ihrary Archives, NewYOI-kCity, NY. Outgoing Correspondence: Book VII. I .ctrcrs rcprinted in Dowel,

Charles II. Dowel (193()), IX.46. On I,'lellling, sec I~laise, Time Lord (20()()); Creel, "Sandford Flellling"

(J ':l(0); older Iilcralurc includcs lhapec, Sandjiml/1lellling (1915). Quotation inIlklning, "'Ibrestrial Tillie" (I 87(»), 1.

47. I"icnling, "'llTrestrial Time" (187(»), 14--15.48. Ibid., 31, 22, ;ll1d 3()-37.49. I,'lellling, "I ,ongitmlc" (I 87<J), 53-57; attack on thc Ilrench position OIl 63.50. (;lcveland Abbe, I IS Signal ()ffice, to Sandford Ilictning, 10 March I i)80.

Banwnl to lilellling, 18 March, () April 1880, amI 2<)April 1881. All BaIllard toIllcllling letters Sandford Illclning l'apcrs, National Archives of Canada, Ottawa,O)ltario, Me 2') I~I Vol 3. File: Baring-Bamard. 11m Baruard showing a watch, seePrf)cee<iillgs ojthe American Metrological Society (18~B).

51. Bantard to Ille1ning, 11 [uuc 1881, Sandford Illenling Papers, NationalArchives of Cau.uln, Ottawa, Ontario, Me 29 HI Vol :;. Ilile: I)aring-Bamard;Slllyth, "Report to the Board of Visitors" (1i)71), RI2-R20, on RIlJ; response toSlllyth's work more generally by Baruard, "'I 'he iVletrology" (1884). On Smyth andhi~ natnral thcologieal metrology, see Schaffer, Metrology (I <)'J7).

52. Airy to Baruard, 12 [uly 188J, Fleming Papers, vo!. 3, folder 19.53. Banwrd to Fleming, 19 Angllst, :; September, and 8 September 1881, qno-

tation from 3 September. Sandford Fleming Papers, National Archives of Canada,Ottawa, Ontario, vol. 3, folder 19. On the shambles of 'lhumsou's appointment:

B'lntard, "A Uniform System" (1882).54. [olm Rodgers to I lazcn, 1J [unc 1881. United States Naval Observatory LS-

M vol. 4.55. "Report of the Committee" \Dceember 1882\.56. Co!. II. S. Haines (Gen. Mgr., Charleston & Savannah Railway) to W. 11.

Allen, 12 March 1883. William F. Allen Papers, New York Public T.ibrary Archives,New York City, NY. Incoming Correspondence: Box 3, book I, 72.

57. Allen, Rel)ort on Standard Time (lH83), 2-6. W. F. Allen, Scrapbook, atWidener Library Harvard University.

58. Allen, Report on Standard Time (18K'S), 5.59. Ibid., 6.60. Figmes on the number of letters and telegrams from Allen, "llistory" (1884),

42; figmes on the number of lines running from different cities' times from Bartky,"Invention of Railroad Time" (1983), 20.

61. Newspaper article, unsigned, in letter to W. F. Allen from F. C. Nuncn-machcr (Central Vermont Railroad), 23 November 188"3.William F. Allen Papers,New York Public Library Archives, New York City, NY. Incoming Correspondence:Box 5, book IV, 158; E. Richardson (for D. D. Jayne and Son, Publishers, Philadel-phia) to W. Ii. Allen, 5 December 1883. William ]i. Allen Papers, New York Pub-lic I .ibrary Archives, New York City, NY. Incoming Correspondence: Box 5, bookV,48.

()2. See, for example, tclegram of Col. A. A '.1;lllllagc (Cell. 'J I-allsporl.lVlgr. ofthe Missouri Pacific Railway), ill Allen, "Il istory" (1884),42; S.W. Cummings(Central Vermont Railroad) to W. F, Allen, 2CrNovelllbcr 18~n. William ]i. AllenPapers, New York Public Library Archives, New York City, NY. Incoming Cone-spon.lcucc: Box 5, book V, 18; and George Crocker (Asst. SlIPt., Ccutral Pacific R.It San l'raucisco) to W. F. Allen, 8 October 1883. William l.Allen Papers, NewYork Pllblie I .ibr.uv Archives, New York City, NY. Incoming Correspondence: Box4, book 11,97.

6:;. John Adams (Ccn. Supt., Fitchburg Railroad) to W. F. Allen, 2 October1883. William Ji. Allen Papers, New York Public Library Archives, New York City,NY. lncomins; Correspondence: Box 4, book II, 68; W. ]i. Allen to John Acl.nus, 4October 188:;. Willian] Ii. Allen Papers, New York Public I .ibrary Archives, NewYork City, NY. Iucoiuiru; Corrcspoudcucc: Box 3, book VII, 299.

64. Proceedings of General Time Convention (II October 1883).65. Ibid.66. I,tH U.S. am! Canada, Proceedings of the Southern Railwav Time CrJllvcll-

tion (17 October 188:;). '67. Proceedings of the General Time Convention (11 October 1883).68. W. F. Allen to Mayor Franklin Edson requests shift of New York time to 75th

meridian; followed by Edson to Alderman, 24 October 1883, in J. S. Allen, cd.,Standard Time (1951),17.

69.7 November 1883, in 1- S. Allen, cd., Staiulard Tinie (1951), is.70. Barnard to Fleming, 22 October 18fB.Fleming Papers.

11·.1III.'

71. ele Bernardiercs, "Dctcrminutious rclcgraphiquc" (1884). On de

Bcrnardicres: Dossier SlIT Octave, Marie, Gabriel, Joachim de flenwrdieres, Novem-

ber 1886. Arch ivcs of the Service h isloriquc de 1a marine, Vincennes, No. 2879.

72. Figurc; details from www.porthellrIlo.org.l1k/refl.ibraryIColIstruction.html.

(accessed 14 February 2()02).

73. Crccn, J~efJ()rt Oil 'l'elegra/J/zic Deletnunation (1877), ')-Hl.74. He/JOrt oitlie Superintendent of Coast Slirvey (1861), n.75. Before the Civil \lVar, the process had a rather improvisational quality. Duel-

ley Observatory ill Albany, New York, for example, aimed to determine its relative

position to New York City by loftillg a wire from a small wooden bllildillg usscm-

bled 011 the observatory site to the private residence of astronomer Lewis M.Ruthcrfurd, esquire, al Second Avenue and I':lcventh Street ill New York Cily. By

B. fl.. Could with observers Ccorge W. Dean with I':dwanl Coodfel\ow, fl.. 10:.Winslow and fl. .' I'. Mosman, appendix 18, ill J<el;ort of the Sll/JerilltellClent 0( the

Coast Surve» (18(l2), 221-n.7(). lutrodnctiou, in Report of tlic SU/lerilltelldent of the Coost Surrey (1864);

also ibid. Could, appendix I il, I 54-S(): I{e/Jorl of the SU/lcrillielldellt or the COdstSurvey (18(l»), csp. 21-2).

77. I{e/)()rl of the SII/Jeril/te/l(lell/ or the CO(/st SlIn'ey ('8()7), esp. 1-8 and ibid.

Could, appendix 14, t SO-51.

7S. /{el)()rt or {he Superintendent. of /he (;O(/st SlIlvey (I S()7), (lO.

7(). See, for example, Preseoll, Ilis/O/y (18(l6), csp. ell. XIV; l'i1111, "CroWillg

Pains atthe Crossroads" (197()); aud Provinci.il Historic Sile, "Ilc.rrt's COlIll'lI1

Cahl c St.uion" (www.lark.ieee.eallihr:lrylllearls-e011Ielltlllisloriclprovsile.lllllll ,

accessed 011il April 20(2).

80. On Coulcl's earlier America: I work ,lIld Iris adopliou of Brilislr techniques,

see Barlky, Selling Tillle (2()OO), (d-·n. On tire transatl.mtic work, see Could, ill

]{e/Jort of/he Superiuietulcu! o(the Coast Survey (l S(l9), (lll-(l7.

81. Cuuld, in /{efJOrl or tile Sllllerilltem/ent of the C()<I:;{ Survey (I S(9), () I.82. Cuuld, in RefJOrt of the Superintendent of the Coo»! SlIn'ey (I S(9), (l1, ().

81. /{ef)()rt of the Suoerintendent of the COlf~t Survey (187~), 16-1 Ii; uppcuclix

IS in /{efJOrl o(the Superintendent (IS77), 1(l)-()4. Triangle in ibid., 1M.84. C rccu, l\e/JOrt 011 the 'l'elegrafJhic Detetni inaiion ( 11)77).

S5. Creon, Davis, and Norris, 'l'e/egra/J/zic De termination of /,rmgil.lldes (18S0).

So. Ihid., S.87. Ibid., 9.

t-iil.Davis, Norris, and Laird, Telegraflhic Determination of! lJJlgiludes (1885), 10.

89. Ihid., 9.

90. de Bcrnurdicrcs, "Dctcrrninatious tclcgra phiqucs" (1884).

91. La Porte, "Dctcnnination dc la longitude" (1887).

92. Rayct ami Salah, "Dctcrmiuation de 1<1longilude" (1890), B2.

93. Annex III in International Conference at Washington (IS84), 210.

94. Septieme COllference GeodesiqHe lutemaiionale (1883), 8.

95. lntetnational Conference at Washingtoll (I HS4), 24.96 Ibid, 37.

97. Thiel., )')-41,011 W9H. lbid., 41.

99. Ibid., 42-47, Oil 47.

100. Ibid., 42, 44, and 49-50.101. Ibid., 51.

102. Ihid., 52-54.

I ()~. Ihid., 54.

1()4. Ibid., (l2-M, ou M.

105. Ihid., (l)-(lK, quotations on 6), «r, 68.

106. Ibid., ()8-(,!).

107. lhid., 76-80.

1OS. lbid., J .cfaivrc 01191-'>2; adoption of the metric system on 92-9~: Thorn-

SOli on 94; tire vote, see 99.

109. lhid., 141.

no. Ihid., 159 and 180.

III. On the history of the revolutionary calendar ill France, see Haezko, "l .e

Calcudricr rcpublicain" (1992); Ozouf, "Calendrier" (1992).

112. lnternational Conference at Washington (1884),183-88, on 184.

..

CHAPTER 4

I. Janssen, "Sur lc Congrcs" (1885), 716.

2. /\1 tire Paris 'telegraphic Conference of 1890, the assembled urged adop-

t ion of a universal time that would be set for all the world by the lime of clocks

at lire prime meridian: ef. Docllments de la Ccmterence Telegraphiqlle (IH91),60S-I).

3. I Iowarcl , l'ranco-Prussiau War (197<.J), quotation on 2, see also 43.

4. Huchol«, Moltlw (1991), ch. 2 aucl ~,esp. 146-47; also Bucholz, Moltke andthe Cernian Wars (200]), 72-7'3, 110-11, amllC)2-0).

5. The cstablisluncnt of uniform lime is discussed ill Kern, Culture (1983),11-14; und iu I Iowsc, Greenwich (1980), 119-20. Si1l1011 Schaffer uses the Wells

time machine ,IS a guide through to the turn-of-thc-ccuturv intersection of the

mcclumizcd workplace, literary and scientific engagcment with time in "Time

Machines" (in his "Metrology," 1997).

G. Molrkc, "Driltc Bcrathung des Rcichshaushaltsctats" (I il92), 3il-39 and 40;

339

NOTES TO PAGES 159-173 NOTES TO PAGES 173-194

trans. Sandford Fle1hing, under the titlc "General von Moltkc 011 Time Reform"(1891),25-27.

7. Fleming, "Gclleral von Moltke on crime Reform" (1891), 26.

S. Newspaper clippings from the Cambridge University Library, including

P.S.L, "Fireworks at the Royal Observatory," Castle Review (n.d.); N igcllIamilton,

"Crccuwich: lIavil\g a Co at Astronomv." Illustrated London News (1975); ane!

Philip 'l aylor. "ProPaganda by Deed-th~'Creenwich Bomb of IS94" (lI.d.). Con-rad, Secre/Agent (11)53), 2S-29.

9. Lallcurauc], L/lll1ificatioll internatianale des heures (IS97), 5-6.10. Ibid, 7.II. [bid., S ami 12.

12. ibid., 17, IS, and 22-n.1:;. Poinc.uc, 'l~.apport sur la proposition des [ours .istrououuquc et civil"

Im)51·

I 'f. l'rcsidcut of ~hc Bureau on ,()]Igitude, 15 February IS97, 1)ecimalisalioll dll

lenu»: et de la cireOl)ferenee, executiug all order of the Minister of Public Instruc-

tion, 2 October IS') (l. Fr()]!1 Archives Natioualcs, Paris.

