MathematicalToolsinaDigitalWorld
7th September2012
Aninvestigationintotheirdevelopmentandtheirimpactonthewiderworldfrom
theperspectiveofdigitalculture
byAnthonyDurity
May2012
DigitalCulture/
DepartmentofArtandCultureStudies/
UniversityofJyväskylä
i
Finalyearthesis, Jyväskylä2011–Cork2012
FromAnthonyDurity
AtUniversityofJyväskylä, centralFinland
IntheInternationalMaster’sDegreeinDigitalCulture
Supervisors
(senior)RaineKoskimaa
(junior)KristófFenyvesi
ex-Supervisors
SusannaPaasonen
KimmoLehtonen
Publishing, copyrightandlicensinginformation:
AnthonyDurity, copyright©2012
Somerightsreserved
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Publishedonlinevia https://kirjasto.jyu.fi/publish-and-buy/publishing-your-thesis
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seetheCreativeCommonswebsiteformoredetails.
Acknowledgments: (innoparticularorder)SusannaPaasonen, RaineKoskimaa, Kristóf
Fenyvesi: allofJyväskyläuniversity; RonanFarrellfriendandeagle-eyededitor; GiovannadiRosarioforshowingmehowandencouragement; AnneDurityandLeoDurityforunceasingsupport; JonneArjorantafortranslatingtheabstract; PamelaJones
ofGroklawfame, TonyWassermanofCarnegieMellonuniversity, CarloDaffaraof
Conecta, MartinMichlmayrofCyrius, DianaHarrelsonofcyber-anthro.com: forhelpfulpointers, adviceandinformation; DarrelC.Ince, LeslieHatton&JohnGrahamCummingfortheirtimelyNaturearticleandcorrespondence; toallwhorespondedto
myquestionnairesandfollow-upquestions.
ii
Abstract
HumanistinentiedekuntaAthenaeumPL 3540014Jyväskylänyliopisto
puh. 0408053412, 0408053404
[email protected].fi
twitter: @jyuhum
Käyntiosoite: Seminaarinkatu15A-rakennus
Avoinna: maklo10-16ti-toklo9-16peklo9-15
Onmonianäkökulmia, joistadigitaalistakulttuuriavoidaantarkastella. Matematiikan
jamatemaattistentyövälineidenyhteyskaikkeendigitaaliseenonyksinäistänäkökulmista. Tämäviittaamatemaattistenohjelmientutkimukseen. Pääasiallisetlähestymistavat, joitavoidaannoudattaa, ovatmatematiikanharjoittaminen, soveltaminenjakoulutus. Tämätutkielmakeskittyyharjoittamiseenjasoveltamiseen, jättäenhuomiottakouluttamisen.
Tässätutkielmassaosoitetaanmitenkasvavassamäärintietokoneistettumaailmamme
vaikuttaamatematiikanharjoittamiseen. Mikäänmatematiikanosa-aluekuvaamisesta
teoreemantodistukseeneiolejäänytkoskemattomaksi. Esimerkkinätästäohjelmoin
fraktaaliuniversuminosajoukon, L-systeemin, osaksitutkielmaa. Matematiikkaasoveltavien
ihmistentyöonhelpottunutheidänpystyessäänautomatisoimaantehtäviään, ovathe
sitteninsinöörejä, tutkijoitataitaiteilijoita. Olentuonuttätäesiinkeskittymällämatemaattisentaiteenviimeaikaiseenkasvuun.
Kulttuurijaideologiavaikuttavatkaikkiinelämänosa-alueisiin, eikäohjelmistonkehitysolepoikkeus. Keskeisiäkysymyksiäovathallintajavapaus, suljetutjärjestelmätja
läpinäkyvyys. Sillä, mitenohjelmistojakehitetäänoneettisiä/pragmaattisiaseurauksia,
sillävoiollalainopillisiaseurauksia, tieteellisessäkäytössämatemaattisillaohjelmistoilla
onepistemologisiaseurauksia, jasenlisäksiovattaloudellisetseuraukset. Selvitinensintekijänoikeuksienjahenkisenomaisuudenoikeuksienhistoriaa-sittentarkastelin,
mitennämätoimivatviitekehyksinäohjelmistoalalla.
Voidaksenivertaillailmaisiajaavoimenlähdekoodinmatemaattisiaohjelmistojasuljettuihinohjelmistoihinlaadinjoukonkyselylomakkeitajakäytinniihindigitaalisenetnografianmetodologiaa. TämätarkoittiavoimenlähdekoodinSage-projektinkäyttäjien
jakehittäjienjasuljetunlähdekoodinMathematicankäyttäjienjakehittäjienkanssapuhumista. Annoinmyösyksityiskohtaisenyleiskatsauksenmolemmistajärjestelmistäennen
kuinanalysoinsaamanivastaukset.
Therearemanyvantagepointsfromwhichtogainaperspectiveondigitalculture. The
intersectionofmathematicsandmathematicaltoolswithallthingsdigitalisonesuch
vantagepoint. Thisimpliesaninspectionofmathematicalsoftware. Thebroadlines
thatcanbetakenarethepractice, educationandapplicationofmathematics. Thisthesisfocusesonpracticeandapplication, disregardingeducation.
iii
Withregardstheformeritisshownhowthepracticeofmathematicsitselfhasbeen
affectedbytheincreasinglypervasivecomputationalnatureofourworld. Fromvisualisationtotheoremprovingnoareahasbeenuntouched. I programmedasubsetof
thefractaluniverse, L-Systems, intothethesistodemonstratethis. Inthelattercase
thosewhoapplymathematicshavebeenaidedbytheautomationoftheirtasks: bethey
engineersoracademicsorartists. I havefocusedontherecentgrowthinmathematical
arttohighlightthis.
Cultureandideologyaffectallareasoflife, andthedevelopmentofsoftwareisnoexception. Atheartareissuesofcontrolandfreedom, lock-inandtransparency. Howone
developssoftwarecanhaveethical/pragmaticconsiderations, itcanhavelegalramifications, whenwegetintohowmathematicssoftwareisusedinsciencethereareincreasingepistemologicalissues, finallythereareeconomicones. FirstI lookedbackwardin
timetosurveythehistoryofcopyrightandintellectualpropertyrights–thenI consideredhowtheseframeworksoperateinthesoftwareworld.
Inordertocompareandcontrastfreeandopensourcemathematicalsoftwarewith
proprietarysoftwareI composedasetofquestionnairesandusedthemethodologyof
digitalethnography. IntheendthismeanttalkingtousersanddevelopersoftheopensourceSageprojectandusersanddevelopersoftheproprietaryMathematicapackage.
I alsogaveadetailedoverviewofbothsystemspriortoanalysingtheresponses.
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TableofContents
1
Prefatoryremarks
1.1 Thesedigitaltimes . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Thetopicofthisthesis . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3 Coda, whatis meant bydigital? . . . . . . . . . . . . . . . . . . . . .
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Researchoverview
2.1 Thesisoutline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Overviewofsourcematerial . . . . . . . . . . . . . . . . . . . . . . .
2.2.1
Mathematicalart, fractals, chaos, computeralgebrasystems . .
2.2.2 Freeandopensourcesoftware, hackerculture, softwaredevelopment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.3 Variousviewpoints: legal, economic, ethical, epistemological .
2.2.4 Othernotablesourcesofmaterial . . . . . . . . . . . . . . . .
2.3 Methodologicaldecisions . . . . . . . . . . . . . . . . . . . . . . . .
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Theimpactofmathematicshavinggonedigital
3.1 A bird’s-eyeviewofmathematicalsoftware . . . . . . . . . . . . .
3.2 Historicaldevelopmentandstateofplay . . . . . . . . . . . . . . .
3.3 Anexcursionintoafractalworld . . . . . . . . . . . . . . . . . . .
3.3.1
Kochcurves(curves, islandsandsnowflakes) . . . . . . . .
3.3.2 Sierpi�skitriangle . . . . . . . . . . . . . . . . . . . . . .
3.3.3
Fractalplant . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.4 Hilbertcurve . . . . . . . . . . . . . . . . . . . . . . . . .
3.4 Theflighttoabstraction: abstractexpressionandmathematicalart
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4 Thecultureandideologyofintangiblemedia(data)andsoftwaredevelopment
(code)
4.1 Theoriginofcopyright . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 HistoryandsnapshotofFOSS . . . . . . . . . . . . . . . . . . . . .
4.3 Thetarpit: softwareprogrammingishard . . . . . . . . . . . . . . .
4.4 Legal, economic, ethical, epistemologicalangles . . . . . . . . . . . .
4.4.1 Legal: no, all, orsomerightsreserved . . . . . . . . . . . . . .
4.4.2 Economic: theneweconomy . . . . . . . . . . . . . . . . . .
4.4.3 Ethical: pragmatismversusethics . . . . . . . . . . . . . . . .
4.4.4 Epistemological: thecaseforopencomputerprograms . . . .
5
Specificcomparisonandquestionnaires
5.1 Compareandcontrastopenversusproprietarytools . . .
5.2 Sage . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.1
Lead-uptoopensourcequestionnaire . . . . . . .
5.2.2 Feedbacktoopensourcequestionnaire . . . . . .
5.2.3 Follow-upquestionstoopensourcequestionnaire
5.3 Theproprietaryworld . . . . . . . . . . . . . . . . . . .
5.3.1
Lead-uptoproprietaryquestionnaire . . . . . . .
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6 Summaryofresultsandconclusion
6.1 Brieffinishingremark . . . . . . . . . . . . . . . . . . . . . . . . . .
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Endnotesandcitations
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Appendix
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5.4
5.5
5.3.2 Feedbacktoproprietaryquestionnaire . . . . . .
5.3.3
Follow-upquestionstoproprietaryquestionnaire
Results . . . . . . . . . . . . . . . . . . . . . . . . . . .
WhatI learntaboutposingsurveys . . . . . . . . . . . .
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“Patternsareeverywhere,
Bestnottoreadtoomuchintothat.”
Pythagoras(toanacolyte), 3rd BookoftheApocryphaGeometrica
1
Prefatoryremarks
1.1
Thesedigitaltimes
Humanityislivinginthedigitalage. Inthespanofafewgenerationstheworldhas
beentransformedutterlybythemicroelectronicrevolution. Mostrecentlytherehas
beenthetransitionfromwiredtowireless–allwithinthespaceofahandfulofdecades
–thismeansthattheveryatmosphereissuffusedwithdigitalinformation. Gadgets
that were the fodder of the wildest pulp science fiction mere decades ago have now
becomeubiquitous, everyday, commonplace. Everyerahasabeat[Luhmann, 1982, cf.],
[1]towhichitthrumsandhums. Thischaracteristicfeatureeventuallybecomesthe
callingcardofthatera. TheRenaissanceandtheEnlightenmentbeingtwoperiods
thatspringtomind. MoreparochiallytheVictorianerainBritainortheGildedAge
oftheUnitedStatesorthe BelleÉpoque eraofcontinentalEuropecometomind; less
parochially[Vattimo, 1988, cf.] thereisthelabelModernity.
A characteristicfeatureofthecontemporaryworldiswhatistermed churn intechnicalcircles, forcedobsolescenceandsoforth. Withwhatmayonlybeduetotheperspectiveofbeinginthenow–withthe(dis)advantagesoflookingbackovercenturies
andallthelossofdetailthatentails–thepastseemstohavebeenalotmorestaticthan
now, oratleastsoitwouldappear. Thepastappearstohavebeenalotmoreuniform
andstableoverlongerperiodsoftimethannow. Technologicalprocessseemstohave
goneonatsnailspaceincontrastwiththeheadyonrushingintothefuturethatappears
toexemplifycontemporarytechnologicalprogress.
Youwillnoticealotofequivocationintheprecedingparagraph. Many, “itseems”,
many“itappears”. Thereasonforthishesitancybeingthatthisresearcherisunclear
as to the accuracy of these observations, whether they are particular to our contemporarytimesorwhetherpeoplehavealwaysfeltthisway. Itcouldbethatthisisjust
how time always appears from the human vantage point as it unwinds, unfurls and
unloopsfromday, toweek, tomonth, toyear, todecade, tocentury. Theseremarks
areintroductory/preparatory, theyare–thoughI shareLyotard’s“incredulitytoward
metanarratives”[Lyotard, 1984]{pg. xxiv}–commonknowledge. Thedistantpastwas
alargelystaticaffair, kingdomscameandwentbutalwayswithpeoplelivinginfeudal
conditions. Therewasasliverofaristocracyandroyaltythatcontinuedonandonvia
hereditaryclaimsratherthanmeritocraticorelectedmeans. Workderiveddirectlyfrom
thelabourofhumansandanimals. Whatmetal-workingtherewasresultedinweaponry
andjewellery. Knowledgewasstoredupaslore, guildsguardedthislore, itwaspassed
onfrommastertoapprenticeintheguild-house–horticultureandhusbandryfromparenttochildinthefield. Withoutmuchinaccuracyandinaroughcomparisontonowadaysitcouldbesaidthatwhatpeopleknewtheyknewheuristically[Foucault, 2002, cf.]
ratherthananalytically. Thesewerepre-scientifictimes, thescientificmethodwasnot
evenclearlyelaborated. Wethinkofthosepeople, ourdistantancestors, assleepwalk-
1
ers–themorecynicalamongstusclaimthatwesleepwalk[Koestler, 1959, cf.] through
lifetothisday.
Andwhatisthecharacteristicofourage? IsittheSpaceAge? TheDigitalAge?
TheAtomicAge? TheInformationEra? Thereissomuchchangeintheareaoftechnologyalonethatitwouldbehardtopointtoanyoneoverarchingdefiningfeature.
WhichiswhyperhapsthatthenebulousrubricPostmodernityhascaughtontheway
ithas. OrarewelivingintheEraofGlobalisation? AndwiththevoicesfromTahrir
Squarestillringinginourearscouldwesaythatwehaveentered, globally, theDemocraticEra? Andthoughtheworld’sgreatmonotheisticreligions–thoseofAbrahamic
origin–stillholdswayovervastnumbersofpeople, couldwenotcautiouslyatleast
whisperitthatweseemtobeonthebrinkofaSecularAge?
Mypointisthatitwilltakehundredsofyears, ifwesurvivethatlongasaspecies,
tosettleonanoverarchingdesignatorforthesetimes, thosethatarepresentasthisis
written. Untilthen, letusagreefornowthatoneofthehallmarksofthetimeswelive
inisthatof pervasivecomputation andleaveitatthat.
Therearesevenbillionpeopleonthiscrowdedplanetrightnow. Asof2011there
werealmost6billionmobile-cellularsubscriptionsinthepossession[2]ofpeoplearound
theglobe. Asyouknow, eachmobilephoneisaminiaturecomputerandtwo-wayradio.
Formostpeopleapartfromourclothing, andthenourwallet, themobilephoneisthe
nextonthelistofitemswecarryaroundwithus. Computingisnowpervasive, soon
itwillbeubiquitous. AsWilliamGibsonhassaidmanytimes, “Thefutureisalready
here–it’sjustnotveryevenlydistributed.”[3]Itmaynotbethecasethisveryday, but
withintwogenerationstherewillnotbeaplaceontheplanetwithoutaccesstomobile
technology, itisinconceivablegivencurrenttrendsthatitcouldbeotherwise.
Itisasimpleobservationthatthedigitalisparthardwareandpartsoftwaresoitcan
besaidthatthenatureofthedigitalisthusatwo-foldnature. Bifurcatingagain, softwarehasadualnature, sourceandbinary. Thehardwareisthesubstrate, thesoftwareis
thefluidlogicthatcongealsontop. Hardwareissilicon, wires, transistors, capacitors,
resistors, microelectroniccomponents. Thewidthofthepathwaysincontemporary
microchipsaremeasuredinnanometers-soI couldjustaseasilyhavesaid, nanoelectroniccomponents. SiliconfabricatorslikeIntel(x86), GlobalFoundries(x86), Samsung(ARM),Qualcomm(ARM),IBM (POWER) havereachedthestagewherethey
arepackingbillionsoftransistorsontoeachhigh-endmicroprocessor. ThefastestsupercomputershavetensofthousandsofprocessorsandterabytesofRAM.Theirperformanceismeasuredinthepetafloprange. Computingpowerisincreasingrelentlesslyandfollowingaverystrictpowertopriceratioandithasdonesoformanyyears,
aswitnessedbytheMoore’sfamouslaw(GordonMoore, ex-CEO ofIntel). Thishas
alsobeendubbedtheLawofAcceleratingReturns. Thistrendisapparentlysouniformandsopredictable, fromonetelecommunicationgenerationtothenext, thatsome
technologists[Kurzweil, 2005]havepredictedatechnologicaleschaton-atechnologicalrupture, anageofsuper-intelligentmachines. Thisistheinformaticfringeofeschatologywithitsownattendanttechno-rapturewhoseapproachingeventhorizonof
hyper-intelligentmachinesistermedthesingularity.
2
1.2
Thetopicofthisthesis
Weinthehumanitieshavetograpplewiththeimplicationsofthisacceleratingdigital
change. Ifwearetoviewallthisfromamostabstractofperspectivewemightusethe
toolsofphilosophy. Ifwearetostaywithinthescienceswewouldusethetoolsofsociology. Ifweweretotakeaninterdisciplinaryandmoregroundedapproachwewould
workwithinthetraditionofculturalstudies. Researchersinthehumanities-properly
calledthedigitalhumanities, ifthefocusisexclusivelyontheareaofinformationand
communicationtechnologies-candecidetotakealookoftheimpactofthedigitalin
anynumberofways. I havedecidedtofocusonsoftware, thatmalleablepartofthe
digitalnature, andinparticularmathematicalsoftware.
Thisthesisisanexplorationofthestateofplayinmathematicalsoftwaretools, both
opensourceandproprietary. Thegoalistoexaminethesetoolsfromtheperspective
ofhowtheyarebuiltandhowtheyareused, bothscientificallyandartistically. The
goalistoexplorehowmathematicshasbeenalteredbythistransitiontothedigital.
BecauseofthisI needtolookatmathematicssoftware as software–howdoesitfitinto
theusualfabricofsoftwaredevelopment. Muchhasbeenwrittenaboutthepracticeof
softwaredevelopment, whether, likeDonaldKnuth, onecallsittheart[Knuth, 2009,
cf.] (orcraft)ofsoftwarecreationorwhether, asismorestandardinacademia, onecalls
thedisciplinesoftwareengineering[Ghezziet al., 2002, cf.] reflectsonhowyouview
thepracticeasitrelatestoothertradesandprofessions. Alsotobeexploredishow
mathematicalsoftwareonadigitalplatformopensupentirelynewvistasintherealmof
visualisationthatsimplydidnotexistbefore. I amnotgoingtolookatsimulationand
modellingbutI shalllookathowmathematicalsoftwarethroughrealtimevisualisation
hasallowedhumanitytobegintocomprehendbetterthechaoticandfractalnatureof
theworld. Finally, alsotobeexaminedishowthisenablingtechnologyisseepinginto
artintheformof, asI seeit, alogicalsuccessortoabstractexpressionismandgeometric
artviathediverseandvibrantgenreofmathematicalart.
OnapersonallevelallowmetoexplainhowI havearrivedatparticulartopic. My
bachelor’sdegreeisinphilosophyandmathematics. True, I couldbynomeanscallmyselfamathematician, I donothavefirst-handknowledgeabouttheday-to-dayactivities
oftheworkingmathematician. Butthereisapartofmethatisfascinatedbymathematics–Mandelbrotsets, theinfinitesimalcalculus, mathematicallogic, numbertheory,
younameit, I finditinteresting. Unfortunatelymypassionexceedsmyability. I will,
alas, nevergetveryfarintotheworldofmathematics, soI seethisthesisasawayof
beingapartofthemathematicalworld. Thefree(asinfreespeech, notasinfreebeer
–libertyversusgratis)andopensourcesoftwareangleenablesmetolinkmathematics
tomydigitalculturestudiesbecausesoftwareisaprimemanifestationofthedigital,
andbecausefreeandopensourceapproachestosoftwaredevelopmentarefluctuations
inculture. Thevisualmathematicalartefactsangleenablesmetolinkmathematicsto
mydigitalculturestudiesbecauseartisalwaysamanifestationofculturethoughoddly
enoughwhenjoinedwithmathematicsitseemstobringaboutcreationsthattranscend
anyoneculturesuchistheuniversalaspectofmathematics. Thefractalandchaosangle
enablesmetolinkmathematicstomydigitalculturestudiesbyshowinghowtheway
studyandresearchinthedigitalhumanitiescanberadicallydifferent[4]fromthesort
ofdigitalprintingpressideologythatpermeatesthehumanitiesatpresent.
3
Howarealltheseareasexpressionsofcultureorfluctuationsinculture? Theway
I seeit, cultureisthesumtotalofnon-universalbehaviouraltraitsinhumans. I usuallyhelpmyselfalonginthisunderstandingwiththefollowingrefrain, cultureishow
peopledothingsdifferentlytogether. Bythislogiccultureisneversomethingpurelyindividual, individualsarevesselsofculturebutcultureisexpressedonlycollectivelyand
neveruniversally. A primeexamplethatI useforexplainingthistomyselfistheobservationthateveryonedancesbutthatdifferentgroupsofpeoplehavedifferingcostumes,
stylesandtraditionsofdance. Cultureisinthedifferences, itisapatinaorlayerover
theuniversal. Withrespecttosoftwaredevelopmenttherearemanyculturaldifferences
insoftwaremethodology, someofwhichbearnorelationtosoftwaredevelopmentas
anengineeringdiscipline. Peoplewhobelieveinfreesoftwareoropensourcesoftware
believeinthepragmaticorethicalbehaviourofsharingthesourcecodetotheirlabour.
Thecontraryculturalstanceisproprietarysoftwarewherethesoftwareisnotshared.
Therearemanynuancesbutthatisthegeneralgist.
Thisthesiswillcontainadistinctbias. I believethatthefreeandopensourcesoftwaremethodologyisthebetterwaytobuildreliablesoftwaresystems, systemsthatare
lesshostiletotheusersofthesoftwarethanclosedorproprietarysoftware. Taking
thisintoaccount, notonlyshallI exploretheterrainofopensourcemathematicaltools
versusproprietarytools(thissurveyI will, ofcourse, performinanunbiasedfashion)
butI shallalsolookatwaystohelpfosterandimprovetheopensourceecosystemof
mathematicaltools.
I havegivenaflavourofthetopic, I nowturntotheapproach. Ifyouwillpermitme
tosay: I haveadifficultywiththeword approach andwithhowitisusedinacademic
contexts. Formethewordsuggeststhedirectionfromwhicharesearchergoestowards
theirresearchspace, ratherthanasynonymformethodologywhichishowI amcoming
toaslowrealisationthatitisemployed. Consideramountainclimber. Theapproach
tothesummitistheangleofattackassuch, itsaysnothingaboutthetoolstheclimber
uses–I wouldpreferifapproachheldontoitsoldclothingratherthanbeingcoerced
intonewgarments. Withthatbriefbutpertinentdiversionoutofthewayletmediscuss
myproposedmethodology. AsisappropriatetohumanitiesandculturalstudiesI shall
performqualitativeresearch. Myaimistointerviewmathematicalsoftwaremakers,
adherentstobothfreeandopensourcemethodologies. I aimtomakeasurveyofthe
impactofmathematicsandcomputersonart. Theapproachwillbedigitalethnography
(pleaseseesubsection 2.3)say–toalargeextentphilosophicalasthatismybent.
Inthehumanitiesthecomputeristreatedasafancydesktoppublishingtool. The
processistheresearchitself. Theresultsarestatic. Ifthereisanythingthatcouldbe
learntfromthedigitalandnetworkrevolutionisthatresearchcouldbecomeacollaborativeopen-endedaffairandresultscouldbepresentedinan–tousethatratherpassé
word–interactivemanner. WhatdoI envisionbythis? Pictureifyouwillathesiswhere
thechartsandgraphscanbemanipulatedbythereader. Alreadythethesishasbecome
ahyperlinkedaffair, somethingsomundanethatitescapesourattention. Butwhatis
moreamazingthatbeingabletofollowalinkinachainofinformationinstantlysothat
youretrievethenextpieceofinformationstoredonamachinethousandsofkilometres
away? Itseemsthatweinthedigitalhumanitieswriteuppageafterpageaboutall
thenewaffordancestherevolutioninICT bringsandyetarecontenttoletthisnatural
progresswashgentlyoverourshoresleavingusundisturbed.
4
1.3
Coda, whatis meant bydigital?
Itisanobservationofminethatculturalstudiesoverlapswithmediastudiestosucha
largeextentitisdifficulttorememberthatthereisalifebeyondmedia. Truthbetold
mediaanalysis, forwhateverreason, makesupalargepartof(digital)culturalstudies
andasitisobvioustoanyonethatthemediahasbeenimpactedgreatlybythetransition
todigitaltechnologieswhatweappeartobeleftwitharenumerousarticlesanalysing
onlinesub-culturesandtheaffectofthedesktoptechnology, mobiletechnology, and
internettechnologyonhumanbehaviour.
Inthe LanguageofNewMedia LevManovichasserts[Manovich, 2002]thatthe
languageofthenewmedia(andbyimplicationcode)thatnowsurroundsusisthelanguageofthemachine, ormoresuccinctlythedigital. ThenatureofthislanguageaccordingtoManovichshallbedealtwithnow.
Manovicharguesthattherearefive“principles”ofnewmedia: numericalrepresentation, modularity, automation, variability, andculturaltranscoding. Inthefirstcase
ourrealworldissampledandquantised–thecontinuousbecomesbinarydigits. Inthe
secondcasethemediaobjectsthemselvesarecomprisedofpartsthatcanbemanipulatedindependentlywhilekeepingaunifiedsystemicintegrity–asimilarobservationis
madeforcodeasitisfordata. Thethirdcasereferstotheprogramabilityofthisnew
environment. Thefourthcasereferstothemalleabilityandfluidityofthebitsandhow
theinterfaceisdecoupledfromthecontent; italsoreferstohowconstantscanbereplacedbyvariablesindata. Thefinalcaseseemstorefer(I sayseemsbecauseI could
notcommitmyselftosaywithabsolutecertaintyI gotthisprinciple)tohowthesenew
propertiesaffectculture–transcodingmeaningtogofromoneformattoanother.
IntheWhatNewMediaIsNotchapterhesays: “Havingproposedalistofkeydifferencesbetweennewandoldmedia, […]FollowingaresomeofthepopularlyheldnotionsaboutthedifferencebetweennewandoldmediathatI willsubjecttoscrutiny:”{pg.
49}Newmediaisanalogmediadigitised, alldigitalmediasharethesamedigitalcode,
new media (and code also) allows for random access, involves a loss of information,
copiedendlesslywithoutdegradation, isinteractive.
Hereweencounterthedigital. Whatisthedigital? Infact, whatisamedium? Here
ismytakeonit. Wordslikemedium, text, andsoonhavetheirrootsinthephysical–lettersonapage, theairasacarrierofsoundwaves. Whenphysicistsusethetermmedium
theyrefertoaspecificphysicalobjectthathasspecificphysicalproperties. Whenwesay
thatprintisamediumweareusingtheterminaslightlymoreabstractsense. When
Manovichputs“theInternet, Websites, computermultimedia, computergames, CDROMsandDVD,virtualreality[5]”{pg. 19}togetherinalist(thoughhesaysthatthis
listisculledfromtopicsofdiscussioninthepopularpress)whatexactlyishedoing? I
assertthatheisbeingvague.
I donotthinkweneedahaphazardlist. Forinstance, wehavenoproblemsaying
thatprintisamedium, thingslikebooksandleaflets, posters, mail, newspapers, photographsareprintedontopaperandcardandphoto-paper. SoCD-ROMsandDVD
areopticalmedia. Theyhaveaname, thisistheirname. Computergames? These
aremedia? Computergamesaregames. Gamesarenotmedia. Though, inonesense
imagineifyousaidthatnotonlyisprintamediumbutsoarebooks–inthiswaycard
gamescouldbemediabutthatdoesn’tfeelright. Letussaythatcomputergamesare
5
storedonandaccessedfromdigitalmediabutarenotmediathemselves. Howabout
computermultimedia? Thisisvaguerandmoreabstractstill, weevenhavetheword
mediainmultimedia–inwhatsenseisthewordbeingusedhere? Multimediaisalready
anoldfashionedword, I onlyseeitusedtodescribemultimediacourseswherethestudentlearnsdigitalaudiomanipulation, digitalimagemanipulation, 3D modelling, web
sitecreation. Dotheeducationprovidersseeeachcraftasamedium? Possibly. Letus
leavethispuzzletoonesideforthemoment. Istheinternetamedium? Arewebsitesa
medium. Thewebisonlyapartoftheinternet, justlikeemail, podcasts, VoIP,andso
on. Ifthewebsitesandtheinternetarebothmediathenmediacanbenestedandthere
isnoreasontothinkthatemailisnotamedium. Isemailamedium? Isitpartofthe
newmedia? Ifemailisamediumthenisordinarymailamedium?
