that software could not be created that wouldrun a program as efficiently as the tediousmachine-language programs, this eclecticgroup proved the doubters wrong. Programsin Fortran not only ran efficiently, but alsochanged the way people thought about soft-ware and made the computer much morewidely accessible.

Lohr recounts the numerous computerlanguages created after Fortran, along withthe intriguing personalities of their creators.He takes the reader on a fascinating tourthrough Cobol to Unix and C, throughBASIC and Visual BASIC, and Algol to Pascal and C&&. By this time, the stage is set for the personal computer and the rise ofsoftware as a separate business, and the endof the mainframe era when software wasshipped as part of the computer. Althoughwe have seen many advances that significantlyincreased the utility of the computer, soft-ware development continues to lag behindhardware and limits the performance anduse of cutting-edge computing.

Lohr ends with the creation of the mark-up language HTML for the web and the philo-sophical battle being waged over open-sourcesoftware such as Linux, for which the sourcecode is freely available, and commercial software. It will be fascinating to see how the

battle plays out over the next decade or so. ■

Paul Peercy is at the University of Wisconsin,2610 Engineering Hall, 1415 Engineering Drive,Madison, Wisconsin 53706-1691, USA.

In the eye of the beholderIt Must Be Beautiful: GreatEquations of Modern Scienceedited by Graham FarmeloGranta: 2002. 224 pp. £20, $25

Ian Stewart

When Robert Recorde invented the equalssign he justified his choice of two parallellines on the grounds that “no two thinges canbe moare equalle”. His inspired symbol, nowindispensable in science and mathematics,forms an iconic decoration for the dustjacketof It Must be Beautiful.

The beauty of equations passes most ofthe human race by. But now we have a bril-liantly readable book that absolutely revels inthat beauty. Graham Farmelo has assembleda star-studded cast of authors and encour-aged them to wax lyrical about their favourite

equations. The book’s main message is theone that Paul Dirac scrawled on a Moscowblackboard in 1955: “Physical laws shouldhave mathematical beauty.”

The essays are arranged in chronologicalorder, based on the date of origin of the equation. Farmelo kicks off with the Planck–Einstein equation for the energy of a quan-tum of radiation, the discovery that startedthe quantum revolution. His essay is mainlyhistorical, and the characters come to lifebefore our eyes. Einstein turns up in severalessays, probably because he set himself such high standards. We are told that the poetPaul Valéry kept a notebook to jot down hisideas, and asked Einstein if he did the same.“Oh, that’s not necessary,” said Albert. Thenhe added wistfully: “It’s so seldom I haveone.” The ideas he did have, though, werestunning. It falls to Peter Galison to remindus of Einstein’s most famous equation. It is, of course, L4mV 2. That’s how Einstein firstwrote it, if it seems unfamiliar.

Physics takes up about half of the book.Roger Penrose makes a valiant effort toexplain general relativity, and tells us that thetotal energy of the gravitational waves radi-ated by Jupiter is about that of a 40-watt light bulb. Arthur Miller dishes the dirt onSchrödinger’s equation — and his love life.Frank Wilczek revels in Dirac’s relativisticequation for the electron, and Christine Sut-ton does a wonderful job on the Yang–Millsequations. The rest of the book is more varied:Igor Aleksander on Shannon’s equations forinformation, Robert May on the logistic mapof chaos theory, and John Maynard Smith on evolution. All of the essays are excellent,but some are more excellent than others.

Oliver Morton’s contribution is ratheroffbeat: the Drake equation, used to estimatethe prospects of finding intelligent aliens. AsJack Cohen and I point out in our forthcom-ing book Evolving the Alien (Ebury Press), theequation itself is open to serious criticism —as, even more so, is its extension in Peter Wardand Donald Brownlee’s Rare Earth(Coperni-cus, 2000). But its history is fascinating. Evenmore fascinating is Aisling Irwin’s account of the Molina–Rowland equations, whichexplain why chlorofluorocarbons destroyozone, and predicted that they would. Thoseequations may just have saved the planet.

Finally, Steven Weinberg muses wisely onthe staying power of a good equation, point-ing out that all of the equations in the bookare actually wrong — and are all the betterfor it. A comprehensible and insightfulmodel beats an exact description any day.

It would have rounded off the discussionif at least one purely mathematical equationhad been included — maybe Euler’s e i p411,or one of Ramanujan’s partition formulas.The beauty of equations resides in theirmathematical form and implications; appli-cations relate to their importance as modelsof the real world. But the two are linked,

book reviews

264 NATURE | VOL 416 | 21 MARCH 2002 | www.nature.com

The Nuremberg Chronicle, more correctly knownas the Weltchronik, or Chronicle of the World, wasan extraordinary Renaissance achievement, andone of the most important works ever published.It is an illustrated encyclopedia of the world as it was known in Germany near the end of thefifteenth century. Most of its knowledge is drawnfrom the Bible, but it also records contemporaryevents, including the falling of a meteorite on theAlsace, and some history of medicine. It includes

maps of important cities, and a map of the world— just too early to include Columbus’s newfindings. Compiled by Hartmann Schedel inNuremberg, the book was illustrated byrenowned artists and engravers includingAlbrecht Dürer, who went on to becomeGermany’s best-known Renaissance painter.Taschen has now published a luxurious fascimileof the massive chronicle (£40, $60, 60 euros),with extensive commentary in several languages.