15. Commission ele deeil1lalisa(ioll du teinb«, :; March I~97.11>.Ibid., O.17. lhid., ::.

IS. Nohlcmairc to President locwv, 6 March 18()7; priutcd in Cmml1issioll dedeei111<1iisalioll dlll~/1lIJS, :; March 1897,5.

10. IkJ'l];Jr(licre~ to Monsienr lc l'rcsidcnt clu Burea\l des 1,ongitudes, 1 March

1wn, printed in CO'11Il1lissioll de deciIHulisulio/l du lelllf)~, -; March Iwn, 7.20. Ilme;1l1 de I a Societe francaise de Physiq\le to M. Ie Miuistrc du COJll-

iucrcc, approved b~ the Conscil de ]a Socic:tc OJl 22 April I W)7; reproduced in

[auct, "Rapport sur lcs projets dc rcformc" (1S07), 10.

21. In a(lditioll t',o the factor of 4 just mentioned, the division of the circle into

400 parts had a fac~or of 6 to COllver! 24 hours of time per day into tire 400 grads

that divided tire cin,::le (dividing 24 by 400 yieldul ,I factor of 6); the filial factor of

9 cntered when ()n~ wanted to couvert between old ;Inglcs .md ucw oucs-multi-

plying by 36() and di ividing by 4()O. The chart itsclf is reproduced in Poincare, "Rap-port sur les resolllti(\)]\S" (IS07), 7.

22. The Sarrallt\on system is presented in Sarrautou, Heure tlecuna!« (lS07),

with Sarrautou's COt nhihutiou dated April I K06.

n. Commission: de decimalieation du temp», 7 April IS07, 3.24. Cornu, "La: Dccimalisation dc l'heurc" (IS97).25. Ibid., 390.

26. Poincare, "1, .a dccimalisalion de I'hcure" [IS07], 678 and 679.

27. Note pour Monsieur lc Ministrc, 29 November 1905, Archives Nationalcs,

Paris, F117/2921.28. Sarrauton, Deux Projet« de loi, addressed to Loewy at the Bureau des Lon-

gitudes, 25 April 1899, Obscrvatoire de Paris Archives, I, 7, and 8.

29. La Grye, Pujazon, and Dricncourt, f)itlerences de longitueles (IS07), A 3.

30. Headrick, Tentacles (1088), 110-13.

31. La Grye, Pujazou, and Dricncourt, f)ifTerences de l()llgitllde~ (1S07), A6.

32. Ihid., AI), citation on /\S4.

33. La Cryc, Pujazou, and Dricucourt, Differences de fongitude~ (IS97),

A135-36.

34. IIcadrick, Tentacles (198S), 115-16.

'35. A discussion of the Paris-London longitude campaign can be found in

Christic, Telegra/Jhic Determinations (1006), v-viii and 1-8, and further references

therciu. On the desirability of a redetermination, see the International Geodetic

Confcrenee, Paris, 1898.

36. I.ccturcs of 18lJZ-,)3 rcpriutcd in Poincare, Oscillatio/lS Electriqlles (lS94);

idem, "I<tnde de la propagatioll" II,)04L 0]] subm.uinc case, see 454.

'37. /{e/JOrl of the Superintendent or the Coast Survey (IS60), 116.

38. l.ocwy, I ,c Clerc, aud de Bcruardicrcs, "Dctcnniualion des (liffercnccs dc

longitude" (] SK2), A26 and A203.

'30. Rayc! and Salats, "Determination de la longitude" (IS00), BI 00.

40. 1.a Crye, l'ujazon, and Driencourt, Diflerence~ de longitueles (IS07), Al 34.

41. Calinou, t::tude sur les diverses grClndeurs (18')7), 20-21.

42. Caliuou, 1::11{(lesur fes diverse» grandeurs (IS07), 23 and 26. lonucr Poly-

technician Jules Andrade said much the same thing ("there is an infinity of admis-siblc clocks") in Iris book OIl the foundations of physics, Lecons de nieclianiquef)hysiCfue (Paris, IS0S), 2, which he Finished Oil 4 September 1807. Poincare cited

this work too ill "The Measure of Time" to support the contention that when we

choose one clock over another it is a matter of couvcnicncc, not of one running

true aud the other wrong. Though Poincare pursued the quantitative "scientific"

notion of silmultancitv while Bergson attended principally to the qualitative expe-

ricncc of time, Bergson's Time and Free Will (I18S01, 200]) focused attention on

the meaning of time.

43. Note pour Monsieur lc dircctcur, 20 March 1000. Archives Nationales,Paris, F/17 113026. Martina Schiavon tracks the role of the army, surveying, and the

savant-oisicier in her richly documented study, "Savants ()fllcier~" (200 I). For a tex-

tured study of colonialism and surveying (and lllany further references) see Bur-

nett, Masters (20{)O).

44. Compte» reiulus de ['Association Geoc/esique lntemationale (IS09), 3-12

i~

I.'

~.'"!fi~~-'':/'''

:1,..·.::.OJ~~'

NOTES TO PAGES 193-207 NOTES TO PAGES 207-218

October 1898, 130-33, 143-44; Poincare's remark ill Comptes rendus de I'Academiedes Sciences 13] (1900), Monday, n [uly, 218.

45. Headrick, Tentacles (1988),116-17.

46. Poincare, "Rapport sur Ie projet de revision" (1900), 219.

47. lbid., 221-22.

48. Ibid., 225-26.49. Coinbte« rendus de I'Association Geoc/esique lntemationale (J 901), 25 Sep-

tember-6 October 1900, session of 4 October, also Basset, "Revision de l'arc"

(1900),1275.50. Compte» reiulus de I'Academie des Sciences 134 (1902); 965-66, 968,969,

and 970.51. Compte» rend liS de l'Academie des Sciences 136 (1903), Sol.52. COII/ptes reudus de [,Academie des Sciences 136 (1903), 861-62.

53. COIn/Jtes reiulus de ['Acac/(hllie des Sciences 130 (19m), S62 and H6H; on the

destn rction. Com/Jte.~ rentlus de I'Acac/emie des Sciences 1 3S (1904), I () 14-15 (Mon-

day 25 April I()()4); native informants, Compte: rendus de {'Academie des Sciences140 (19()5), 99K and 999 (Monday 10 April 19(5); quotation from Comptes reiulusde /'Acade11lie des Sciences B6 (19m), 871.

54. 1 ,<I 11rent Roller, Hellri Poincare. Des Mathematiqlles (I La Phi/osophie. f::llIdedu IJarcolirs intellectuel, social et {JOtiliqlle d'un uuttheniaticien all debut du siecle,ullpublished doctoral disscrtution. University ofNaney 2,1999,165.

55. Poincare, "Sur lcs I'rincipcs de la mccauiquc"; origillally fro II I Rihliotheqlledu Congres international de /)hilosophie Ill, Paris (llJO I), 457-lJ4; urodificd and

reprinted ill Poincare, Science aiu! 11ypothesis [1902], ch, 0,90.

56. Poincare, "The Classic Mechanics," in Science and flY/JOllIesis 11902], cli.

6, 110, lO4-0).57. Poincare, "i lypotlrcscs ill Pllysics"; origillally "Lex relations entre la

physique cxperimental<.: ct la physique mathcmatiquc" in Revue generale des sciencespures et appliquees 11 (1900), 116~-75; reprinted in Science and HY/Jothesis [1902],

ch. 9,144.58. Poincare, "Intuition and Logic in Mathematics"; originally "Du rfile de l'in-

tuition ct de la logiquc CII mathernntiqucs," in Comptes Rendlls du deuxieme COl1-

gres iniernaliouai des mathematiciens tem! <'1 Paris du o-J2 aOllt 1900; reprinted in

Poincare, Foundaiion« of Science (1982), 2l0-1!.

59. Poincare, "La thcoric de Lorentz" [1900],464.

60. Lorentz, Versltch einer Theorie 11895].61. Poincare, Electricite et optique [19011. 530-32.

62. Christie to Poincare, 3 Angnst 1899, accompanied by Christie to Loewy, I

December 1898, and Christie to Colonel Basset (Directeur du Service Ceo-

graphiqlle de l'armcc), 9 February IH99. Obscrvatoire de Paris, ref. X5, C6. Poin-

care to Christie, 23 June 1899,9 August 1899, and undated (but probably shortly

after 9 August 1899), all from Christie Papers, Cambridge University Archives,

MSSRG07/261.

63. Poincare, "La theorie de Lorentz" [1900], 483.

(l4. Suppose 13 sends a signal to A at noon across the distance from A to B, AB.

B shonlcl set his clock at noon plus the transmission time (the usual procedure). Butthe speed in the left-going direction is c + V, so the transmission speed in the head-

wind direction t(headwind) is AB/(c + v), and, conversely, transmission time in the

tailwind direction is AB/(c - v). The "true" time of transmission from 13 to A is half

the round-trip time, 1I2It(headwind) + t(tailwind)], while the apparent time ol truus-

mission is [ust t(tailwind). So the error committed by using the apparent time of

transmission is the difference between true and apparent transmission times, or

I':rror = 1I2[I(hcadwill(l) + t(tailwind)]- t(tailwind)

Using the definitions of t(t<lilwind) and t(he<ldwind) above:

l':rror = 1/21AB/(c + v) - AB/(c - v)1 = lIZAB(c + v - c + v)/(c' - v' ) = ~ ABvlc'.Darrigol rightly points out that most historians of relativity have ignored this

clock coordination interpretation of local time, Electrodynamics (2000), 3 )9-60;

also Miller's wide-ranging Eimtein, Picas.wJ (200!), 200-15; for further references,

see Stachcl, Einstein's Collected Papers, vol. 2 (1989), 30811.

6). Poillcare eiles Physicie1ls, unpubl. correspondence from the lIenri Poincare

Archive: All1lCXC1, document 205, 31 January 1902.

(ll. Poincare et les Pliysiciens, unpubl. correspondence from the Henri Poincare

Archive: Auncxc I, document 205, 31 [anuary 1902.

()7. Poincare, The Foundations of Scie1lce (1982), 352.

()8. Sce the excellent discussion in Henri Rollet, Henri Poincare. Des Mathe-maiiques (/ la I'hi/osofJ/zie. L::tlldes du barcours iniellectuel, social et politique d'iuimatheniaticien <llL dehut. du siecle, unpublished doctoral dissertation, University of

Nancy 2, 1999, 249ff, quotation on 263; also Debarbat, "An Unusual Use" (1996).

69. Poincare, "].c Banquet du II Mai" (19tn), 63.

70. lbid., 63-64_

71. Dcbarbat, "An Unusual Use" (1996), 52.

72. Darboux, Appell, and Poincare, "Rapport" (1908),538-49.

73. Poincare, "The Present State and Future of Mathematical Physics," origi-

nally "I :I;:t<lt actucl et l'avenir de la physique mathernatique" [24 September 1904,

Congress of Arts and Science at St. Louis, Missouri], in Bulletin des Sciences Math-eniatiques 28 (1904), 302-24. Reprinted in Poincare, Valeur de la Science (1904),123-47, this quotation on 123.

74. Poincare, "The Present State" [1904], 128.

75. Ibid.

76. Ibid., 133. Translation modified: "ell retard" should be "offset to a later

343

I

J

I'

-------------"---------------

344 NOTES TO PAGES 218-227

time" ~the clocks do not run "slow" in the sense of running at a slower rate, ital-ics added.

77. Ibid., 142 and 146-47. Poincare et les Physiciens, unpubl. correspondencefrom the Henri Poincare Archivc: document 124, 191-93, letter from Poincare toLorentz (n.d.) but sometime shortly after Poincare's return from Saint-Louis.

n. Lorentz. "l':lectromagnetic phenomena" (1904).79. Poincare, "Los 1.imitcs de la loi dc Newton" (1953-54), 220 and 222.80. Poincare, "La Dynamiquc de l' electron" 1190HI, 567.HI. Poincare, "Sur ]a Dynamiquc,' reprinted in his Mecanique Nouvelle (1906),

22; discussed by Millcr, Einstein (l9Hl).82. Poincare et les Physiciens, unpubl. corrcspondcncc from thc l Icuri Poincare

Archive: letter 127, I .orcntz to Poincare, HMarch 1906.