ButI feelthatprintisthemediumandthatmailisauseoftheprintedmedium
andnotamediuminitsownright, otherscoulddisagree. Whatisitaboutdigitalmail
thatmakesiteasierformetofeellikeitcouldbeamedium? Medium, inLatinmeant
“theoneinthemiddle”whichisintermediaryinEnglish. (Ifamediumisachannelor
acarrier, thenmailandemailaresub-channelsorsub-carriers–whichshowsthatthe
designationinformationsuperhighwayisnotthatwideofthemarkafterall.)
Takingastepbackinordertosurveythelandscapebetter, howisnewmediato
becharacterised? Ifnewmediaisanythingatallitisdigitalmedia. Sowhereverthe
bitcanresideisadigitalmedium, likeintheconduitsoftheinternet, thepixelsofyour
monitor, inopticalmedia, thewiresinthecircuitryofthemagicboxoftricksinfront
ofyou, intheregistersoftheCPU,inthecellsofthememorychips, inthemagnetic
polesoftheparticlesontheharddrive. Thisyoucouldsayisourdigitalinfrastructure.
Shouldwecollapsealltheseplacestogetherandcallitadigitalmedium? Itseemsmore
likeadigitalrealmthanamedium. Besidessomeoftheseplacesareusedforstorage,
somefordisplay, someformanipulation, andsomefortransmission. Itislikehaving
thesheafsofpaperandthetypesettingmachineandtheprintingpressarrayedonthe
deskinfrontofyou, maybethat’swhytheycallitdesktoppublishing.
Soistheinternetamedium? Butwhatistheinternet? Well, theinternetisthepipes,
thecomputersandtheprotocols. Bitsmovearoundaccordingtoprotocols. Because
thebinarydigithasbeenfreedfromtheparticularsubstrateofanyonemedium. The
bitisaddressabletouseapieceofcomputerjargon. Thusthesymbolisaddressable. I
realisethatI keepreferringtoprinthereasifitwerethecanonicaloldmediumbutI feel
mymusingsholdsforallnon-digitalmedia, withprintthesymbolisimpregnatedinthe
medium–ifyouwanttocopyabookyoumustphotocopytheentirepage, symbolsand
all. Thisistheoldmediaway. Becauseitappearsthatanythingatallcanbeencoded
numericallyonceyouagreeonaconventionforencodingthenitappearsthatnearly
anytypeofobjectcanberepresentednumerically. Thechemicalsequenceofmolecules
forinstance. Vocalpatterns. Thehue, saturation, colourandluminosityofanimage.
Entirebooks. Encyclopædias. Itismyassertionthatthedigitalmediaaremulti-format
ormulti-modalbecauseoftheunifyingunderlyingrepresentationandaddressabilityof
thebit.
AnotherwaythatI lookatallthisisthroughthelensofmetaphor. Take, “Thistext
isavehicleformyideas”. N.KatherineHaylesshowsusofcoursethatthereisnoideal
textassuch, letussaythatweareusingthewordtextinthenominalistsense, notinthe
Platonicsense. Canwesay, “Thisbookisavehicleformyideas”? Surewecan. Butdo
6
youmeanthebookinyourhand? Orallthebooksprinted? Soyoumeanthetext. The
bookstoresthetext. Thebookisacontainerforthetextinsomewaythatthetextisa
containerofyourideasthroughthebeautyandmagicoflanguage. Ifthetextisavehicle,
thevehiclemustmoveoversomesurface. Letusseeifthemetaphorholds. Imaginethe
textisatrainoracarthenthesurfacemustbeatrackoraroad. Isthesurfacethebook?
Orisitprint? Youcouldalsosay, “Thissongisavehicleformyideas”or“thispoem”
or“thisstory”or“thisfilm”soclearlythevehiclemetaphorworksacrossmediums. So
eventhoughthesurfacesvarythemetaphorworks. Youwouldn’tsay“thisinternet”or
“thiscomputer”butyoucouldsay“thismultimediaextravaganza”or“thisweb-comic”or
“thisvideo-game”sowecanseethatManovich’slistisindeedhaphazardasitappearsto
containobjectsfromdifferentcategories. Whatisinterestingisthatwecalltheinternet
(anditsHTTP subsettheweb)theinformationsuperhighwaysoweseeitasasurface
forvehiclesinsomeway.
Sonowthatweareattheconclusionofthisoverlylongsynopsishavewearrivedat
anyconclusions? Wehavecometotherealisationthatwithnewmediaandwithcomputercodethesymbolsofthecontentarereadilydivorcedfromthemediumitself. I do
notknowwhattocallthis. Manovichisrighttobesuspiciousofthe’randomaccess’
principlebecauseitdoesn’tcapturethefullideabutitdefinitelycapturessomeofit.
LikeI saythejargoninthecomputersciencefieldisaddressabilitybutthenagaindictionariesareindexedandwehavepagenumbersandtablesofcontentsbutthenagain
theseonlyallowyoutogotocertaincrudepartsoftheseworks, nottoeachandevery
symbol. Sowehaveautomatedbit-levelgranularityandaddressabilityinthenewmedia. WhenitcomestomodularityI cannotthinkofasinglebookthatisnotbrokenup
intochaptersoranewspaperintosectionssoI thinkmodularityisnotafeatureunique
tonewmedia. Asthebitisanundifferentiatedmeaninglessobjectweneedformats
andencodingsystemstoturnastreamofbitsintoameaningfulchainofinformation.
Alsoweneedtosaywheretheboundariesoftheobjectsareandweneedtoinitiateand
terminatedigitalconversationssoweneedsynchronisationtechniques.
Whatismostinstructivetomearethetechnicaldetailsofculturaltheorists. Itappearstothisreaderthatthemorewaffleandverbosethework, themoreitisguaranteed
thatthetextisshortonorfudgesthetechnicaldetail. Caseinpoint, otherresearchers
inthedigitalhumanities, forinstanceHayles(whoI’vealreadymentioned)andEspen
J.Aarsethgointofairlyaccurateandcomprehensivetechnicaldetailintheirvarious
works. Manovichstaysonthelevelofculturaldiscoursewhichisalwaysgoingtobe
vague. Whenhedoesventureintotechnicalterrain: “A computerprogramwrittenby
aprogrammerundergoesaseriesoftranslations: high-levelcomputerlanguageiscompiledintoexecutablecode, whichisthenconvertedbyanassemblerintobinary”heis
superficiallycorrect. “A computerprogramwrittenbyaprogrammerundergoesaseries
oftranslations”–yes, theyarecalledcompilationpassesbutalsoacomputerprogram
canbeinterpretedsotheycouldbecalledinterpretationpasses. Asintopassoversomethingwhileprocessingit. “High-levelcomputerlanguageiscompiledintoexecutable
code”–no, asI saiditcouldbecompiledorinterpretedsowhynotjustsaytranslated?
Thecomputerprogramiscalledthesourceandtheresultiscalledthetarget. There
maybeanumberofintermediatestepsbutthecompilerorinterpretergenerallyproducesobjectcode, notexecutablecode. “whichisthenconvertedbyanassemblerinto
binary”. Anassemblertranslatesassemblycodeintomachinecode(binarycode)but
7
rarelynowadaysdocompilersorinterpretersgenerateassemblylanguagesoanassemblerisrarelyinvoked. Whatactuallyhappensisthatalinkerturnsobjectcodeintoexecutablecodebyresolvingsymbolsandthisexecutablecodeisbinarycode. Thedetails
areavailableinanyrecentbookoncompilertheory.
A noteonthetoolsI use: I amwritingmythesisitselfinLATEX[6], anopensource
documentationpreparationsystemtraditionallyusedinthescientificandtechnicalcommunity. Rather than hand-crafting the document I am using a package called LYX
whichwhenitisbehavingtakescareofthenittygrittymechanicsandletsmegeton
withtheactuallytaskofconvertingmyobservationsintosomethinghopefullyworthwhile.
8
2
Researchoverview
2.1
Thesisoutline
Therearethreemainpartstomythesis: sections(3)‘Theimpactofmathematicshaving
gonedigital’, then(4)‘Thecultureandideologyofintangiblemedia(data)andsoftware
development(code)’andthen(5)‘Specificcomparisonandquestionnaires’. Theremainingsectionsbeing: the(1st )‘Prefatoryremarks’sectionbeingamerepreamble; andthis
sectionhere, the(2nd )‘Researchoverview’, beinganoverview; thethesisconcludeswith
section(6)‘Summaryofresultsandconclusion’. Allthereferences, betheycitationsor
endnotesandwhethertheyrefertoelectronicorprintresourcesarecontainedinsection
(7)‘Endnotesandcitations’andfinallysupportdocuments(onlinesurveyformsandthe
like)arelistedinthe Appendix.
Section(3)tracestheoriginsandgrowthofmathematicalsoftware. I showhow
onebranchofmathematics, thatdealingwithchaosandfractals, hadtowaitforthe
developmentofadequatehardwareandsoftwarebeforeitcouldbeexplored. I show
howmathematicalsoftwareisnowchangingtheartlandscape.
Section(4)tracestheoriginsandgrowthofintangiblecreations–previouslythe
domainofthoughtandtextonly. Withtheriseofthebit(bothdataandcode)humanitiesnotionsofpropertyhavehadtoadapt(bothmediaandsoftware). Inconcreteterms
thismeanslookingat: theoriginsandevolutionofthenotionofcopyright, thenatureof
howsoftwareiscraftedwhetherproprietaryoropensource, thepatentingofintangible
objects, thenatureoftheneweconomyinthenetworkedsociety.
Section(5)analysestheresponsestotwoquestionnaireswhosequestionsarerelated
toissuesI grapplewithintheprevioussections. Thesequestionnairesaredirectedat
developersandusersofaleadingopensourcegeneralmathematicalsoftwaretooland
atthedevelopersandusersofaleadingproprietarymathematicalsoftwaretool. Both
toolsareequallycapableofworkingwiththemathematicsandgeneratingtheartfound
insection(3)andbothprojectsareembeddedinthesystemofregulations, cultureand
ideologydiscussedinsection(4). I extendtheanalysisbyconsideringissuesfromthe
perspectiveofthephilosophyofscienceandpointtorecenttheoreticalworkinthisarea.
2.2
Overviewofsourcematerial
Thissubsectionrunsthroughtheavailablesourcesofinformationandwhichofthose
sourcesI haveused. Oneofthefirsttasksofanyresearcherissurveyingthelandscape
of existing research to see what prior research is applicable to the research at hand.
Thisincludespopularandspecialistnon-fiction(drawnfromcourseworkandbeyond),
academicpapers, articleswithinjournals, andencyclopædiaentries.
Asregardscourseworkonlyacouple, certainlynomorethanahandfuloftitleswere
strictlyrelevanttomytopic. Itisnotthatmythesistopicfallsoutsidetheallowedlimitsofourcoursebutratherthatthecourseitselfonlytangentiallytouchestheareaof
thecraftofthedevelopmentofsoftware(includingmathematicalsoftware)andtheimpactofthedigitalonmathematicalart. Inthemaincourseworkrelatedtoparticipatory
culture, newmedia, methodologicalissuesininternetresearch, andtheoriesofdigital
9
cultureinformedmyresearch. ExamplesincludeCharlieGere’s DigitalCulture, essaysbyWendyChunsuchas OnSourceryandDaemons, orCodeasFetish, Hayles’s
HowWeBecamePosthuman, EspenAarseth’s Cybertext: PerspectivesonErgodic
Literature, andasseeninthepreambletoLevManovich’s(thoughitcontainsflaws)
TheLanguageofNewMedia. WhetheritisbecauseI haveaperennialinterestinsuch
mattersI foundthatissuesintheseworksrelatingtoopennessandtransparency, access
andcontrolariseagainandagain-wecouldbetalkingabouttheareaofsocialmedia,
electronicpoetry, ordigitalaesthetics. Forinstance, whentalkingaboutbloggingand
citizenjournalismourclassconcentratedonthewhetherbeingabloggerqualifiesone
asbeingajournalist, wespokeabouttheinstantglobalreachofablog, wetalkedabout
theinteractivenatureofcommentingsystems, theside-steppingofthemassmediaand
withthattheabilityofdirectlyspeakingtruthtopoweralbeitwithasmallervoicethan
traditionalwell-knoworgans.
2.2.1
Mathematicalart, fractals, chaos, computeralgebrasystems
I have drawn a lot of material from the New Encyclopædia Britannica, 15th edition,
which I have found to be invaluable [Enc, 1982a]. I have also drawn on two recent
artexposés: PhilipSteadman’s Vermeer’sCamera: UncoveringtheTruthBehindthe
Masterpieces andDavidHockney’s SecretKnowledge: RediscoveringtheLostTechniques of the Old Masters [Steadman, 2001, Hockney, 2006]. I have relied on The
FractalGeometryofNature byBenoitB.Mandelbrot[Mandelbrot, 1983]. InasimilarveinI haveextractedvaluableandlearnedscholarshipfrom ChaosandFractals by
Heinz-OttoPeitgenandDietmarSaupeandHartmutJürgens[Peitgenet al., 1992]. I
havebeeninspiredbytheBridgesseriesofconferences. BridgesconcernsMathematicalConnectionsinArt, Music, andScience. The2011washeldattheUniversityof
Coimbra. FromtheproceedingsI havedrawntwoworks: TheArtofComplexFlow
Diagrams byAnneBurns[Burns, 2011]and A Nine-andTwelve-PointedStarPolygonDesignoftheTashkentScrolls byLynnBodner[Bodner, 2011]. FromtheassociatedexhibitionI havedrawnon AestheticExplorations byNathanSelikoffand Biscuit
Land byMehrdadGarousi. I havebeeninemailcorrespondencewithallfourartists.
2.2.2
Freeandopensourcesoftware, hackerculture, softwaredevelopment
I madeuseofavideofromTheBerkmanCenterforInternet&SocietyatHarvardUniversityaboutthebook CommonAsAir byLewisHydewhichisalookatthehistory
ofthecommons[Hyde, 2011]. TheCathedral&TheBazaar byEricS.Raymondhas
beenakeytextformeasitisakeyvoiceoftheopensourcerevolution[Raymond, 2001]
–itisoneofthefirstsociologicaltakesonthefree-software/opensourcemovementby
aninsider. DreamingInCode byScottRosenbergabookconcerningamuchtalked
aboutopensourceprojecthelpedshapealotofmythinking, thoughI donotquote
itdirectly[Rosenberg, 2008]–itgivesadetailedbusinesshistoryofandinsightinto
the high-profile Chandler project. Just For Fun by Linus Torvalds and David Diamond [TorvaldsandDiamond, 2002] a biography of Linus Torvalds and his baby,
Linux–againI haven’tquoteditbutitwasinstructional. FreeAsInFreedom bySam
Williams[Williams, 2009]–abiographyofRichardStallmanandhisbabies, theGPL,
10
Emacs, GNU andtheFSF.Online. TheMythicalManMonth byFrederickP.Brooks
[Brooks, 1995] –aclassicofsoftwaredevelopmentliterature, positedthatsoftwaredevelopmentdoesn’tscalebythrowingmorepeopleattheprobleminthesamewayas
otherengineeringtasks.
2.2.3
Variousviewpoints: legal, economic, ethical, epistemological
RiffingonAdamSmith’s WealthofNations isYochaiBenkler’s WealthofNetworks
whogivesaneconomist’stakeonnetworkeffectsastheyrelatetointangibleproducts
[Benkler, 2006]. TimWudelineatesthehistoryofmonopolyinthetelecommunicationsindustrywithhistext TheMasterSwitch [Wu, 2011]. TheStanfordlawyerand
policyinfluencerLawrenceLessighaswrittenmanybooksandisadrivingforcebehindtheCreativeCommonsoneofwhoselicensesthisthesishasbeenbroughtoutunder. Hehas FutureofIdeas [Lessig, 2001]whichisavailableonline, also FreeCulture
[Lessig, 2005]and Code2.0 whichiswhatI’vedirectlyquotedfrom[Lessig, 2006].
2.2.4
Othernotablesourcesofmaterial
Sagedocumentation[Steinet al., 2011]whetheronlineorlocaltutorialsandmanuals
hasprovedinvaluable. MathematicadocumentationandWolframMathworldhasproved
veryusefulalso[7].
2.3
Methodologicaldecisions
AsI amlookingintothepastinanumberofways(thehistoryofcopyright, thehistorical
changesinart, theco-developmentofmathematicsandmathematicalsoftware)I shall
employHistoricalResearch. BecauseofmynatureandbackgroundI oftenstriveto
generalisefromparticularsoncehavingdelineatedthehistoryofatopicandsoI employ
alotofPhilosophicalResearch. Thesameholdstruewhenanalysingthestructureof
theworldaroundus, asinwhenI lookatthenatureoftheneweconomyorthenature
ofthedigitalI againusephilosophicaltechniquesinformedbyvarioussources.
Quiterecentlyithascometomyattentionthataresearcher, DianaHarrelson, inthe
UnitedStatesiswritingathesisonthecommunitysurroundingtheFedoradistribution
ofLinux. I havecorrespondedprivatelywithher. Shehasclassifiedherworkasdigital
ethnography[8]. ThisseemslikeasuitableoverallmonikerforwhatI amtryingtodo
withmythesis, indeeditseemslikeasuitablemonikerformanyoftheinvestigation
indigitalcultureandthedigitalhumanities. Itisethnography(athickdescriptionof
humansocialinteractions, usingGeertz’sterminology)withadigitaltwist.
Inthinkingaboutmethodologicaldecision-makingI havedrawnonheavilyfrom
threesources, anonlineresearchmethodresourceofJyväskyläuniversity[9], the ParadiamDialog editedbyEgonGuba[Guba, 1990]andthe SageHandbookofQualitative
Research editedbyNormanK.DenzinandYvonnaS.Lincoln
[DenzinandLincoln, 2005]. NowthatI haveposedmyquestionnairesandgarnered
theresponsesI havetakenbothananalyticandsyntheticapproach(analytic–isthere
anythingmoretobelearnedfromtheindividualresponsesthanmeetstheeyeonthe
11
surfacelevel?; synthetic–whatkindofgeneralconclusionscanbedrawnwhenallthe
responsesarelookedattogether?).
Astothemethodologicalissues(bywhichI meanethicalones)I amlikelytoface
nowthatI amawareoftheterrain. EthicallyifI useinformation“publicly”availableon
theinternetI willdomyutmosttoacknowledgetheoriginalsource, contactthesource
wherepossible, andtorespecttheintentionsofwhoeverpostedtheinformationonline–onedoeswhentakinginformationfromaprintedwork. Non-ethicalissueswill
involvetheaccuracyoftheinformationI receivefromthepersonsI interview, thecomprehensivenessofthefeature-setcomparisonI compile, andthefidelityofthehistorical
accountI provide.
12
3
Theimpactofmathematicshavinggonedigital
3.1
A bird’s-eyeviewofmathematicalsoftware
Mathematical software is software used to analyse, model, visualise or calculate numeric, statistical, symbolicorgeometricdata. Thiswouldbeanuncontroversialdefinitionofmathematicalsoftware.
Thisisapersonalobservationmadefromanassessmentofindicesofmathematical
softwaresothelistbearsrepeating–numeric, statistical, symbolicorgeometric.
Letmequicklypointoutthatthereisabsolutelynoconsensusonanyoftheterms
involved. Termsasseeminglyobviousandtransparentas number or numeric atfirst
glanceareupondeeperinspectionfraughtwithremarkabletensions. Also symbol or
symbolic areamorphoustermssurelyapplicablewellbeyondthedomainofmathematics. Theterms geometry or geometric, statistics or statistical areperhapstheleastcontestedofthetermsunderscrutiny. (Whythisissocanbeshowntobethecaseorexpandeduponinanappendixperhaps, thisistherealmofthephilosophyofmathematics
andfarbeyondthescopeofthisthesis.)
Beyondthis, whatarewetosayofmathematicalsoftwarethathasasitsprimary
functionsomethingotherthanthemanipulationofmathematicalentitiesorobjects?
Whataboutwordprocessing, documentprocessingortypesettingsoftwarewhoseprimaryfunctionisthecreationofnon-mathematicaldocumentsbutotherwiseprovides
exceptionalhandlingoftheinputtingofmathematicalsymbols? Word byMicrosoft
Corporation[10], InDesign byAdobeCorporation[11], and LATEX[6]areallexamplesof
these. Thenconsiderpiecesofsoftwarethatallowustoexplorefractals(using Benojt[12]
forexample)orchaoticmapssuchastheLorenzattractor(using 3DAttractors[13]for
example). Inthesecasestheoutputispictorialorevenartisticinnature. Theseare
partlymyconcern, butmostapplicabletomearethosepiecesofsoftwarethathaveas
theirprimaryfunctionthemanipulationofmathematicalentities
Tobacktrackorrewindamoment. Fromanotherperspective(followingWiedijk
amongothers, seebelow)mathematicalsoftwareisgenerallysubdividedintotwoparts:
computeralgebrasystems(CAS,sometimescomputationalalgebrasystems)andautomatictheoremprovers(ATP).Youmaythinkofthefirstsortasglorifiedcalculators,
plottersormodellers. Youmaythinkofthesecondlotasmoresophisticatedderivers
orsolvers. Thebulkofthewealthgeneratedforpurveyorsofmathematicalsoftwareis
derivedfrompackagesbelongingtothefirstgroup, thatis, CAS.Thesecondgroup
existmoreintherealmofacademicresearchratherthanaspartoftheproductportfolioofasoftwarevendor. OfCAS,someofthesepiecesofsoftwarecostthousandsof
dollarsandarethefruitofinnumerableperson-hoursofwork. ATP isamuchmorerecentadvancementinthefieldofmathematicaltools. ThisisasopposedtoCAS which
cantracetheirrootsbacktomechanicalmathematicalaidssuchasthehumbleelectronichandcalculator, thesliderule, theBabbagedifferenceengine, theabacus, even
thepenandpaperafterafashion. ATP wasjustnotpossiblebeforetheadventofthe
digitalcomputerandindeedsuchareitsgoalsthatthesuccessofATP isintimately
intertwinedwiththesuccessoftheprojecttocreateartificialintelligence. I willspeak
aboutthisareaofmathematicalsoftwarenow.
Thefirstrealheadlinesuccessinthisarea(computer-aidedproofs)wasintheprov13
ingofthefourcolourtheorem[14]. A shortpaperbyAndreeaS.CaludefromthedepartmentofmathematicstheuniversityofAuckland, NewZealanddetailsthecontroversy
thatthisfeataroused[Calude, 2000]
Halmosexplainsthataproofdonewiththeuseofthecomputerhasthesameamount
ofcredibilityasonedonebya“reputablefortuneTeller”, asthesemachinesaresimilarto
“oracles”sincetheyhavecertainphysicalpropertiesthatwehaveyettounderstand. Similarly, Deligne, fromtheInstituteforAdvancedStudy(a1978FieldsMedalist)shares
thesamepointofview: “I don’tbelieveinaproofdoneonacomputer. Inaway, I am
veryegocentric. I believeinaproofifI understandit, ifit’sclear. A computerwillalso
makemistakes, buttheyaremuchmoredifficulttofind”.{pg. 5}
Whatisundeniableisthatanaudittrailwasnecessarytoprovethatthealgorithmthat
themathematicianshadusedhadperformedasstated. Also, thealgorithmitselfwas
anobjectofintensestudyandintegralpartoftheproof. A sortofman-machinesymbolicsymbiosis. I cannotunderstatetheprofoundconsequencesofthisformathematics. Whentakentoitslimitswecouldseethatwecouldaskamachine, “IstheRiemann
hypothesiscorrect?”, anditmayreply“yes”or“no”andhowwouldweverifyintotality
itsreasoningforifitweresimpleortrivialwe(humans)couldhaveperformedtheproof
ourselvesinthefirstplaceandnotleftittothemachine–ifontheotherhandthemechanicalreasoningisnon-trivialthentheverificationwillbenon-trivialalso. Inessence,
whatwouldhavetobedoneistoprovethetheoremproverandascanbereadilysurmisedthisisan actaadnauseam. WhatwehavehereistheHaltingProblem, butunder
anotherguise. Itshouldnotbeasurprisethatwefinditlurkinghere.
Perhapsawordaboutthefourcolourtheoremisinorderheretogivethereadera
senseoftheterrain. ItwasfirstaskedbyFrancisGuthriein1852whatistheminimum
numberofcoloursthatareneededtocolouramap(reallyatwodimensionalsurface)
dividedintoarbitraryregionssuchthatnotwoadjacentregionsshareacolour. What
isniceaboutthisquestionisthatitissimpletostate, easytovisualise, andfiendishly
difficulttoarriveatadefinitivesolution. Overtheyearsamaximumupperbound(of5)
wassetbyHeawoodin1890butneveranabsoluteminimum. Eventuallyamethodwas
devisedin1976byKennethAppelandWolfgangHakenthatinvolvedgeneratingallthe
possiblepermutations(asetof1,936(sub)mapsintotal)oftwodimensionalregions, methodicallypaintingandrepaintingthemandallthewhilecheckingfortheleastnumber
ofcolours. Itwasrealisedthattheprocesswouldbetootedioustobedonebyhand,
thealgorithmwastranslatedintoacomputerprogramandtheresultof4wasarrived
at.
Onecanseehowthesolvingofthefourcolourtheoreminvolvedcraftingcustom
codededicatedtothatoneproblem. ATP generalisesthisbyallowingthemathematiciantospecifyaxiomsinamathematicalreality, thesoftwaremaythenbeaskedifa
certainstateofaffairscanbereachedfromtheknowledgeithasbeenfedandintheprocessitmayeitherproveordisprovetheorems. Howtheyperformthisfeatisbeyondthe
scopeofthisthesis.
GettingbacktoCAS.ThoughI calledCAS software“glorifiedcalculators, plotters
ormodellers”thisisamulti-billiondollarindustry. Asyoucanimaginethesesoftware
14
packageshaveafargreaterrangeofapplicabilityandutilitythanpackageswhichperformsinglepurposetaskssuchasstatisticalfunctionsorgeometricfunctionsorwhat
haveyou. Besides, themoregeneralpurpose(andatthesametimecommerciallysuccessful)packagescontainstatisticalorgeometricorotherfeatures–thisiswhatmakes
themgeneralinthefirstplace. ThereareessentiallyfourhighprofilegeneralCAS packages: MATLAB[15]byMathWorks, Inc., Magma[16]bytheComputationalAlgebra
GroupattheUniversityofSydney, Maple[17]byMaplesoftandMathematica[18]by
WolframResearch. ThereisnocomparativelysuccessfulFOSS equivalenttothese
packages. ThenearesttomymindisSage[Steinet al., 2011]whichiswhyI havechosentodirectaseriesofresearchquestionsatthedevelopersofSage.
Keepinmindthatthereareliterallyhundredsofpiecesofmathematicalsoftware[19]
asthiscomprehensiveonlinetaxonomybyFreekWiedijkshows. IndeedWiedijk’scriteriaforcategorisationrequiresthattheitemunderscrutinyhavesomethingtodowith
mathematics, havesomethingtodowithcomputers; furthermore, theitemsmustbe
active, publicandsignificant. MycriteriacoincidewiththelastthreebutaswasmentionedabovemyconcerniswithCAS ratherthantextualauthoringsystemsorother
systemsthatdonothavethemanipulationofmathematicalentitiestoproducemathematicalresultsastheirprimaryfunction. Wiedijkimposesastructureofninecategories
on“mathematicsinthecomputer”: twoarenon-softwaresowemaysafelydiscardthose,
oneisinconnectionwithauthoringandtherestdivideintoCAS andATP.A useful
distinctionthatWiedijkmakesisoneofdifferentiatingbetweenproofcheckersandtheoremproverswiththeformeractingasanaidtothereasoningofahumanandthelatter
workingoutastrategytosolveaspecifiedtheoreminitsownright. Wiedijkdoesnot
distinguishbetweenthevarioustypesofCAS whichinawaywouldbelikedelineating
thepiecesofsoftwarealonglinesofmathematicalfunctionsuchasgeometryorstatistics
andsoon.
3.2
Historicaldevelopmentandstateofplay
Thehistoryofmathematicalsoftwareisinterwovenwiththedevelopmentofcomputersandcomputersoftware. Ashasbeenstatedanddocumentedinnumerousplaces
(seeforexamplethefirstchapterofGere’sDigitalCulture[Gere, 2002])computersare
anoutgrowthofthecapitalistsystem, specificallythelatecapitalistphase, andinparticularthemilitaryindustrialcomplex. Thisnarrativeisubiquitousanditisdifficult
todisavow. Themilitaryhasalwayshadrecoursetoavailofthetalentsofmathematicians, notablyinballistics, owingtothefactthatprecisionisavirtueinwar; deception
andsecrecyusemathematicsastheircloakinthemurkytrade-craftofespionage.
That is not to say that mathematicians have always been the willing tools of the
generalsbutpatriotismandmonetarygainarecharmingseductresses. Itiswellknown
amongmathematiciansthatGodfreyHaroldHardy, knowssimplyasG.H.Hardy, a
committedpacifist, saidin A Mathematician’sApology[Hardy, 1940], “Noonehasyet
discoveredanywarlikepurposetobeservedbythetheoryofnumbersorrelativity, and
itseemsunlikelythatanyonewilldosoformanyyears.”{pg. 44}Whathemeantbythis
isthathewashappytopursueareasofmathematics, puremathematics, thathadlittle
applicationtotherealworld. Itisinthistextaswellthatweseethetropeofbeautyand
creativitywhichisoftenseenindescribingtheartofsoftwareengineering.