A Renaissance world view

© 2002 Macmillan Magazines Ltd

which was Dirac’s point. Many of the mostbeautiful equations of mathematics originat-ed in questions posed by science. But somebeautiful equations didn’t, and that ought tobe said, too. Let’s hope there is a sequel. ■

Ian Stewart is in the Department of Mathematics,University of Houston, Houston, Texas 77204-3476, USA.

A milestone for anew millenniumThe Human Genomeedited by Carina Dennis & RichardGallagherPalgrave: 2001. 156 pp. £19.99, $30

Daniel Cohen

The sequencing of the human genome was thelast major goal to be set by leaders of science in the twentieth century. Its achievement wascertainly as spectacular a triumph as thelaunching of the first spacecraft or landing onthe Moon. It was also an amazing example ofcooperation and competition between scien-tists, government funding agencies, charities,and public and privately funded projects. In a symbolic way it is a manifestation of the dramatic cultural changes that humanityundergoes at the turn of a new millennium.

Nature was an active supporter of the project to sequence the human genome, promoting ideas, lobbying for more fundsand publishing outstanding achievements,including a completed draft sequence. So it is natural to see two senior editors of Naturecompiling a book on this epochal achieve-ment. The book is aimed at both non-specialists and students in the field, and presents the goals, history and consequences of obtaining the genome sequence. With a foreword by James Watson, the bookdescribes early achievements in DNA struc-ture and human genome mapping, followedby a detailed account of the dramatic courseof events that led to the sequencing thehuman genome ahead of schedule.

The style is very clear and the authors present not only the facts, but also the spirit of this dramatic race. Although it is probablytoo early for a full understanding, the authorshave tried to assess the future impact ofhuman genome sequencing on biology, medi-cine and society. The book contains very goodillustrations and historical photographs ofkey participants of the project. The originalarticle reporting the sequence obtained bythe public consortium, with schematic genemaps and accompanying papers, makes upmore than half of the book. It will be a pleasure for any scientist to have this mile-stone book in their personal library. ■

Daniel Cohen is at GENSET, 24 rue Royale,F75008 Paris, France.

book reviews

NATURE | VOL 416 | 21 MARCH 2002 | www.nature.com 265

Knowing neuronsA dynamic installation highlighting the fluidityof brain functionMartin Kemp“The work is a homage to the beauty and sheercomplexity of the structure and its steadydevelopment, its genetically-driven growthinfluenced by experience.”

“The complexity and beauty of its structure…reflects the developmental constraints that shapedits growth.”

These two quotes are from writers extolling thewonder of the neuron, as disclosed by modernneurobiology. The first is from Andrew Carnie,one of the ‘researching artists’ featured in theexhibition “Head On. Art with the Brain inMind” at the Science Museum in London (on view until 28 July 2002). The second is fromRichard Wingate of the Medical Research Centrefor Developmental Neurobiology, King’s CollegeLondon, in whose laboratory Carnie wasintroduced first-hand to “the distributed circuitrywhose logic remains one of the greatest mysteriesof biology” (Wingate again).

Their shared experience was the result of oneof eight such collaborations set up by the curatorsof the exhibition — Caterina Albano, Ken Arnoldand Marina Wallace — under the aegis of theWellcome Trust. The other artists are Osi Audu,Annie Cattrel, Catherine Dowson, Letizia Galli,Claude Heath, Gerhard Lang and Tim O’Riley.

In building up his three-dimensionalvisualization of the brain, Carnie looked back tothe pioneering work of Santiago Ramon y Cajal.Cajal used thin slices of tissue, impregnated with resin and stained by a method invented byCamillo Golgi, to construct an imaginative spatialpicture of the cellular structure within the brain.Using Golgi stains, Cajal was able to infer the

composition of different brain regions and evento suggest the direction of information flow. Cajaland Golgi were awarded Nobel prizes in 1906.

The modern resources available to Carnie,such as laser-scanning confocal microscopes andMRI scans, can be used to create compellingspatial arrays and to transcend the static picturesof morbid anatomy, capturing the three-dimensional dynamism of the living circuitry.Carnie was drawn into the amazing worlds of the proliferation, migration and connectivity of neurons in the developing mind, particularly as drifting memories are laid down.

What Carnie set out to capture in hisinstallation, Magic Forest (above), was not anillustration of brain physiology but an evocationof the fluid flux that is the essence of neuronaltransformation, as the growing cells extend theirbranches to communicate with companions nearand far. Two projectors stand three metres aparton plinths at either end of a darkened space. Theyalternately project 160 slides on to three largegauze screens. As the images dissolve into oneanother, the forest grows and diminishes, comesand goes, builds and collapses, layer by layer, in anendless loop of generation and decay.

At these cutting edges of creative visualization,the tasks of the artist and the scientist both beginat the boundaries where knowledge runs thin.The artist gives vent to his awe through the magicof visual suggestion; the scientist through aninsatiable urge to explain ‘how’.

“It has been a breathtaking experience.” Thewords are Carnie’s, but they could have been saidby any scientist grappling with what Wingate callsthe “slices, fragments and snapshots” that“remain, for the time being, the basis of ourunderstanding of neuroanatomy”.Martin Kemp is in the Department of the History of Art, University of Oxford, Oxford OX1 2BE, UK.

Science in culture

© 2002 Macmillan Magazines Ltd