C II A 1''1' I': R 5

1. Scc the excellent work on lime in Switzcrlancl, Messerli, Gieicilllziissig,pitnkt-lich, sclmell (1995), esp. ch. 5. For biographical details on Mathias l Iipp, see de Mes-tral, l'iol1l1ierssuisses (1960),9-34; also Weber and lavrc, "Malthaus I Iipp" (1897);Kahlcrl, "Matlluius Hipp" (1989). On l lipp's relation to the astrouomcr I Iirsch, andthe myriad ways in which the new tccllllologics of time and simnltuncitv precisionjoined the history of experimental psychology to astronomy, see the exccllcnt worksby Canales, "I':xit thc I!rog" (20(ll); Selllllidgcn, "Time and Noise" (2()()Z);and Char-loltc Bigg, Behilld the / .ines. S/Jcelro,w;o/lic 1';lIler/J1'isesill Early Twentieth Century/';uro/le, unpublished doctoral dissertation, l luivcrsily of Cambridge, 2()02.

2. On l Iipp, Kahlcrt, "Mattluius I lipp" (1989). Landes's work, Revolution inTillie (1981),217-1 n, is excellent on the Swiss watch industry, though he focusesOil clock production and no! 011 networks.

~. See I<'avarger,L'/:;leclricite (1924), 40R-()9.4. "Die ZUkUllit dcr ocffcnllichen Zeil-Angaben" (12 November PNO);l\IIerle,

'"lcmpo!" (1lJ8',)), J 66-7R cited in Dolun-v.m ]\OSSUlll,History or the /lour (1996),150.

S. Favarger, "Sur la Distribution de l'hcurc civile" (1902).6. Ibid., 199.7. Ibid., 200.8. Ibid., 201.9. Kropolkiu, Memoirs (llJ89), 2H7.10. Favarger, "Sur la Distribution de l'hcurc civile" (1902), 202.11. Ibid., 203.12. Ibid. Newspaper quoted in Jakob Messerli, Cleiclzmiissig Piinktlich Schnell

(1995),126.

NOTES TO PAGES 228-234 345

13. Einstein, "On the Investigation of the State of thc Ether" [IS951; Einstein,"Autobiographical Notes" (1969),53.

14. Urner, "Yom Polvtcchnikum zur ETH," IlJ-23.15. For example, Einstein's notes on Weber's lectures, in Collected Papers, vol.

1, 142. Weber's own work ranged over a variety of topics in experimental andapplied subjects: temperature dependence of specific heats, the cncrgy distributionlaw for blackbody radiation, alternating current circuits, and carbon filaments. Edi-tors' note, Collected Papen 1, 62; Barkan, Nernsi (llJ99), 114-17.

16. Einstein's notes on Weber's lectures, in Collected Pa/Jers (Translation), vol.

1, 51-53.17. EillStein to Mileva Marie, 10 September 1H99, item 52, ill Collected Pa/lers

(Translatioll), vol. 1, 132-33.JR. Einstein to Mileva Maric, August lR99; Letter 8 in Einstein, Love Letters

(1992),10-11; also in Collected Pcurers ('l1-anslatiol1), vol. J, 130-31. On Einstein'sspecific knowledge of aspects of electrodynalllics, see Holton, Thematic Origim(1973); Miller, Einstein's Relativity (19Rl); and Darrigol, Electrodynamics (2000).

IlJ. On Einstcin and the ether, see editors' contribution, "Einstein on the l~:lce-trodynamics of Moving Bodies," in Collected Papei«, vol. J, 22 3-2 5, and Darrigol,Electrodynamics (2000), 373-S0. On Einstein's early use of the relativity principle,

ibid., 379.20. Einstein to Mileva Marie, May 190 1, item 111, in Collected Po/lers (Trans-

laiion], vol. 1, 174.2J. Einstein to Mileva Marie, June 1901, item 112, in Collected Paper» ('l1'(/ns-

laiion}, vol. 1, 174-75.22. l·:instein to Jost Win icier, RJuly 1901, item 115, in Collected Papers (Trans-

lation), vol. 1,176-77. On Einstein's battle, see Rcnn's excellent article, "Contro-versy with Drudc" (1997), 315-54.

23. Department of Internal Affairs to Einstein, 31 July 1901, item 120, in Col-lected Papers (Translation), vol. 1,179.

24. Einstein to Marcel Grossmann, September 1901, item 122, in CollectedPapers (J)'(!Jzslation), vol. 1, 180-S1.

25. Einstein to Swiss Patent Office, 1HDecember 1901, item 129, in CollectedPapers (Translation), vol. 1, 18H.

26. Einstein to Mileva Marie, 19 December 1901, item 130, in Collected Papers(Translation), vol. 1, IH8-H9.

27. Einstein to Mileva Marie, 17 December 1901, item 12R, in Collected Papers(Translation), vol. 1, lR6-S7.

28. Einstein to Mileva Marie, 19 December 1901, item 130, in Collected Papers(Translation), vol. 1, IS8-89. Translation modified.

---'"

..•.

29. Einstcin to Milcva Marie, 28 Decem her 1901, itcm l 31, ill Collected PalJers(lhl11s/a/iol1), vol. 1, 189-90.

30. 1':illSteill to Milcva Marie, 4 April 1901, ile1ll96, in Collected Papers (TrallS-lation), vol. I, I62-()3.

31. 1':iIIStcill, advertisement for private IeSSOIlS,S February 1902, item 135, inCollected l'alJers (Tramlatiol1), vol. 1, 192.

,)Z.I':illstein to Milcva Muri c, I'ehru;ny Il)OZ, item 136, in Collected Papers('1falls/a lion}, vol. I, I92-<n

)3. Soloviuc, iutroductiou 10 I':instein, Letters Ln Solovine (1993), 9.34. See l lollon, Thematic Origills (1973), ch. 7.35. Mach, Science of Mechanic» II WHI, 27Z-7).3(,. 1':iIlStcill, "I':rnsl Mach," I /\priI191(), document 2<), ill Collected Papers,

vol. (), 2KO.

) 7. PC:trSOII, (;/'(1111111<11' of Science 1:])';<)21, 204, 22(), and 227.)0. I':illslcin, icller« to So/mille (1983), 8--(J. Mill, System o(Logic (l<Xl5), 322.3<). I<insleill, leitcr« to So/oville (1<)83), :-;.-<);Oil I<insteill .un] Mach, see

11011011, Theil/otic ()rigills (I <)7'»),ch. 7. Other works 1";11 Soloviuc reedls the gronpdisclIssing were those by Ampcr«, I<ssai (1004); Mill, S)'stem o(/.ogic (I <)()S); .md

l'carsou, (:/'{/1111110roj'Sciellce 1.1W)2[. I'oill(';m:, Wi,~sel/schali IIlid I 'Ylmlhese (I <)(H).40. l'oillc;l!(\ Wissellscll"li IfW/ I IYI){)these (1904), 2:-;()-K9.-+I. I':illskill to Sch lick, 1·+l Icccu rlx-r 191 S, dcxmucnt I ()5, ill Collected PalJcrs,

vol. 8a, 221; (;o//eded PalJers (Twlls/atioll), I() I.42. Mosl orten ll«: I .iuclcm.ums rcndercd ]'oincare's convention hy lihereiflkom-

meu; but, for example, wlrcu l'oillc;m:: arglled againsl the philosopher K lc Roy illScience and I 1)'IJ(Jthe.,is (I'. xxiii) thal elwnl-;c<l. l'oillcarL' wrote, "SOIlIC people havehccu struck hy Illis ch.nuclcrist ic of tree couvcntion [French: "de libr« convent ion,"Science el I IYIJOthese (24)lw"ich In;IY be r<.:eogl,ized in ccrtuiu flll1lLnncnlal prin-

ciplcs of t lrc sciences." The l,indenl;lI111s put the relevant phras« as ..... dellChatukter [reier konventioueller I'esiset;:lIlIgen ... " (Poincare, \NissellschaflllndI 'Ylmthese (1<)04), XII I).

-+3. I':insll'in 10 Solol'illC, 0,0October 1'J2-f, ill I':illsleill, Letters to S()/()ViHe, (,'l.One Ihinks (inter al ia) of Mas Planck, lhc firsl Ellnolls theorist-supporter of rcla-livity, who clisd.rincd "couvcuicncc" lalk in physics, eelebralillg instead that whichwas universal <111<1invariant. See, for example, l lcilbrou, J)ileflll1las (I <)96), -+R-52.

+l. I':instcin, "i\lllohiographischc Ski/'.ze," ill Seelig, cd., Ilelle Zeit, Dunkle Zeit(1956),12. I':insteinlo Milcva Maric lcbruary 1902, item 10,7, in Collected {'alJers(Tral1s/ation), vol. I, 1<)";.011 2 JUlie ]<)()Z I':illstein was notified officially tl1;lt hehad the joh <II Hie Paten 1Office ,It au annual sabry ofSfr 'l,5()(), item H(), ill Col-lecied Po per« (Trans/ation), vol. l, 194-95; see also item 141, 19 [unc I<)OZ, 1<)5;and that he was to aSSU1l1Chis duties 011 I July 1<)02: ilclll 142, 19().

NOTES TO PAGES 242-249 347

45. On Poincare's views on dynamics and kinematics, see Miller, Frontiers(1986), parts I, Ill; Pat}', Einstein PhiiowfJhe (1993), 264-76; and Darrigo!, ":lec-trodynamics (2000).

46. Here is not the place to offer a full tcchnicul reconstruction of all aspects ofEinstcin's path to special relativity. The reader is referred to all excellent short syn-thesis in Stachcl ct al., "Einstein ()1\ the Special Theory of Relativity," cditnri.tl notcin Collected Pa/Jers, vol. 2, 250,-74, esp. 264-65. For further development of early

history, see, for example, Miller, Eillstein's Relativit), (1981); Darrigol, ":/ectrody-fUlIllics (2000); and Pais, Subtle Is the Lord (19RZ).

47. Fluckigcr, Albert 1':ilZsteill (1974), 5R.48. I':illstein to I JaIlS Wohlwend, 15 i\ugust-3 October 1902, item 2, in Col-

/ected Papers (Trans/atioll), vol. 5,4-5.49. Fluckigcr, Albert ":illsieil1 (1l)74), 5K.50. Fliiekiger, AlbertI':instein (1974), (,7; I':instcin to Mileva Marie, September

I<)()), item 1\ in Collected Pa/Jers (Lranslaticm}, vol. 5,14-15.51. References cited in Pais, Subtle Is the I ord (19R2), 47-4R, who cites Fluck-

iger, Albert f':imtein (197-+).52. Nicolas Stoichcff, patcnt '30224 submitter] () J;I1\I1<1ryI<)()4 issued 1<)()4;

i\11Icric;1l1 J':1cctrieal Novelty, "Stromschliessvorrie htllllg ;111clcktrisclrcn Pcnclcl-wcrkcn," patent 31055 submitted 16 March 1904 and issued 1905.

q. According to the lists of patents provided in Berner, initiation (c. 191 Z),

eh.IO.5-+. l lundrcds of relevant patents are listed in the IOIlTl/al Sllisse d'hor/ogerie clur-

iug Ihe relevant years (1902-05). Sadly, the Swiss paten I office dutifully destroyedall papers processed by Einstein 18 years after their creation; this was sl.mda«] pro-ccclurc on patent opinions, and even Einstein's famc led to no exception. See l'iiIs-illg, 1':il1steill (1997), 104.

55. The most del ailed linkage bctwccu I':instein's patent work and his scientificwork is on iiyromagnctic compasses and J':instein's production of the l.iusrciu-clcl laus effect, see Calison, flow l':xIJcril11el1/s /<lId (1l)~7), ell. 2; in addition, seellughes, "Einstein" (19<)3), and Pycnson, YoulIg f':insteil1 (]<)R5). On I':instcin'sassignlllent to evaluate electrical patents, see Fluckigcr, A/hert l':instein (I <)74), ()Z.

56. Fliiekiger, A/bert Einstein (1974), 66.57. J. Einstein & Co. uud Sebastian Koruprobst, "Vorrichtuus; zur lImwand-

lnng del' unglcidJ\n:issigen Zcigeraussehl~ige von Elektri"itiils-Messern ill cineglcichJll~issigc, gradlinige Bcwegung," Kaiserlichcs Parcutamt 53546,26 FebruaryIR<)O;idem, "Ncucrung an clektrischcn Mess- und Anzeigcrvorrichtungen," Kaiser-Iichcs Patcntamt 5'3:-;46, 21 November lRR9; idem, "Fcdcmdcs Rcibrad", 60361,n February lR90; "Elcktrizitatsztthlcr dcr Firmn J. 1'~illstcill & Cic., Munchen(Systcn: Komprobst)" (1891), 949. Also see Frenkel and Yavclov, Einstein (in Russ-

I:I

i,I'II'II

I

OTES TO PAGES 253-271 349

ian) (1990),75 ff., and Pyenson, Young Einstein (1985), 39-42. Further on the links

between electric clocks and electricity measuring devices, see, for example, Max

Moeller, "Stmmschlussvorrichtung an elektrisehen Antriehsvorrichtungen fuer

elektrisehe Uhren, Elcktnzitatszahlcr und dergl." (Swiss patent 24342).