15
Theoriginalcomputerswerespecialpurposemechanicaldevicesforspeedingup
computation. Theywerenevercalledcomputers. Theywereoneoffdeviceslikethe
PascalPascaline, theLeibnizWheel, theJacquardloomandtheBabbageDifference
EngineandAnalyticalMachine. Thefirstactualcomputerswerethefemaleoperators
thatattendedtothecalculatingmachinesoftheearly20th century. Whetheritwascalculatingballistictrajectoriesortallyingupacensusthesemachineswerealwaysspecial
purposedevicesandanymathematicalsoftwaresuchasexistedwasboundupintheir
operation. Softwareimpliesadistinctentityfromhardwareorfromtheether-wareof
abstractalgorithms. Itwasn’tuntilthenotionofstoredprogramswiththeVonNeumannarchitectureofcomputingdevicescouldweinanywaybegintotalkaboutsoftwareasathinginitself. Therewasnorecognisablesoftwareindustryuntilcomputing
hardwarebecamefullycommoditised. Assuch, therewasnosuchthingasmathematicalsoftwareperse, atleastnotindependentsoftwarepackageswhethercommercially
availableorotherwise.
Thehistoricaldevelopmentofmathematicalsoftwarefollowsthecourseofsoftware
ingeneral. Mainframetomini-frametomicrocomputer. Specialpurposetogeneral
purposetomassmarkettoacertainextent. ThefirstCAS systemscanbetracedbackto
the1960s. Thehistoryofmathematicsisawell-troddendisciplinewithasizeableliterature.1 Buttheconjoiningofthetwo, ahistoryandoverviewofmathematicalsoftware,
beingarelativelyrecentphenomenon, isapathlesstroddenintermsoftheavailable
literature. TherearebooksrelatedtothisaspectorthataspectofmathematicalsoftwarebutnonethatI havefoundthatwouldappeartotackletheintersectionofthese
topics. ThreevolumesthatI havediscoveredafterapainstakingandexhaustivesearch
aretheproceedingsfromthe2002, 2006and2010internationalcongressesonmathematicalsoftware. Eachvolumeissplitacrossmathematicaltopics. Asyoucanseefrom
thedatesI havejustgiventhecomprehensivefieldofstudyisveryrecent(atthetimeof
writing).
Inanyeventitseemswecantracethistypeofmathematicalsoftwarebacktothe
1960s. REDUCE seemstolayclaim[20]tobeingoneofthefirstearlyattemptstocreateageneralcomputeralgebrasystem. Orrather, anattempttocreateasystemthat
allowedtheautomatedprocessingofFeynmandiagramsmetamorphosedintosomethingthatistakennowadaystobeaCAS.
Andnowletuslookathowcomputershaveallowedmathematiciansandartiststo
explorepreviouslyinaccessiblemathematicalvistas. I refertothevisualdisplayofmathematicalorquantitativedata. AsEdwardR.Tuftehaspointedout[Tufte, 2001]inthe
IntroductionandchapteronAestheticsinhisseminalbookVisualDisplayofQuantitativeInformationthefieldisquiteyoung, perhaps200to250yearsold. WilliamPlayfair, aScottishpoliticaleconomistandengineer, developedorimprovedupongraphicalmethodsofstatistics. Upuntilthelatterhalfofthe20th centurytherenderingof
thesetypesofgraphicswasdonemanuallybutwiththeadventofthecomputeranew
fieldcalleddigitalimageprocessingwasborn. Whenappliedtomathematicsitselfthis
allowsmathematicianstovisuallyapprehendtheinformationthatliesbehindtheiralgorithmsandequations. Whenappliedtoartitallowsartistsaccesstomathematical
1 SimilarlyasizeableportionoftheAmazon’sforestshavebeenfelledtosoakuptheinkspilledinthename
oftheartofsoftwareengineering.
16
landscapeswhichattimessharesimilaritiesbutatothertimesdivergewildlyfromthe
imaginingsofthepre-digitalpast.
3.3
Anexcursionintoafractalworld
ThesearethewordsoftheAmericanmeteorologistEdwardN.Lorenz(1917-2008),
whowhileatMIT cameacrossbychancewhatisnowcalledthebutterflyeffect,
Well, thisallstartedbackaround1956whensome[…]methodsof[weather]forecastinghadbeenproposedasbeingthebestmethodsavailable, andI didn’tthinkthey
were. I decidedtocookupasmallsystemofequationswhichwouldsimulatetheatmosphere, solvethembycomputerswhichwerethenbecomingavailable. […]I finally
foundasystemoftwelveequationsthatwoulddothisandfoundthattheproposed
methoddidn’tworktoowellwhenappliedtoit, […]I hadasmallcomputerinmyofficethen, soI typedinsomeoftheintermediateconditionswhichthecomputerhad
printedoutasnewinitialconditionstostartanothercomputationandwentoutfora
while. whenI camebackI foundthatthesolutionwasnotthesameastheoneI had
before; thecomputerwasbehavingdifferently. I suspectedcomputertroubleatfirst,
butI soonfoundthatthereasonwasthatthenumbersthatI hadtypedinwerenotthe
sameastheoriginalones, these[formerones]hadbeenroundedoffnumbersandthe
smalldifferencebetweensomethingretainedtosixdecimalplacesandroundedoffto
three hadamplifiedinthecourseoftwomonthsofsimulatedweatheruntilthedifferencewasasbigasthesignalitself, andtomethisimpliedthatiftherealatmosphere
behavedasinthismethod, thenwesimplycouldn’tmakeforecaststwomonthsahead,
thesesmallerrorsinobservationwouldamplifyuntiltheybecamelarge.[21]
Theraisond’êtrefortheexistenceofthedisciplineofdigitalculture, orforthatmatterthedigitalartsorhumanitiesisthatacademiahascometorecognisethathumanity
isatakindofinflectionpointinitsdevelopment. Atanypointinhistorythisresearcher
wouldhavebeenbringingthereadersattentiontothisfactthroughthemediumofthe
printedword. Thehumanitieshaveembracedwordprocessinglikeallotherinstitutional and individual actors. This embrace is an embrace with no end, though the
printedwordhasbeentherecordofman’sfolliesandtriumphsforcenturiesnowthe
truththatthebookbeganitsdeclinewiththebirthofdesktoppublishingisinconvertible. Weadmiretheimmediacy, thefluidity, theeaseofeditinginthedigitalrealmindeedtheboundandprintedvolumeisonlyeverthefinallinkinthechain, boundup
withtheeconomictransactionofconsumerandproducer. Andnowwithelectronicreaders, e-readers, ontheinexorableincreasewhosekillerappsareconvenienceand
portabilityeventhatlinkwillprizedapart.
Aspractitionersofelectronicliteratureandelectronicpoetryareawarethetextis
(or rather I should say that in the right hands it has the potential to be) now a textual/computationalhybrid. Theworksofthisexperimentalavant-gardesidestepsthe
regulardistributionchannelsashasbeenthecasewithallexperimentalproseandpoetry
downthroughtheyears. Limitedsetofpractitioners, limitedaudience. Thereis, however, anothergroupofpeoplewhocreatecomputational/textualhybrids-theusersofa
17
certainclassofmathematicalsoftwaretools. Someofthesearescientistsandengineers,
someareartists. Allharnessthepowerofdigitalcomputerstobringthemathematicsin
theirdocumentstolife: equationscanbedrawnincartesianorhyperbolicgeometries,
statisticscanbeplotted, thearcaneandcomplextypographyofmathematicalstructures
canbedonebymachineratherthantediouslybyhand. Themetaphoristhenotebook.
A notebookiscomprisedoftextandcomputation. Ofcoursethereisamarkeddifferencefromelectronicpoetryandelectronicliteratureinthatthetextisattheserviceof
themathematicswhereasine-poetryande-literaturethecomputationalnatureofthe
workisbroughttobearonthetextinordertoenliventhetext.
Mostwordprocessingordesktoppublishingortypesettingtoolshavebuiltinscriptinglanguageswhicharedesignedtoautomatetediouswordprocessingandtypesetting
tasks. Thesearenormallybundledintosmallmodularunitscalledmacros. Theyarethe
stuffofnightmares. Thereisatraditionamongprogrammerstomakethefunctionalityofthecomplexpiecesofsoftwaretheycreatescriptable. Thisallowsthetool-user
tobuildthefunctionalitythattheprogrammerdidnotseefittoprovidebecauseitwas
deemedthatonlyasmallportionoftheuser-basewouldbenefitfromsaidfunctionality.
I canthinkofveryfewcomplexpiecesofsoftwarethatdonothaveapluginsystem, a
macrosystem, abuilt-inscriptinglanguageorwhatever.
Thecomplexsystem, TEX,thatI amusingtowritethisthesishasascriptablecore.
Itisatypesettingsystemthatcancreatebeautifuldocumentsandunderstandsmathematicalnotationverywell. Thismeansthatdocumentswithformulaecanberendered
withease. Pushedfurtheritcanbeusedtoturnmathematicsandalgorithmsintopictures.
LetmeshowyouwhatI meanbyabriefexcursionintotheworldoffractals. Inthe
processofshowingyouI aiminsomewayprovideconcreteexamplesofwhatispossible
whenthecodex[Aarseth, 1997]{pg. 8}(asAarsethcallsthetraditionaltext)meetsmathematicalsoftware. Itisanexampleofhowacademiccultureofresearchandexposition
mustchangeinthefaceofthedigital.
Itisbesttogiveabriefdescriptionofwhatfractalsare. Theyaresystemsthatexhibit
self-similarity, scale-invariance, non-integerdimensionality. BenoitMandelbrot, born
inPolandofJewishdescent, coinedthewordfractalinhisinfluentialworkTheFractal
GeometryofNature. Itisoftenthoughtthat fractal isshortfor fractionaldimension,
thenon-integerdimensionalityI mentionedbeforebutthisisnotthecase.
I coined fractal fromtheLatinadjective fractus. ThecorrespondingLatinverb frangere means“tobreak:” tocreateirregularfragments. Itisthereforesensible–andhow
appropriateforourneeds! –that, inadditionto“fragmented”(asin fraction or refraction), fractus shouldalsomean“irregular,” bothmeaningsbeingpreservedin fragment.
[…](Since algebra derivesfromtheArabic jabara =tobindtogether, fractal and algebra areetymologicalopposites!){pg. 4}
Whatdoesitmeanforasystemorfiguretonon-integerdimensionality? Themathematicalnotionofdimensionisnotassimpleasoureverydaynotionwhichmeans extended
inspace. Itmeansthatunliketheeverydaynotionsoflinesof1dimension, planesof2,
volumesof3, fractalsmayhavein-betweendimensionality. Thereasonthatthiswent
18
unnoticedforsolongisbecauseallfractalshaveapotentiallyinfinitenature–theonly
thereasonwhypicturesoffractalsarepossibleisbecauseacut-offisusedtoterminate
theiterativeprocessofcomposingthefigure.
Whenspeakingoffractalgeometrywearespeakingofageometry, ametricormeasureofageographythatbearsnorelationtotheEuclideankind. Euclideangeometry
istheintuitivegeometryofthepoint, thestraightline, theflatplane. Thisgeometryis
sointuitivethatitpresumedtobetheonlygeometryandofcourseitmatchedthedata
fromoursensesperfectly: 3spatialdimensions, 1temporaldimension. Inthislimited
universefractalgeometries, hyperbolicgeometriesandelevendimensionalsuperstring
geometriesareunthinkable.
AccordingtoMandelbrot, “A fractalisbydefinitionasetforwhichtheHausdorff
dimensionstrictlyexceedsthetopologicaldimension.”
Thekeyideahereisthatfornormalobjectsareintuitivegraspingoftheirdimension
wouldbethedimensionthattheobject’sboundingfigurewouldhave. Insuchcasesthe
Hausdorffdimensionandthetopologicaldimensioncoincideandarethefamiliarsmall
integerunits. TheHausdorffdimensionforirregularobjectsistypicallynon-integer.
Forinstance, theSierpi�skitrianglehasafractaldimensionof log3 / log2 whichisapproximatesto1.5849625indecimalnotation.
Here is a quotation from ”A Fractal Life” by Valerie Jamieson in New Scientist
(November2004).
The Mandelbrot set is the modern development of a theory developed independentlyin1918byGastonJulia[1893-1978]andPierreFatou[1878-1929]. Juliawrotean
enormousbook–severalhundredpageslong–andwasveryhostiletohisrivalFatou.
Thatkilledthesubjectfor60yearsbecausenobodyhadacluehowtogobeyondthem.
Myuncledidn’tknoweither, buthesaiditwasthemostbeautifulproblemimaginable
andthatitwasashametoneglectit. HeinsistedthatitwasimportanttolearnJulia’s
workandhepushedmehardtounderstandhowequationsbehavewhenyouiterate
themratherthansolvethem. Atfirst, I couldn’tfindanythingtosay. Butlater, I decidedacomputercouldtakeoverwhereJuliahadstopped60yearspreviously.
Somuchmoreofouruniversebecomescomprehensiblewhenwerealisethatphenomenathatwetooktobeunrelatedturnouttobecapableofbeingmodelledinsimilar
ways. Paradoxicallyatheoryaboutchaosbringsatypeoforderfromchaos. Perhaps
one shouldn’t draw too much from an off-hand remark by Benoît Mandelbrot but I
thinkitisnotablethatdigitaltechnologywasinstrumentalinenablingthistransition
fromthegeometriesofintuitiontogeometrieswhichdefyintuition.
OnetypeoffractalistheL-System. ThisisshortforLindenmayersystemsafter
theHungarianbotanistbiologistAristidLindenmayer(1925-1989)introducedanddevelopedtheconceptin1968whileattheUniversityofUtrecht. Hewonderedifthere
wasasimplemathematicalwayofdescribingthegrowthofplantsandalgae. Hefound
thatsomeofthegrowthcouldbedescribedusingasimplerewritingsystem, whatwe
wouldknowtermaformalgrammar. Itwaslaterfoundthatmanydifferentmathematicalentitiescouldbedescribedusingthesamerewritingsystem. I amabletoshow
demonstratethemherebecausethelanguageTEX supportstheirdescription.
19
Rulesarelabelledwithcapitalletters. A ruleissuchthataletteristransformed
intosomeotherstringwhereastringisasequenceofcharactersinaveryrestricted
alphabetmadeupofthedesiredlettersandplusesandminuses. Therulesmustbe
mutuallyrecursivethoughinorderthatonemayiterateasmanytimesasonewishes. In
theendoneinterpretsthelettersaslines(drawforward)andtheplusesandminusesas
indicatingtheangles(turnacertaindirection)betweenthelinesdrawn. Onestartsoff
thewholeprocesswithanaxiom, aninitialstartingvalue, whichisoneofthelettersin
thealphabet.
3.3.1
Kochcurves(curves, islandsandsnowflakes)
Thefirstfractal, thefirstL-SystemthatI shallpresent, isknownastheKochsnowflake
orisland. Helge von Koch (1870–1924) wasaSwedish mathematician who firstdescribedthecurvethatnowbearshisnameinarticlesin1904and1906.[22]Itisbuilt
bystartingwithanequilateraltriangle. Oneremovestheinnerthirdofeachside, then
onebuildsanotherequilateraltriangleattheplacewherethesidewastakenaway, and
soonandsoon. Bynecessitythismeansthatnumberoftrianglesscaleupasthesize
ofthetrianglesscalesdown. Fittingthreesuitablyrotatedduplicatestogethergivesus
theKochsnowflake. TheKochsnowflakecanbesimplyencodedasaLindenmayer
systemwithinitialstring ”F + +F + +F ” (whichgivesusanequilateraltriangle–as
opposedtojust F whichwouldonlygiveusaline). Thecurvehasthestringrewriting
rule ”F ” → ”F − F + +F − F ”, andangle 60º. Thezeroththroughthirditerationsof
theconstructionareshownbelow.
.
.
.
.
.
.
.
.
Figure 1: Kochsnowflakeorisland: iterationsonetothree
ThereadermayfinddescriptionsoftheKochcurvefrompage89to93of Chaos
20
andFractals (1992). Itleadsintootherspace-fillingcurvesbytheGiuseppePeano(18581932)andDavidHilbert(1862–1943). Theauthorhopesthatthishasbeenillustrative.
3.3.2
Sierpi�skitriangle
TheSierpinskitriangle(andifyouwantwiththeorthographySierpi�ski), isafractal
namedafterthePolishmathematicianWacławSierpi�ski(1882-1969)whodescribed
itin1915. ItisanattractivefixedsetanditisalsocalledtheSierpinskigasketorthe
SierpinskiSieve. However, similarpatternsappearalreadyinthe13th -centuryCosmati
mosaicsinthecathedralofAnagni, Italyandotherplaces, suchasinthenaveofthe
romanBasilicaofSantaMariainCosmedin. EscherproducedstudiesofSierpinski
gaskettypepatternsfromthetwelfthcenturypulpitoftheRavellocathedral, designed
byNicola di BartolomeoofFoggia. Originallyconstructedasacurve, thisisoneof
thebasicexamplesofself-similarsets, anotherexampleofamathematicallygenerated
patternthatcanbereproducibleatanymagnificationorreduction.
UnliketheKochsnowflake, whereoneruleisusedtoproducethedesiredresult,
theSierpinskigasketisproducedusingapairofrecursivelyreferringrules ”F ” → ”G −
F − G” anditsmirror ”G” → ”F + G + F ”. Theaxiomthatstartsitalloffmayeither
be F or G andtheangleisagain 60º whichmakessensebecausewearetalkingabout
triangles.
.
.
.
.
.
.
Figure 2: Sierpi�skitriangle: iterationsfivetoseven
TheSierpinskicarpetisafractalwithveryspecialtopologicalpropertieswhichwe
shallnotdwellonhere.
21
3.3.3
Fractalplant
Here, F meansasusual drawforward, − means turnleft 25º, and + means turnright
25º. X heredoesnotcorrespondtoanyparticulardrawingactionbutisinsteadused
tocontroltheprogressivechangesofthecurve. Theoperationhasastack(whereyou
cansaveandrestorestatebypushingandpoppingitemsontoandoffthestack. [ is
equivalenttorememberingthecurrentvaluesfortheangleandposition, whicharethen
putbackwhenthecorresponding ] isencountered. Againtworulesareusedtoproduce
thefractalplant. Theyare ”X ” → ”F − [[X] + X] + F [+F X] − X ” andthemuch
muchsimpler ”F ” → ”F F ”.
.
.
.
.
.
.
Figure 3: Fractalplant: iterationsthreetofive
I cannotfindwhooriginatedthisfractal, itcouldwellhavebeenLindenmayerhimselfasitdealswithabotanicalstructure.
3.3.4
Hilbertcurve
A Hilbertcurve(otherwiseknownasaHilbertspace-fillingcurvebecauseitsspatial
limitistheplaneonwhichitresides)isacontinuousfractalspace-fillingcurve. Itwas
firstdescribedbytheGermanmathematicianDavidHilbertin1891.[23]Itwasintended
22
asavariantofthecurves, alsospace-filling, discoveredbyarithmeticpioneerGiuseppe
Peanoin1890.[24]
Owing to the fact that it is space-filling, its Hausdorff dimension, which I mentioned earlier but did not strictly define, is 2 (precisely, its image is the unit square,
whosedimensionisanintegerwhosevalueis 2 asweknowinanydefinitionofdimension; itsgraphisacompactsethomeomorphictotheclosedunitinterval, withHausdorffdimension 2).
Hn isthe nth approximationtothelimitingcurve. TheEuclideanlengthof Hn is
n
2 − 21n , i.e., itgrowsexponentiallywith n, whileatthesametimealwaysbeingbounded
byasquarewithafinitearea.
Again, apairofrulesisusedtodescribetheHilbertcurve. Heretheyare: ”L” →
” + RF − LF L − F R + ” anditsmirror ”R” → ” − LF + RF R + F L − ”. Theaxiom
is L andtheangleis 90º.
.
.
.
.
.
.
Figure 4: Hilbertcurve: iterationstwotofour
Ifyouimagineiteratingthissequencetoinfinityyoucanseehowthe“curve”will
eventuallyfillallthespaceintheplane.
3.4
Theflighttoabstraction: abstractexpressionandmathematicalart
Theearly20th centurysawaflighttoabstractioninart. WhenI speakofarthereI am
primarilyconcerningmyselfmoreorlesswiththebranchesofpaintingandsculpturein
moderntocontemporaryart, thevisual(orplastic)artsingeneral. I donotreferhereto
theatre, nortodance, normusic, norliterature, nordecorativedesignsuchasmosaicor
tilingorstainedglasswork–atleastnotinthecontemporarycontext–inthepastsuch
casesmaybetouchedonasthereaderwillpresentlydiscover.
23
Flightimpliesafleeingfrom. Whatdepictioninartfledfromwasthesemi-accurate
representationofthenaturalorfantasticalworld, amodeofrepresentationthathad
longreignedtotheexclusionofothermodes. BeitaTurnerlandscape, aRembrandt
portrait, aGreco-Roman2 statue, orafantasticalscenefromHieronymousBoschor
GustaveDoréthekeyideasofperspectiveandfigurativerepresentationunderpinned
Westernart. OutsideofEuropean/Americanartthetechniqueofsimulatedperspectiveatinfinitywasusedlesstogirdorunderpinthepictorialscenebutagainthedesire
forafaithfulrepresentationofanaturalorfantasticalscenewasevident. Theonlyslight
deviationfromthisobservationthatcomesimmediatelytomymindaremandalas, ageometricsacredartoftheHinduandBuddhisttraditions. (I havebeentoldthatthere
areaspectsofthisslightdeviationintheartoftheMerkabahtradition, Mayanfolkart
andsymbols, andthearchitecturalplansofGothiccathedrals. I donotbelievethat
theseexamplesdetractmuchfrommyobservation.) However, theseareabstractonly
inthepictorialsenseastheyarerichinformulaicsymbolismoncethemindhasbeeninitiatedintothetradition-thoughclearlytheintentionistovisuallyoverloadthecognitive
processes.
2 I reallydonotmeantoprivilegetheWest. Thedesiretocreateadisinterestedartappearstobeauniversal
humantrait, expressedinsong, dance, monument, storytelling, craft. I usemyexamplesinaniconicfashion,
tocalltothemindofthereaderaparticularexamplethatsignifiesaglobalratherthanparochialparadigm. I
couldhavesaidAssyrian, orEgyptian, Scythian, Mycenaean, Minoan, andsoforth–anyancientpeoples.
24
Figure 5: Kalachakra, sandMandala[25]–TibetanBuddhistsacredgeometry
Therearemanytheoriestoaccountforthisflighttoabstraction. Whenstudying
thephilosophyofartinGalwayasanundergraduatemyprofessorFelixÓ Murchadha
describedtheaestheticshiftusingthepaintingsofKandinsky. Heusedthejargonof
phenomenologyandthevisuallanguageofthepointandthelineandtheplane. What
followsisasynopsisofKandinskyfromthe15th editionoftheEncyclopædiaBritannica
whichshouldhelptosetthescene[Enc, 1982c],
Amongthevanguardartistswhochangedthehistoryofartintheearlyyearsofthe
20th century, theRussianpainterandaesthetictheoristWassilyKandinskyoccupiesa
specialnicheofhisown, forheisoftenreferredtoasthecreatorofthefirstpureabstraction–thefirstpicturethatbrokewiththeWesterntraditionofdepictingrecognisable
objects. Hisabsolutepriorityinthisrespect, likemosthistoricalfirsts, isopentoargument. But, inhispaintingsandhiswritingjustbeforeandjustafterWorldWarI,he
wascertainlyoneofthemostundeviatingandmosteloquentofEuropeanabstractionists.{pg. 376}
25
ThejargonofphenomenologyaslaidoutinanarchitectonicfashionbyEdmundHusserl
(1859–1938)lendsitselfwelltoadescriptionoftheprocess(es)thatKandinskyandhis
contemporariesweregoingthrough. But, I wouldassert, onlyincidentally. TheconceptionofphenomenologywhichHusserlandothers–EdithStein(1891–1942)andMauriceMerleau-Ponty(1908-1961)forinstance–formulatedisastudyofthestructureof
experienceandnecessarilyamountstoaformulationofhowtheobjectsofrealitybecomeobjectsofconsciousness. Thereistalkof εποςηἕ, bracketing, phenomena, intentionality, noumena, andsoon. Theprocessentailsacertaindetachment, anabilityto
suspendbelief, orbracket–theprocessisnecessarilyoneofabstractionandisonlyone
wayamongothersfordescribingthisprocess. Itisonedoorofmanyintotheworldof
metaphysicsfromtheconcreteworld. ThisiswhyI saythatasadescriptionoftheearly
20th centurymoveinartitismerelyincidentalratherthaninstrumental.
Toimagineawarontherepresentationalmodeonemustlookfor casusbelli. I
wouldlooktotechnologicalroots. Itstrikesmethatallsuchtheories(theoriesofthe
flighttoabstractioninart)musttakeintoconsiderationthebirthofthedaguerreotype.
Thisliberatedthehandoftheartistinthesamewayastheprintingpressliberatedthe
handofthescribe. Whereasthescribecopiesasourcetext, thesourceforthecamerais
asnapshotofreality. ManRayhassaidinaninterview[26],
I paintwhatcannotbephotographed, thatwhichcomesfromtheimaginationor
fromdreams, orfromanunconsciousdrive. I photographthethingsthatI donotwish
topaint, thethingswhichalreadyhaveanexistence.
Wecanseethattheflighttoabstractioncamesometimeafterthemid-to-late19th century. Kandinsky, whoiscreditedwithsomeoftheearliest’pure’abstractpieces, was
operatingintheearly20th century. Intheinterveningtimethepotentialofthecamera
forfixingrealityontoathinsheetofpaperwasbeingabsorbedandgrappledwith. The
samecanbeseeninsculpturewhichstartedassumingmoreopenformsandbeganto
beconcernedwithformitself.
26
Figure 6: Kandinsky’s OnWhiteII (1923). CentreGeorgesPompidou, Paris.
Ithasrecentlybeenshown[Hockney, 2006, Steadman, 2001]thatmanyoftheold
masters used cameras (both obscura and lucida), mirrors and lenses to project light
ontocanvasasatechniqueorshortcutindepictingreality. Nowwiththecamerabeing
perfectedtherewaslessandlessaneedforrealisminart, lessaneedforpaintingovera
projectedimage. Competitionbreedsdiversityperhaps. Whyshouldartholdamirror
uptonaturewhenachemicalprocesscoulddothesameandjustasaccurately? Thatit
isarelativelyunknownfactthatsomeofthegreatestpaintersintheWestusedthistrick
isduetothesecrecyoftheguilds. OnecangobacktoPlatoandAristotletofindsome
ofthefirsttheoriesaboutthepurposeofart. A keyinnovationinartwasAncientGreek
theatre. Howitdevelopedisunknownbutonetheoryisthattheperformancesgrew
outofearlierfertilityritualsthatinvolvedanimalsacrifice, notablygoats. Tragedycan
27
betranslatedasgoat-song[Enc, 1982b]. AnothertheoryisthattheGreekplaysbelong
moretoaMysteryCultthananythingelse. Thesecultsorritualswouldhaveinvolved
apriestofsomesort. Eventuallyachoruswasadded. Thepriestrolemorphedslowly
intoaleadingactorrole. Ritualcallandresponseevolvedintosemi-narrative. Itisoften
difficulttorememberthattheatre, painting, sculpturedidnotarrivefully-formedinto
theworld. PlatoandAristotlewerereactingtothisculturalinnovationwhendeciding
aboutthepurposeandfunctionofartinsociety.
A numberkeytermscropup: mimesis, tragedy, comedy, catharsis. Tragedyishigh
seriousthatentailsanemotionalrupture. Comedyisbase. Mimesisisauthenticreflecting. WhatI amcallingfigurativeartcouldalsobecalledmimeticart-artthatimitates.
Thereadermaybewonderingwhythisdetour-likeexcursus. Itisplaintoseethatearly
theorydictatedthatartbe about something. Itwasimbuedwithstructureandsymbolism. PlatoarguedthatartbeingapaleimitationofrealitywhichitselfwasapaleimitationoftheidealworldoftheFormswasthereforeadegeneratepracticewhichcouldstir
uptheirrationalinthepopulacewhereasAristotlearguedthatartwithproperthemes
andcontentcouldbetherapeutic.
