bshm christmas meeting 7 december 2019
TRANSCRIPT
BSHMChristmasMeeting
7December2019
DepartmentofComputerScience,UniversityofWarwick,Coventry,CV47AL
PROGRAMME&ABSTRACTS
Programme
09.30CoffeeandRegistration
09.55Welcome(MarkMcCartney,President)
10.00HelenRoss(Stirling):Dicuilandtriangularnumbers
10.40SteveRuss(Warwick):VisionsintheNight:Bolzano'sAnticipationsofContinuity
11.20Coffee
11.40JaneWess(Independent):FromNewtontoNewcomen:MathematicsandTechnology1687-1800
12.20BSHMAGMandlunch
13.50Shortmembertalk:TroyAstarte(Newcastle):OntheDifficultyofDescribingDifficultThings
14.10Shortmembertalk:CatalinIorga(ENTC,romania):KnownandUnknownInAl-Kashi'sMathematics
14.30RobinWilson(Open):Huntingandcountingtrees:theworldofCayleyandSylvester
15.10Tea
15.30ChrisPritchard(Independent):Fromcollectingcoinstosearchingthearchives:Personalreflectionsonbecomingahistorianofmathematics
16.10MartinCampbell-Kelly(Warwick):VictorianDataProcessing
17.15Finish
OrganisedjointlywiththeDepartmentsofComputerScienceandMathematics,UniversityofWarwick
ABSTRACTS
HelenRoss(Stirling):Dicuil(9thcentury)ontriangularandsquarenumbers
DicuilwasanIrishmonkwhotaughtattheCarolingianschoolofLouisthePious.HewroteaComputusorAstronomicalTreatiseinLatininabout814-16,whichcontainsachapterontriangularandsquarenumbers.Dicuildescribestwomethodsforcalculatingtriangularnumbers:thesummationofthenaturalnumbers,andthemorecomplexmethodofmultiplication,equivalenttotheformulan(n+1)/2.Healsostatesthatasquarenumberisequaltotwiceatriangularnumberminusthegeneratingnumber,equivalentton2=[2n(n+1)/2]–n.Heregardedthemultiplicationformulaasnovel.ItwasinfactdescribedinthethirdcenturyADbytheGreekauthorsDiophantusandIamblichus.Itwasalsoknownasasolutiontoothermathematicalproblemsasearlyas300BC.ItreappearedintheWestinthesixteenthcentury.Dicuilthusfillsagapinourmedievalknowledge.SteveRuss(Warwick):VisionsintheNight:Bolzano'sAnticipationsofContinuity
MuchofthemathematicalworkofBernardBolzano(1781-1848)presentsachallengetohistorians.Howshouldwebestintegrateintothemainstreamofhistoricalnarrativewhatappeartobeoriginalandwell-documentedinsightswhichwereunknown,orunrecognised,intheirowntime,butwhichwererediscovereddecadeslater?Threeexamplesfromtheearly19Cwillbereviewed:neighbourhooddefinitionsofgeometriccontinua(line,surface,solid),theconstructionofanon-differentiablebutcontinuousfunction,andtheconceptof'measurablenumber'whichjustifiedtheso-called'axiomofcontinuity'andidentifiedwhatlaterbecameknownasrealnumbers.Risingtothischallengeforhistory,andrenderingaccuratelytheresultsofBolzano'sthinking,canneverthelessbeaninspiration(ifnotaninfluence)forlatermathematicians.TwoexamplesfromBolzano'sworkoninfinitecollectionswillbeoffered.Finally,someobservationswillbeattemptedontheroleofcontextinassessingwhatconstitutesananticipation.JaneWess(Independent):FromNewtontoNewcomen:MathematicsandTechnology1687-1800
Thistalkpresentsasmallcontributiontoalargeprojectinvolvingaboutfiftyhistoriansofmathematicsglobally.Itwillformachapterinvolumefourofasix-volumesetontheSocialHistoryofMathematics.Mysmallpartinthisis‘MathematicsandTechnology1687to1800’.
The18thcenturywasatimeofdevelopingindustrialisationandimperialism,whichwerechangingthenatureofthephysicalandculturallandscapeinEurope.Forbothpurposesmathematicswasincreasinglyappliedto‘technology’,awordimplyingtheuseoftoolsandmachines.Thetalkwillexploretechnologiestowhichthenewcalculuswasapplied,andtechnologieswhichinvolvedlargenumbersofpeoplebecomingmathematicallyliterateforthefirsttime.
Thetopicscoveredhavebeendividedintothosewhichservedthepurposesofindustrialisationandthosewhichservedimperialism.Undertheformercamelandmanagement,construction,watersupply,transportandpower.Underthelattercamenavigation,shipdesign,ballistics,andalcoholomtery.Thetalkwilltakefourexamplesfromthesetopics,arguingthatthenewcalculuswasnoteffectiveinmanyreal
situations.Ontheotherhandthenumberofpeoplecompetentatmathematicalmanipulationincreasedconsiderably.