58. Swiss Patent Office to Einstein, 1 1 Decem her 1907, item 67, in CollectedPalJers (Tram/otion), vol. 5, 4(i. On Einstein's interest in dynamos, see Miller, Fron-

tiers of Physics (l9B6), eh. i. Einstein insisted that he only took \ 'P the role of expert

witness if he judged the side he was defcnding to be in the right. For example, ill

192H he defended Siemens & lIalskc against Standard Telephoncs & Cables

Ltd. -see Illighes, "Inventors" (199i), 34.

59. Calison, Ilow Experiments End (l987), ch. 2.60. I':instein to l Iciurich Zangger, 29 JlIly ]917, ducumcnt 365, in Collected

Paber«, vol. Ha, 495-96.6J. 1':1111J labichtto Jo:iusteill, 19 l-cbru.uy 1908, item 86, in Collected P(//Jers

(Trans/afirm), vol. S, 5H-(ll, 011 ()o.

()2. On "the little machine" see editors' essay ill Collected Papers, vol. 5, 51-54;

Fiilsing, I';in.~f.ei/l (I ,)97), I ~2, 241, and 2()7-7H; Jirellkel aud Yavclov, I';imtein(1990), ch. 4.

()~. l':instein to Albert Cockcl, brch Il)09, item l44, ill ColledeclPalJers(Tralls/aiioll), vo]. S, 102.

64. I':instcin to Conrad 1Llbicht, 24 December 1907, item ()9 ill Co/leciedI'd/lers (TrallS/atioll), vol. S, 47; Liustcin to Jakob L1I1I), after I November 1')08,

itciu J 25 in Collected I'a/Jers (Tralls/alioll), vol. 5, 'YO. "1 am presently Gnryi"g on

:111extremely iutcrcslint; corrcxpondcncc with I L A. I .orcnlz 011 the radiation proh-

ICIll. 1 .rcluurc lhis man like no other; I might say, I love him." l':instein to [nkob

laub, 19 May I ()()'), item 161 ill Col/eded Pa/Jers (Ii'wls/at-i(m), vol. 5, 120-22, on

1zr.()5. C. Vigrellx .u«] I,. Brillic, "Pcudulc avec dispositif clectro-maglldique pour

lc rcglage de sa nrarchc," patent ~~H15.(l). liustcin, "l Iow I Created the Theory" (19HZ). Compare remarks that I':ill-

stein recorded on a diseograph ill 1924: "After seven years of reflection ill vain

(IH9H-1905), the solution carne to me suddenly with the thought that our concepts

and laws of space and time can only claim validity insofar as they stand in a clear

relation to om experiences; and that experience could very well lead to the alter-

ation of these concepts and laws. By a revision of the concept of simultaneity into

a more malleable form, I thus arrived at- the special theory of relativity." Einstein,

in Collected Papers (li'allslation), vol. Z, 2(i4.

67. Joseph Sauter, "Comment ['ai appris a conuaitrc Einstein," printed in

Fluckiger. Albert Einstein ill Bern (1972), 156; Folsiug, Alheri Einstein (1997),

155-56.

68. Einstein to Habicht, May 1905, document 27, in Collected Papers (Trans-

lation), vol. 5, 19-Z0, on ZOo69. Einstein, "Conservation of Motion" [19061 in Collected Papers (Transla-

tion), vol. 2,200-206, on 200.

70. Cohn, "Elcktrodynamik" (1904).71. Einstein, "Relativity Principle" [1907 j, docurnenr 47, in Collected Papers,

vol. 2, 43Z-88, on435; Collected PU/Jers (Trans/atioll), 252-311, on 254 (transla-

tion modified); also I':insteill to Stark, 25 September 1907, document 59 in Col-

lected Papers, vol. 5, 74-75. On Cohn's physics, ef. Darrigol, Electrodynamics

(2000), 368, 382, and 386-92.72. Abraham, Theorie der J<:iektrizitiit: Elektromagnetisehe ') 'heorie der Strahlung

(Leipzig, 1905), i66-79; cited in Darrigol, Electrodynamics (2000), 382.

73. Warwick, "Cambridge Mathcmatics" (1992, 1993).

74. Cited in Calison, "Minkowski" (1979),98, lI2-l3.

75. Calison, "Minkowski" (1979), 97.76. For an cxecllcnt ovcrview of the reception of Minkowski's ideas, see Walter,

"The non-Euclidean style" (1')99).

77. Citcd ill Calisou, "Minkowski" (197')),95.78. Einstein, "The Principle of Relativity and Its Consequences in Modern

Physics" [1910], document 2, in Collected Papers (Tram/ation), vol. ~, 117-43, on

125.79. Einstei II, "The Theory of Relativity" [1911], dOClIment 17, in Collected

Papers (Trallslation), vol. ), 34()-50, on 348 and 350.80. "Discussion" Jiollowing 1.ccturc Version of "The Theory of Relativity," doe-

ument 18, in Collected Paper« (TrallSlatioll), vol. 3,351-58, on 351-5Z.81. "Discussion" Followillg Lecture Version of "The Theory of Relativity," doc-

ument 18, in Collected Paoer« (Trallslation), vol. 3, 351-58,011 356-58; see also

the notes to the original version in Collected Pa/JeTS, vol. 3, on 448-49. Poincare,

La Science (1905), on 165.

82. Laue, Relativitiits/Jrinzip (1913), 34.83. Planck, Eight Lectltres (199~), 120; trallslatioll111oc\ified slightly following

Walter, "Minkowski" (1999), I 06. On Planck's words and Einstein's career, see Illy,

"Albert Einstein," 76.84. Einstein, "On the Principle of Relativity" [1914], document 1, in Collected

Papers, vol. 6, 3-5, on 4; Collected Papers (lhmslation), vol. 6,4.85. Cohn, "Physikalischcs" (1913),10; Einstein, "011 the Principle of Relativ-

ity" [1914], document 1, in Collected Papers (Translation), vol. 6,4.

86. More precisely, this simple triangle shows quantitatively the relation

between time measured in the two frames. Let M be the time it takes light to travel

the distance h (so h = cM). We imagine the light eloek moving to the right at a

',- ..:"."- '--...,:,.~.•. -' .


speed v, and the inclined path of the light pulse to cover a distance D in a time M'(so D = cdt'). In the time M' that the beam takes to reach the top mirror, the

launching point of the light beam has moved to the right an amount b which must

be the speed of the clock multiplied by the time M', that is: b = vM'. So we have a

right triangle (see 5.12b) with all the sides given. Apply Pythagorus's theorem: D'= b' + 17'. Substitute the values ofD, b, and h, and we have: (ci".t')' = (vi".t')' + (eM)'.Snbtraeting (vM')' from both sides and simplifying, we get: M' / M = 1/ --/(I-v'lc 2).This is the crucial result. It says that a tick of the clock at rest that takes M in its rest

frame (here light moving a distance h) is measured by an observer at rest to take a

longer time (M') when the clock is moving at velocity v. For vie = 4/5 the speed of

light, this ratio 1/ --/(l-v2/e') is 5/'3: a elock moving at four-fifths the speed oflight

would be measured by a stationary clock to run slow by a factor of 5/3. Of course

"stationary" and "in motion" are, according to Einstein, entircly relative.

87. Howeth, History (1963). Further on wireless time setting, see, for example,

Roussel, Premier Livre (1922), esp. J50-52. Boulanger and Ferric, La Telegraphie(1909), date the Eiffel'l(lwer radio station to 1903. Ferric, "Sur quelques nouvelles

applications de la Telegraphic" (1911), esp. 178, indicates that planning for wire-

less time coordination began at the start of work 011 wireless; Rothe, le« Apt)lica-Ii01lS de la TelegralJhie (1913), discusses the details of radio-communicated time

coordination procedure.

88. Max Rci!hoffer and Franz Morawetz, "[':inrichhmg zur FernbeUtigung von

clcktrischcn lihrcn mittcls clektriseher Wellen," Swiss patent 37912, submitted 20Angus! I<)()6.

89. Dcpclley, 1£.1 Cables sous-marins (1896), 20.

90. Poincare, "Notice sur la telegraphic sans fil" [1902[.

91. Amoudry, Le General Ferrie (1<)93),83-95.

92. Conference lnternationale de I'heure, in Annales du Bureau des Longitudes9, Dl7.

93. Commission Technique Intcnninistcric llc de Telegraphe sans Fil, 7th

Meeting, 8 March 1909, MS 1060, II 1<'1,Archives of the Paris Observatory.

94. Poincare "La Mecanique nouvelle" (1910),4,51,53-54.

95. (Approval) Ministre de l'Instmetion puhliquc et des Beaux-Arts, a Monsieur

lc Direeteur de I'Observatoire de Paris, 17 July 1909; (Meeting minutes) Commis-

sion Technique Iutcrministcricllc de Telegraphe sans Fil, 10th Meeting, 26 June

1909, both documents MS 1060, II Fl , Archives of the Paris Observatory.

96. Poincare, "La Mccanique Nouvelle" [1909[,9. Manuscript copy is dated 24

July 1909 (Archives de I'Academic des Sciences).

97. Poincare, "La Mccauique Nouvelle," Tuesday 3 August 190<).

98. Amoudry, General Ferrie (1993), 109; see Comptes rendus de I'Academic

des Sciences report 31 January [1910j.


99. Scientific American 109, 13 December 1913,455; see also Joan Marie

Mathys (unpubl. MA thesis, "The Right Place at the Right Time," Marquette Uni-

versity, 30 September 1991).100. LallelIland, "Projet d'organisation d'un service international de l'hcure"

(1912). On the Eiffcl1ower-Arlington exchange, see, for example, Amouchy, GeneralFerrie (1993),117; Joan Marie Mathys (unpublished MA thesis, George Washington

University, 1991); and Scientific American 109, 13 December 1913,445.

IO!. Howse, Greenwich (l980), 155.102. See 11 th and 13th meetings of the Commission Technique Intermin-

istericllc de '['elegraphe sans Fi], 2 I March 1911 and 21 November 1911, lVIS

1060 II Fl Archives of the Paris Observatory.IC)3. U:m Bloch, Le Principe de la relaiivite (1922),15-16. Dominique Pcstrc

characterizes Bloch (and his brother) as physicists who were unusual for their time

in France by writing textbooks that looked positively on the new physics ofthe early

twentieth century and characteristically wrote using a series of progressive gener-

alizations from the concrete to the abstract (no doubt to appeal to their more exper-

imentally oriented colleagues). See Pcstrc, Physique et Physiciens (1984),18,56,

and 117.104. See Bureau des Longitudes, Reception des signaux horaire«: RellseignemelllB

meteorologiqlleS, seismoZogiql1es, etc., iransmis par les postes de telegralJhie sans iil dela 1bur Eifie;!, Lyon, Bordeaux, etc. (Bureau des Longitudes, Paris, 1924), 83-84.

105. Corrections are of many sorts, and include effeets due to the motion of

satellites, the lower gravitational field at the height of the satellites, and the rota-

tory motion of the earth. The relativistic component of the Doppler shift is 1"12c',which for satellite velocities is about seven millionths of a second per day. Because

the speed ofljght is so much faster than the speed of the satellites, most of general

relativity neeclnot be taken into account, but the equivalence principle that is part

of general rcl ~ltivity is significant. (The equivalence principle says that there is no

way to distinguish the physics of a freely falling box from the same box without a

gravitational field.) A more rigorous analysis would take into account (inter alia)

that the satell itcs' orbit is not always in the same gravitational ficld, that the earth

observer may be moving on the surface of the earth, that the earth's gravitational

field is not the same everywhere on the earth's surface, that the sun's gravitational

field affects tl'le earth clock and the satellite clock differently, and that the appar-

ent velocity 0 f light is altered by the earth's gravitational field.106. Neil Ashby, "General Relativity in the Global Positioning System,"

www.phys.lsa.edu/mog/mog9/node9.html(aeeessed 28 June 20(2).

107. Chro nology of activist actions, www.plowshares.se/aktionerlplowcron5.htm

(accessed 19 February 20(2); also see Los Angeles Times, 12 May 1992, "Men

Arrested in s-,::>aee Satellite Hacking Called Peace Activists," Metro part B, 12.

-----·---·-···~~4iiiIiA;r'.k':as:SUaaUSiblIdlCliiik.JdS .•.SSd 42

--~.~==---==~-~~=~----------

108. 'l aylor, "Propaganda by Deed" (n.d.}, 5, in "Greenwich Park Bomb file,"

Cambridge University archives. Serge F. Kovaleski, "1907 Conrad Novel May Have

Inspired Unabomb Suspect," Washington Post, 9 July 1996, AI.