Fast-forwardtwomillennia. Whateverthereasontheflighttoabstractioninart
tookaveryshorttimeoncethelogicoftheprocesstookhold, maybe30years. This
isaninnovationincontent, moresothanstyle. WecantracetheincreasingrealisationofthisnewtypeoffigurationinKandinsky’sworkbywayofexample. Indeedhe
documentedhisownexperimentationinmonographsaccompanyinghisart. KandinskyhimselfnotedhowhewastakenabackwhilelookingatClaudeMonet’sHaystacks
painted in the impressionistic style, that he had a moment where he stopped seeing
thehaystacksthemselvesandjustsawthepaintingforitsformalfeaturesofcolourand
shapealone. ButthiscouldonlyhavehappenedifMonet’spaintingwasalreadytravellingdownapathtowardsabstraction[Enc, 1982c],
I hadthefeelingthatherethesubjectofthepicturewasinasensethepaintingitself,
andI wonderedifI couldn’tgomuchfurtheralongthesameroute. AfterthatI looked
atRussianiconswithdifferenteyes; I hadeyes, thatis, forwhatwasabstract…{pg. 377}
Itisincontradistinctiontolookingupataskyfilledwithsparsefluffycloudsorata
rockyoutcropandbeingstrucksuddenlythatitbearstheshapeofananimalorsome
otherlivingbeing. Thiscoupledwithanimismleadstothereificationoflandscapefeatures. Whatwehavehereisacognitiveopticalillusionwherefictionisproducedfrom
formlessness-itisatypeofover-signification.
Kandinsky’sperceptualdissolutionofthehaystacksisasortofreverseprocess, goingfromfictiontoformlessness–anditisatypeofunder-signification. I donotknow
thetermthatisusedinpsychologytodenotethesetwoinverseprocesses. Inthesame
wayAncientGreektheatretookontheformoftheatrefromsomelesstheatricalform
andperhapsundersomekindofexternalinfluencebeiteconomicorspiritualortechnological. Thispracticeofrepresentingritualisedartificebysymbols, orofinvestingformalactionsorelements(shape, colour)withasymbolicmeaningorcharacteriscalled
symbolism. Inthistheorysymbolism–theflighttomeaning–wouldcontrastwithabstractionism–theflighttoabstraction. Itcouldseemtobethataestheticdevelopments
28
inartaretheresultofatugofwarbetweenthesymbolandtheabstract.
Anotherkeycreativemindinthe20th centurywasDutchartistM.C.Escher. Few
artistsbreakoutofthe“whitecube”intothecollectiveimaginationofanera. Dalíisone
suchartist, Escherisanother.
Figure 7: M.C.Escher, CircleLimitI (1958)withgeodesicsinred.
In1958EscherpublishedRegularDivisionofthePlane, andinthisworkhesays:
AtfirstI hadnoideaatallofthepossibilityofsystematicallybuildingupmyfigures. I didnotknow... thiswaspossibleforsomeoneuntrainedinmathematics, and
especiallyasaresultofmyputtingforwardmyownlayman’stheory, whichforcedme
tothinkthroughthepossibilities.
Again, inRegularDivisionofthePlane, Escherwrites:
Inmathematicalquarters, theregulardivisionoftheplanehasbeenconsideredtheoretically. ... [Mathematicians]haveopenedthegateleadingtoanextensivedomain,
buttheyhavenotenteredthisdomainthemselves. Bytheirverynaturetheyaremore
interestedinthewayinwhichthegateisopenedthaninthegardenlyingbehindit.
29
Escher’smeticulousdrawingshaveasignaturefeelalloftheirown. ThoughanindividualisticartistI thinkI haveshownhowEscher’sintricatesketcheslieonacontinuumof
geometricartisticprogression. AlongwiththelikesofMondrian[Tufte, 2001]{pg. 185}
heblendedgraphicalelementsnormallyfoundoutsidetherealmofartwithatrueartisticelements. Heisatransitionaryfiguretoanartisticmovementthathascomeintoits
owninthedigitalage–mathematicalart.
Themachineliberatestheartistwhoexploresgeometry, symmetry, formula. The
artistisliberatedbythepowerofthemachinetorenderthepatternsintoavisualform.
Furthermorethemachinecancrunchthenumberstirelesslyfortheartist. Theartistis
freetoexploremathematicalspaceinawaythatwassimplytootime-consumingheretofore. Ifarchitectureissaidtobefrozenmusic, mathematicalartistheopeningbarofa
sonata–asliceoftheharmonicbeautyofnumbermadevisualratherthanaural.
Thenodtomusicisnotinapt. AsGiovannaDiRosariohaswritteninan, asyet,
unpublishedpaper[27]:
BenjaminFrancisLaposky(1914-2000)wasamathematician, andartistwhohas
beencreditedwithmakingthefirstcomputergraphics. Hisworkincomputerartisa
formofoscillography, theresultsofwhichhehascalled’Oscillons’or’ElectronicAbstractions’. Laposkysaidthat“Oscillographicartmightbeconsideredasakindofvisualmusic, asthebasicwaveformsresemblesoundwaves”. Hewantedtoreproduce
thedesignsorpatternsofnaturalforms, curvesduetophysicalforces, orcurvesbased
onmathematicalprinciples, suchasvariouswaveforms(sine-waves, squarewaves).
Letuslookatsomepuremathematicalartisticpiecesnowtoexhibittheprogression
takingplacenowadays.
30
Figure 8: AnneBurns, ComplexFlowII (2010)12”x12”Digitalprint. Inspiredbythe
vectorfieldof f (z) = z 11 alongthreecirclescenteredattheorigin.
AnneBurnsworksatthedepartmentofmathematicsatLongIslanduniversity,
NewYork. Inherpaperinthe2011Bridgesproceedings[Burns, 2011]shesaysthatthe
waysheachievesimagesthatshelikesisbyportrayingacontinuouscomplex-valued
functionasavectorfieldoveritsdomain. Distinctivefeaturesofthefunctionssuchas
singularitiesandwhatshecallstheirmultiplicitiescanbereadilymadeoutbyplotting
thefieldoveragridwherecoloursaregivenvaluesbasedonfunctionsoflengthfrom
theoriginand/ordirectionfromtheorigin. Bylimitingtheviewtocertainpathsand
byexperimentingwithdifferentmetricandangularfunctionsthecolourscanbevaried.
Byexploitingrotationalsymmetryimagesthattheartistfindsbeautifulcanbefound.
Firstconcentratingonasquaregridwhosecenterwasazeroorpoleofthefunctionunderconsideration, f (z), andplottingthevectorwithtailateachgridpoint, and
lengthanddirectiondeterminedbythevalueof f (z), thepictureswerenottooinspir1
ingunlessanexoticfunctionsuchas f (z) = e z near z = 0 waschosen. I beganexperimentingwithdrawingthevectorfieldsalongpathsenclosingsingularpointsand
31
scalingthelengthandassigningthecolorofeachvectorusingavarietyofformulas.
Evenassimpleafunctionas f (z) = z n , for n anonzerointeger, inspiredtheimages
inFigures1and3. Thesubjectofvectorfieldsandflowsisamajorsubjectforstudy;
howeverinthispaperI willdescribejustafewideasforproducinginterestingandartisticimages. Theseideasshouldbeaccessibletoastudentwithalittleknowledgeof
calculusandcomplexnumbers. UsingActionScript/Flash, animationsoftheimages
are easily produced. In this paper a complex valued function of a complex number,
f (z) = u(x, y) + iv(x, y), isinterpretedasavectorinthecomplexplaneemanating
from z = x + iy andthedomainisrestrictedtoasmallregionthatcontainsthe“interesting”points, suchaszerosorpolesof f .
Burnsfoundinspirationfromtwomathematicalsources: thefirstabookcalled Visual
ComplexAnalysis andthesecondanarticleintheFebruary1996issueofMathematics
Magazinetitled OnUsingFlowstoVisualizeFunctionsofaComplexVariable. She
wastakenabackbythediagramsofwhatshecalls“flows”. Sheusedtheopportunityto
explorethenasanexcuseforlearningActionscriptbyAdobeCorporationwhichhasat
itsdisposalvector-basedgraphicscapabilities.
Figure 9: LynnBodner, Figure9ofT9N12 (2011)TheInd0729patternfromtheWade
collectionontheleftcomparedwiththeauthor’scroppedTashkentScrollspatternon
theright.
NextweshalllookatthegeometricreconstructionsofLynnBodner. Shedescribes
the process of reconstructing nine and twelve star polygons from Islamic geometric
tessellationsfoundonascrollattheInstituteofOrientalStudiesattheAcademyof
32
SciencesinTashkent, thepresentdaycapitalofUzbekistan. Tashkentisacitywhose
namemeans“stonecity”andinwhosemuseumsrestswhatisconsideredtobetheoldestQu’ranonrecord, apparentlydatingfrom655. LynnBodnerisatthemathematicsdepartmentatMonmouthuniversityinNewJersey. InherpaperintheBridges
2011proceedings[Bodner, 2011]shesetsherselfthetaskofreconstructinghowitwas
theoriginalartisans(withoutmensuration)cameabouttheirpatterning, apatterning
BondercallsT9N12. Themethodofcompass-and-straightedgeisused, amethodas
oldasEuclid. SheusesamathematicalsoftwareprogramcalledGeometer’sSketchpadbyDynamicGeometry.
Thepatternasawhole(asyoucanseefromthefigure)consistsofalmostregular
nine-pointed, regulartwelve-pointedandtheleftoverirregularpentagonalstarpolygons. Thescrolls(theso-calledTashkentScrolls)comprisefragmentsofarchitectural
sketches. ThesesketchesareattributedtoaguildofarchitectsoranUzbekmaster
builderplyingtheirtradein16th centuryBukhara. Theindividualtessellationsarecalled
repeatunits, theycanberepeatedbyjoineduptilingonaplane. TheirisalsoascrolllocatedattheTopkapıPalaceMuseumLibraryinIstanbul, theTopkapıScrollcomprises
114IslamicornamentaldecorativesketchesofasimilartypetotheTashkentScrolls,
T9N12doesnotappearintheTopkapıScroll. ItisputforwardbyHarvardprofessorGülruNecipo�luthatthesketches“servedasan aide-memoire forarchitectsand
masterbuilderswhowerealreadyfamiliarthroughexperiencewiththecodedgraphic
languageusedinthem”.
33
Figure 10: MehrdadGarousi, BiscuitLand (2010)20”x20”digitalprint
Wemovenowfromcontinuouscomplexvaluedfunctionsandstarpolygonsbackto
theworldoffractals. MehrdadGarousiusesasoftwarepackagecalledMandelbulb3D[28]
toproduceallhisworks. Thisisapackagethatallowsartiststoexplorefractalsin3D
space. Thereisanexplorationwindowthatallowsforquickmovingaroundandthen
atanytimeasnapshotcanberaytracedforamoredetailedlook. Garousiisnotaprogrammerinthewaythenextartistis, heismoreanartisticcybernaut.
ConcerningthisworkGarousifeltthatthelandscapeheendedupwithwascomposedofamaterialthatremindedhimofbiscuits, hencethetitle. Hesaysthatthemathematicalstructureofthecompositionhasbeenworkedaccordingtotwoconnectediterations. Thereisaniterationthat“slicesandhatchescubesofmaterialverticallyand
horizontally[…]onethatdrillsthecenterofthefrontfaceofeveryslicedcube”. The
resultissomethingliketheabovefigurewiththehollowedoutareasbeingquiteunusualwiththedistinguishingorangecubicshapesleftover. Asistypicalwithchaotic
iterationsverysmallperturbationsintheformulacauseunpredictablecomplexityand
behaviourtocometothefore.
34
Figure 11: NathanSelikoff, AestheticExplorations (2004)A 4×4matrixofhighquality
images, representingasmallportionoftheparameterspaceoftheseparticularattractors.
Finallywereturntothestrangeattractorsofchaostheory. Inanemailcorrespondence with me Nathan Selikoff has communicated that he began “playing” with the
strangeattractoralgorithmin1999. Hisartworkhasbeenexhibitedingalleriesand
othervenuesthroughoutEuropeandtheUnitedStates. Hestudiedfineartandcomputerscience. HeusesacustomprogramwrittenintheprogramminglanguageC++,
theindustrystandard3D apiandlibraryOpenGL andGLUT.
Allowmetoparaphrasehistechnicalnotes. SelikofffirstgenerateshisstrangeattractorartworkwiththecustomprogramwrittenusingC++, OpenGL,andtheOpenGL
utilitytoolkitGLUT.HesaysthatthealgorithmthatheusesforgeneratingtheattractorsisdetailedinCliffordPickover’sChaosinWonderland. Thesizeofthefinalartworkdeterminesthedensityofpixelsthatheneeds, betweenahundredthousandand
afewbillionpixelsbeingplottedbyiteratedfunctionswhichsimulatethestrangeattractorequations. HethenusesPhotoshoptocolourintheattractorsusinggradient
mappingwiththeinitialrendersin16bitgrayscaleimages. Howtheresultingimageof
theattractorappearsdependsonasmallnumberofcoefficientsanditsmutation(that
35
istosay, whichequationsituses).
Hisprogramallowshimtoexplorevariousaspectsofthestrangeattractorheis
workingon–hecanmoveabouttheobjectinsimulatedthreedimensionalspacebyrotating, panningandzoomingtheviewportintothedigitalworlds. Theprogramallows
himtoadjusttheparametersoftheequation. Oncetheprocesshasarrivedatapleasingimagehesaveitsparameterssothathecanthenrenderitanothertimeatahigh
resolutionanditisonlyatthispointthathetransferstheimagesintoPhotoshop. In
Photoshopheisabletotweakthecolour, contrastandfinerdetails.
ThesourcecodeforhiscustomprogramhasnotbeenpublishedbutSelikoffdoes
havecodetutorialsonhiswebsite.
Thisleadsthisinvestigationfelicitouslyontothenextsection: aninvestigationinto
howthedisclosureorlackofdisseminationofintagibleassetsimpingesonvarioushumanendeavoursbeitartisticorengineering.
36
4
Thecultureandideologyofintangiblemedia(data)and
softwaredevelopment(code)
4.1
Theoriginofcopyright
In CommonasAir [Hyde, 2011]LewisHydedefendstheconceptofthe culturalcommons. Howhasourculturalheritage, thestoreofideas, art, andinventionswehave
inheritedfromthepast, cometobeseenas intellectualproperty? Somepeople[29]argue thatthere is nosuch blanket termasintellectualproperty andintellectual propertyrights. Theyargueagainstlumpingallthreecategories, copyrightlaw, patentlaw,
trademarklawintothesamebasketastheyarequitedifferentbeasts. Theyalsoargue
thattheworksapplicabletotheselawsverymuchdonotbehaveliketraditionalpropertyanyway. Havewe, LewisHydeasks, takentheconceptof ownership toofar?
Thereisafascinatingtalk[30]givenattheBerkmanCenterforInternet&Society
atHarvarduniversityinwhichtheauthorofCommonAsAirdiscussesthatverysame
bookandthentakesquestionsfromthefloor. ThisisHyde’sthirdbookafter TheGift
and TricksterMakesThisWorld (neitherreferencedhere). Allthreeinvestigatethe
relationshipofartistsandtheirartwiththesocietytheyinhabitbutwhereasthefirst
twofocusonthepossibilityofartyoumightsay, thethird, theoneinquestion, focuses
ontheincreasingimpossibilityofcreativeexpressioninaworldwheretheintangible
hasbecomepropertyandcorporationsexertmoreandmorecontroloverwhatisand
whatisnotpossiblewithourstoreofheld-in-commonscientificandartisticartefacts.
TowardsthebeginningofhistalkHydequotesfromoneoftheclassics, workembeddedinthebedrockofEnglishliterature. PiersPlowman (datingfromthe1360s,
accordingtoBritannica), or William’sVisionofPiersPlowman[31], isthetitleofaMiddleEnglishallegoricalnarrativepoembyWilliamLangland. FromitHyderecallsfor
usthisline, “Humanintelligenceislikewater, air, orfire, sharedonearthincommon”{5
minutesin}. Theconcepthereisthatideascannotbechaineddown. Thisisatime
pre-moveabletypeandpre-Gutenburg. Themostfluidchannelforthetransmissionof
ideaswasnotinprintbutorally. Printhadthebenefitoflongevityandpermanence, but
itwasdifficulttoreproduce, andthusdifficulttotransmitandre-transmitideas.
Whatismeantbythatline, “shared[…]incommon”? Itseemssimpleenough. Neitheryou, norI canlayexclusiveclaimtothefruitsofthehumanmind, whathasbeen
wroughtbyintelligenceandimaginationiscommontoall. Atthattimethiswasaselfevidentuncontestedconcept. Indeed, inordertopreventothersstealingtheirideas
scientistsusedtobeverysecretive. Therewasnopeerreview, therewerenojournals.
Manyofthegreatestscientistsandmathematicianscloselyguardedtheirdiscoveriesin
theirownlifetime. I shallnotciteanyspecificcasesindetailbutI dorecallhavingread
thatbothGaussandNewtonwereverysecretive. Partofthereasonbeingbecausethere
wasatthetimenolegalframeworktoprotectinventorsandauthorssothattheycould
benefittemporarilyfromthefruitoftheirlabor, therewasnowidelyheldconceptofthe
intangibleasproperty; notyet. (Notethattherehadbeenajudgmentinthe6th century
inCelticBrehonlawenunciatedthus, “AstoeveryCowitsCalf, sotoeveryBookits
Copy”whichwasarulingbyDiarmaid, HighKingofIreland, againstColumbafor
theactofplagiarizingaLatinpsalterofFinianofClonard.) I amuncertainastohow
37
pervasivethisrulingwasorwhetheritextendedbeyondtheshoresofIreland.
TransferringtotheothersideoftheIrishSeaweencountertheideaofthecommons. ThenotioncomesfromunusualpropertyarrangementsinEngland(andother
regions)infeudaltimes–say, 9th tothe15th –centurywhereaplotoflandcouldbegrazed
incommonbythelivestockofthepeopleinacommunity. Thecommonsdenotedcertainaccessandusagerights. Generally, thelandwaspartofamanor, andalordowned
thelandofthemanor. Therewerealsocaseswherethelordwoulddemandasliceof
theproducefromthissharedturf. Atanyratetheserfsandpeasantsandplot-holders
wouldsharethesecommonplots, itwouldbeheldincommon, noonecouldlayclaim
toit. Thiswasnotcommunismasthestatedidnotowntheland–thoughthecrown
andthechurchwerethetwobiggestlandownersinthecountrybackthen, todayin
theUK itistheForestryCommissionwhichisthestewardofthelargestpercentageof
land, andthusthecommonpersonviathegovernmentcanlayclaimtothissliceofthe
sceptredisle.
Fromthisnotionofaphysicalcommonshasevolvedthenotionofaculturalcommons: scientificfacts, folktales, oldculturalartefactsthatareheldbythestate, the, and
soforth. ThisiswhyHydesays, “Weallhaveinheritedaculturalcommons, andliveinit
andcontinuetocreate”, and, “Wehaveaccesstoalltheintangiblecreations”, and, “Allof
thisbelongstoallofus”, and, “Allofuscanusethesethingswithoutaskingpermission”.
Intothatworldarrivedpaperpulpingandmilling(exactdatesoforiginunknown),
blockprinting(7th century), moveabletypefirstly(11th century)andtheprintingpress
(15th century). Thiswas, ofcourse, averyslowprocess, takingcenturyuponcenturyof
refinement. Initiallythegoverningclasses(thatisthecrown, royalty, nobility, aristocracyandlandedgentry)andthechurchwereverypleasedwiththeseinventionsasitaffordedthemaneasiermeansfordisseminatingtheirproclamations, decreesandteachingsbuttheyalsorealisedthatviewsandopinionscontrarytotheorthodoxywould
benefitfromthesetools. Thusthegovernmentdevisedaschemewherebyonlycertain
printinghousessanctionedbystateweregivenrenewablelicensetotradeandproduce
certainworks(importingwasgenerallybanned)totheexclusionofotherprintersfora
limitednumberofyears; thiswastheoriginalpatentpermission, arighttoprintselect
worksbythecrowneffectivelyinperpetuity. Eventuallyeachpublishedworkhadtobe
registered. Fromthisstate-sanctionedmonopolygrewamorepowerfulentity, called
theStationer’scompany, aguildofprintinghouses. InEnglandbytheendofthe17th
centuryitspowerhadbecometoogreatandin1695parliament3 didnotrenewitslapsed
collectivelicense. Thingsremainedinlimbosome15yearswhenahistoricpieceoflegislationwasproposed, theCopyrightActof1709whichwasputintoforcein1710. As
thiswasduringthereignofQueenAnne, ithasbecomeknownastheStatuteofAnne.
Thislawgrantedashort-termrightofownershiptotheauthorofthework. Thedurationwas14years, plusaonetimerenewableperiodofanother14, giving28apossible
maximum28yearsintotal. This, surprisingly, wasanovelconcept. Andindeed, this
conceptappliedtothephysicalcontainer, thebook, andverbatimcopiesthereof. Verbatimcopyingwasillegal, thenotionthatitwastheideascontainedwiththeprinted
andboundcontainerwhichweresubjecttothisnovellawisnotthecase.
3 Inthemid-17th centuryparliamenthad(asyouwillrecall)replacedthemonarchyofthelandastheenactor
oflaws, theUnitedKingdomhadbecome, viatheCromwellianrepublic, aconstitutionalmonarchy.
38
Thisnotionofcopyrightspreadthroughouttheglobe. Itwasanattempttosolve
the problem of public goods. It attempted to balance the wishes of the author, the
reader, andthetrader. A shockingconceptI realiseinthisdayandagewheresomeone
canbesuedintobankruptcybecausetheydownloadedahandfulofcopyrightedcommercialpopsongsfromtheinternet. Thewordpunitivespringsreadilytomind. But
enoughabouttheillsofthe21st century, letusreturntothe18th . Thereasonguildshad
sprungupwasbecausetheywereavehiclefortradesecrets, tricksofthetradeliterally.
Again, thecopyrightact, andtheevolvingnotionoflimitedliabilityallowedinventors
andauthorstocapitalisetemporarilyontheirworksandnotloseeverythingthrough
unsoundinvestments. Bothoftheselegalframeworks(copyrightandlimitedliability)
protectcapitalandhaveunderpinnedcapitalism’srise. Becausethetradesmanisopenly
protected, theguildsandtheirsecretshavediedout.
AsHydesaysinhistalk, theideaofpropertyentailscertaintypeofrightofaction.
Itentailstherighttoexclude. Inthepast, hepointsoutinterestingly, workswerenot
copyrightedbydefault, onehadtoregisterone’swork, nowadaysHydenotesthatthe
simplewritingdownofashoppinglistorlaundrylistwouldbydefaultbecopyrighted
toitsowner. Wethinkthatwemust“©AnthonyDurity, 2011”orwhateverbutthatis
notthecaseatallnowadays, alloneneedsisproofofauthorship; copyrightisenabled
bydefaultwhichisinkeepingwithcapitalism’sdrivetocastthenetofprivateproperty
aswideasitpossiblycan. Alsointhepastthecopyrightactonlyappliedtoverbatim
copying. Thus, translationsandabridgementsweredeemedfairgame. Itiswasonly
muchlaterthatcopyrightwasseentotocovertheintangibleideasinaworkandthe
abilitytospawnderivativeworkswasrestricted. A derivativeworkcanbe, asI said, a
translation, anabridgement, ormoreup-to-date, amashup, aremix, apastiche, andso
on.
TheideaofwhatisfairgameornothasbecomeenshrinedunderthebannerofFair
Use. Thelawsdefinewhatapersonoraninstitutioncandowithaworkdespiteitbeing
undercopyright. Educationalcopyingispermitted. Personalverbatimcopyingispermitted. Andsoforth. ThereisanotoriouslawintheUnitedStatescalledtheDigital
MillenniumCopyrightAct(DMCA) whichallowscorporations(oranyonegenerally,
butcorporationsinpractice)tosubvertfairusethroughtechnologicalmeans. Hyde
mentionsthisinpassing. Itappliestomanyartefactsinourdigitalworld. Thelaw
hasbeenexercisedmanytimesandisbeingactivelychallengedbytheAmericanCivil
LibertiesUnion(ACLU) andtheElectronicFrontierFoundation(EFF),whocanbe
viewedasstaunchdefendersoflibertyorcranklibertariansdependingonwhichtraditionalsideofthefenceonesits.
Hydeshowusthatwhilecopyrightisabooninthatitincentivizes/motivatescreativity, italsocanleadto“bullying”and“badbehaviour”. Hegivesustwocourtroomexamples: DieboldversussomestudentsthattriedtopublishevidencethatDiebold’selectronicvotingmachineswereflawed–thistookmanymonthsandsuckedup$150,000in
legalfees; theestateofJamesJoyceversusCarolSchloss–whichtookseveralyearsand
$240,000. InthefirstexamplethestudentswerebroughttocourtusingtheDMCA
becausethevotingmachineshadelectronicanti-circumventionmechanisms, theend
resultisthattheyweresuedundercopyrightlaw, whichisasbizarreanapplicationof
copyrightthatI canthinkof. Thesecondexampleisanexampleoftheabuseofregular
copyrightlaw, thetermof14yearsisnowadistantmemory–itisnow95yearsinthe
39
States.
I havenotrelatedHyde’sinterestingtyingtogetheroftheidealsofafunctioning
democracyandthecommons, I havenot mentionedhisworkingoutof theconcept
ofagonisticpluralism, andI haveonlytouchedonhisretellingofthetwoenclosures
orfencings-in, thefirst-agrarian, thesecond-moreintangibleleadingtoourmodern
conceptof“intellectualproperty”. Butitisenoughtoleadusontotheuseofcopyright
insoftwarelicensing.
Fastforwardfrom1710to1970.
4.2
HistoryandsnapshotofFOSS
It all started with a printer so the story goes. I have culled most of this story from
FreeasinFreedom [Williams, 2009]bySamWilliamsbutthebulkofwhatI shalldescribe here is best described as modern folklore. Richard Stallman was working at
theArtificialIntelligencelabattheMassachusettsInstituteofTechnologyasasoftwareprogrammer. Thoughthesepeopleusedtoprefertodescribethemselvesas’hackers’[appendix/endnote]. Thiswasthelate1960s, early1970s. TheMIT AI labhadreceivedagiftfromthepeopleoverattheXeroxPaloAltoResearchCenter. A printer, a
laserprinterinfact. Itwasmanytimesfasterandagooddealmoreaccurate. Itsuffered
fromaflawthough, whichwasthattheprinterbecameoccasionallyjammed. Nowas
ithappenedthepreviousprinterhadhadthisproblemandStallmanhadrectifiedthe
flawbyhackingatthesoftwaretogetittosendamessagebackoverthenetworkto
anyonewhowaswaitingonajobintheprintqueue. Simplyputthemessagesaid, “The
printerisjammed, pleasefixit.” Andsomeonewould.
Theproblemwasthatinthiscasethisnewprinterdidnotcomewiththesource
code. SoStallmancouldnotperformthesametime-savinghack. WhenStallmantracked
downanengineer, RobertSproullitwas, ofthesourcewhobythattimewasatCarnegie
Mellon(soStallman’sversionofthestorygoes)SproullrefusedtogiveStallmanthe
sourcecode. StallmanclaimsitwasbecausetheSproullassertedthathewasboundby
anon-disclosureagreement(NDA) notto. AnNDA isalegallybindingcontractthat
requiresanemployeenottotalkabouttheworktheyaredoingfortheiremployeruntil
aperiodoftimehaselapsed. Theyarecommonlyusedatstartupswheretheideabeing
developedisnovelandwherefirst-moveradvantageiskey. AnNDA isusedtoprotect
theinnovativeandrevolutionarynatureofapieceofworkfromcompanieswithdeeper
pocketsormoreexperience. Theyarepartandparcelofanentirecommercial, dareI
say, capitalistethos.
InWilliamsownwords, “Likeapeasantwhosecenturies-oldirrigationditchhad
grownsuddenlydry, Stallmanhadfollowedtheditchtoitssourceonlytofindabrandspanking-newhydroelectricdambearingtheXeroxlogo.”
A certaintypeofhackerethic[appendix/endnote]hadbeeninculcatedinStallmanat
theMIT AI lab, thisshareandsharealikeethichadrunupagainstthebrickwallofcommercialcompetition. Xeroxwantedtomonetizethetechnologiesthatitsresearchers
weredeveloping, Xeroxwasn’tacharity, itseemsreasonablethatXeroxwouldnotwant
todistributethesourcecodeforitsnewmarvelalongwiththehardwareeventhough
thiswasthetraditionatthetime. Whatitboilsdowntoishowserviceabletheitem
thatyouhaveboughtis. Ifsomethingiswrong, shouldyoubeabletofixityourselfor
40
shouldyousenditofftoaspecialisedengineer? StallmanwantedtofixtheMIT AI lab
printerhimselfandhadbeenthwarted.
ThiseventactedasacatalystforStallman. Hehadneverbeenovertlypoliticalor
interestedinwhatwashappeninginsocietyinanabstractwayoneimagines. Buthere
waswhatfeltlikeapersonalsnub. HowmuchofthestoryisapocryphalI donotknow
atthisremovebutI haverelayedthefactsasI havethemtohand. Thiswasatrend
inthehardware/softwareindustryatthetime. Youmustrememberthatcommercial
systemsweredeliveredwithschematicsandwereessentiallytransparentdevices. Not
thatitwasunthinkablenottodocumenteveryaspectofeverypieceofhardwareyou
sold, firmwareandsoftwareincludedbutitwasjusthowtheindustryoperated. Ifa
customerpurchasedoneofthesedevicesfromyoutheywantedtoknowhowitworked
andhowtofixitwhenitstoppedworking.