TroyAstarte(Newcastle):OntheDifficultyofDescribingDifficultThings
Inthe1960s,afullformaldescriptionwasseenasacrucialandunavoidablepartofcreatinganewprogramminglanguage.Akeypartofthatwasathoroughandrigorousdescriptionofthesemantics.However,inthedecadessince,thefocusonprovidingthishassomewhatdiminished.Whywasformalsemanticsonceseenassocritical?Whydiditnotsucceedinthewayshoped?MyPhDwasspentresearchingtheearlyhistoryofprogramminglanguagesemantics,withaparticularfocusontheIBMLaboratoryViennaunderHeinzZemanek,andtheProgrammingResearchGroupatOxfordUniversityunderChristopherStrachey.Itcouldalsobeseenasanhistoryofmodel-based(ratherthanalgebraicoraxiomatic)semantics.Inthistalk,Iwillpresentthekeyfindingsofmyresearch,asawaytowhetmyaudience'sappetiteformythesis,andarguethatformaldescriptionwasacrucialpartoftheformationoftheoreticalandformalcomputerscienceintheEuropeantradition.CatalinIorga(EdmondNicolauTechnicalCollege,Romania):KnownandUnknownInAl-Kashi'sMathematics
ThispaperisfocusedonthemagnificentmathematicalworkofJamshidAl-Kashi,oneofthemostimportantscholarsofIslam.
Helivedinthe15thcenturyandwasagreatmathematicianandastronomer.Hisremarkablemathematicalbookis“TheKeytoArithmetic”(MiftahAl-Hisab)whichremaineduntranslatedandunknowninWesternEuropeuntiltheendof19thcentury.ThelawofcosinesisknowninFranceasAl-Kashi’stheorem(Theoremed’Al-Kashi)andhiscontributiontodecimalfractionsissosignificantthatformanyyearshewasconsideredastheirinventor.Al-Kashiobtainedaccuratevaluesof2πandsin1oinbothsexagesimalsanddecimals.Hisaimwastocalculateavaluewhichwasaccurateenoughtoallowthecomputationoftheboundariesoftheuniverse.Al-KashialsodiscoveredaveryinterestingalgorithmforcalculatingthenthrootswhichisaspecialexampleofthetechniquesgivencenturieslaterbyRuffiniandAbel.Thepropertiesofbinomialcoefficientswerediscussedinhis’’TheKeytoArithmetic”ofc.1425.
ThepaperalsocomprisesmanyothermathematicaltechniquesandmethodsusedbyAl-Kashi,oneoftheoffspringsofHouseofWisdom(BaytAl-Hikmah)ofBaghdad.RobinWilson(Open):Huntingandcountingtrees:theworldofCayleyandSylvester
Wheredidtheword‘graph’(inconnectionwithgraphtheory)comefrom?Howmanyparaffinsaretherewithagivennumberofcarbonatoms?InthisillustratedtalkIshalloutlinesomecontributionsofArthurCayleyandJamesJosephSylvester,withparticularreferencetotheenumerationoftreesandchemicalmoleculesbetweentheyears1857and1889.Nopreviousknowledgeofgraphtheoryisassumed.
ChrisPritchard(Independent):Fromcollectingcoinstosearchingthearchives:Personalreflectionsonbecomingahistorianofmathematics
Asomewhatself-indulgentlookathowsomeonewithabentformathematicsandacuriosityaboutthepastmadethatjourneytowardshistoricalresearch,withafewwell-knowncharactersmakinganappearanceontheway,includingArchimedes,Brahmagupta,Cardano,PeterGuthrieTait,FrancisGaltonandGeorgeDarwin.MartinCampbell-Kelly(Warwick):VictorianDataProcessing
Large-scaledataprocessingdidnotbeginwithaccountingmachinesandcomputers--itbeganinthe1860swiththefirstindustrial-scaleoffices.Theseofficesemployedhundredsorthousandsofclerkstoprocesscountlessthousandsoftransactionsperday,entirelybyhand.Althoughtheseofficesdidtheirdataprocessingwithnothingmoresophisticatedthanapenandledger,theydevelopedastonishinglycomplexandrobustsystemsperfectlyadaptedtowhatcouldbedonewiththemostprimitivetechnology.ThistalkwilltakeyouonanillustratedtourofsomemajorVictorianoffices,includingtheBankersClearingHouse,theCensusOffice,thePrudentialAssuranceCompany,theCentralTelegraphOffice,andthePostOfficeSavingBank.Thecentralmessageofthetalkisthatwhiletechnologyevolves,informationprocessingsystemsandstructuresareextraordinarilypersistentandsometimeshaverootsthatgoback150years.
TheNewYorkClearingHouse,c.1864.Theimageshowsportersandtellersofthe54NewYorkbanksexchangingchecks--eachexchangetookabout10seconds.