109. This has been pointed out lllany times: Infcld,Albert Einstein (1950), 23;

Holton, Thematic Origins (1973); and Miller, Einstein's Relativity (I 9fl I), and

idem, "The Special Relativity Theory" (l9H2), 3-26. Einstein docs refer to

"Lorentz's theory" in the text (hut no footnote).

110. Myers, "From Discovcry to Invention" (1995),77.

II I. By law, patent officcrs werc taught to look for originality. In Switzerland

that lumt for novelty had a specific mcaning: "Discoveries do not count as new, if

at the time of their registration in Switzerlaud, they are well enongh known that

their development by the technically adept is .rlrcady possible." The contrast with

neigh boring countric» is worth lloting. In France rejection for lack of originalily is

based 011 "publicity" given 10 prior work, while in Ccnuany a similar refusal could

be made if Ihe iuvcutiou had been either reported in an official puhl ication of the

last century or if its use was so well known that its employment by other technical

people appeared possible. According to turu-oj-l hc-ccnlurv paten! manu.rls, Swiss

law lay closer 10 Ihe French; origimlily ill Swilzerland mcuntthatthc invcntiou

was not 'Icln:dly known in Swil/.crbnd regardless of wlwlmighllie dormant in an

obscure foreign publicaliou.

112. Sell<llll.e, Paicnlrcch! (JlJ()1), ·n.In. Ibid., B-H114. 1':illSlein, '" I 'Ire World as I See II," ill idem, ulea« and ()/lilliolls (llJ 54), I ().

6. "Discours elu Duc M. de Broglic" in Poincare, Livre du centenaire (1935),

71-78, on 76.

7. General conclusions by Poincare, in Langevin and de Broglie, Theone du ray-onnement (1912), 451.

8. I have retranslated this quotation and also corrected a spurious insertion that

seems to have crept into the secondary literature. The phrase gegen die Relativi-taetstheorie simply docs not appear in the original. Einstein to Heinrich Zanggcr,

15 November 1911, item 3D 5, in Collected Pa/Jers, vol. 5, 249-50.

9. Poincare to Weiss, editors of Poincare Papers date as ca. November 1911.

Poincare et le« Phvsiciens, unpubl. correspondence from the Henri Poincare

Archive ZUrich.

10. Darboux, "Eloge historiquc" [1913], Ixvii.

II. Poincare, "Space and Time" (1963),18 and 23.

12. Ibid., 24.

13. Poincare, "Moral Alliance," Last Essays (1963),114-17, on 114, 1l7; on the

last days of Poincare, Darboux, "I~:logc" (l91 6). Sce the excellent discussion of

Poincare's political engagement ill Laurent Rollct, Hemi Poincare. Des Mathema-tiques a la Philoso{Jhie. /i:tude dU/J<lfcOWS niielleciuel, social et /Jolilique d'un inath-ematicien au debut du siecle, unpublished doctoral dissertation, University of Nancy

2,1999, esp. 2H)'-H4.

14. "Discours elu Prince Louis dc Broglic" (1955),66.

15. Poincare, Foundation» of Science (19H2), 352 (translation slightly modified).

16. Ibid., 232.

17. Sherman, Telling Time (1996).

18. "Lcttrc de M. Pierre BoulTOUX ir M. Mittag-Leffler" 118 June 19111, in Poin-

care, Oeuvres, vol. II (1956), 150.

19. Both quotations, ef. l':instein, Ideas and Opinions (1954), 274.

20. Eimtcill about the religious spirit of science in Meill Welthild 119>41,reprinted in idem, Ideas and O/Jinions (1954), 40.

21. Editors' introduction to vol. 2, Einstein, Collected Papers, xxv-xxvi.

22. EillStein to Schlick, 21 May 1917, Collected Paber: (Translation), vol. 8,

333. Also as Holton has argued in Thematic Origins (1973) that Einstein's empha-

sis on metaphysics changed over time.

23. Favarger, r:ri:lectricite (1924),10.

24. Ibid., I I.25. Representations ofEinstcin's relativity as a culmination of inereasingly accu-

rate "no-nether" measurements arc rife; perhaps the most scholarly attempt to

locate Einstein's formulation as a mere variant of the early nether-electron theories

is to bc found in Edmund Whittaker, History of the Theories of Aether (1987),40,

where the chapter "The Relativity Theory of Poincare and Lorentz" includes the

remark: "Einstein published a paper [in 1905] which set forth the relativity theory

1. I':iusteiu, "On the Relativity Principle awl the Conclusions Iklwn From It"

119()71, docuulcul47, ill Collected Pa/Jcrs, vol. 2, 432-8H; in Collected Paper«(Transla/ion), vol. 2, 252-55.

2. I':illslein did cite Poincare's work on llrc inertia of encrgy in I':instein's 1906

derivation of E = me' (W llic Principle of Conservation of Motion of the Center of

Gravity" 119061, document 15, ill Collected Papet« (TwlI.slatioll), vol. 2, 200-2(6);

then in ("On the Inertia of energy" 119071, document 45, in Collected Paper«(Translation), vol. 2,238-50). I':instcin rc-omittcd Poincare when l':instein again

wrote on the inertia of energy.

3. Poincare, "I .a Mccauique Nouvelle" 119091, 9. Manuscript copy is dated 24

July 1909 (Archives de l'Acadcmic des Sciences).

4. ElgUet, AjJreS ['Ecole (1927), 41.

5. Einstein, "On the Development of our Views Couceruing the Natu rc and

Constitution of Rarliation," document 60, in Collected Papers (Translatioll), vol. 2,

379.

353

354

of Poincare and Lorentz with some amplifications, and which attracted much atten-tion. He asserted as a fundamental principle the constancy of the speed of light.which at the time was widely accepted, but has been severely criticized by laterwriters." See Holton, Thematic Origins (l973), esp. ch. 5 and Miller, Einstein's Rel-ativity (1981).

26. Schaffer, "Late Victorian metrology" (1992), 23-49; Wise, "MediatingMachines" (1988); Culison, Image and Logic (1997).

27. I<illsleill to Solovine, Princeton, 3 April 1953. in Einstein, Letters to Solovuie(1987), 143; translation corrected.

28. l':imteill to the son and sister of Michele Besso, 21 March 1955, Alhertl':ill-stein Michele Hesso Cotresbondance (1972), 537-39.

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Alfaro, Eloy, 191Allen, William F., lIS, 122-26,127,

152-53,33611Allgemaine Elektrizitiits Cesellsehaft

(AEG),249almanacs:

astronomical, 163sunrise/sunset times in,

126Alsacc-Lorraine, 50American Association for the

Advancement of Science, 123American Metrological Society,

113-15, 151American Society of Civil Engineers,

123anarchism, 159, 226, 289Andes, mapping expedition in,

193-98Andrade, [ules, 314, 34 ilzAnschiitz-Kaempfe,249-51Anschiitz-Kaempfe, Hermann, 250,

251antimcridian, 119, 146, 161anfipositivism, 324Aristotle, 37Arthur, Chester A., 123, 144-45Asia, 134Asia, in global electromapping net-

work,142

INDEX

Page numbers in italics refer to illustrations.

Abbe, Cleveland, 114, 115, 149-50,151

Abraham, Max, 242,260,277,291absolutes:

of movement, 56-57of time, 13, 14, 19, 26, 27, i», 38,

44,190,236-38,239,253,267,271,304

Academy of Sciences, 65-()6, 85, 87,91-92,129,130,138,143,156,219,308,325

Quito expedition overseen by,193-94,196-97,211

Acta Matizcmatica, 65, 68, 71action-reaction principle, 203, 209,

218Adams, John Conch, 149, 150A. De Peyer and A. Favarger ct Cie,

222AEG (Allgemaine ElektriziEits

Gesellsehaft), 249Africa, in globallllapmaking network,

175-80,176,178Agostinelli, L., 248Air Force, U.S., signal technology of,

285, 289Airy, George Sir, 120-21, 180Alder, Ken, 333nalgebra, vs. geometry, 64Alembert, Jean Le Ronel d', 239

w.

asteroids, orbital motion of, 68-69,70, 72-75

astronomy:in clock coordination, 182datc-chungc times in, 153, 162-63in longitude determination,

m-32, n3, 140-41Atlantic Ocean:

longitude mappiug of, 102-')telegraph cables across, 13U,

B3-38,183-1)4atomism, 52,81Aubin, David, )3417Aveuarius, Richard, ZiS

Bain, Alexander, 30Barkan. Di.m.: Kon 110S, 34511Baru.rrcl, l-rcdcrick A. P., 113, 114,

11'J-20, 121, 122, 123, 12ilBurrow-Green, JlIlIC, 33211Bartlics, Roland, 2ilBartky, Ian It, 3H-·35n, 33811Bccqucrcl, Ec1nWild, <)5-96Bccqucrcl, l lcnri, %,166Bergsou, llcnri, 32-BBerlin, Ccnnuny:

master clock of, 3l, 22)Paris clock coordination with,

186-87Berlin Observatory, 223Bern, Switzerland:

clock synchronization in, 30, 31,222-23,227,244,244,245,248,253

patent office in, 30,243, 244-51,244

train station of, 30, 31Bertillon, Alphonse, 214Besso, Michele, 235, 253,254,255,

261,327

INDEX

Bigg, Charlotte, 333n, 34411Birkhoff, Ceorge D., 301Bloch.Leon, 283-84, 35111Boer War, 193Bologna Academy of Science, 156Boltzmann, Ludwig, n 5Bonaparte, Prince Roland, 194Bond, W. C., \03, 104Bonnefoy, Marcel Paul, 54Bonnet, Ossian, 54Bordeaux Observatory, 142-44Bmsnct, Jacqllcs-Benigllc, 296, 326Boston, Mass.:

clock-coorclii ration system of,1117-8

standard lime adopted ill, 12(1-Z7BOlldenoot law, 173-)4BOllgllC!',Pierre, 193Hourdiu, Martial, 159, 22()BOlllrollx, Aline Poincare, 54, 5()

Boutroux, 1':Jllilc, 54-)(1,81,314,315

"Brain of I':imlcin" (Burthcs), 2XBrazil, in globaltdcgraplt network,

n7-39, J4(), 143Hrclcuil Observatory, iN, 91,95British Cable, 175-77Brock, David C., 332/1Broglie, l.ouis cle, 303-4Broglie, Maurice de, 297Buchcrcr, /\lfrcd, 294Bureau des l.ollgitlldes, 100, 308

I':iffel radio lillie backed by, 276,284,314

global mapping efforts of, 43,128-29,130-31,141,142-44,174-79,176,180,182,185-86,191-98, 211, 314,316,32'3

011 Paris-London longitudinal

difference, 180-82Poly technicians at, 53presidents of, 41, 48,129, 181,

188,206,308,314Quito mapping expedition of,

191-98,211, 316on time decimalization, 163, 173,

174,314Burnett, Graham D., 34111

Cahan, David, 33111Calinon, Auguste, 56-57, 81,

188-89,314Canales, [imena, 34471Canary Islands, prime meridian set

ill, 147-48Carnap, RlIdolf, 266Cassidy, David, 3291l, 330nCatholic Church, J 53, 198Cauchy, Augustin 1.ouis, 49, 51celestial mechanics, 32, 62-75

as chaos vs. stability, 66,69-75

three-body problem in, 62-66,68-75, 301

Celestial Mechanics (Laplace), 153centimeter-gram-second system

(CCS),166Central and South American Cable,

142chaos, 72, 74-75Charlemagne, 86Chicago, Ill., observatory time signals

in, 112,126Christie, William, 206church clocks, 96,312circumference, degrees of, 163-65,

167-69,171,34011Civil War, U.S., 132, 133, 136,314( .larke, Colonel, 121

Index 373

clock coordination:American method of, 103-7,105,

106, 314by astrouoiuical observation, 182as democratic goal, ';22-23early efforts at, ';0-31, 34,40,