Asthemachinesgrewmorecomplexandastheusersofthesemachinesbecamefurtherandfurtherremovedfromtheengineeringtraditionitbecame1)impracticaltoprint
pagesandpagesofmanuals, 2)beabletorelyonthefactthatyourcustomercoulddecipherthosemanuals. Itcannotbedeniedaswellthattherearesomegenuinecommercial
motivesforslowlycomingtotherealisationthatacompanyshouldwithholdinformationfromitscustomerbecauseitfirstlydisempowersthecustomerandmakesthem
morereliantonthesalescompanyespeciallyifwhatthatcompanysellsisnon-standard
andsecondlyitcutsdownoncosts, lessuser-facingdocumentationislesscostly-ina
forprofitenvironmentwherethereisnocounterbalancetothesecommercialchoicesa
corporationwillonlynaturallytrytomaximiseitsprofits.
Stallman’sadmixtureoftalentsthatmadehimaneffectivecoder, hisnaturalsocial
disposition, hisplaceinacademia, thesnubbing, theactionsofXerox, allcombinedto
spurhimtocreateprogramsandworktoensurethatthesourcecodeforthoseprogramswerefreelyavailable. FromthisgrewGNU4 ,anattempttoprovideacomplete
operatingbasedonfreesoftware. Everycomputerneedsanoperatingsystem(OS).
Stallman’sgoalwastocreatetheGNU operatingsystem. Forthatheneededacompiler, thetooltoturnsourcecodeintobinaryblobs. Forthatheneededaneditor. This
chickenandeggproblemiscalledbootstrapping. A wholesequenceofsoftwarearchitecturalmovescanbecalledbootstrapping, orthebootingupofanOS canbecalled
bootstrapping. StallmanhadlongworkedonaneditorcalledEmacssoheturnedhis
attentiontothecompilertoolchainwhichwascalledGCC,ortheGNU C compiler
asC wasthelanguageStallmanchosetowritetheoperatingsysteminasC wasthe
languageusedtowriteUnix. TheGNU operatingsystemwastobeaUnixlikeOS.In
ordertosafeguardhisworkStallmanmadethefreeavailabilityofthesourceanironclad
agreementbyexplicitlyfreeingthesource[32]bycraftingalicenseguaranteeingtheuser
certainrightswhileenforcingcertainobligationsontheuser–akindofquidproquo
agreement–theusergetsaccesstothesourcesolongastheuseragreestoreleaseany
modificationsthatheorshemakestothecodeintheeventthattheuserredistribute
thesoftware. Asthisisseenasa hack, repurposingcopyrightlawtoenforcesharing
thesetypesoflicensesarecalledcopyleft licenses, sometimesdenotedso: «. Ifapiece
ofsoftwareiscoveredbyacopyleftlicenseitisfreesoftware. Thelicensewascalledthe
GPL,theGNU generalpubliclicense, itnowstandsatversion3anditisthissocial
4 GNU(4)isNotUnix
41
andlegalhackthathaschangedthecourseoftheindustryofsoftwaredevelopment.
ThesoftwarestackiscalledGNU,thefoundationthatmanagesthestackandlegal
challengesandeverythingelseiscalledtheFSF,freesoftwarefoundation.
Stallman’sfoundationneverbuiltafullOS becausetheirkernel(thecoreoftheOS
–thebitthattalkstothehardware, thebitthatmanagestheapplications)neverreally
tookoff. InsteadayoungFinnishmannamedLinusTorvaldsinbuildingaUnixkernelcloneforhimselfcalledLinuxsucceededinthistask. Thisiswhysomepeopleargue
thatLinuxshouldbecalledGNU/Linuxbecauseitisacombinationofboththesevital
piecesofsoftware. Atthetimeofwriting, Android, Linux’smobilesuccessorbacked
bythewealthandtechnicalabilityofGoogleissettobecometheworld’sleadingsmartphoneOS,andassmartphonesaresettobecomethedominantmobileform-factorthis
meansthatfreesoftwareinthespaceof40years, 20initiallybyGNU alone, thefollowing20inconjunctionwithLinuxhasdisruptedanindustry.
Thestoryofthisideologicalrevolutionintheprocessofsoftwaredevelopmenthas
beendocumentedinmanyplaces. WhyI amdocumentingithereistocontrastthe
historyofthepracticeofsoftwareengineeringwiththesocialethosthatevolvedaround
freesoftware. Thiswewillturntoforamoment.
Thepublicsurfaceofacommercialpieceofsoftwareislimitedtotheproductitself; thesemi-facelesscorporationbehindtheproduct; themarketing, publicrelations,
andadvertisingspendofthecorporation; thetechnicalsupport; thetrade-showbooths;
andnowadaysthecorporatewebsitewhichcanserveasatechnicalpointofcontactor
merelyasanelectronicbrochure.
ContrastthiswithmostFOSS projectswhich, iftheyarelarge, arebackedbyfoundations: thinkFSF,thinkKDE,thinkGNOME,thinkApache, thinkLibreOffice,
thinkLinux. Thesefoundationsarenon-profitsgenerally, buttheyoftenreceivecommercialbacking–soratherthanacorporationmakinganopensourceplaythey’lldirect
fundingtowardsasemi-autonomousfoundation. Thesefoundationsarestewardsof
onechuckoflargesoftwarewithmanycomponentparts–thewayinwhichApacheand
KDE areumbrellasforanecosystemofprojectsthattakentogetherhavealargefootprint. Smallerprojectswillinvolvealoosegroupingofindividualsdonatingtheirtime
andresources. Thatisnottosaythattherearenocorporationsthatbuildtheirbusiness
solelyortooalargeextentaroundFOSS.TheprimeexamplewouldbeGooglewhich
hasleveragedLinuxtobuildthemobileoperatingsystemAndroidandalsoleveraged
WebKittobuildthewebbrowserChrome. ThemoneytofundAndroidandChrome
comesfromthesearchgiant’srevenuestreamininternetadvertising. Docompanies
makemoneyfromsellingFOSS products? Theanswerisyes. OneofthemoresuccessfulsoftwarecompaniesinrecentyearshasbeentheposterchildoftheFOSS world,
Redhat. TheycreateadistributionofLinuxcalledRedhatEnterpriseLinuxwherethey
assembleallthepieces, makesureitallworksandthenprovidecommercialsupportfor
theirefforts. Redhathavebeensosuccessfulandprofitablethattheyemployalarge
numberofengineerstofixkeypiecesofsoftwareintheGNU/Linuxecosystem. This
holdstrueevenifthesepiecesofsoftwarearebackedbyfoundations. Thecommercial
supportmodelishowmanyFOSS companiesderivetheirwealth. Whenyouthink
aboutit, thismakesalotofsense. TheFOSS ethosmeansthattheburdenofengineeringcanbesharedbutbecausethesourceisfreelyavailableitisoftenansimplematterto
getyourhandslegallyonbinarycopiesofthesepiecesofsoftwaregratis. Whatmakes
42
themusefulliesinthecomplexityoftheiroperation. Itmakessensethatpeoplewillpay
peopleforknow-howandexpertiseinmanagingthiscomplexityandasgo-topointsif
somethingshouldgohorriblywrong.
4.3
Thetarpit: softwareprogrammingishard
Softwareengineeringeventhoughitiscalled engineering isafarfromprecisediscipline.
Thehistoryofsoftwaredevelopmentsislitteredwithtalesofmammothprojectssufferingmammothoverrunsbothintermsofcostandallottedtime. Softwareengineeringis
notlikecivilengineeringwherethecost, lengthoftime, amountoflabour, materialsand
soforthcanbecalculatedprettyaccuratelybeforehand. I amnotsayingthatthereare
notengineeringworksthatarefraughtwithdisaster, areabortedbeforecompletionor
havemanyinterrelatedunknownquantities. Rathertheolderengineeringdisciplines
havehadmillenniatosolvetheintractableproblemstheyface. Andonceaproblemis
solved(theflyingbuttress, thearch, thesuspensionstay, andalltherestofit)theystay
solved.
Therearetheoriesofsoftwaredevelopment. Therearemodelsthatorganisations
follow. Theyvarybyteam-size, organisationalcomplexity, bureaucracybuttheyare
allveryalike. Thereisapieceofsoftware(asoftwaresystemofindeterminablesize)
thatmustbebuilttofulfilapurpose; thepeoplewhoknowwhatthatpurposeisare
interrogated; specifications, theequivalentofsoftwareblueprintsaredrawnup, those
specificationsareturnedpiecebypieceintocode; iterateuntilcompletion; launchproduct. Therearemanybestpracticesateverystagethathavebeendiscoveredovertime:
optimalteamsizeofindividualteams, test-drivendesign, codereviews, bugandfeature
repositories, coderevisionsystems. Andstillprojectsgooverbudgetandovertime.
A managerinIBM calledFredBrooksnoticedthisandsetaboutanalysingina
semi-scientificwaythepracticeofsoftwaredesignandtheresultwasabook, The Mythical Man-Month[Brooks, 1995], that has become a sort of software developer’s bible
alongwithanumberofothersacredtextslike DesignPatterns byGammaetal.
[Gammaet al., 1994]. Brooks notes in the preface that his slim tome had sold over
250,000copiesbyits20th anniversaryedition, theeditionI haveaccessed.
Themythicalmonthtowhichthetitleofthebookrefersistheideathatifyouhave
X amountofmen(theyarealwaysmen, sorryladies)workingonaproject, i.e. theinfamousditchdigging, thenifonespeedsuptheirrateofworktwofoldordoublesthe
sizeoftheteamthenthetimetakentodigthatditchortoproduceaN widgetsinan
assemblylinewilldecreasebyonehalf. ThisisatheFordistmodelofproduction. What
Brooksnotedwasthatcounter-intuitivelyaddingmoreengineerstoasoftwareproject
thatwasalreadyexperiencingdelayscausedevenmoredelaysroughlyspeaking. Why
isthis? Buildingsoftwareisnotalinearprocess, itappearsthatthereisasignificant
amountofoverheadintermsofcommunicationbetweenteammembersthatonlyisexacerbatedextrateammembersandfurthermorethecostoftrainingupnewmembers
onanynon-trivialprojecteatsintothetimethathasbeensetasideforactuallybuilding
theproduct. Youalsocannotassemblylinesoftwareconstructionbecauseeachindependentmoduleintheprojectmustbemoreorlessnearastatewhereitcanbeprovably
workingatanygivenmomentwhichmeansthatallteammembersworkingonindividualmodulesmustbeworkinginacoordinatedparallelfashion. pg. 17“Thebearingof
43
achildtakesninemonths, nomatterhowmanywomenareassigned”.
NowitisinterestingthatBrooksnotesthatcertaintypesofsystemareharderto
producethanothers. Ifwetakea standaloneprogram asourunitofmeasurementhe
claimsthatwiththeexperienceoftimehecametobelieveacertainruleofthumb. There
isathreefoldincreaseinoutlayifonewantstoturnonesprogramintoa programming
product, thismeansthatitisgeneralised, tested, documented, maintained. Similarly
thereisathreefoldincreaseinoutlayifonewantstoturnonesprogramintoa programmingsystem, thismeansthatitsinterfacesareregularandthatitcanbeintegratedinto
systems. Finallycombiningbothtogeta programmingsystemsproduct (likeaportable
operatingsystemsay, oraportableofficesuite, oraportablecompilertoolchain)takes
ninetimesasmucheffort.
Thefourthchapterclaimsforanylargesoftwareprojectthatthevisionofthesoftwareasatotalitymustgothroughonemind. EverychapterofTheMythicalManMonthfeaturesanengagingpieceofartwork, inblack-and-white. A beautifulrepresentationofReimsCathedralisthepieceofartworkforthefourthchapterwhichis
entitledAristocracy, Democracy, andSystemDesign.
EricS.Raymondhasahypothesisthatthereisasilverbulletofsorts-themethodologyoflibresoftware. Inaseminalessaythathassincebeenpublishedthoughitisavailablefreelyforanyone’sedificationontheinterwebsisTheCathedralandTheBazaar.
IfyouhavealreadyguessedthatthecathedralinquestionisBrooks’scathedralthenyou
wouldberight. Raymond’ssuggestionisthattheveryprocessofadheringtoamodel
wherethesourcecodeisfreelyavailablecircumventssomeoftheage-oldargumentsthat
Brooksrose. HethenhasapragmaticoutlookonlibresoftwarecomparedtoStallman’s
ethicaloutlook. ThepotentialproblemwithBrooks’sanalysisisthatsoftwareprogramminganddevelopmenthadessentiallybecomeisolatedactivitiesthatonlyallowedsoftwarereusewithinthosesilos. Formanyyearscommercialsoftwaredevelopershadbeen
hypingoneormoremodelsofreusabilitythatdidnotincludesourcereusabilityormodificationbecausethebusinessmodelaroundsoftwarehadcoalescedintotheideathat
youeithersoldprograms, buildingblockcomponents(programmingproducts)with
interfacesforstackingandlayering, orprogrammingsystemsproducts, againwithout
thesourcebarringexceptionalcircumstanceslikeyouweresellingtothegovernment
orthemilitary.
TheCathedralandTheBazaarisstructuredbyaseriesofpithyaphorismsdesigned
toinculcateinthereadertheessentialtraitsofgoodopensourcedevelopment. Number6is, “Treatingyourusersasco-developersisyourleast-hassleroutetorapidcode
improvementandeffectivedebugging.” Hegoesontosay, “Thepowerofthiseffect
iseasytounderestimate. Infact, prettywellallofusintheopensourceworlddrasticallyunderestimatedhowwellitwouldscaleupwithnumberofusersandagainst
systemcomplexity, untilLinusTorvaldsshowedusdifferently.” Andtheninthenext
paragraph, “Infact, I thinkLinus’scleverestandmostconsequentialhackwasnotthe
constructionoftheLinuxkernelitself, butratherhisinventionoftheLinuxdevelopmentmodel. WhenI expressedthisopinioninhispresenceonce, hesmiledandquietly
repeatedsomethinghehasoftensaid: «I’mbasicallyaverylazypersonwholikestoget
creditforthingsotherpeopleactuallydo.»”
FredBrooks’sclaimisthatthenon-parallelisableportionofsoftwaredevelopmentis
thathalfofthescheduleshouldbedevotedtotestingofonekindoranother, component
44
testingandearlysystemtesting, systemtestingitself, andbetatesting. TheLinuxmotto
asenunciatedbyRaymondis: givenenougheyeballsallbugsareshallow.
4.4
Legal, economic, ethical, epistemologicalangles
Legal, FOSS isboundbylicensesbackedbythelegalsystem–economic, itisaqualitativelydifferentmethodfordevelopingsoftwareandtherearemonetaryimplications
bothproandcon–ethical, therearesomewhoarguethatfreesoftwareisasocio-ethical
phenomenonandotherswhoarguefromapositionofpragmatism–epistemological,
bywhichI meantheinterplayofFOSS withthemethodsofscientificdiscoveryand
howwecometoknowwhatweknow.
AsthereaderwillhavebeenabletomakeoutfromthepottedhistoryI haveprovidedseveralcaseshavebeenmadefortheeffectivenessofonemethodofsoftwaredevelopmentoveranother. Themostradicaldeparturefromtheengineeringorthodoxy
isthestanceofStallmanandpeoplewho, likehim, believethattheissuessurrounding
thesharingofcodeareethicalissues. Theybelievethatityour(moral)dutyasagood
neighbourtoshareyourcode. Others, likeLinusTorvaldsandmanyothers, believethe
whatisatstakeismorethepragmaticdecisionofbuildingbettersoftware. Theybelieve
thatsharingsourcecodeleadstohigherqualitysoftware, andwhatsoftwareengineer
wouldnotwantthat?
Legalmattersareanotherconcern, freeandopensourcesoftwarelicensesaresurprisinglysimplelegaldocuments. Theyprovidecertainassurances, theydemandcertainrequirements. Theycomeindifferentflavoursdependingonwhichfreedomsthey
tendtoemphasize.
Rightstoatangibleorintangibleentity(creativework)aregenerallyseenaslegal
rights. Withregardtothepaternityoftheworklawyersnowtendtodifferentiatebetweenthemoralrightsofanauthorandtheeconomicrightsofanauthor. Thereason
thattheyareseenaslegalrightsisbecausetheyarenotseenaspartoftheinalienable
rightsofapersonbutstemfromtheseinalienablerights. Moralrightsdifferformeconomicrightsinthatmoralrightspertaintoissuesof attribution -requiringthatthe
correctauthorbeattributedorcreatingaworkanonymouslyorpseudonymouslyand
havingthatveilprotected. Notethatthesemoralrightshavenothingtodowithethics,
theyareaconceptofcopyrightlaw. Moralrightsalsopertaintothe integrity ofthe
work, itisthemoralrightofanauthorthatisaffectediftheworkhaspiecesremoved
duetocensorship. Theeconomicrightsofanauthorobviouslypertaintotheabilityof
theauthortoreceivejustrenumerationfortheuseofthefruitsoftheircreativeefforts.
4.4.1
Legal: no, all, orsomerightsreserved
PublicDomain(norightsreserved) Worksinthepublicdomaininformallyrefersto
creativeworksthatarepubliclyavailable, freeforalltouse. Formallyaworkmayenter
thepublicdomainoralwayshavebeeninthepublicdomainbecausetherightstied
totheworkmayhavebeenforfeited, areinapplicableormayhaveexpired. Examples
couldbe:
• forfeited: Anauthormaywaivetheirrightsonaworkallowingthatworktoenter
45
thepublicdomain. Thisvariesfromplacetoplacesothatinsomejurisdictionsan
authormustasserttheirmoralrightsandeconomicrightsinordertobenefitmateriallyandprotectagainstinfringement-inotherjurisdictionstheseareaccrued
totheauthorbytheactofcreationandmustbeexplicitlywaived.
• inapplicable: ThisconceptrelatestoprehistoricnaturallanguageslikeItalian,
Finnish. ItcouldperhapsapplytoinventednaturallanguageslikeEsperanto,
Loglan, Klingon, Elvishandsoforthbutthishasneverbeencontestedlegally.
AsthisthesisgoestoprintOracleissuingGoogleoverthecopyrighttotheprogramminglanguageJava, thefirstsuchcase–itwouldsetaprecedentifOracle
wereabletoassertcopyrightoverthelanguageitself(ratherthanaparticularimplementation). A rulinghasbeenpasseddownattheEuropeanlevelupholding
Google’sposition.
• expired: Whenthecopyrightonaworkexpiresitentersthepublicdomain. Works
predatingcopyrightlawareseenaspartofthecommonheritageandfolklore.
Fullcopyrightorcopyleft(allrightsreserved) Copyrighthasbeenthestandardlaw
pertainingtocreativeworkssincethestatuteofQueenAnnein1790. Thishaschanged
infoursignificantwaysdownthroughtheyears. Thefirstchangeisthelengthofthe
termofthecopyrighthasbeengrowingeverlongerastimegoesby. Whatwasoncea
methodofprotectingauthorsfrompublishers(andnowadaysusers, butinthosedays
copyingwasaprivilegedtask-onehadeithertobeliterateorownapress, bothprivilegedpositions)isnowamethodofextractinglongtermrevenuefromacopyrighted
work. Thisstiflesreuseandremixculture. Thesecondisthatcorporationsarenow
legalpersonsandcanownassertcopyrightovercopyrightableworks. Thelifetimeof
corporationscanbemeasuredinthecenturiesandthesecorporationscontinuallypress
forlawstobeamendedwithlongerandlongercopyrightterms. Thethirdchangeis
copyleftwhichwehavediscussedbeforeanditisaproductofourdigitalworldandthe
essentialchangeinthenatureofdigitalworksfromtraditionalworks. Thefourthisthe
mostrecentinnovationandcanbethoughtofamiddleground, somerightsreserved,
examplesofwhicharegiveninthenextsubsection.
TheGPL,BSD,MIT,Apachesoftwarelicensesallrelyonstrongcopyrightlaw.
Whensituationsoccurwheresomeoneorsomecorporationusesapieceofsoftware
thatiscoveredbyacopyleftlicenseanddoesnotadheretothetermsofthelicensethey
areinbreachofcopyright. Usuallyinthecaseofatraditionalworkthiswouldentail
republishingtheworkwithoutpermission, inthecaseofcopyleftthebreachwouldinvolvemakingmodificationstoapieceofsoftwareandredistributingitwithoutmaking
thosechangesavailable, forexample. Transgressormustberigorouslysuedforcopyrightinfringementorthelicenseswillbeseenashaving“noteeth”.
TheCreativeCommons(somerightsreserved) Inelectronicmediaotherthansoftwareausecasewasfoundwhereitmightbedesirabletogiveupsomebutnotallrights
toaworksothattheworkcouldberemixed/reused/mashed-up. Thisworksespecially
wellforaudioandvideo. Oftentimesanauthorwilljustwanttobecreditedfortheir
workandnotcareatallwhatisdonetotheworkitself-ergo, theyareconcernedwith
46
attributionandnottheintegrityofthework. Thisallowsforfiner-grainedcontrolover
thework, amoremeasuredandsubtlelettinggo, amorenuancedapproachedthanthe
allornothingapproachofpublicdomainorfullcopyright. Thisthesisforinstanceis
licensedunderpermissivecreativecommonstermswiththeknowledgethatitowesits
existencetothehardworkofmanyothersandthoughitisadistillationandreworking
ofmanymindsisnotaworkofstronglyoriginalcharacterandthusdoesnotneedthe
fullrightsofausualcreativecopyrightedwork.
4.4.2
Economic: theneweconomy
Thatbringsusthefinalpartofthissection–theneweconomy. Theriseofdigitalmediahasbroughtthenotionofpiracyinfromthehighseasandintoourlivingquarters.
Thenotionofpiracyrestsagainonthenotionofproperty, propertyintransitthatis
stolen. Whenapersonillegallydownloadsatune, illegallystreamsamovie, illegally
copiesapieceofsoftwareitissaidthattheyareinvolvedinpiracy. Thepiracyofintangiblemediaisnotlikethepiracyofthehighseasbecausewhenapersonconsumes
oneoftheseitemstheyhavenottakensomepieceofcargointransitandfurthermore
whenintangiblemediaiscopiedtheoriginalisnotdestroyedsowhatwehavehereis
aproliferationofgoods. Itisnottheftinthetraditionalsense. Indeed, asrecentlyas
thismonth, GoldmannSachssuedaformeremployeeSergeyAleynikovformillionsof
dollarsbecausetheemployeehadleakedsomeoftheirsoftware–theysuedforcode
theftandespionage. Unfortunatelyforthemandinaccordancewithcenturiesoflegal
traditionthecourtruledagainstthembecausecodeisnotseenastangiblepropertyby
thelaw[33]andsocannottechnicallybestolenandsoMr. Aleynikovwhilehedidcause
GoldmannSachsharmbyreleasingproprietarycodehecannotlegallybesaidtohave
stolenitandsohecannotbechargedwiththeft. Themosthecouldbechargedwithis
copyrightinfringement whichisnotlegallytheft.
ChiefJudgeDennisJacobswroteaspartofthecourt’sunanimousdecision: “Because Aleynikov did not «assume physical control» over anything when he took the
sourcecode, andbecausehedidnotthereby«deprive[Goldman]ofitsuse,»Aleynikov
didnotviolatethe[NationalStolenPropertyAct]NSPA.”
Jacobswentontoadd, “Wedeclinetostretchorupdatestatutorywordsofplainand
ordinarymeaninginordertobetteraccommodatethedigitalage,”. Andfurthermore,
“TheenormousprofitsthesystemyieldedforGoldmandependedonnooneelsehaving
it,”Jacobsruled. Pointingoutthatthecodewasnottobesoldonorlicensedtoothers,
headded: “Because[thehigh-frequencytradingsystem]wasnotdesignedtoenteror
passincommerce, ortomakesomethingthatdoes, Aleynikov’stheftofsourcecode
relatingtothatsystemwasnotanoffenseunderthe[EconomicEspionageAct]EEA.”
Thesamelogicextendstootherformsofdigitalmedia.
Whetherapersonexcludesanotherpersonfromaspaceintheworldbyenclosingit,
byfencingitoff, eithervirtuallyornotitcouldbesaidthatthispersonwantstomonopolisethispartoftheworld. A commoncontemporarymythisthat informationwants
tobefree –what is trueisthatdigitalinformationisveryfluidandisnotgenerallydestroyedasitiscopiedfromplacetoplace. Artificialbarriersmustbeerectedtocounteractthisfluidity. Technicalbarriersinvolvingencryptionandelectronicsigningcalled
digitalrightsmanagement(DRM) isonemechanism, legalbarrierssuchascopyright
47
infringementisanother. Theseareissuesofmonopolyandplurality, controlandfreedom, transparencyandopacity. Anothermethodemployedisintocontrolthepipes.
TimWushowsinTheMasterSwitchthateverytelecommunication(theinternetisthe
fifth)systemtodatehasendedupinthecontrolofamonopolyoroligopoly. Another
internetage-mythisthattheinternetisimpervioustothissortofrestriction, theinternetissomehowinherentlyopen. Wushowsthathistoricallythisisarecurrentbelief, a
beliefthathasalwaysturnedouttobefalse.
Specifically, whatweneedissomethingI wouldcallaSeparationPrincipleforthe
informationeconomy. A SeparationsPrinciplewouldmeanthecreationofasalutary
distancebetweeneachofthemajorfunctionsorlayersintheinformationeconomy. It
wouldmeanthosewhodevelopinformation, thosewhoownthenetworkinfrastructureonwhichittravels, andthosewhocontrolthetoolsorvenuesofaccessmustbe
keptapartfromoneanother. Atthesametime, theSeparationsPrinciplestipulates
oneothernecessity: thatthegovernmentalsokeepitsdistanceandnotinterveneinthe
markettofavoranytechnology, networkmonopoly, orintegrationofthemajorfunctionsofaninformationindustry.
Wu advocates a type of Separation Principle along the lines that are meant to keep
congress, the judiciary, and the executive office in the constitutional republic of the
UnitedStatesseparate. Thisseparationofpowersinvolvingatri-partitestructureis
meanttogivestabilityandbalancetothenation. LawrenceLessigarguesfromthelevel
ofprotocolinCode2.0–heshowsthatthereisnothingintheelectronicarchitectureof
theinternetprotocolsthatshouldbearoutthenotionthattheinternetisimperviousto
capture,
ThisregulatoriswhatI call“code”–theinstructionsembeddedinthesoftwareor
hardwarethatmakescyberspacewhatitis. Thiscodeisthe“builtenvironment”ofsocial
lieincyberspace. Itisits“architecture.” Andifinthemiddleofthenineteenthcentury
thethreattolibertywasnorms, andatthestartofthetwentiethwasstatepower, and
duringmuchofthemiddletwentiethitwasthemarket, thenmyargumentisthatwe
mustcometounderstandhowinthetwenty-firstcenturyitisadifferentregulator–
code–thatshouldbeourcurrentconcern{pg. 121}
BothWuandLessigcautionvigilance. I wouldarguethatthereisapropensitytothink
oftheinternetasapublicspace. ThisisamisconceptionI wouldargue. Itisas, I said
earlier, morecorrecttoviewitinaninfrastructuralwayasanetworkofnetworkswitha
hubandspokelayout. Allthesites, onthewebatleast, areinterconnectedbythezerodimensionalityofthehyperlink–thismakesitadenselypackedspaceofprivatespaces
withnopublicspacewhatsoever. Itisonlyifthesite’ssystemallowsforpublicparticipation, asinawiki, thatanyofthespacescouldbesaidtobepublic. I canemphasize
thispointbypointingoutthatitisimpossibletohaveapublicdemonstrationonthe
internet, themostthatispossibleistomountadistributeddenialofserviceattackon
specificprivatespaces. Similarlytherearenopublicspacesonwhichtoscrawlgraffiti
Banksy-like, theinternetandthewebjustarenotshapedlikethistopologically.
48
Finally, fromaneconomist’spointofviewYochaiBenklerarguesthat,
Perhaps the most amazing document of the consensus among economists today
that, becauseofthecombinationofnonrivalryandthe“ontheshouldersofgiants”effect, excessiveexpansionof“intellectualproperty”protectioniseconomicallydetrimental, wastheeconomists’brieffiledintheSupremeCourtcaseofEldredv. Ashcroft.
Thecasechallengedalawthatextendedthetermofcopyrightprotectionfromlasting
forthelifeoftheauthorplusfiftyyears, tolifeoftheauthorplusseventyyears, orfrom
seventy-fiveyearstoninety-fiveyearsforcopyrightsownedbycorporations. Ifinformationwerelikelandoriron, theideallengthofpropertyrightswouldbeinfinitefrom
theeconomists’perspective. Inthiscase, however, wherethe“propertyright”wascopyright, morethantwodozenleadingeconomistsvolunteeredtosignabriefopposing
thelaw, countingamongtheirnumberfiveNobellaureates, includingthatwell-known
marketskeptic, MiltonFriedman.{pg. 38}
Intangiblemediaandcodeissubjecttononrivalry. Unlikephysicalstuff, physicalobjects; whereifI buythestuffI depriveyouoftheobject, intangiblegoodsdonotoperate
inthisfashionandaresaidtobenonrival. And, ifanideaisletlooseintheworlditcan
bebuilton–plotlinescanbereused, algorithmsduplicated. Mathematicalsoftwareis
subjecttoalltheperspectivesgiveninthissection. Theproductionofmathematicsas
itcomestodependonmathematicalsoftwarewilladjusttotherequirementsofthelaw
ratherthantherequirementsofscience.
4.4.3
Ethical: pragmatismversusethics
Itmaynotbeimmediatelyobvioushowthechoiceofwhichsoftwareonerunsonones
computercanbeanethicalchoice. AsI havementionedbeforethereareactors, like
LinusTorvalds, withinthefreesoftwareandopen-sourceworldwhoviewtheirchoice
todevelopnon-proprietarysoftwareasapragmaticdecision–thatistosay, theyview
thatthefreesoftwaremethodologyproduces better codethantheproprietarymethodology. “Itstartedgainingattentionwhenitwasobviousthatopensourcewasthebest
methodofdevelopingandimprovingthehighestqualitytechnology.”
[TorvaldsandDiamond, 2002]{pg. 227}Theflipsideofthisistheethicalangle. Someone, likeRichardStallman, viewsthischoiceinethicalterms, theybelieveitis morally
wrong todevelopproprietarysoftwarefordistributionbecause, theysay, thatdecision
hasanti-socialconsequences. “Stallmanneverthelesscantakesolecreditforbuilding
thefreesoftwaremovement’sethicalframework.”[Williams, 2009]{ch. 13}Inresponse
theproprietaryworldhasrespondedtothethreatfromLinuxandthefreesoftware
movementwithoutrighthostility–witness, “Linuxisacancerthatattachesitselfin
anintellectualpropertysensetoeverythingittouches,”[34]. Thissuggeststhecamps
arealignedalongculturalandideologicalfaultlineslendingcredencetothebeliefthat
indeed theconsequencesofonesdecisionsinthisrespectareinfactpartlyethicalin
additiontopragmatic.
49
4.4.4
Epistemological: thecaseforopencomputerprograms
AsI waspreparingthisthesisanarticlewaspublishedinNaturethatwasmostfortuitous. ItspeaksdirectlytotheepistemologicalconundrumI havealludedtoanumber
oftimes. Theargumentgoesthus. Themethodsofsciencerequirethatallthepartsof
anexperimentbereproducible, tosatisfytherequirementoftestifiabilityandfalsifiability. Priortothecomplexsoftwaresystemsofthelast50yearsthisamountedtomerely
havingaccesstotheexactsametoolscalibratedintheexactsamewaysasotherscientific
teams. Tothebestofmyknowledgethetheoriesunderpinningscienceneverrequired
absolutetransparencyofthetoolsinquestion. Inpracticeonceatoolisengineeredto
asufficientprecision, towithinacertaintoleranceoferrorthenalliswell. Thisisnot
possiblewithsoftwareastheexamplesfromchaostheoryshow–essentiallyonewould
needidenticalhardwareandsoftwaresetups.
Theauthors, DarrelC.Ince, LeslieHatton&JohnGraham-Cumming, arguethe
caseforopencomputerprograms. I shallweighthemattermyself, thenI shallpresent
theirviews.
I mentionedearlieraboutGaussandNewtonbeingquitesecretiveintheirwork.
Peerreviewedpublicationssimplydidnotexistasaconceptafewhundredyearsago–
itisarelativelyrecentmoderninvention. Ittooksometimebeforeitwasrealisedthata
cultureofopennessisnecessaryforevidence-basedscience. Copernicuswenttoworkas
anassistantforTychoBrahebecauseBrahekeptthemostmeticulouscalculationsbut
heinnowaysharedthatdatawithanyoneoutsidehisastronomylab. Asthephilosophy
ofsciencedevelopedinthetwentiethcenturytheideathatyoucouldsimplyasserta
proofandletituptootherstobelieveyouornotfelltooneside. Itcametobeseenthat
notheoryiseverfullyprovenbutmerelythebestcandidateormodelformeasuringand
predictingrealityoutofmanycompetingtheories. Thebestonecandoisfalsifyatheory,
disqualifyit, onecannevercategoricallyproveatheory. KarlPopperwasinstrumental
inmakingthisworldviewwidespread–andthiswasintheearlytomid20th centuryso
notthatlongagoatall.
Likeallotherfields, sciencehasbecomecomputerized. Tomymindthismeansthat
thereshouldbeacertainelevatedrequirementforcomputerprogramsusedinscientific
research–thereareepistemologicalconcernsI believe. I wouldn’tgosofarastosay
thatwithholdingthesourcecodeforthecomputerprogramsusedinscientificresearch
isanti-scientificbutI feeltheactdoesresideinaquestionableplaceonthecontinuum
ofscientificintegrity. Stallmancontendsthatallproprietarysoftwareisessentiallyantisocial. WhilethislineofreasoningseemsplausibleI feelthatastrongclaimsuchasthis
isunnecessarilyprovocativeandwouldonlytrulymeritattentionifsomekindoflegal
frameworkwasbeingputintoplacetomakefreeandopensourcesoftwareanuntenable
pursuit. I dofeelthatintheareaofscientificresearchsomekindofstrongclaimcouldbe
madethatthewithholdingofsourcecodeisanti-social. Asmathematicsissuchalarge
partofsciencethisplacesacertainextraburdenonthemakersofmathematicalsoftware
I feel–insomewaysyoucouldsaythatwehaveregressedtothetimeofNewtonand
Gaussinthisonerespect. Thisissurelyalessthanidealsituation. Thesemenprofited
fromtheirsecrecy, wemustaskourselvesifthisisthesituationwewantsociallyastime
progressesandcomputersandcomputerprogramsbecomeevenmoreembeddedand
enmeshedintothefabricofsociety.
50
HereistheabstractoftheNatureauthors,
Scientificcommunicationreliesonevidencethatcannotbeentirelyincludedinpublications, buttheriseofcomputationalsciencehasaddedanewlayerofinaccessibility.
Althoughitisnowacceptedthatdatashouldbemadeavailableonrequest, thecurrent
regulationsregardingtheavailabilityofsoftwareareinconsistent. Wearguethat, with
someexceptions, anythinglessthanthereleaseofsourceprogramsisintolerablefor
resultsthatdependoncomputation. Thevagariesofhardware, softwareandnatural
languagewillalwaysensurethatexactreproducibilityremainsuncertain, butwithholdingcodeincreasesthechancesthateffortstoreproduceresultswillfail.{abstract}
Theyhavetworeallifedatasetswhichcontainthesetypesoffailure: datasetsknownas
HadCRUT andCRUTEM3producedbytheUnitedKingdomMeteorologicalOfficewiththeaidoftheUniversityofEastAnglia’sClimaticResearchUnit, datasets
usedbygeologiststositeextremelyexpensivemarinedrillingrigs.
Theysaythatthereisthepracticeofincludingtextualdescriptionsofalgorithms
(theydonotusethetermpseudo-codebyI haveseenthattermusedinsimilarcontexts)
buttheygoontosaythatthisisinadequate. Theysaythatthesourcecodethatsupports
somepublishedscientificresult(ordataset)mustbereleased–owingtoambiguities
innaturallanguage, variabilityinhardware, andfloatingpointrepresentations, inconjunctionwithprogrammingerrors.
Theycite4reasons: theencouragementofnon-institutionalresearchers, thebenefits of extra teaching material, reusability of modules, improved scientific accuracy
quicker. I couldn’tpossiblydojusticetotheentirearticle–I encourageanyonewith
interestintheareatoreadit, itisquitebrief, lucidandapproachable.
Thisconcludesthegeneralinvestigationintosoftwarepractices, cultureandideology
–asmentionedearlierthenextdivesintoacoupleofspecificmathematicalsoftware
ecosystems.
51
5
Specificcomparisonandquestionnaires
5.1
Compareandcontrastopenversusproprietarytools
NowthatI havegivenadetaileddescriptionofthesoftwaredevelopmentlandscape
ingeneralitisthecorrecttimetomakeananalysisofoneparticularcategoryofsoftware, namelythesoftwareofinteresttothisthesis, mathematicalsoftware. Thisisby
nomeansaforensicanalysisofcodequality, workingpractices, andsoforth. Instead
aquestionnairewasposedtotwogroupsofpeople, therewasnotimelimitimposed.
WhenalltherespondentshadcomebacktomeI madeananalysisoftheresultsand
wentbacktothemwithanumberoffollow-upquestionstailoredtoeachindividual.
Noteveryonewhohadrespondedthefirsttimerespondedthesecond, unfortunately.
AsI pointoutbelow, owingtosomebadlystructuredinitialquestionscouplewitharegrettablelackofprecisionmyfollow-upquestionswerethereforeanattempttoclarify
earlierfudges. Thisexplainsthe unfortunately.
Minewasnotalargequestionnaire, norwerethenumberofresponsesoverwhelming, norweretheresponsesincrediblydetailed. WhatI succeededinobtainingwasan
(I believe)authenticsnapshotofthestateofmindoftheactorsinthisparticularniche.
Becauseofthesmallsamplesize, andbecauseI seenoreasonnotto, I ampublishing
theactualresponses as-is, barcorrectingafewtypos. I amrandomisingthecomments
becauseI seenoreasontoallowanyonetoreconstructanyparticularindividualstotality
ofresponses–I aminterestedintheaggregateresponse, thegroupresponse.
I willturnfirsttotheopensourcecrowd, thentotheproprietarycrowd.
5.2
Sage
5.2.1
Lead-uptoopensourcequestionnaire
TheSagemissionstatementaccordingtoitswebsite: “Createaviablefreeopensource
alternativetoMagma, Maple, Mathematica, andMatlab”.[35]A “viablealternative”will
havefivedistinguishingfeatures(andI paraphrase): itwillhavethe mathematicalfeatures ofMagma, Maple, Mathematica, andMatlabwith comparablespeed; itwillhave
beautifulinteractive2dand3dgraphics; itwillhaveanotebookinterfaceandanintegrateddevelopmentenvironment; itwillprovidemanyeducationalbooks(fullundergraduatecurriculum); itwillcomewithcommercialsupport(e.g., customisednotebook
servers).
Asyoucansee, thegoalofSageistodisruptamulti-billiondollarnichesoftware
industry. Whywouldagroupofacademicswanttodothat? Howsuccessfulhavethey
been? InordertoanswerthesequestionsI askedtheprojectmemberseightquestions
thatI hopedwouldessentiallyelicittheiropinionswithoutbluntlyposingthoseexact
questionsinquitesopugnaciousaway. Herearethosequestions.
1. :-WhatisyourroleandhowlonghaveyoubeeninvolvedinSageMath?
2. :-Whatisyourbackgroundandwhatmotivatedyoutobecomeinvolvedinthe
project?
52
3. :-WhatisyourpersonalopinionaboutthequalityofSageMathandthequalityof
opensourcemathematicaltoolsingeneral? Howdoesthisrelatetoproprietary
tools?
4. :-Whatisyouropinionofproprietarysoftwaremathematicaltools? Doyouuse
any?
5. :-WhatisyouropinionabouttheGPL andfreesoftwarelicensesingeneral?
6. :-Inthebroadarcofscientificresearchanddevelopment, howdoyouseeyour
involvementinSageMath?
7. :-Arethereanyviewsandopinionsyouwouldliketosharewiththeworldregardingthesetopics: considerthisyoursoapbox.
8. :-IsthereanythingI amnotaskingthatyouthinkI shouldbeasking?
I receivedsevenanswersafteralittleproddingandcajoling. I’dliketotakethisopportunitytoremarkuponthejourneytoreceivingtheseresponsesfromthisFOSS project.
I initiallyaskedoninternetrelaychat(IRC) astowhetherparticipantsintheproject,
betheyusersordeveloper, wouldliketotakepartinasurveyonopensourcemathematicalsoftwareformythesis. I wasdirectedbyakindandhelpfulsoultothedeveloper
mailinglist. I subscribedtothemailinglist(towhichI amsubscribedtothisday)and
postedamessagewiththequestionnaireinOpenDocument(text)format, aformatI
presumedwouldbeamenabletosuchagroupofindividuals. I receivedbuttworesponsesandI thoughtthatthispartofmythesiswasscuppered. A numberofpeople
repliedtomesaying: thisisaniceideabutyoushouldhavemadethisawebsurveybecauseitishandierorbecauseitwouldbepossibletoreplyanonymously. Andalso: why
wasI askingsomanydetailedpersonalquestionsinthequestionnaire. Thisannoyed
andbemusedmebecausea)thedocumentwastohandandinafree(asinfreedom)formatasanattachmenttotheemail, b)I wasnotaskingparticularlysensitiveinformation
andI hadguaranteedI wouldnotdisclosetheidentityoftherecipients, c)I hadletitbe
knownthattheycouldanswerasmuchoraslittleastheyliked. Afterwaitingacouple
ofmonthsandreceivingnootherrepliesinadditiontothefirstpromptandgenerous
twoI relented. I turnedthedocumentI hadpreviouslypreparedintoaGoogleDocumentsformthatisatheartaspreadsheetandposteditagaintothelist. I alsosuggested
thattherewouldbeamaterialrewardintheformofapieceofArduinohardware. This
timeI gotfiveresponses, notoneofwhichchosetoenterthedataanonymouslyand
notoneofwhichwereanyofthepeoplewhohadharanguedmeaboutthesloppiness,
ill-judgednature, ortheinsensitivitytoissuesofprivacyandidentityofmyinitialpost.
Moralofthestory: considergivingpeoplemultipleavenuesinwhichtorespond, do
allowanonymityandpseudonymityunlessonehasagoodreasonagainst, realisethat
peoplecanbequitewillingtocreatemoreworkforyouwhilehavinglittleintentionof
contributingthemselves.
Theexactquestionnaireforms, bothoftheOpenOfficeOpenDocument(text).odt
varietyandtheonlineGoogleDocsvarietyareincludedintheappendixofthiswork. As
youcanseetheyarethesamebarringtherequirementofpersonaldata. BeforeI getto
theanswersI wasgivenI wouldliketogiveWilliamStein’sviewsonwhattheimpetus
53
fortheprojectis. I amcullingthisinformationfromanintroductoryvideo[36]thatis
hostedonSage’swebsite. Steinisoneoftheproject’sfounders–andsoisundoubtedly
inakeypositiontobeabletoarticulatetheseviews. Heisaprofessorofmathematics
attheuniversityofWashington.
AccordingtoSteintherequirementthatSageadheretothemathematicalfeatures
oftheBigFourallowsthemtoeasilydecidewhatpartsofmathematicstoincludein
theirproject. Furthermore, afeatureisnotdeemedacceptableunlessitperformsas
speedilyasthefeatureinacommercialproductitisemulating. Theneedforbeautifulinteractive2dand3dgraphicsstemsfromthedesirebothtouseSageasavaluable
teachingaid(andsotogiveitapushintoacademia)andfromthenecessityofbeing
abletoadequatelyvisualisethemathematicalsymbolsandobjectsyouareprototyping
andbuilding. Withrespecttothenotebookinterfaceandintegrateddevelopmentenvironment(orIDE touseitsshorthand)SteinsaysthatbothEmacsandEclipsehave
beenspecialisedtoallowprogrammerstogetprogrammaticaccesstoSage. Whilethis
isfineitisobviouslyonlysuitableforprogrammersandisabarriertoregularusersof
mathematicalsoftware. A notebookinterfacewouldbringthefamiliarpenandpaper
interfacetoalargeraudienceasthepreferredmethodforinteractingwithSage. Tothat
endSteinsaysthatinabout2007heandAlexClemeshadevelopedaweb-basedgraphicalinterfaceforSage, choosingthewebmodelasitiscross-platformandallowsfor
collaboration. InorderforSagetobeaviableplatformforuseinacademiaitisnecessaryforthestudentstohavehighqualitydocumentationthatexplainshowtouseSage
itselfandalsohowtoworkwithcertainareasofmathematicsinSage. Steinpointsto
thewebsite[37]whichcontainsbooksondifferentialcalculus, ellipticcurves, modular
forms, linearalgebraandmore. A finalpointemphasisesthatinstitutionstypicallyneed
theassuranceofpaidsupportinordertobeabletohavetheknowledgethattheycan
getsomeoneontheendofanemailorphonewhentheyrunintotrouble. Thehacker
oropensourcemantraofRTFM (ifyou’llbegmypardon)doesnotapplyhere.
Sage(whichatthattimewasanacronymforSoftwareforArithmeticGeometry
Experimentation)wasstartedin2005. DavidJoynersoonjoined. Steinhadadesire
forasystemlikeMagmaforhispersonalresearchandforhisteaching, butheneeded
ittobeopensource. JoynerhadaneedforthecodingtheoryfunctionalityofMagma
sotogethertheybuiltontopofPARI[38]whichhadbeenstartedin1985inFranceand
GAP[39]whichhadbeenstartedin1986inGermany. PARI providesnumbertheory
functionality, GAP providesgrouptheorycapabilitiestherebyprovidingcodingtheory
capabilities. TheglueininthisisthegeneralprogramminglanguagePython.
WhywasMagmanotgoodenoughforSteinandJoyner? OnemusttakeintoconsiderationthatSteinhadusedMagmafor5yearsandhadcontributedthousandsof
linesofcodetoMagma. Thefollowingreasonsaregiven:
Expensiveforcollaborators; Thismeanscolleaguesandstudentshadtopartwith
quitealotofmoneytoworkwitheachother. ThoughMagmahaddiscountsforpeople
outsidetheUS (aso-called“thirdworlddiscount”)ittypicallycostseveralmonthssalary
dependingonthecountry. Thiswasseenasahinderancetofrictionlesscollaboration
ifavibrantresearchprojectwastobebuiltatopofMagma.
Closed; Althoughstate-of-the-artalgorithmsareusedinsideMagmatheyarecompletelysecret. TheprojectisrunbytheuniversityofSydney, itistreatedlikearesearch
projectbutthealgorithmsandcodethatisdevelopedisusedforcommercialgain. In
54
theinterestsofsciencetheseshouldbeavailabletomathematiciansinthesamewaythat
everylineofatraditionalproofis.
Frustrating; ProfessorJohnCannonwhoistheheadoftheprojectattheuniversity
ofSydneyexertsastrongcontroloverwhatgoesintotheproject. ThustheMagma
projectishighlycentralisedandcommunity-buildingishindered. Steinpersonallyhad
somecodethathehaddevelopedforautomatedtestingofMagmarejectedbyCannon.
HereweseeparallelswithStallman’spersonalsnubbingbySproull.
Staticlanguage; ThoughthemathematicalcapabilitiesofMagmaaresuperbthe
bridgelanguagethatisusedisnotaspowerfulasgeneralpurposecomputerprogramming languages. An example given is the inability to create user-defined data types
whichispossibleinanydecentmodernprogramminglanguage. Thesearecalledtype
extensions. Generallyspeakingalanguagewillprovidetheuserwithamechanismfor
extendingthetypesystemofthelanguageinacontrolledfashion.
Onerouscopyprotection; MagmausesacopyprotectionschemethattiesthelicensedinstanceofMagmatotheMAC5 addressofthemachine. Obviouslythismeans
ifyouwanttorunMagmainavirtualmachine, ortransferittoanewmachine, orifyour
networkcardbreaksthenthevalueofyourcopyofMagmasuddenlybecomeszero.
Otherlanguagedeficiencies; Followingonfromthegripeabouthowstaticthelanguageistheremarkthatmanyotherfeaturesfrommodernprogramminglanguagesare
missing. Suchas: noexceptionhandling, noeval(), nonamespaces, andsoon.
Smalldevelopercommunity; BecausethedevelopercommunityofMagmaismade
upofresearcherswhoaregivenaccesstothecodebaseandbecausethereisnopublic
mailinglistthedevelopercommunityatanyonetimeremainssmall.
Subpargraphicshandling; Magmahasnographicaluserinterface, atleastinthe
sensethatMapleorMathematicaorMATLAB dobutbecauseMagmaissofarahead
oftheseintermsofnumbertheoryitisquitepainfulthatitislackinginthisarea.
Inefficientbugtracking; Thereisnopublicbugtrackerorlistofreportedbugs.
Bridgelanguageisnotcompilable; Inordertoachieveveryhighspeedsoneneeds
tobeabletoultimatelyeithercompilethelanguageyoutalktothemachineintomachinecodeorhaveajust-in-timeinterpreterthatdoesthisforyouonthefly. Because
MagmadoesnotdothistheonlywaytoachievethisinMagmaistowriteC codethat
interfaceswiththeMagmasourcecodebutbecauseveryfewpeoplegetaccesstothe
sourcecodethisavenueisblockedtogeneralMagmausers.
Afterhavinglookedatthereasonsforgoingitaloneletusgetbacktotheresponses
tomyquestionnaire. InadditiontotheeightquestionsI askedtherespondentstoprovidemewithanameorpseudonym(ortoleavethisfieldblankiftheywishedanonymity)
andtoprovidemewithdetailssuchas: emailaddress, website, nationality, nativelanguage, profession, presentoccupation, presentposition, employer. Allturnedouttobe
fromacademia: students, lecturers, professors–EnglishandSpanisharetheirnative
languages. ItwasonlyafterallthesepiecesofinformationwererequestedthatI askedif
therewere Anyother(personal)informationthatyoufeelmightbeofrelevance. Withoutanyfurtheradoherearetheresultswhichhavebeensubjectedtoscrutiny, both
5 Theuniquenumericidentifier(xx:yy:zz:ww:uu:vv)assignedtoeachlocalareanetworkethernetcardbe
itwiredorwireless.
55
analyticwhereI unpackanyextradetailandsyntheticwhereI connectthevariousdots.
5.2.2
Feedbacktoopensourcequestionnaire
SpeakingabouttheirroleandhowlongtheyhavebeeninvolvedinSageMath –
• “Observerandcritic.”
• “Myinvolvementisnotveryextensive. I wenttoa”SageDays”inMay2010. I organizedaSageDaysinMay2011, withabout30participants. I amintheprocess
ofrefereeingacoupleofpatches. OnepatchofmineisupontheSage-Combinat
patchserver.”
• “Beeninvolvedsince2006. Didsignificantworkonnotebookinitsearlydevelopmentcycle, otherinvolvementhasbeenfocusedonperformance/consistency.”
• “I started using it for computer assisted proofs related to my research in early
2009. Now, I contributewithsomecodetothemainbase.”
• “1month”
• “I havebeeninvolvedinSagesincelate2010. I havesubmittedseveralpatches
(whichhavebeensincecommitted)andbugreports. Basically, I amanintermittentdeveloper.”
• “I’vebeeninvolvedwithSagesincearound2007. I’vecontributedlotsofcodeto
variouspartsofSage, mentorednewcontributorsandusers, andI thinkI may
bethede-factoheadofsagenotebookdevelopmentnow(butthereisnosuch
officialposition, it’sjustthatI thinkI havethecurrentmastertreeandnooneelse
isdoingmuchworkonit).”
FromthiswecanseethatnoneoftherespondentshasmorethanfiveorsixyearsexperienceonSage, thisisincontrastwiththeproprietaryworldwheretherespondentsin
thatcasehave18, 20, even35yearsofexperience. Wecansurmisebytheoccupations
whichinvolvelecturers, professors(retiredorotherwise)thatthesepeoplehavemany
yearsofmathematicsandcomputerscienceexperiencebutgenerallyfromanacademic
pointofview; itistheyouthfulnessoftheSageprojectthataccountsfortheshortnessof
time. Increatingafully-roundedCAS systemtheyare25to30projectyearsinarrears.
Because Sage is a piecing together of many sub-projects some of those sub-projects
willhaveaconsiderablylongerlife-spantodatethanSageitself. Foryouredification
these[40]arethecomponentsusedbySage. Thespeakstotheorganicnatureofthe
project, its independently bottom-up approach and top-down – a sort of integration
ofparts, almostlikeaGNU/Linuxdistributionwhichneverthelessissteeredtowards
Sage’sowngoals. Iftherewereastudyfollowingthisresearchitshoulddelveintothe
componentssendingquestionnairestothemailinglistsofthesub-projects.
Speakingabouttheirbackgroundandwhatmotivatedthemtobecomeinvolvedinthe
project –
56
• “I feelI knowaboutcomputeralgebraandprogramminglanguagesgenerally. I
learnedaboutSageandwasimpressedbyitsnaïveapproachtoprogramming,
mathematics, andmanagement.”
• “I liketheideaofcooperativeendeavours. I alsothinkthatthepossibilitytocontributetothegrowthofSagemakestheprocessofwritingone’sowncodemore
interesting, andprovidesmotivationtodocumentitandpolishit(whichinthe
longrunisprobablyusefulformeevenifI wouldn’tdoitwithoutadditionalmotivation). Italsofeelslessofanimpositiontoaskmoreexperienceddevelopers
forhelpifthecodeI’mwritingmighteventuallymakeitintoSage.”
• “Sometimesproprietarytoolsaregood, buttheymaynotbe.”
• “I amamathematician(lecturer). Initiallymymotivationwasusingittohelpme
solvemyproblems, butlateronI gotinterestedoncontributingtoit.”
• “Hobbiest. Usingsagetobuildwebsiteforphysicspublicationsandexperimentalprojectdevelopment. Thereasonformyinterestinsageissimple, I issupposedtobeabletodoalmosteverythingMathematicacando, &it’sfree. I have
determined that sage is far from ready for prime time use as it’s extremely unfriendlytomostofuswhoaresimpledabblersinthisarea. I feelthatitmaywell
succeedasaviabletoolinafewyears. ItiscurrentlyunderVERY heavydevelopment&requiresalottomakeitusefulasa”toolforthemasses”. Thatisthearea
thatI havechosentoworkon. I’mintegratingsageintoamediawikiinstallation
thatwillallowreal, productive, useasatoolfordoingrealscience&publication
qualitymaterial. Atleastthatismyintention.”
• “I amahighschoolstudentinterestedinmathematicsandopensourcesoftware.
I knewPythonprevioustofindingoutaboutSage, andwantedtofindsomegood
mathlibraries. I triedsomeothers(NumPy, SymPy, etc.) butlikedSage’sintegratedapproachbetter.”
• “I have a PhD in math and a B.S. in computer science. I needed software to
computerankformatricesoverfinitefieldsformyPhD thesis, andwasusing
Magma, butswitchedtoSage. I alsoneededsoftwaretocomputevariousgraph
theoryparameters, andSageconvenientlyhadlotsofcodetodothat. Finally, I
wasaskedbyWilliamifSagecouldincludeadatabaseI built, whichpulledme
alittlemoreintothedevelopmentcommunity. ThenI workedongraphtheory,
linearalgebra, graphics, andotherpartsofSage. Thecommunitywasfriendly
andincluding, soI becameacontributor. SageDaysandIRC werebigfactors
inconnectingwiththecommunity.”
Fromthiswecandetectmultiplemotivations, someclear, somenotsoclear: thereis
cynicism, thereisthescratchingofyourownitchthatwastalkedaboutbefore, thereis
theartandcraftofdevelopment. Someonespeaksofthechallengeofdevelopingones
codeoutintheopen, thereisafeelingthatthisraisesthebarandforcesdocumentationtobewrittenduetooutsidescrutinyandfinallythereisbecominginterestedinthe
projectthroughhavinguseditforsomeotherpurpose.
57
SpeakingaboutthequalityofSageMathandthequalityofopensourcemathematicaltoolsingeneralandhowthisrelatestoproprietarytools –
• “CodewrittenoriginallyforSage? Someofitisverypoor. I amunawareofany
high-qualitycodewrittenspecificallyforSage, buttheremaybesome. Mostopen
sourcemathtoolsareunfinishedandunmaintained.”
• “I don’thaveaglobalopinionof”SageMath”. I doreallylikethefactthat, with
Sage, ifthereareissues, youwillgetanhonestresponse, andmightbeableto
participateinfixingaproblem(shouldyouuncoverone).”
• “I thinkSageisimproving, butstillhasalongwaystogo.”
• “The quality is very good, through a bit inconsistent in different areas. In my
particularareasofexpertisetheonlyproperproprietarycompetitionisMagma.
I don’tknowifI couldcalleithersystembetterthantheother.”
• “Sageisontherighttrackasitseemsheadedtowardsomethingthatcanperform
asdoesMathematicaonlyfree&opensource. AsfarasI cantellallofthese
mathematicappsneedtobeoverhauledsothattheypresentaMUCH easier
tousgraphicinterface. Therealworlddoesnotanylongerusecommandline
inputs. Somethingthatismoreakintotheinterfacepresentedbyappssuchas
Texmaker, orthegraphicsappslikeblenderwouldbeevenbetter. I don’thave
anyexperiencewithproprietarymathtoolsotherthanMathematica.”
• “I amverypleasedwiththequalityofSage, althoughitisinconsistentsometimes
due to it having to interface with many different software. The lower-level libraries(e.g.. NumPy)arealsoexcellent.”
• “Thisisaverybroadquestion. Insomecases, thequalityisexcellent; insome
cases, verypoor. AsforSage, I feelthatthequalityisgood, butcould(anddoes)
improve. A lotofmyworkisinpolishingthingstohavebetterquality.”