312-13electric distribution of, 30, 33,

35-36,52,187-88,207,225-27,257,258,259

with light sigll<lls, 19-22,45,270,271,272,285,295,297,310,34971-5011

longitude determination linked to,H, 35-3(), 44,101-3, 112,130, 182, 312

mathematics of electric signals in,52

multiple straius in modernist movetoward, 39-41, 311-21,327-28

patents connected with, 246-48,247,253,257,273

pneumatic systems of, 93-95, 93,94,225,226

precision of, 109-10, 112,273,276,281,285,288-89

public protests against, 289radio transmissions used in, 247,

271-84,274, 283, 284, 2!l5,303,305, 314, 350n

by railroads vs. observatory lilliesignals, 110-12, 114-15

satellite-based, 285-89, 287, 35111in special relativity thcory, 18-23,

20,21, 253-63,292-93,301-2,311,327

in Switzerland, 30,31,32,46, 2Zl,222-24,223,224,227,244,244,245,248,253,272

"iil ;I.~~.J

,

!"i:.. :.,.'I.~:·,.·~I~;~t

374

clock coordination (continued)technology vs, theoretical basis of,

306-8,309-10tclcgraph transmission time consid-

crcel in, 182-83U.S. promotion of, 107-13

clocks:astronomical, 51-52, 170atomic, 285,288OIl churches, 96, 312as couvcnicn t mcasu rcmcnl for-

mal, UN, 34hlon dccimal tnnc systcm, 15), 1')4,

163electric pcudul.r dcsigllCd for, 222,

24(),253minute hands 011, 95as rccording mcclumisms, 222scagoing, III1-3

coal mines. 41, 57-J)2, ()1Coast :llld Ccodclic Smvey, U.S.,

101, 1()3, nz, l'n, 180, 18),184,192,114

Cohn, I':lllil, 258-CJ(), 270, 285, 291,2')4

Colin, Captain, 278Columbus, Christopher, 131compasses, gyroscopic, 250- 51, 252,

34711Comic, Anguste, 239Congress, U.S., 1z:;

OIl prune mcridi.m, 144-45river survcys ordered by,

132Connaissance des Temp», 148, 163Connecticut, railroads vs, observatory

time signals ill, 110-12Conrad, joseph, 159-60, 289conventionalism, 77-83

of geometry, 77-78, 79-80, 81-82,

INDEX

200pedagogical, 80-81in philosophy, 32-36,81,188-90,

199-201,315in physics, 199-201,240-41,

305-6ol simultnucilv, 33, 36-37,44, 129,

182,186-88,189,190,211,239,306-7,309,315,319

Convention of the Meter, 84-85, 86,90,145,161,186,240

conventions, intcruational, :;8, 315as diplomatic iuslrm ncutx, 92prime meridian as, 145-46proliferation of, 90-91, 145-4()telegraph transmission limc

rctlcctccl in, 18()·-87of weights and mc.rsurcs, 84-91l,

,~8,C)], 92,145, »))11Comu, AHi'ccl,95, 181

ustrouou rical clock built by, 51-.52,170

on dccnualizntion, 164, 1(>9--71clcctrosvuchrouizaliou .mulyzccl

by, 52,229, )11al Polvtccluriquc, 49,51,52,5),

54, 80, 229critical opalcsccucc, 40Critical Study of Mec:lwnics (Cali-

11(11),56--57Cunllingham, I<hcllczer, 262curves, 64

Davy, Humphrey, 58Davy lamps, 58, 61, 62day, start of, 153, 162-63Dean, George, 132, 135, 136-37Dearborn Observatory, 112Dcbarbat, Suzanne, 34311de Bcruardicrcs, Octave, 129-30,

1)7,141-42,143,184,186Decazcs, Due Louis, 84, 85decimalization, 182

of circumference, 163-65, 167-69,171,340n

of electrical units, 166-67, 171-73of metric system, 86, 92of tiruc, 43,153-55,154,163-73,

174,188,211,212,240,314Dedckind, Julius Wilhelm Richard,

238de la Cryc, Bouquet, 163-65, 192de 1<1Noe, General, 164Delaune, M., 174Descartes, Rene, 79-80differential equations, 63-65, 66, 298,

317diplomacy, international conventions

as instruments of, 92Disclosure Oil Universal History

(Bossuct),296Dolim-van ROSSllll1,Gerhard, 33411,

)4411Douccy, l<mile, 58, 59, 60Dowd, Charles, 115, :;36nDreyfus, Alfred, 213, 214-15,305Drudc, Paul, 232, n4Dudley Observatory, 338nDumas, Jean Baptiste Andre, 85-86,

90

Dakar, Scnegal, time-synchronizedmapping project at, 175,176,177-79,171),180,191,316

Darrigol, Olivier, :;4311,345n, H(m,34911

Daston, Lorraine, 33111earth:

clock time based on rotation of, 237

Index 375

satellite surveys of, 287-88shape of, 146, 19/-92, 195,199,

316Eastern 'lclegraph Company, 138eclipses, solar, 131, 148,326Ecole des Mines, 53, 54, 57, 58,

228Ecole Polytcclmiqne, 48-54, 56,67

alternative theories presented at,52,81,82

in electric timc coordinationproject, 95

entrance cx.nniuations of, 49,50I<'I'I Ivs., 228-29history of, 50-52mechanics theory as factory stamp

of, 49, 297theory vs. practical application at,

42,49-53,63,228-29,305,308,33ln

Ecole Professionelle Superieure desPostes et Telegraphes, 273,282-83, 284

Ecuador, French mapping expeditionto, 191-99,195

Eddington, Arthur, 326Edison, Thomas, 275Edson, Franklin, 127Eidgenossische Teehnisehe

Hoehsehule (ETH), 228-30,231,232,233,240,244,263,269, 309

Eiffel, Gustave, 276Eiffel Tower, radio signals transmitted

from, 275-77, 278-79,280-82,283,284, 286,287,303,314

Einstein, Albert:academic appointments of,

299-300, 322, 326

Einstein, Albert (continued)antiauthoritarian stance of, 46,

232-:)3,235, 243,292, 297,310

childhood of, 34elocks in milieu of, 30,243-44,

244,253,254,2155Oil elock synchronization, 19-22,

20,2./, 23,24,25,34,36-37,47,242,253-58,260-61,271,282, 292-S>3, 310

education of, 228, 229, 230, 231,2)2-")3,236-40,244,263,309

electromechanical devices as fasci-nation of, 46, 251-53

01] energy, 2), 240, 242, 510, :;521lether theories rejected hy, IS, 16,

17-18,47,204,227--28,230-3], 2H-35, 260, 262,267-(18,279-80,295,297,302,310,317,323-24

falllily buxiucss of, 249, 25()011 fotu-dilllcllSional spacetime,

2(IS,26(1-67on general relativity, 288, 322, 32(1,

35171on impact of special relativity the-

or~2~268, 26~270, 327later career of, 326-27light-signal elock proposed by,

19-22, 270-71,272, 297, 310,H9n-35011

on Lorentz, 202, 237, 242, 260,34811

on Mach, 2"37magnetic atom theory of, 251mass/energy equation of, 23, 310,

352nNazi-era attacks on, 311

INDEX

on Newton, 131905 relativity paper of, 14-16,

253-58,260,285,290-93,303-4, 3481)

observable procedures required by,24, 25-26, 269, 323-24

othcrworIdy public image of,27-28,46,255

in patent office, 27,30,31,38,41,47,221,223,233-34,241,243,244-51,253,273,291,294, 309, 523, 325, 3461l,347n, 348n

Poincare's influence OIl, 33-34,221,238-39,243,257-58,294-95, 35211,3531l-541l

Poincare's meeting with, 2s>6,297,299, 300

political beliefs of, 26-27, 292, 322on quantum physics, 25, 297-98,

299,317,318scientific milieu of, 24,191,294,

299, 326-27, 553n-54nscicntific philosophy of, 24, 25, 26,

236-40,241, 268-69,2S>8,300,310,316-19,320

simultaneity addressed by, 18-19,24,25,29-30,31,33,36-")7,41,46-47,237,271-72,313

on solitude, 27on rhcnnoclynamics. 240, 243as tu tor, 231, 23 5011 velocity of light, 16-17,3541)writing style of, 290-92

Einstcin, Hermann, 247,250Einstein, Jakob, 249,250Einstcin-dc Haas effcct, 252, 3471lFkcland, Ivar, 332nelectrical industry, standard units of,

145,166-67,171-73

electricity:etheric theories on, 15-16,202,

205practical applications of, 23

electrodynamics, 18, 24empiricism, idealism vs., 81encrgy, 321

conservation of, 216, 218, 240,242, 352n

mass vs., 23, 310, 352nengineering schools, 51EnlighteJlment, 43, 100, 128, 155,

304,316entropy, 240, 241,32]ephciueridcs, 63, 75equator, ]45, 150equivalence principle, 351nECITI (EidgcJl(issische Teclmische

Hochschule), 228-30,231,232,233,240,244,269,309

ether, 23, 44, 45,87,202-6,204,207-12,216-17,220,241-42

contraction hypothesis on motionin, 204, 205, 206,209, 218,219, 242, 279, 280

Einstein's rejection of, 15, 16,17-18,47,204,227-28,230-"31,234-35,260,262,267-68,279-80,294-95,297,302,310,317,323-24

Euclidean gcometry, 76, 77, 78, 79,92,200,264

Euler, Leonharcl, 64Evans, F. J. 0., 146-47

Faidherbe, Louis, 175falling bodies, mechanics of, 16Favarger, Albert, 224-27, 246,2157,

259, 322-23I'~1ye,Herve, 129, 168

Index 377

Felix, Victor, 58Ferdinand, Archduke, 323Ferrie, Gnstave-Auguste, 276Ferro (island), 147-48, 149, 151, 161fields, 202Fizeau, Armand-Hippolvtc, 87,95,

203Fleming, Sandford, 114, 116-20,

118,121,122,128, ]51Fliickigcr, Max, 34711,348nFiilsing, Albrecht, 32971,3471), 348nForster, Wilhelm, 84, 92, 223France:

anarchist actions ill, ] 59British cable control resented in,

176-77,180,193,274-75,282, 305

coal mincs of, 41colonies of, 175, 187, 193,280,

282,314decimalized time proposed in, 43,

153-55,1154diplomacy of, 92in global electromapping effort,

136-37,141-44,143,175,191-98,195,280,314

Greenwich prime meridianresisted in, 119, 146, 147-52,155,159-62,174

metric system designed in, 86,90,98,148,149-50,163

patent criteria in, 35211political metaphor of time coorcli-

nationin,41radio time systems in, 272-81,274,

275-82,283,284, 303, 305science education in, 48-54, 297

Franco-Prussian War, 50, 51, 157, 214Frelinghuyser, Frederick T, 123,

146

~----------------.----------- .

French Revolution, 41, 86,129,153,154,155,163,174,213

functions, thcory of, 201

GaJileo Galilci, 16, 17Galison, Peter, 32911, :nOn, 3471l,

H8n, 34911,35411General Review of Railroads, 98-100General Time Convention of Rail-

road Officials (1883), 115,123, 126-27

Geneva, Switzerland, elock coordina-tion in, 222, 223, 224

geometry:algebra V.I., 04four-dimcnsionnl, 263-(i(i, 267as group, 76-77non-Euclidean, 76, 71\in Polytcchnique curriculum, 51,

BIllas practical convention, 77-78,

79-80,8]-82,200Gcorgia, Shenll<Ill's march through,

132Ccrmauy:

in Franco-Prussian War, 50, 51,157

multiple time standards in, 99,156-58

uutioual uuity of, 41, 156-57,282,292

patent criteria ill, 35211time coordination in, 30, 35,

156-59,282Gettysburg, 137Ciedymin, [erzy, 33311Gilain, Christian, 33211Global Positioning System (GPS),

285-89,287,320,35111Godin, Louis, 193

DEX

Gonnessiat, Francois, 194Gooday, Graham, 33311Goroff, Danicl, 33211Gould, Benjamin, 133, 134, 135, 136Gouzy, M., 174Grammar ofScie11ce (Pearson),

237-38gravity, 215,288,35111Gray, Jeremy, 33211,33311Croat Britain:

colonies of, 180, 192-93decimalization resisted in, 164electrical clock-coordination ill, 106physics in, 199, 2()2radio-time system adopted in,

281-82telegraph cable manufactured in,

13(), 144undcrscn-cablc system of, 100, 114,

175-77,176,180,102,274-75, 2~2, 30')

Great Eels/ern, 134Great Pyramid, 119, 120Cree», Francis, 137, 131\-~0, 142Crccnwich Ohservatory:

bomb detonated at, 159,226011 Paris longitude discrepancies,

180-82,206-7,2~0as prime meridian, 43, 119, 121,

146, ]47, 151-52, 156,159-62, 174

radio-time rceeivers at, 281time zero placed at, 99, 127, 146,

174,280U.S. telegraph-cable link cstab-

lishcd with, 130, 136Grossmann, Marcel, 233, 234groups, 76-77Cruenbaum, A, 333ngutta, 130

Guyou, Captain, 165, 168gyromagnetic compasses, 2S()-51,

252, 347n

Habicht, Conrad, 236, 251, 252, 253Habicht, Paul, 251, 252Haller, Friedrich, 2:B-34, 241, 243,