A nonuniformopiniononcodequality. Thisshowsthatthereisnometricassuchfor
determiningcodequality. Thetrickinessofcreatingprecisequestionnairesisevident
here. Codequalitycouldrefertothe, shallwesay, beautyofthesourcecodeitselfand
itcouldrefertohowfreefromdefectstheproductis. TheSageprojecthasquitea
detaileddeveloperguide[41]whichandtherearedeveloperguidelinessuchthatevery
patch(codefragmentthatimplementsafeatureorfixesabug)mustbeassociatedwith
acorrespondingticketandshouldbeaccompaniedbyunittests. Alluservisiblemathematicaltasksmustbeaccompaniedbydocumentation, asystemcalleddoctestschecks
forthis.
Speakingaboutproprietarysoftwaremathematicaltoolsandtheirusethereof –
• “OccasionallyI useMathematica, whichI findinterestingbutsometimesfrustrating.”
58
• “I haveusedMapleabit, butnotenoughevertogetcomfortablewithit. I’vealso
heardmyfriendwhousesitmorecomplainingaboutvariousissues(inparticular
thewaynewreleasesbreakhisoldcode), whichdidn’tencouragemetogetbetter
acquainted.”
• “I useMathematicaoccasionallytoseeifitcansimplifyintegrals/sumsI needfor
research.”
• “I usedsomeearlierinmycareerforlackofbetterchoices, butI don’tlikenot
beingabletounderstandhowacertainalgorithmworks.”
• “I haveusedMathematica. Waytooexpensive.”
• “I useWolframAlphawhenI needaquickanswertoaquestion. Foranyother
mathematicallyintensivetaskI useSage. I alsouseMathematicaonoccasion.
Ithasmanyfeatures, butI dislikethelanguageandprefertouseopen-source
software.”
• “I useMathematicaoccasionally. I thinktheyareuseful, andcertainlypouralot
ofresourcesintocomputationalmathematics, whichisgreat.”
ItisclearfromtheresponsesthatthereisbutonetoolthatthepeopledevelopingSage
feeltheyareupagainst. AndthattoolisMathematica. Withthisismind, andhavingtriedcomparingthetwopiecesofsoftwareI thinkthatthedocumentationshould
providetutorialsforusersmigratingfromMathematicatoSageinordertoeasethe
transition–largesoftwarevendorshaveconsistentlydonethis. I canthinkofMicrosoft
WordhavingcreateddedicatedhelpsectionsforWordperfectusers[42].
SpeakingabouttheGPL andfreesoftwarelicensesingeneral –
• “GPL,inmyopinion, isabadidea. ”LGPL”issometimesuseful. I preferaBSD
stylelicense. Yes. I justgotanotefromsomeonethatMaximacouldnotbemade
availableintheMacappstorebecauseGPL madeitimpossible.”
• “I don’thaveafinelyhonedtechnicalknowledgeoftheGPL.Itseemstowork
adequately, anditseemstobe(mostly)standard–thosearethemainimportant
things.”
• “I’dprefertouseafreerlicensethantheGPL.”
• “I don’tfeelentitledtotalkabouttheGPL orotherfreesoftwarelicenses. I am
justgladwehaveawayofmakingourresearch/codeeasilyaccessibletoeverybody. I haveafavorableattitude. Butifyouareaskingaboutadisputewhether
itisbettertouseGPL,BSD,ApacheorMIT-typeopenlicensesthenI amnot
sureonwhattosayasI don’tknowthespecificsofGPL (oranyotheroftheselicenses)wellenough. Therearehalfadozendiscussionsonsage-develaboutcompatibilitiesofdifferentlicensesandendlesslyarguingwhetherwecanorcannot
ship/distribute/linkagainstsomelibraryreleasedin(pickyourfavoritelicense).
Andhonestlyallthatdiscussionboresmetodeath, I justwanttodomymath.”
59
• “Excellent!!”
• “I amverysupportiveoffreesoftwarelicenses; I licenseallofmycodeunderopensource.”
• “I liketheGPL,andalsolicensethingsas(modified)BSD orMIT.I thinkthey
aregreatlicensesinmanysituations, butarenotthebestthinginsomesituations.”
Theresponseshereshowthataproject-widepolicyonwhichlicensemostbenefitsSage
andforwhatreasonscouldbedeveloped. Thiswouldnotbealotofworkandwould
clearlyhelptheSageproject. Asthetransparentnatureoftheprojectisakeydifferentiator(regardlessoftoolcapability)thechoiceoflicenseisareflectionofhowtheproject
asawholeviewthenatureofthattransparency. InthecaseofLinuxthebenevolent
dictatorforlifeMr. TorvaldshasstatedwhyhelikestheGPLv2andwhyeveninthe
faceoftheorganisationbehindtheGPLv2supersedingitwiththeGPLv3heisgoing
tostickwiththeolderversionduetohowheviewsthechangestheFSF hasmade.
SpeakingabouttheirinvolvementinSageMathinthecontextofthebroadarcofscientificresearchanddevelopment(amendedresponses) –
• “Nomorethanotherprograms. I’dliketoknowthattheprogramthatgivesme
accesstomybankaccountiskeepingmypasswordsecure, sowhynotdemand
thatitbeopensource? Inreality, opensourcecodewillbereadbyalmostno-one.
Justasinrealityproofsinmathjournalsarereadbyalmostno-one.”
• “SoI guesstheshortansweris: no. Transparencyofexperimentwasn’tabigmotivatorforme, becauseI mainlyadheretothemodelwherebywhatyoupublish
areyourproofs, notyourexperiments(betheycomputer-aidedornot). It’snot
thatI thinkthisistheonlymodelformathematics, butitisthemodelthatI am
usedto, andI thinkthereissocialpressuretoadheretothismodel.”
• “Thisquestionmakeslittlesense. Inthebroadarcofresearchanddevelopment,
I’mamathematicianandSageuser. Thisleadsmetosubmittheoccasionalbug
report; veryrarelytocontributingtoSage.”
• “Inanidealworldyes, butattheendofthedayI (andmostofmycolleagues)will
ratherusesomethingthatworksthansomethingwithanicelicense. Mypersonal
reasonstogetinvolvedwithsagecamefromtheneedofdoingsomespecificcalculationsthatcouldnotbedoneinanyexistingsoftware. Sageprovidedmea
niceframeworksothatI wouldn’tneedtocodeeverythingfromscratch. ButI
wouldn’thavegotinvolvedwithsagejustbecauseofitstransparencyifithadn’t
beenoutofneed.”
• “Asfaras’experimental’resultsdevisedfromproprietarysoftware, welltheywould
seemtobeproprietaryandshouldbejudgedbythepeercommunityassuch. In
myopinion: non-verifiableresultsthatclaimtobe’proven’bysoftwarewrittenby
theexperimenters, whereby’theexperimentors’donotprovidethecodeinvolved,
shouldbeadjudgedas’non-verifiable’unlesstheproducingcodeisalsoverifiable.
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Doesthatmeanthattheymustrevealthecode? NO!Itjustmeansthattheircredibilityshouldbecalledintoquestion. ThecurrentgoingsonattheCernfacility
regarding’particlesmovingfasterthanthespeedoflight’isexactlythisscenario.
Thoughtheirclaimsmaybetrue; everyoneinphysicsiswaitingfortheothershoe
todrop. Why? becausetheyarenotrevealingalltheirprocesses.”
• “Notverysignificant; onlyrelativelyminorpatchesfornow. However, I willbe
submittingapatchforphysicalconstants, whichcouldbeusefulforeducational
purposes.”
• “I seeatrendinscientificresearchanddevelopmenttowardsopensoftwareand
materials(likeopenfreetextbooks, etc.). I seemyinvolvementinSageaspushingthattrendalittlefurther, openingupopportunitiesforeveryonetolearnand
grow.”
TheseresponsesoriginallyshowedthatalmostnobodycouldseethatwhatI wasdrivingathereisthecaseforopencomputerprograms. I haveamendedtheseanswers
withthoseonesI receivedinthefollow-up. Indeed, itwasthelackoffeedbackonthis
point, apointI seeascrucialtotheoverallscopeofthisthesis, thatmotivatedmeto
solicitclarificationintheformofacoupleoffollow-upquestions. Asyoucanseethe
epistemologicalconcernsthatI raiseinsubsection(4.4.4)arenotanissueforusersand
developersofmathematicalsoftware–pragmaticconcernsaretheoverridingfactors.
Speakingaboutfurtherviewsandopinionstheywouldliketosharewiththeworldregardingalloftheabove –
Nobodyhadanythingfurthertocontribute.
SpeakingaboutwhetherthereisanythingthatI amnotaskingthatyouthinkI should
beasking –
Againthewaslittleinthewayofaresponseexceptforthehelpful, “Sure, youcouldask,
«Whatdoyouthinkmathsoftwareshouldlooklikeinthefuture?»and, «Howmight
wegetfromheretothere?»”ThisI thinkisveryforwardlooking, andI includeditinmy
follow-upquestions.
5.2.3
Follow-upquestionstoopensourcequestionnaire
Speakingaboutwhattheythinkmathsoftwareshouldlooklikeinthefuture. How
mightwegetfromheretothere? –
• “Usuallypeoplewhoconsiderspendingalargepartoftheirtimewritingsoftwarealsohavetofindawaytopayforfood, clothing, shelter. Nowitcouldbe
thatthereareenoughpeoplewhowillwriteprograms, free, butwilltheybethe
bestequippedtodoagoodjob? Maybesomeacademics, whosepayissomehow
relatedtoresearchgrants, papers, etc. Asyoumayrealize, theVAST majority
offreesoftwareisbuggy, ill-designedjunk. Thereareafewexceptions, butthey
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arerare. Therearewhat500,000”apps”foriphone? Howmanyprogramson
sourceforge? I thinkitisfairtoexpectthatmostopensourcemathprograms
(i.e. user-contributed)willbelessthanfullyprofessional. (i.e. debugged, tested,
documented, efficient, robust, etc.)”
• “Asregardswhatmathematicssoftwareshouldlooklikeinthefuture, I don’thave
astrongopinion. I thinkpartofwhatmakesSagealivelylocusofactivity(which
ispartofitsvalue, aswellasbeingpartofwhatmakesitfun)isthatthereisalotof
roomforpeopletojumpinandhelp, andI’mcuriouswhetherthatwillcontinue
indefinitely. Atsomepoint, perhapsthesensethattherearesimpleanduseful
additionswaitingtobemadewilldiminish–soparadoxically, improvementsto
thesoftwaremayleadtoitsbecominglessusefulasacollaborativeproject.”
• “Itshouldbeaseasytouseasapencil&paper, forindividualprojects; orachalk
boardforcollaborativeprojects. Itshouldbecompletelyintegratedintographics
productiontoolssothat”seeing”theresultsisassimpleashittingthegraphing
functiononaspreadsheet.
Farbetterinputtoolsthatworkinaubiquitousmanner; touchscreensthatuse
standardmathnotation(orotherstandardnotation; chemical, electrical, etc. )
forallareasofscience. Perhapsgridmapped’workpads’withasimpledrag&
dropprocessforstandardnotation, sothatwecanputonthedisplayexactlywhat
wewouldputonpaper.... Wearecurrently’makingthewagonpullthehorse’:
i.e. weusershaveto’learn’awholeprogramminglanguagejusttobeabletoget
thecomputertoprint/displaymathsymbols. Learningadvancedmathisthough
enough. Usingitpurposefullyisthechallenge. Spendingalotofextraefforton
gettingacomputertodisplaywhatwearesayingisjuststupid. Theyaretools
andshouldbeuseful.”
Whatcanbeseenhereisthatthereisadesireamongdevelopersandusertoseethe
computerdisplaymimicthedomainspecificnotationalreadyacquiredontheroadto
masteringsomediscipline. Itisseenthatthebuilt-inlanguageofthemathematicalsoftwarepackageisyetanotherthingtolearn, anobstaclethatgetsinthewayofdoing
usefulwork. Someexpresshopethatthisbarrierwillbeovercome, somearefarless
optimistic.
5.3
Theproprietaryworld
5.3.1
Lead-uptoproprietaryquestionnaire
AspartofthisthesisI wasabletocontactpeoplewhoareinvolvedwithcommercial
software. Thiswasenabledbyoneofmysupervisors, theveryhelpfulandsupportive
KristófFenyvesi. Overthecourseof2days, onthe14th and15th ofDecemberI received
ten responses. One of these responses was too casual, uninformative and expletiveriddentobetakenseriously. Sonineintotalthen. Thisisslightlymorethanthesurvey
I distributedtotheSagecommunitytowhich, asI say, I receivedsevenresponsesin
total.
AsI saidbefore, butitisworthreiteratingit:
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Thepublicsurfaceofacommercialpieceofsoftwareislimitedtotheproductitself; thesemi-facelesscorporationbehindtheproduct; themarketing, publicrelations,
andadvertisingspendofthecorporation; thetechnicalsupport; thetrade-showbooths;
andnowadaysthecorporatewebsitewhichcanserveasatechnicalpointofcontactor
merelyasanelectronicbrochure.
Corporationsextractwealthfromsoftwarebytreating, andthismayseemobvious, the
expressionofthesoftwareasaproduct–thatistosaycommercialproperty. Intheera
ofshrink-wrappedsoftwarethisisenabledbythedualnatureofsoftwareitself. A deliberatewithholdingofthesourceisperformedinordertosafeguardthebinaryproduct,
theideabeingthatthiscorporationhasamonopolyonthesourceandcorresponding
buildsystem, themethodologyofturningthatsourceintoabinaryblob. Thisiswhy
thetermproprietarysoftwareisapt, andnotthetermcommercial. Itisplainasdaythat
inverseofcommercialisnon-commercial, andwhereasmanysmallFOSS projectshave
verylittleturnover, mostFOSS projectshaveacommercialaspecttothemevenifthey
arenon-profits. Tothinkotherwiseistoelidethecommercialactwiththecapitalistic
act.
Manycommercialentitiesstructuretheirbusinessesinsuchawayastowithholda
pieceofinformation. Onecanthinkofpharmaceuticals, onecanthinkofbrewing, one
canthinkofmanyareas. Inthetransitiontothedigitalworldtherulesandregulations
thatboundthematerialworldwereslowlyreworkedforthedigitalworld. Thuswe
havecopyrightpreviouslyappliedtotextnowbeingappliedtosourcecode, wehave
therubricintellectualproperty, wehavepatentsnowapplyingtointangibleobjects.
Theeffectistocreatewhatsomepeople[citation]viewasan artificial scarcity.
ThepublicsurfaceofaFOSS projectdiffersconsiderablyfromthatofacommercial
pieceofsoftware. Whereasbydefinitiontheactivityonacommercialprojecttakesplace
behindcloseddoorstheactivityinaFOSS projectcanexhibitvaryinglevelsofopenness
andtransparency. Theremaybechatroomswheredevelopersand/orusershangout.
Theremaybepublicmailinglists. Theremaybeawikiorablog, theremaybeabug
andfeaturetracker. Infact, mostFOSS projectshavealltheseavenuesofinteraction
andmore. Producersofproprietarysoftwarehavethesepathwaysofinteractionaswell
but they are internal to the corporation that owns the piece of proprietary software.
FOSS projectsdonotneedtheseavenuesbuttonothavethemissortofanathemato
theideologythatmotivatespeopletoengageinthismodeofsoftwaredevelopment.
Thisisalltosaythatthepublicpersonaofacorporationisbrochure-like, managed–
allimage, nevermereprocess. Theirimpactontheworldbeyondtheirproductarewhat
arecalledexternalities. Thisreferstohowtheyaffectthereenvironmentbeyondthe
insertionoftheirwaresintothemarketplace. Theseexternalitiescouldbeintheareaof
pollution, politics, harmtothebiosphere, harmtothefood-chain. Thiscanbringthese
entitiesincontactwiththelegalsystemwhichbecomesonerecordofacorporations
existence.
IntheenditturnsoutthatI wasveryfortunatethattherespondentstomyproprietaryquestionnairewereemployeesofWolframResearchorusedWolframResearch’s
premierproductMathematica. Inthelightoftheprecedingparagraphitcouldbesaid
thattoknowMathematicaistoknowWolframResearch. MostoftheinformationI
providehereI haveculled, unlessotherwisestated, fromtheofficialcorporatewebsite
63
andacertainonlineencyclopædiawhichshallremainnameless. Thisinformationiseasilyaccessible, non-authoritativebutneverthelessforthepurposesofthisthesisentirely
adequate.
Theprivatecompanywasfoundedbyitsnamesake, physicsdoctorateandauthor,
StephenWolfram. Itwasfoundedin1987tocommercialiseapieceofsoftwarethat
Wolframhadbeendevelopingforanumberofyearsprior. Thisworkwasbornout
of[citation]andthisbecameMathematica. Todaythecorporationisamulti-national,
spanningatleast4countries: theUS,UK,Japan, France–ithasfourhundredplus
employees. A regularsingle-userlicenseforMathematicausedinacommercialenvironmentcosts$2495. A studentlicensescost$140. ProductslikeMicrosoftOfficeare
similarlydiscounted. Onecouldneversellacarfor$24,950foruseincommercialenvironmentbutsellstudentsthesameonefor$1,400. Itisunthinkable. Thisamazingthe
differenceincostshowsthatthecostofsoftwareisnotinthebits, atall.
Withallthatoutofthewayherethenarethetenquestions, twomorequestions
thantheFOSS group, wereasfollows:
• A :-Howlonghaveyoubeeninvolvedinmathematicalsoftware?
• B :-Whataretheprojectsyouareinvolvedinandwhatareyourmainroles?
• C :-Whatisyourbackgroundandwhatmotivatedyoutobecomeinvolvedmathematicalsoftware?
• D :-Whatisyouropinionoffreeandopensourcesoftware(FOSS) mathematical
tools? Doyouuseany?
• E :-DoyouhaveanyopinionontheadvantagesordisadvantagesofFOSS mathematicaltoolsandhowtheyrelatetoproprietarytools?
• F :-Whatisyouropinionaboutcopyright, softwarepatents, theGPL andfree
softwarelicensesingeneral?
• G :-Inthebroadarcofscientificresearchanddevelopment, wheredoyouseethe
placeofmathematicalsoftware?
• H :-Inthedevelopmentofthearts, wheredoyouseetheplaceofmathematical
software?
• J :-Arethereanyotherviewsandopinionsyouwouldliketosharewiththeworld
regardingthesetopics: considerthisyoursoapbox.
• K :-IsthereanythingI amnotaskingthatyouthinkI shouldbeasking?
Asbefore, inadditiontotheseriesofquestionsI askedtherespondentstoprovideme
withanameorpseudonym(ortoleavethisfieldblankiftheywishedanonymity)andto
providemewithdetailssuchas: emailaddress, website, nationality, nativelanguage,
profession, presentoccupation, presentposition, employer. Itwasonlyafterallthese
piecesofinformationwererequestedthatI askediftherewas Anyother(personal)informationthatyoufeelmightbeofrelevance. IncontrasttotheSageprojectthetarget
64
groupwasnotwelldefinedandconsistedonlyofpeopleI couldreachthroughmysupervisor. However, thisisnotamajorproblemasI initiallyhadonlyhopedtosurvey
developersofopensourcemathematicalsoftwareandsoonecouldconsiderthissecond
groupofrespondentsasbonusdata. HereisarundownoftheninerespondentsthatI
feltreturnedwithvalidandinterestingtalkingpoints.
Takingthequestionsinorder.
5.3.2
Feedbacktoproprietaryquestionnaire
Speakingaboutthelengthofinvolvementinandaroundmathematicalsoftware –
Bartwowhohadlessthan5yearsdirectinvolvementinmathematicalsoftware. All
respondentshadmultipledecadesofinvolvement, wearetalkingaboutclaimsof18, 20,
30, and35years. Thismeansthatthesepeoplehaveseenhowthissoftwarehasevolved
withtheintroductionofthemicrocomputerandtheinternet.
Speakingabouttheprojectsandtherespondents’mainroles –
• educator: “CAD toolsforcircuitlayoutCAD toolsforconceptualphaseofarchitectureCAD toolsformachiningmechanicalpartsCAD toolsforgeometrical
sculptureMathematicalvisualizationmodels”
• user/engineer: “MathematicalgraphicsandanimationwiththeprogramWolframmathematica”
• educator: “I aminvolvedinteachingregularlytheseprograms:
DERIVE,PHASER,useofEXCEL todomathematicalcalculations, recently
Mathematicaforstudentsofmathematics, physics, engineering, economics, cognitivescienceetc. I alsousetheminapplicationsandresearch, andalsointeachingsubjectsnotdirectlyconnectedwiththem(e.g. differentialequations).”
• developer: “user interface development for Mathematica, primarily interactive
graphics”
• datacurator: “oilrigdata-catalogdatakeyboarddata-catalogdataquasicrystals
-computingaperiodiclattices”
• developer: “Implementation and/or debugging of symbolic computation algorithms. Thisincludesfunctionalitythatistogreaterorlesserextentsapproximatenumeric, exactnumeric, or(almost)purelysymbolicinnature. Areasincludeequationsolving, linearalgebra, optimization, numbertheoryrelatedfunctions, ”classical”computeralgebra, andmore.”
• architect: “SMP:creator, architect, companyco-founderMathematica: creator,
architectandcompanyfounder&CEO Wolfram|Alpha: creator, architectand
companyfounder&CEO”
• businessperson: “CreatingmathmanipulativesandbooksforK-12educationand
creatingmathematicalart. I handleallrolesrelatedtotheseactivities.”
65
• QA:“I usefilesthatotherpeoplecreateusingmycompany’sproprietarymath
softwareproduct. I usethesefilestoprocessdata, toautomaticallygenerateunit
tests, todownloadandmanipulatesourcecode, andtomanuallyoptimizeother
aspectsofthewebproductI workon. I donotactuallydevelopsoftware, butI
understandsomecodeandhavemadechangestolegacymathsoftwarecodein
thesourcefilestofixminorissues.”
IncontrasttoSagethesepeopleliveandworkoutsidethewallsofacademia. Foralotof
themhowtheyputbreadonthetableisthroughthepracticeofsellingcraftedsoftware.
Thisdifferenceinperspectivecomesintoplaythroughoutthereplies. A goodrangeof
experienceandpositionsisrepresentedwhichbolsterstheusefulnessofthedata.
Speakingabouttherespondents’backgroundsandtheirmotivationforbecominginvolvedinmathematicalsoftware –
• science/academia: “MathandPhysics. –A strongloveforgeometry.”
• science/industry: “Educatedasamechanicalengineer. Mymajorinterestsisto
depictnaturalphenomena, includingmathematicaltheoremsandoperationof
machines.”
• mathematics/academia: “I amamathematicianbytraining, startedtoteachcomputerscienceinthenineties, andrealizedhowgoodatoolDeriveand-laterMathematicais.”
• comp sci?/industry: “I have always been interested in interactive graphics and
workedinsomefieldrelatedtothesame. I usedMathematicainmydissertation
workandthoroughlyenjoyedexploringwithit. Whentheopportunityaroseto
workforWolframResearch, I sawitasachancetocontributetoaqualitypiece
ofsoftwarethatI lovedusingmyself. I lovemathematics, butithasalwaysbeen
importanttometoconnectthemathtographicalresults. Mathematicahasgiven
methatopportunity.”
• mathematics/industry: “lotsofprogrammingatayoungage, exposuretospecializedmathematics, individualresearchTrainedasmathematicianingradschool.
Vagariesofjobmarketledmetothislineofwork.”
• science/industry: “PhysicsPhD.Wantedtohavetoolsformyownandotherpeoples’scienceandtechnology”
• science/academia: “Mytrainingandearlyprofessionalactivitieswereinsemiconductoranddeviceresearch. I haveusedmathematicalsoftwareasrequiredto
completeprofessionaltasksandtodesignproductsforK-12education. I have
alsousedmathematicalsoftwaretoaidinthedesignofmathematicalartandto
explorerecreationalmathematics.”
• science/industry: “MybackgroundisinBiologyandPhysicalAnthropology, in
whichI haveaBachelor’s(undergraduate)degree. I workedasanundergraduateassistantinaHumanBiomechanicslabandaBalanceandGaitlab. Thescientificlabexperienceandtheadvancedcomputerproficiencythatwasrequired
66
formyresearchintheselabsmademeadesirablecandidateformycurrentmath
softwarecompany, whowerelookingforpeoplefromavarietyofscientificbackgroundswhounderstoodprogrammingandcouldhelpoptimizesoftwareand
managebugfixes. TheyhiredmebeforeI evengraduatedcollege, andI was
flattered. I finishedmydegreeandhavebeenhereeversince.”
Mosthavebackgroundsinscienceormathematics, onlyonehasacomputerscience
background. Thisimpliesthatmathematicaltoolsarefartoospecialisedforordinary
softwareengineersinthemain. Takenwiththeresultsfromtheotherquestionnaire
wherealltheparticipantsareinmathematicsdepartmentsinacademiaI thinkallows
ustomaketheclaimthattheengineersofmathematicalsoftwaretoolsaredrawnfrom
asmallerpoolthanisnormalforsoftwareprojects.
SpeakingabouttheiropinionofFOSS mathematicaltoolsandwhethertheyuseany
–
• positive/doesnotuse: “Thisisagoodthing. ButI havenotpersonallyusedit.”
• none/doesnotuse: “I donotusefreesoftware, becauseI amcontentwithWolframMathematica.”
• positive/doesnotuse: “I knowsomethingaboutSage, thiswillbeathreatening
alternativetoMathematica-intenortwentyyearsfromnow.”
• negative/doesnotuse: “Veryfew. Opensourceisagreatwaytoharnesscollectiveprogrammingpower. Butit’snotthebe-all, end-allanswertotheworld’s
softwareneeds. Someprojectsrequirethecontrolandthoughtfulnessthatopen
sourcecan’tprovide. OneofthestrengthsofMathematicaisthatsince*all*ofthe
designhasgonethroughonebrain—StephenWolfram’s—itallworkstogether
verysmoothly. A systemascomplexasMathematicawouldbeamessifitwere
designedopen-source.”
• none/doesnotuse: “Someinterestbutnoexperience”
• negative/does not use: “I do not use any. My opinion is that some are good,
thoughfewarewellmaintainedoverthelonghaul. Butstablefunctionalitytends
tobewellregardedinsomeofthesetools. Thehypeabout”opensource=more
reliable”isgarbage. I refer, byandlarge, tothepaperavailableatthefollowing[44]
links[43], andtovarioustalkingpointsthathavegrownaroundthiswork.”
• none/doesuse: “Weusequiteafewsuchlibrariesinourtechnologystack”
• negative/doesnotuse: “MostFOSS toolshavelimitedcapabilities, andI have
onlyusedthemonoccasion.”
• positive/doesnotuse: “I donotuseanyopensourcemathematicaltoolsbecause
I donotuseanymathematicalsoftwareinmydailylifeotherthanatwork. I am
aproudsupporterofopensourceandfreesoftware, however, andI haveheard
verygoodthingsaboutSage.”
67
Itwouldseemthatpeopleinindustry, atleastthissmallsample, haveanoverallpositiveviewonFOSS mathematicaltoolsbutdonotappeartouseanypersonally. Some
FOSS toolsrelatedtomathematicsareusedinthetechnologystackofproprietaryproducts, presumablysuchtoolscarryaBSD licenseorsomethingsimilar.
SpeakingabouttheadvantagesordisadvantagesofFOSS mathematicaltoolsandhow
theyrelatetoproprietarytools –
• none: “Notenoughknowledgetocomment.”
• none: “n/a”
• nospecific: “I thinkthereisalevelwhichisnottoohighrequiredbypeoplewho
aresayengineers(oreconomists, chemistsetc. ifyoulike). Peoplewhostudy3-4
semestersattheuniversityandarenotspecializedinamathematicallyorcomputationallyintensivearea(suchase.gquantumchemistry). Theneedsofthese
peoplearewellfulfilledeventodaybyMaple, Mathematica, orevenDeriveor
Sage.
Peoplewhoareinterestedintheuseofprogramsinmathematical(ormathematicallyintensive)researchneedthebestprograms. ThereasonI likeMmaisthat
ithasbeenplannedmorethan20yearsagoandnotisnotaresultofpatchwork.
Anotherreasonisthatyoucanuseanyoftheprogrammingparadigms, eventhe
bestfittingonetoyourproblem.
I donotcarebugs, theywillexistforever, butalargegroupofuserswilleliminate
those.”
• “Qualityisoftensurprisinglygood, butinmyexperience, usuallyslowerthanproprietarytoolsandnotasnicelydesigned.”
• none: “Noopinion”
• “Advantages: Easiertoalterifonefindsbugsandhasthetime, inclination, and
expertisetofixthem. Canshareworkwithcolleagueswhomightnothaveit, providedthesoftwareisreadilyavailableandeasytoinstall. Easiertocontributeto, if
one(orone’sstudents)is/aresoinclined. Disadvantages: Maintenanceisgenerallynottoogreat, especiallyregardinglegacybugs. Inthisrespect, onegetswhat
onepaysfor. Interfacestendnottobetoogood. Overalldesignisoftenweak
duetopatchingtogetherworkfromvariousprojects, disparatecontributors, or
insomecases(e.g. Sage)evenentirelydifferentprograms. Itisabithardertorequestnewfunctionalityandactuallyobtainit, unlesssaidfunctionalityhappens
tobesomethingofinteresttothecurrentdevelopers. Thatistosay, the”market
place”(howsoeverconstrued)hasrelativelylessinfluencehere. Thereisagreater
chanceofprojectforking, thusdiminishingtosomeextentthechancesfordecent
codemaintenance.”