244-46,249,291Harriet 'Iubman-Sarah Connor

Brigade, 289Harrison, John, 102,312Hartford, Conn., New York time used

in, 1io.nHarvard Collegc Observatory, 103,

106-7, ios, 109-11,112,126,136

Headrick, Daniel R., 34111heat, 229-30, 231, 240, 243Hei]hron,]. L, 3461lHeinzmann, Gerhard, )2911, )3311Heisenberg, Werner, 24Helmholtz, Hermann, 80, 230Hermite, Charles, 65, 71, soHertz, Heinrich, 230, 235, 2];Hipp, Mathias, 30, 221-22, 224, 257,

34411Hirsch, Adolph, iN, 145, 146,222,

344nhistory, categories of, 38-39Holton, Gerald, 32071, 34511,34611,

35211, 353n, 35411homoclinic points, 72, 74Howse, Derek, 339n, 351nHughes, Thomas, 347n, 34811Hugo, Victor, 138, 326Hume, David, 26, 238,239-40

idealism, empiricism vs., 81Illy, J., 349nindustrial production, international

Index 379

conventions in, 90information sciences, rapid develop-

ment of, 321intercontinental ballistic missiles,

285interferometer, 87, 203-5,204,242International Bureau ofWcights and

Measures, 84, 89, 227International Congress of Arts and

Science, 215International Congress on Chronorn-

etry,224Intcmational Geodesic Association,

191-92,196International Ceodetic Confcrencc,

182intuition, mathematical, 66-68, 76,

201-2Ireland, international cable links

with, 134-35

Janssen, Jules, 147, 148-49, 150-51,152,153-55,156

Janssen, Michel, 32911[eanroy, Eugenc, 58Jerusalem, as prime meridian loca-

tion, 156Jordan, Camille, 71joyce, James, 319[uif (master miner), 58Jiirgen, Rcun, 34511

K (kilogram), 88, 89, 90, 91Kaiser, David, 329n, 33111Kant, Immanuel, 55, 57,76,81-82,

316Kaufmann, Walter, 220, 294Kelvin, William Thomson, Lord,

105, 121, 135, 138, 152Kern, Stephen, 33911

kilogram, prototype of, 84, 88, 89, 90,91

kinematics, 18, 242Klein, Felix, 79, 201-2Kleiner, Alfred, 234, 244, 207Kornprobst, Sebastian, 249Kronecker, Leopold, 71Kropotkin, Peter, 226

Lacombe, M., 1971,<\Conclaminc, Charles-Marie, 193Lagrange, [oscph-Iouis, 64I .allcmaud, Charles, 160-()2, 196,

197,198,202,280,281lanuncl, Rudolf, Z()~Landes, David S., 34471Laplace, Pierre-Simone clc, ()4, 14lJ,

153, 1o')latitude, natural prime of, 145latitude measurements, )4--35I .aub, Jakob, 2')2Laue, Max V()II, 2(>lJ,294, 2lJ5Law of Nations, 121Le Clerc, 1'., \1)6Lcfaivrc, Albert, 14(), 151-·')2Lcibniz, ClJltfried Wilhelm, 150I.e Roy, I<dollard, 34(mLe Verrier, Urbain, lJ5, %, lJ7, lJ~,

lOO, 114, 180Lie, Sophus, 79-80light:

clocks coordinated with signals of>IlJ-22, 45,270, 271, 272, 2~5,2lJ5, 2lJ7, 310, 34911-5011

constant speed of, 16-17,271,310,351n, 35411

critical opalescence of, 39-40electric, 23metrological standards based on

wavelength of, 3Bn

INDEX

as waves in ether, 15, 17Lindemann, F., 346nLindemann, L., 34611Lobaschcwski, Nikolay lvanovich,

Z3lJLocke, John, 239Loewy, M., 164, 165, 109, 173, 181,

186,206longitude:

length of mcridial arcs of, 191practical applications of, 43zero point of, see prime meridian

longihlde, detcnnination of:astronomical observations in,

HI-32, 1'33,140--41clock syuchrouivution and, 34,

35-36,44,101-),112, ]30,182-83, )12

clccrromapping efforts Oil, 129,J)O, ])2--44, 140, 145,l7S-lm, 176, 178, IlJ4-lJH,1<)5,200, ')]4

moon movements used in, 102,131-32

of Paris vs. Crccnwich, IHO-H2,20()-7,314

radio-lime precision in, 273,276-77, 2RO, ')03

telegraph transmission lime in,183-87, IlJO

transatlantic, 102-3, I 33-3K,IH3-84

I. ,(Jug Range Aid to Navigation(LOMN), system, 285

Lorentz, Hendrik A, 26, 189,202-12,231,234-35,237,20],269,277,297

contracti on hypothesis of, 204,205,206,209,218,219,220,242,279, 280, 310

Einstein's admiration of, 299, 34811local time posited by, 44, 45,

205-6, 207, 208, 209-10, 2 II,217,218,219,241,242,254,257, 25H, 262, 27R, 279,280,294, 2lJ5, 307, 309, 313

relativity concepts of, 44,302,35311

M (meter), 87-90, H8, lJ1, 92, 33311Mach, I':rnst, 26, 235, n6-37, 23~,

2,)lJ, 240, 266magnetism, ctheric theories on, 202,

205Magny luilling disaster, 58-61,61,

()2,315mapmaking, 112

electric lclcgrapl: cables used in,4')-44, 12lJ, no, 133-34,B(l-n, ])lJ-44, 140, 143,14'), 175-77,176,179,180,IlJ2-lJ3, 194-99, 195, 323

l-rcnch-Euglish rivalries in, 180,192-93

C I'S tcehnology in, 287-88intcrnntiouul conventions on, 91sea-going clocks used in, ]0\-3signal lransuiissiou-time correction

in, 183-R7, IlJOof spuccti 11IC,286U.S. beauty of, lJ9-!OO

Marchand, Captain, 180Marie, Milcva, no, n2, 233, 234,

2'35,246Mascart, I'Jcuthere, 275mass:

conservation of, 21 5-16, 218cnergy vs., 23, 310, :;5211

master clocks, 30, 32, 33, 223mathematics:

conventional ism in, 79-80

Index

differential equations in, 6~-65,66,298,317

logieists vs. intuitionists in, 66-68,201-2

in Polytcchniquc curriculum, 51,228-29,33111

of three-body problem, 62-66,301

topology ill, ) 1, 301Maurain, Captain, 1lJ6, ]97,202Maxwell, James Clerk, 23, 202, 210,

Z30, 235,237,268Maxwell's equations, 15,44, 2,1measurement, technology of, 87,

33)1l"Measure of'l'imc, The" (Poincare),

32-33,174,175,186,200,266, Hill

on olcctro-coordiuatiou of clocks,3\ 35-36, I 87-R8, 207

CCfln<1npuhlicatiou of, 238-39on cwtouiau laws, 190on sunultuncily as convention, 33,

7,6,129,182,189,190,239,30o

mechanics:

cxporimcntal vs. theoretical,IlJ9-201

ill Polytcclmique curriculum, 4lJ,297

relativity principle and, 16, 17lcissncr, Ernst, 269

Memoirs of C1 Revolutionist(Kropotkin),226

Mercator, Cerard, 119Messerli, Jakob, 245, 34411meter, prototype of, 84, 85, R7-90,

H8, 91, 92, 98,161,33311metric system:

decimal character of, 86, 92

mctric system (continued)French design of, 86, 90, 98, 148,

149-50,163geodcsic origin of, 86, 161internatiollalizatioll of, 86political symbolism of, 90spreading adoption of, 85-87, 98,

152, 170Mcxico, in telegraphic uclwork, I ~9Michclson, Alhert, 1->7,20~-5, 2()4,

217,242,201-62,294midllight, dale challge at, 153, 162military:

railroads ill rapid deployment of,1v: J 51)

signalleelmology of, 275-7(l, 280,2H3, 21->4,21)r:;,2R~ 289

smveys used by, 132Mill, Johll Stuart, nl), 240Miller, Arthnr L, 32911, »011, )4117,

14511, )4(1II, )4711, ,5211, ,')411Millkowski, I lcnu.u In, II), 2(l,-65,

2m, zes, 2CH, 295mirror g;llv:Jllolllders, I35->(l, I ~I->Millag-I.cfller, Ciist;l, 65, 68, U),

70-71, WiMoille, flelnmlh Carl Bernhard VOIl,

157-59,224,282,292IllOIIlClltlllll, posiholl vs., 2"f-251lI01lCY,decilllalization of, 92MOllgc, Caspard, s 1, 33111moon, 149

longitndc dctcrmiuatinn based Oil,102,131--32,133

Morley, f'~dward Williams, 242,2(:.1-62, 294

MOllchez, Emcst, lklMyers, C.·eg, 35211

apolcon. I, Emperor of the French,

INDEX

153,228National Archives (France), standard

meters preserved in, 86, 89,92

Nature, 65aval Observatory, U.S., 121-22,

127,nOnavigation.

longitude determination ill, 4~,m

radio lime signals used in, 276NAVS'JAR CPS satellites, 289Navy, U.S.:

glohal clcclrolllapping (.:rfort~ of,])7-40. 140, 141

gllid'lIlcC systems developed hy,2il2,21->5

radio clock -yncluouizatiou of,272, 274, 2711, 21->2

Neptune, discovcry of, 95, 12 I, 149,150

Newfoundland, tclegraph Jiues to,I N, 135, l,()

ell' Method~ of Celestial Mechallics(l'oincarc:5),74

Newton, Sir Isaac, 150, 212,277, 2%Oll plallclary motion, 62, 75second phase of physics dcrivcd

from, 2 1')-16on shape of c: rrth, 191011 timc as ah~olute, I ~, 19, 26, 27,

29, 31l, 44, 190, n(l, 237, 304L'WYork, .Y.:

Alhany's longi tude VS., 'BIlIJGreL'nwich lii uc adopted by, 123,

127, ~37~1regional railro.ad time kcycd to,

110,111-12,126Nile River, coloi iial rivalries on, IIlO,

193

obel Prize, 210Noblemaire, M., 105-66numbers, theory of, 2G~Nye, Mary Jo, 331n

observatories:longitude mappers' construction

of, 134-35, 131l-40, 140,

177-78prime meridian positioned at, 147railroad time vs., 1l0-12, 114-15time systems operated by, 106-12,

126,12ilU.S.-Emopeau links of, 132see a/so s/Jecific observatoruss

occultation, ] 32, 13:;Olesko, Kathryn, 'BIII, 333nOlympia Academy, 236, 237, 23:-;-39,

257, 2()O, 7,2(l-27"011 the Dynamics of the 1':Jeclron"

(Poiucarc}, 21<'>,2<,>5"On the Electrodynamics of Moving

Bodics" (Einstein}, 14,2<'>0-93

"On the Part Played by Polytechni-cians in the Scientific Work ofthe xrx Century" (Poincare),48-49

optics, 5 IOscar II, King of Sweden, 65Ottoman I':mpire, start of day in, 153

Pais, Abraham, 32911, 34711Paris, F1'8l1(:c:

anarchist actions in, 159-601870 siege of, 148electric clock-coordination system

in, 95-98, lOO, 311longitude of, 180-82, 183, 20ti-7,

280,314

..~-------- ...

Index

pneumatic clock-coordination sys-tem in, 93-95, 95, 94

Paris Observatory:electric clock-coordination at, 95,

96-98,100,147,311electric-time-based cartography

tied back to, 143, 144, 147longitude discrepancies Oil,

180-82,280,314as prime meridian location,

147-48, 150Paris Telegraphic Conference (I X90),

339nPasteur, Louis, 51patents:

criteria in granting of, 291,35211.presentation style of, 29 \-92Swiss officc of, 2'n-H, 2+l,

244-51,247,253,291-92,323, 346n, 3471l, 35211

Paty, Michel, 32911, 34611, 34711Pautot, Auguste, 59, 60Pearson, Karl, 237-38, 240, 26()Pedro II, Emperor of Brazil, 138, 139Perret, David, 246, 247-41lPerrier, General F., 181, 197Pcrroz, Emile, 59, ()()Peru, clcctromapping of, 139-40Pcstrc, Dominiqnc, 35111l'ctitdidier, M., 54['hclps, S. J ,., I ~9Philadelphia, Pa., railroad lines Oil

time system of, 126philosophy, 314

of conventionalism, 32-33, 36,188-90,199-201,315

influence of relativity theory on,25, 26

of positivism, 239Phrugmcn, Edvard, 68, 69, 70, 71

physicists, theoretical, 202, 323physics:

British, 199,202conventional basis of, 199-201,

240-41,305-6etheric theories in, 15-18,23,28,

44,47,87,202-6,204,207-12,216-17,218,219,220,230-31,234-35,241-42,260,262,267-68,279-80,293,294-95,297,302,310,317,323-24

format of articles on, 290-91impact of relativity th cory on, 13,

267-70,297; see also relativ-ity, special theory of

mcasuring units in, 166-67, 171-73quantum discontinuity in, 24-25,

270,297-98,299,317,318simultaneity in, 189, 313-14

Piaget, Jean, 25Picasso, Pablo, 319Picon, Antoine, 33111Planck, Max, 269-70, 294, 295, 34611planctary motion, 62-65, 66, 189Plato, 212, 264-65, 316pneumatic clocks, 93-95, 93, 94Poincare, Aline, 54, 56Poincare, Henri, 14, 26

on celestial mechanics, 32,62-75,315-16

on clock coordination, 33, 35-36,45,47, 187-88,207,254,257-58,259,282,285,309,310

conventionalist approach of, 32,77-83,174,199-200,240-41,268,302,304,305-7,318,319,34611

on conventionality of time, 33, 36,

INDEX

44,129,182,189-91,200,211,239,306,309,315,34111

Cornu admired by, 51, 53on day's starting time, 162death of, 303, 315on decimalization, 163, 164, 165,

167-69,171-73,182,211,212,215

Dreyfus prosecution critiqued by,213,214-15

education of, 42, 48-54, 57,228,229,232,297,308

Einstein's meeting with, 296, 297,299, 300

e1cctroteehnology journal co-edited by, 41-42,53,169

engineering background of, 41, 42,48,53,54,57-62,61,305,306,315

French cartographic efforts urgedby, 192, 193-94, 199,211,306,316

German translations of works of,238-39,240-41,346n

on global time coordination COI11-

mittec, 38, 211happiness curve plottccl by, 55on inertia of cnergy, 35211intellectual achievcmcnts of,

31-32,48,65-66,78,87,91,221, 303-4, 308-9, 325-26,327

light-signal synchronization of,45,281,285,295,297,313,314

on longitude determination, 34,35-36

on Lorentz's etheric theories, 45,202-3,204,205-6,207-11,216-17,218-20,241-42,254,

257-58,260,261,277,278,279,280,293,294-95,297,299, 302, 307, 313

metaphorical style of, 28-29as mines inspector, 57-62,61,305,

315modernism of, 212, 219,315-16,

320on moral truth vs. scientific truth,

212-13,302-3national security concerns of, 274,

275-76, 282, 305at Paris Bureau of Longitude, 41,

43,48,53,100,128-29,160,181,186,206,211,276,306,308-9,314,315,316,323

on Paris-Greenwich longitudinaldifferencc, 206-7

on philosophy of science, 56, 57,66-68,189,199-202,221,243,268,299,302,304-6,316,319

politics of, 213-14, 302-3on prime meridian debate, 146on progrcss of physics, 215-17,

218,220,235,277-78,279,295-96,297,2<,)8-<,)9,300,

304-5,317on Quito mapping expedition, 19 I,

193-94,194,1%-<.)7,198,1<,)9,206,211,302,316

on radio time system, 273-79, 282,283, 287, 314

relativity principle used by, 17,28,45-46,199-200,212,218-19,277-78,280,301-2,303-4,310,316,35311

scientific milieu of, 190-91,314-15

on simultaneity, 32-37,41,44-46,

Index

57,129,182-83,186,187-88,189-90,200,237,239,242,271-72,281,306-7,309,314-15

sociallintellcctual circle of, 54-56spacctime considered by, 263,

265-66, 295stroboscopic maps created by,

68-69,7~ 72-74, 73, 75,33211

teaching career of, 61, 81, 27 3,282-83, 308

telegraph transmission time notedby, 33, 36, 183, 199

three-bocly problem addressed by,62-66,68-75,301

visual-intuitive approach of, 63-65,66-68,301

work proccss of, 28,46Pollock, Jackson, 319position, momentum vs., 24-25positivism, 239Post Office, U.S., 123prime meridian:

clocks set to time at, 33911clefined, 116as global convention, 145-46atGreenwich,43, 1l9, 121,146,

147,151-52,156,159-62,174international confcrence on, 128,

129, 144-52potential locations of, 119, 123-24,

147-51,156practical motives vs. philosophical

concerns on, 148-52Principe, Gavrilo, 322progressivism, 46, 212, 215projective geometry, 51Proust, Marcel, 319Ptolemy, 148

Pujazon, Cecilion, 177Pycnson, Lewis, 3471lPyramid, Great, 119, 120

quantum physics, 24-25, 270,297-98,299,317,318

Quine, Willard Van Orman, 25Quito, Ecuador, French mapping

expedition to, 191-99,195,202,206,211,316

radio:military use of, 275-76, 280lime transmitted by, 247, 271-84,

274,283,284, 285, 3()i, 305,314, 350n

radioactivity, 218radium, 216railroads:

crashes due to clock inaccuraciesof, 104-5

Ccrmall ll1ilitary strength linkedto, 157

intcruat iouul couvcnl ions used by,90

observatory time signals vs.,110-12, 114-15

rise in clock coordination for, 30telcgraph transmission of, time

used hy, 105,255-56time zones adopted hy, 99, 122-n,

124, 125-28, ] 58reductive materialism, 323Reichenbach, Hans, 266rclativity, gcncral theory of, 288, 322,

326,35111relativity, special theory of:

clock synchronization and, 18-2:;,2(), 21,253-63,292-93,301-2,311,327

INDEX

constant velocity oflight used in,16-18

Einstein's 1905 paper on, 14-16,253-58,260,285,290-93,303-4, :;4811

experimental cOllScqucncesincluded in, 291-92

four-dimensional spacetime and,263-66,267,285,286

mechanics of falling bodies as prc-cursor to, ]6

nineteenth-century physical sci-

cnce and, 2'l-24, 46-47,303-4,310-11, )5311-5411

physics principles allcctcd hy, ] 3,18,267-70,277-78,297,311,327

positivist philosophical roots of,239-40

satellite Iccill1ology adjnstmentsaccording to, 287-89, 287,:;5111

scientific ncccptanc« of, 24-25Rhode Island Carel I)oard Company,

108Richclicu. Cardinal, 147Riemann, Bcrnhard, 80Rockwell Iutcmatioual, 2il9Rodgers, John, 122Rolle!, Laurent, )2017, :;:;117,:;4211,

35311Rome, Italy, international gcodcsic

conference in, 145, 146-47Russia, time unified ill, 99Ruthcrfurd, Lewis lvI., 146, 147,33811Rynasiewicz, Robert, 32911

nized mapping projeet in,175,177-79,191,316

Sampson, Commander, 147San Fernando Observatory, 175, 177,

179Sarrautou, Henri de, 173-74satellites, clocks coordinated by,

286-89, 287, 351nSchaffcr, Simon, 33311,336n, 33911,

35411Schlick, Moritz, 239, 266Sehlieffen, Alfred van, 157Schliemann, Heinrich, 138Sclnnidgcn, Henning, 34411science:

of complexity, 75conventionalist philosophy in,

188-89cdllcationin,48-56,228-30experiment in, 24, 52, 199,

200-201,229,324,33111induction vs. deduction in, 56, 57,

81,99,323-25principles vs. conventions in,

240-41,34611theory vs. application in, 38-39,

49-50,51,53-54see a/so mathematics; physicsScience and Hypothesis (Poincare),

41,48, 211, 238, 240-41, 268,346n

Science of Mechanics, The (Macht),236,237

Secret Agent, The (Conrad), 159-60,289

Seignac-Lcsscps, Governor, 177Senegal, timc-synchronizedmapping

project in, 175-80, 176, 178,187,191

Sherman, William 'Iecumseh. 132

safcty lamps, in mines, 58-59,60,61,62

Saint-Louis, Senegal, timc-synchro-

Index

Shinn, Terry, :;3hzshooting the moon, 131Signal Corps, U.S., 114simultaneity:

as convention, 33, 36-37,44, 129,182, lil6-88, 189, 19(), 211,n9, 306-7, 309, 315,319

observation as proof of, 57see a/so cJock coordination; timeSmyth, Piazzi, 119, 120soJar eclipses, 131, 148, 326solar systcm, chaos vs. stability of, 66,

69-75,310Solovinc, Maurice, 236,238,326,

:;46nSolvay Conference (1911), 296,

297-98, 299South America, IOllgitudinalmap-

ping of, 137-42, 140, 143spacetime, four-dimensional, 263-67,

285,286,295SfJacetime Physics (Taylor and

Whceler), 285,286Sperry, 250-51Stachcl, John, 329n, 34311,346-4711Staley, Richarcl, 33 311Stark, Johannes, 294State Department, U.S., 43, 144,

146statistical dynamics, n 1, 2:; 5, 240Stephens, Carlcne K, ~34nStrachcy, Ccncral, 150Study of the Variolls Quantities of

Mathematics, A (Calinon),188-89

surveyors, 101-3, 112telegraphic, 132-44, .l4(), 183-87,

193-98, .195Sweden, Crccnwich time standard

used ill, 99

Switzerland:clock synchronization in, 30, 31,

32,46,221,222-24,223,224,227,244,244,245,248,253,272

patent office in, 233-34, 243,244-51,247,253,291-92,323, '34611,147n, 35211

'Ianucry, Jules, 56Taylor, Edwin, 235, 286tectonic plates, 238telegraphy, 37-38

in American method of clock syn-chronization, 103-4, 105-6,105,106,107

British undersea-cable network of,100,134,175-77,176,180,192,274-75,282,305

cable construction in, 130clock xynchronizatio» through,

103-4, IOS-6, lO5, J()6,!07globalm<lpmaking enabled with,

129, 130, 1)2-44,140, 143,145, 175-77, 176, 179, J 80,194-'J8, 195, 206,314

iutcruation.il couvcntions 011, 85,90,180

mirror galvallometcrs used for sig-nal cuhauccmcnt in, 135-36,138

North American cable systems of,104

optical, 275transmission time ill, 33, 36,

183-84,190,199undersea cable installation in, 130,

133-34wireless, 32, 273; see also radio

Teske, Charles, 110, III

INDEX

theoretical physics, 202, 323thermodynamics, 231, 240, 242, 321three-body problem, 62-66, 68-75,

301

radio time implemented by, 272,274,278,280-81,282

railroad adoption of time zones in,99,115,122-23,124,125-28

universal comparator, 87, 88Universal Exposition (1851),85Universal Exposition (1889),191Universal Exposition (l900), 48, 98,

224

Index

Weierstrass, Karl, 65, 71-72Weiss, Pierre, 300,301Wells, H, G" 3391lWestern Union, 108West Indies, longitudinal mapping of,

137What Books Say, What Things Sa)'

(Poincare),325-26Wheatstone, Charles, 30Wheeler, John, 285,286Whittaker, Edmund, 35371-5411Wien, Wilhelm, 294William Bond & Sons, 108Wise, M, Norton, 33211,33311,35411Wolf, Charles, 96, 311World 'rime Convention (1884):

day's start addressed by, 153, 162decimalization of time keeping

urged at, 153-55prime meridian decided at, 128,

129, 144--45, 146-52, 156,162

World War 1,175,322World War n, 285Wren, Christopher, 160

time:convenient: choices in measure of,

188-89,239decimalization of, 43, 153-55, J 54,

163-73,174,188,211,212,240,314

intuitive, 36synchronization of, see clock coor-

dination; simultaneitytime, absolute:

critiques of, 14, 26, 27, 236-38,23'J, 253, 267, 271, 304

Newtonian concept of, 13, 19,26,29,38,44,190,236,2'>7,304

time machine, 33911time zones, 116, 160-61, 173-74

railroad adoption of, 99, 11S,122-23,124,125-28,158

'I onclinc de Quarenghi, Abbe,156

topology, 31, 301trade, international convcutions used

in,90Trcsca, Gustave, 95'Iubrnan, Harriet, 289

Venus, occultation of, 132Victoria, Queen of England, 138Vienna, Austria, pneumatic clocks in,

93Vienna Circle, 25, 266, 320Viollet-le-Duc, Eugene, 96

Waldo, Leonard, 107-8, 109, llO-ll,112,114,115

Walker, Sears, 103Walter, Scott, 33211,33311,34911war:

international conventions on,145-46

signal technology used in, 193,275-76,281,285,289

Warwick, Andrew, 32911, 33111,33311,34911

Weber, Heinrich Friedrich, 229-30,244, 344n-451l

Yale Observatory, 107, III

Zangger, Heinrich, 251, 29Jzone system, see time zones

.il.,"II",11

Unabomber, 289United States:

in Civil War, 132clock coordination in, 100-116clcctromapping efforts of, 132-42,

140,143,192industrial distribution of time in,

100military locating systems of,

285-89

einstein´s_colcks_poincaré´s_maps_galison

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