• “Theycanbegoodinprovidingwell-definedlumpsoffunctionality. Theydonot
usuallyprovidepolishedcoherentuserexperiences, orinnovateintheareaofuserlevelfunctionality.”
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• “TheprimaryadvantagetoFOSS toolsiscost. Someproprietarysoftwareistoo
expensivetojustifythecostforthemyapplications.”
• “Theadvantagesarenumerous: thetoolsarefreeandeasilyattainableviainternetdownload. Thecommunityofuserscanalsobethecommunityofdevelopers,
meaningthatthedevelopmentprocesscanfocusonwhatusersactuallyneedand
want as opposed to what some marketing team has decided will generate the
mostpublicityandrevenue. ThemaindisadvantageI haveheardaboutSagein
particularisthatitisunstableandoftencrashes. Ifopensourcesoftwarecrashes,
nooneisgoingtoloseherjobbecauseofit–thereislesspressureonthedeveloperstofixbugssincenoone’slivelihoodisaffectedbymalfunctionsorbreakage.”
WehaveheretheusualrolecallofobservationswithrespecttoFOSS:cheap, inferior
qualitytoproprietarysoftware, easiertofixintheorybutnotinpractice, dangerofforking, goodasgluecodebutnotasgoodattheuserinterfacelevel, frequentlybuggy.
Speakingaboutcopyright, softwarepatents, theGPL andfreesoftwarelicensesingeneral –
• “Freesoftwarelicensesaregreat. Thepatentsystemisbroken.”
• “n/a”
• “MaybebecauseI liveinacountrywhichdoesnotbelongtotherichestones:)?
MaybebecauseI hadtwoearlierstudentsthisweekalsowhocameforadvice
andI didn’taskthemtogotothecashierfirst-andI myselfoftenreceivesupport
fromotherpeopleinthisabsolutelyobsoleteway.”
• “Peoplehavearighttoowntheresultsoftheirprogrammingefforts... ortogive
themawayfreely.”
• “Inaperfectworld, everythingwouldbefree, butinapracticalworlditmaybe
bettertocreatesoftwareusingcommerceasameansforprogress.”
• “Copyrightofsourcecodeisfine, provideditdoesnotserveasahindrancetoindependentdevelopmentofsubstantiallysimilaralgorithms(I believecopyrights
do not cause such hindrances). Software patents are another matter entirely.
Theyseemtobe, generally, ahindrancetothe(bothfreeandcommercialmarketplace. Sufficeittosay, theseissuesaregoingthroughvariouslegalsystems
withsomeimmediacy. Onehopesthelawswillcatchupwithtechnology…The
GPL isaperversity. Theclaimisthatithelpstomakesoftwareuniversallyavailable. InactualfactitservesasamajorbarriertowhattheNSF terms”transferof
technology”. Generallythisinvolvesgoingfromseededresearchfundingtomatureprojectswithinthemarketplace. Moreoftenthannotthislatterstepisin
thecommercialsector, asthatiswherethereisagreaterlikelihoodofadoption,
maintenance, andfurtheranceof(many, thoughbynomeansall)usefulsoftware.
Generallyspeaking, freesoftwarethatisavailablebothforcommercialandnoncommercialusageisbetterpositionedtobedeployed, thusservingtheneedsof
moreusers. SoftwarelicensedasBSD isagoodexampleofsuch; itisusefulboth
infreeandcommercialdomains.”
69
• noresponse
• “I understandtheneedforpeopleandcompaniesthatdevelopsoftwaretocharge
foritinordertopayforthehoursthatgointowritingit. Copyrightsandpatents
arenecessaryinstrumentstoprotectintellectualproperty.”
• “I supporttheEFF andtheFSF andhavebeenusingLinuxathomesinceI was
ateenager. I favormodelssimilartoe.g. RedHat: opensourcesoftwarethatis
stillabletogeneraterevenueandbethemainsourceofpeople’semployment. I
understandthatthisisdifficult, butI wishitcouldbetherealityformoresoftware
initiatives.”
Asthereadercanseetherangeofopinionsondisplayeveninsuchasmallsamplesizeis
remarkable. Cuttingthroughtheextraneousgarbandweseeemotivelanguage, wesee
ideologicallanguage. Inthiswaywecanshowthatmereoutwardculturaldifferences,
thatistosaystylisticallysuperficialonescouldnotevokesuchpolarity. Theculturehas
tobesomewhatgroundedinideology. Itisthenatureofideologythatwithinanideologicalframeworkitscompetingsystemsaremutuallyhostile–thesamecannotbesaid
forcompetingcuisine, hairstyles, ordancemoves6 . ThereadercanclearlyseethedistinctionI referredtoearlier: positiveandnegativefreedoms, freedomfromsomething
versusthefreedomtosomething–hencetheriftbetweenBSD-stylelicensesandGPLstyle. Softwarepatentsareviewed, whenanopinionisexpressed, asahindrancerather
thanahelptotheindustry. Theambiguityoftheterm free inEnglishisstillanissue. As
onewouldexpectwithrespondentsfromthecommercialsector, commercialscenarios
isseenaspragmaticallydictatingreality.
Speakingaboutmathematicalsoftwareanditsplaceinrelationtothebroadarcofscientificresearchanddevelopment –
• “Atthecenter!”
• “I sharethisview: ”Fourcenturiesago, telescopeswereturnedtotheskyforthe
firsttime–andwhattheysawultimatelylaunchedmuchofmodernscience. Over
thepasttwentyyearsI havebeguntoexploreanewuniverse–thecomputational
universe–madevisiblenotbytelescopesbutbycomputers”StephenWolfram”
• “Wheremathematicsisused, mathsoftwareshouldalsobeused”
• “There’snogettingaroundthefactthatmanyscientificproblemsaremathematical, andrequiremathematicalsoftwaretoattack. Thechallengefordevelopers
istomovecloserandclosertothegoaloflettingtheuserspecifywhatsolution
isrequired, andlettingthesoftwarefigureoutthebestwaytogettoasolution.
Toomuchsoftwaretodayrequiresyoutohaveintimatetechnicalknowledgeto
makeanyprogress.
6 Howdoesthisrelatetothetribalaspectsexhibitedwithincultures, forexamplefootballrivalryandthe
like? Oddlyenoughthiscouldbeasortofstrivingforgroupidentitywithinaseaofundifferentiatedsameness
–atleastideologiesprovidereasons, tribalismprovidesonlyonereason–thisplacerathertheotherplace.
70
I agree[…]thatworkingcodeshouldbesuppliedwithscientificarticleswheneverpossible. (Ironically, I findrefereescomplainingwhenI putactualcodein
mysubmissions. SinceI believeitbelongswiththework, I havelearnedtoisolateitinanappendix.)
Myopinionisthatifresearchisfundedbyone’shomeinstitution, thenitgets
tomaketherulesregardingwhatisproprietary. Ifitisfromtaxpayerfunds, I’d
ratherseeguidelinesthatareinthedirectionofeasylicensinganddissemination
of actual code (I have indeed raised this issue with one such funding agency).
I donotparticularlylikethethoughtthatsubmissionsunaccompaniedbycode
(e.g. becauseitisproprietary)mightfacediscriminationintermsofacceptance
forpublication. […]Myreasoningisthis. I seequiteafewarticlesinplaceslike
CommunicationsoftheACM,writtenbyresearchersfromindustry(Yahoo, Microsoft, Google, and elsewhere), that are interesting but touch on proprietary
work. I vastlypreferhavingsucharticlespublished, sanscode, tonothavingthem
atall.”
• “itbelongseverywhere, butnotallthetime.”
• “Numeric software is pervasive. Likewise statistical software. Both are likely
togrowinimportanceas”bigdata”becomesmoreintegraltoscienceandsocial
sciences. Symboliccomputationis, atpresent, moreofaniche. Itisstartingtosee
widerusageinthesciences, technology, engineering, etc. Butitisbynomeans
usedtothesameextentasstatsandothernumericalsoftware. Ofcoursethis
couldchangeovertime, andindeedtherehasbeenaslowbutsteadyriseinusage
ofexactand/orsymbolicmethods.”
• noresponse
• “Muchresearchanddevelopmentisexperimentalinnatureanddoesn’trequire
sophisticatedmathsoftware. However, muchofitdoesrequiremodelingthat
needssophisticatedtools. Inmostofthesecases, atleastintheUSA,acompany
orresearchinstitutionisbehindthework, andthefundsareavailabletopurchase
software.”
• “Mathisthefoundationofeveryscientificdiscipline. I haveneverworkedonaresearchproject, eveninanthropology(whichpeopleerroneouslyassumeisalways
a”soft”science–notsowithphysicalanthro!) thatdidnotmakeextensiveuse
ofmathematicalsoftware. Oncethestudyisproposedandthefundingsecured,
thedataisgathered. Oncethedataisgathered, thedataisprocessedwithmath
software. Thisprocessingconstitutessometimes70-80%ofthetimespentonan
entireresearchproject. Mathsoftwaresitsattheverycoreofmodernresearch.”
Without a doubt, the ability to perceive the role that mathematics and by extension
mathematicalsoftwareplaysintheshapingoftheworldbutatthesametimenotto
graspthefactthatadegreeoftransparencyisnecessaryforthefullbenefitsofthisshapingtobeaccruedbyeveryoneisafunctionofideologicalandculturalbias.
Speakingaboutmathematicalsoftwareanditsplaceinrelationtothedevelopmentof
thearts –
71
• “Onenewpowerfulandflexibletooltocomplementothermeansofcreatingart.”
• “ThereisacategorycalledMathematicalArt, butI thinknicepicturesthemselves
arenotart.”
• “Animation, filmmaking, perhapsalsopainting, (textile)design”
• “Nowthatcomputinghasmademathematicsaccessibleandemployable, there
areenormouspossibilitiesinthearts. Inarchitecture, forexample, theavailabilityofmathematicalcomputinghasopenedupnewformalworldsthatwerepreviouslyinaccessible. Therehasbeenanexplosionofnewarchitecturalformsthat
willonlyaccelerateinthefuture.”
• “It’smoreabouttheartistthanthecomputer. Whatistheplaceofacrylicpaintin
thedevelopmentofthearts?”
• “I donothaveagreatfeelforthis. I canonlysaythatI haveseenfantasticcreations
ingraphicsand, toalesserextent, sculpture, thatwerecreatedprimarilyusing
mathematicalsoftware.”
• noresponse
• “Inthevisualarts, theareaI’mmostfamiliarwith, theuseofmathsoftwareallows
thecreationofnewanduniquedesignsandforms. Forsometwo-dimensionaldesigns, mathsoftwareisneeded, butalotcanbedonewithnon-math-specificsoftwaresuchasIllustratorandPhotoShop. Forthree-dimensionaldesigns, mathspecificsoftwareisoftenessential.”
• “Thereislittlegeneralinterestinmathematicalart, althoughI personallyfindit
fascinatingwhatbeautifulcreationspeoplelikeMichaelTrottandIgorBakshee
havebeenabletoassembleusingMathematica. Intheartworld, though, I don’t
getthesensethatthismediumisrespected. Perhapsitisbecausethemediumof
mathematicalandcomputerbasedartistoonewstilltotheartisticcommunity.
I wishtosharetheobservationthatofthepeoplewhogenuinelydoappreciate
andadmiremathsoftwarebasedart, thevastmajorityaremathematiciansand
scientistsratherthanartists.”
Theanalogywithapreviousmediumdoesn’thold. AsI havearguedforelsewhere–
I donotseethecomputerasamedium, ratherduetothenatureofthedigitalI see
itasamediumofmediums–similarlytheinternetisnotjustanetwork, whatmakes
theinternetdifferentfromwhatprecededitisthatitisanetworkofnetworks. This
isarecursivenessisakeyfeatureofcyberneticsystems. Nootherman-mademedium
heretoforehasexhibitedthisself-referentialnaturesofluidlyasdoesthedigital. Otherwisetheseopinionsspeaktotheongoingslow-burningrevolutioninart, design, and
architecture. Theimpactofcomputersandmathsandengineeringsoftwareonarchitecturewouldbeathesisuntoitself. Itisinterestingthattheideaoftheauthenticity
ofartisquestionedbecauseofthismechanicalintervention, weshouldviewthisasan
opportunityratherthanwithcaution.
72
Speakingaboutwhethertheyhadanyviewsandopinionsthattheywouldliketoshare
withtheworldregardinganyoftheabove –
• “Goodcomputerprogramscanbeanamplifierofone’screativity.”
• “Inspiteofthemanybenefitsofusingcomputers, disassociateyourselfasmuch
aspossiblefromusingthem.”
• “AtthemomentI wouldonlycompareMathematicawithSage, alltheotherprogramsaremuchlessrelevant. (Exceptveryspecializedfields, likeGAP forgroup
theorists.) Wolphram|AlphaandtheplainlanguageinputtoMathematicaisalso
agreatsteptotheHolyGrailofartificialintelligence. I appreciategoogle’sGraph
function.”
• “Archimedean principle: Math and Science tools should not be used for War
computations. Ifpeoplewanttoparticipateinwar, thentheyneedtodevelop
theirowntoolstodoso. Norshouldweteachthemhowtodevelopthesetools.”
• “Regardingtheuseofmathsoftwareinart, I finditincrediblydishearteningthat
mostartistictypesclosetheirmindstothemathematicalandthescientific. They
seescienceandartasthisirreconcilabledichotomy, whereasinreality, doesart
notexisttoexemplifyandexpressbeauty? Andwhatcouldbemorebeautiful
thantheideaofsuperstrings, ortheplotofasystemofnumbersthatrepresentthe
ratiosofpetalsizesinaflower, orafractalrepeatinginfinitely, ortheveryconcept
ofinfinityitself? Evenasimplecolumnofvaluesinaspreadsheetisbeautifulif
thosevaluesarebasedonscientificobservation. Thosenumbersrepresentour
humanneedtounderstandourplaceintheuniverse, toknowmoreofwhoand
whatweare, andI canthinkofnothingmorelovelyintheworld.”
Apartfromthesurvey-orientedresponse(thecontextualresponseshallwesay)these
repliesspeaktomarkedlydifferentaspectsofthehumanspirit: war, creativity, beauty,
dehumanisation. OnecouldsaythatageneralpointthatI havebeenattemptingto
getacrossheavy-handedlyinthisthesisismadehereforme–thefactthatthedigital
heraldsnotjustaboostinspeedbutinexpressivity. Therancoroustwoculturesdivideincontemporaryacademia(seeforinstanceC.P.Snow’s1959 TheTwoCultures
RedeLectureturnedessay[Snow, 1993])echoesthetug-of-wardichotomyexpressed
herebetweenscienceandart. Thedivideisreflectedinthenewpriesthoodroleofhigh
technologyandbigbudgetscience. Thedehumanisationanglehasbeentackledadequatelybytheoreticiansindigitalculture, mostnotablyN.KatherineHaylesforetelling
thecomingepochofposthumanity[Hayles, 1999]inherinfluentialbook, HowWeBecamePosthuman, fromtheturnofthemillennium. WitnessalsoSherryTurkleandher
recenttext[Turkle, 2011], asofthetimeofwriting, AloneTogether.
SpeakingaboutwhetherthereisanythingI amnotaskingthattheythinkI shouldbe
asking –
AsinthecaseoftheSagequestionnaireonlyonepersonrespondedtothisquestion.
However, ratherthangivingmesuggestions-thistimethepersonthankedme, intheir
73
words, “I ampleasedthatyouhaveaskedanythingatall. Mathsoftwareisusuallyseen
asanuglymeanstoatediousend–thisisthefirsttimeI haveencounteredinterestin
itasauniqueentityworthyofstudyandconsideration. Thankyou.” Inthedryand
tediousworldofacademicresearchitiswonderfultogetpositivefeedbackandencouragement. So, nodeardatum, thank you.
5.3.3
Follow-upquestionstoproprietaryquestionnaire
Speakingaboutwhattheythinkmathsoftwareshouldlooklikeinthefuture. How
mightwegetfromheretothere? –
• “I considerthefreeforminputofMmaandofwolframalphausefulformanyusers,
stillI myselfwouldpreferaformascloselytomathematicsaspossible. I amnot
interestedinfancysolutionslikevocalinputetc.”
• “(1)Itwillhaveabetternotionofwhatisfeasibleforcomputations, howlong
theymighttake, andsomeabilitytoletusersknowinadvance. (2)Morenaturallanguage(written), handwriting, andspeechrecognitioninputcapabilities.
Notethatsomeamountofthisexistsalready. (3)Moredeploymentinwaysthat
usersneversee, e.g. controllingdevices(homes, cars, robots, etc.), usewithinAI
(whichinturnisseeingmoreusageincontrollingthings), andingeneralseeing
moreuseinautomatedenvironments. Sorryfortherun-onsentence. Andagain,
notethatthisalreadyishappening, thoughI expectthescaletoincreaseperhaps
vastly. (4)Developmentofmoremathlibraries, bettermaintained, moreeasily
extensible, etc. Thismaybewishfulthinkingonmypart. Probablyataminimum
willrequiremorepublic/privatepartnering. Reasonbeing, librariesdeveloped
foracademicpurposesoftengetinitialfundingbutthendonotgetwellmaintained; thereisusuallyfarlessincentivefortheoriginalauthorstoputresources
there.
Howdowegetthere? We’realreadyheadedinmostofthesedirections, though
atpresentnotsomuchitem1(it’sadifficulttaskingeneral, andthereisnotmuch
inthewayofmarketorotherpressuretoinvestresourcesinit). I seemuchofthis
assimultaneouspushingfromresearchlabs(university, government, andindustrial), andpullingfromconsumerdemand. Orisitpullingfromtheformerand
pushingfromthelatter? I cannevertell.”
• “I don’tknowthatI usemathsoftwareenoughtohavereallythoughtalotabout
howitshouldbedifferentinthefuture. I cancommentthatI woulddomore
withthree-dimensional structuresandalsomoreanimationifitwereeasierto
usesoftwareforthosetasks. I’vealwaysgotseveralthingsthatI wanttodowith
mytime, andI tendnottopursuethingsinthosecategoriesbecauseofthetime
itwouldtakebothtogetuptospeedwiththesoftwaretoolsI wouldneedand
thetimeitwouldtaketocreatethesortofthingsI wanttocreateonceI wasup
tospeed. Somaybethat’ssayingI wouldliketoseetoolsthataremoreintuitive
andeasiertouse. WhenusingMathematica, forexample, you’rebasicallywriting
code, whichisagrindforpeoplelikemethathaven’tdonealotofprogramming.”
74
Again, inkeepingwiththeanswersfromearlierwehavethedesirefortheman-machine
interfacetobemademorenatural, totakeontheformofmathematicsitselfasitisdone
withpenandpaper. Itisarguablethatthereismoreoptimismondisplayherefrom
thosethatchosetoreplytothefollow-up. Itwasdisappointingandhurtthesolidity
ofthedatathatwhileanumberofpeopleagreedtoansweracoupleofmorequestions
(outofthisgroup)onlythreedid.
5.4
Results
I havebeenscrutinisingtheindividualresponses(takingananalyticapproach)enroute
sonowisthetimetodrawsomegeneralconclusionsfromtheresponsestakenasawhole
(syntheticapproach).
Theimpressiononegetsisthatengineers, lecturersandscientistsgenerallytake
a pragmatic approach to software – this means that they will reach for the tool that
doesthebestjob. Therearethosewhoareobviouslypassionateaboutopen-source
mathematicaltoolsbutgiventhesizeoftheentireecosystem(Linux, BSD,LibreOffice,
Firefox, mostrecentlyandnotablyAndroid, ...) mysuspicionshavebeenconfirmed
thattheentireopen-sourcemathematicaltoolssectorisunderdevelopedvis-à-vistheits
proprietarycounterpartandlagstheecosystemasawhole.
Regardingoverlap. Itwouldappearthereareveryfewexclusiveusersofeitherproprietaryorfreesoftware. ItappearsthatmostcontributorstotheSageprojecttryto
pushthingsforwardsothatthererelianceonproprietarysoftwareisdiminished. Allof
theartistsuseproprietarytoolstotheextentthatoneartistevendevelopsproprietary
customsoftware–I amnotsurehowmuchofanissuethisisfortheartisticcommunity.
Certainlyepistemologicalconcernsarenotasimportant.
Almostnorespondentfromeithercamphasthoughtofthebigpicturequestion
abouttheuseofmathematicaltoolsdeeplyconnectedwiththearcofscientificprogress,
infactmostmisunderstoodmyquestion.
5.5
WhatI learntaboutposingsurveys
Askforonlyonepieceofinformationineachquestion. Doaskwhatformaleducation
thepersonhasreceived, ifany. Whenaskingaboutsoftwareaskaboutthenamesof
theindividualsoftwarepackagesused, notvaguemarkerslikeprojectsorcategories.
Doaskwhetherornotitisokaytocontactthepersonforfollow-uporclarifyinginformationiftheyhaveleftanemailaddress. Dostatethattheresearchisseriousandthat
casualanswersarenotappreciated. Ifyouaskpeopletovolunteeranyfurtherpersonal
informationtheywillnot.
75
6
Summaryofresultsandconclusion
Thefinalpartofthethesisistohand. Nowisthetimetorecap. Itisanunenviabletask
todisentanglemathematicsfromitssurroundings, fromtheworldarounditsotospeak.
Thesameobservationholdstruewhenwespeakofthedigitalworld. Mathematicsis
inexorablyinterwovenwiththewayofhumanlifeanditscyberneticsubsetthedigital
humanlife. Butlikenearlyeverystoryconcerningtheartefactsofcontemporarylife
mathematics(beitthepractice, educationorapplication)hasitselfinturnbeenaltered
bytheimpactofthedigitalworldactingonit. Thisthesishasfocusedonsomeofthose
alterations.
A wordabouttools: thetraditionaltoolsofthemanipulatorofmathematicshas
beenprimarilythepenandpaper.TherehavebeenmechanicalaidssuchasthecompassandT-square, thesetsquare, thetallystick, theabacus, therulerandthesliderule. Thesehavebeeneclipsedbyelectroniccomputation. Themanipulatorsofmathematics, I amthinkinghereofeducators, researchers(mathematicians, thosewhodeal
solelyinmathematics), engineers, actuaries, statisticians, artists, architects, thesemultipleanddiversefieldsalongwiththeordinaryandeverydayuserofelectroniccalculators
havebenefitedfromthecomputerisationofmathematics.
Mathematicaltoolsastheyexistinadigitalworldismathematicalsoftware. With
thatinmindthisthesishaslookedatmathematicalsoftwarefromanumberoforthodox
angles.
I haveassembledthevariouspartsofthisthesistogivesomeunifyingstructureto
thetotalityofthisthesis. Thewordmathematicshasadoublemeaningrenderingits
usetobeambiguousattimes. (InEnglishatleast)itreferstoasharedformallanguage
andadiscipline. Contrastthiswithothersimilarwordsthatreferpurelytoadiscipline,
likebiologyforinstance. Unlessthisdistinctioniskeptinmindsomeconfusionshall
arise. ItmustbestressedthatinthisthesisI refertomathematicsthediscipline, which
iswhyI speakofpractice, educationandapplication.
Insection(3)I havetriedtotouchonhowthepracticeandapplicationofmathematicshasbeenaffectedbymathematicshavinggonedigitalbytakingalookatthat
intersection, atmathematicalsoftwarethatistosay. WithrespecttothepracticeI have
delineatedontheonehandthegrowingdependenceoncoremathematicsoncomputationalproofsandontheotherofdigitalimagingbeinganimmediateaidinthevisual
explorationofmathematicallandscapes. HighlightedalsowasthecoalescenceofcomplexsystemsaroundpackagescalledCAS,computeralgebrasystems. Thesepackages
wouldbetakenupagaininsection(5)inmoredetail. WithrespecttoapplicationajourneywastakenintheworldofmathematicalartandindoingsoI attemptedtoplacethis
fieldalonganorganiccontinuumofsorts–thisisnowtheexplorationofvisualspace
itselfwiththeaidofmathematics.
Insection(4)thefocuswasturnedonasubjectthathasaremarkablysparsecorpus
inthefieldofdigitalhumanities(WendyChunexcepted). I havegivenaveryclinical
legal-historicalaccountofcopyrightandthenshowedhowtheissuesoftheintegrityand
paternityoftheworkandhowtheissuessurroundingthecommonshastakenonanew
lifeintherealmofsoftwaredevelopment. Personalandprivateinterestsconflictwith
thesocialrequirementofsomesortofdigitalcommons. MovingfromthehistoricalI
attackedtheproblemspacefromanumberofangles, theseanglesasI havementioned
76
afewtimesnoware: epistemological, legal, ethical/pragmatic, economic.
Buildingonstrandsofstudyfrombothsection(3)and(4)I wasfinallyabletosituate
thequestionnairesinthetheoreticalcontextoftheprevioussections. Thesequestionnaires, directedatbothopen-sourceandproprietaryactors, alongwithanintroduction
andcritiqueofeachofthetypeofsoftwareusedbytheseactorsroundedoutthemeat
ofthethesis. TheapproachI tookwastointerweavetheactualresponsesthemselves
witharunningcommentaryfollowedbyahigh-levelsummary.
6.1
Brieffinishingremark
Someofthegoalsofthisthesishavebeenmet, othershavenot. Inthefirstcaseanadequatepictureofthelandscapeofmathematicalsoftwarehasbeengiven. Inthesecond
thoughthevarioustopicsarelinkedbymathematicalsoftware, andthoughthedisciplineofdigitalcultureanchorsallthatgoesoninthesepagesitwouldperhapsbeen
wisertochooseanarrowersubject-matterandtopursuethatindepth.
I believethatI haveshownthatitispossibletogroundthestudyofdigitalculture
andthedigitalhumanitiesinamodeoflearningthatismorefocusedonthestuffofthe
digitalbothpracticalandtheoreticalthanisthenormatthemoment. I believethatthis
meansteachingthefundamentalsofhardwareandsoftware, understandingsoftware
developmentmethods, creatingbridgestothosedisciplinesthatareviewedasbeenon
thesciencessideofthefenceratherthanthehumanities. Inevitablysocietyitselfwill
enforcethesechangessoitwouldbebetterifthechangecamefromwithinacademia
thanwithout.
77
7
Endnotesandcitations
A thingisfunnywhenitupsetstheestablishedorder.
Everyjokeisatinyrevolution.
GeorgeOrwell, Funny, butnotVulgar7
Theendnotesareintheordertheyappearinthebodyofthetext. Thereferences
andcitationsinthefollowingsubsectionarelistedhereinalphabeticalorder–theyear
inbracketsistheoriginalyearofpublicationintheoriginallanguage. I havealsosuppliedthepublicationyearofthecopy/editionthatI haveaccessed. I haveattempted
toincludethetranslatorandtheyearoffirstpublicationinEnglishfortextsthatwere
originallypublishedinalanguageotherthanEnglish. Thesereferencesaregenerated
automaticallybythedastardlycombinationofRefWorks, JabRefandBibTEX (using
LYX); andtheformatisAPA-like.
Standardlegaleseboilerplate: all(registered)trademarksandlogosaretheproperty
oftheirrespectiveowners.
7 http://www.tinyrevolution.com/mt/archives/000006.html
78
Endnotes
[1] Publicdomaintext.ModernHistorySourcebook: ImmanuelKant: WhatisEnlightenment? (1784):
http://www.fordham.edu/halsall/mod/kant-whatis.asp
[2] Theworldin2011courtesyoftheInternationalTelecommunicationUnion:
http://www.itu.int/ITU-D/ict/facts/2011/material/ICTFactsFigures2011.pdf
[3] “HeisreportedtohavefirstsaidthisinaninterviewonFreshAir, NPR (31August
1993)”, asreportedby:
http://en.wikiquote.org/wiki/William_Gibson
[4] MarkkuEskelinen&RaineKoskimaa, Introduction:
http://cybertext.hum.jyu.fi/articles/19.pdf
[5] In TheTheaterandItsDouble.“Discussingthe”mysteriousidentityofessence
betweenalchemyandthetheater,”Artaudarguedthatthetheatercreatesavirtual
reality– ”laréalitévirtuelle” –inwhichcharacters, objectsandimagestakeonthe
phantasmagoricforceofalchemy’svisionaryinternaldramas.”
http://fusionanomaly.net/antoninartaud.html
[6] ThehomepageoftheLATEX softwareproject, atypicaltypesettingtool:
http://www.latex-project.org
[7] ThehomepageofWolframMathworld, curatedbyEricWeisstein:
http://mathworld.wolfram.com
[8] FromanexchangewithDianaHarrelson, PhD StudentinHumanComputerInteraction, whosharedaPDF ofherPhD,FedoraPracticum, withme:
http://www.cyber-anthro.com/
[9] Jyväskyläuniversityhostsawebsitededicatedtoresearchmethods, bothqualitativeandquantitative:
https://koppa.jyu.fi/avoimet/hum/menetelmapolkuja/en
[10] ThehomepageforMicrosoftWord, atypicalwordprocessingtool:
http://www.microsoft.com/word
[11] ThehomepageforAdobeInDesign, atypicaldesktoppublishingtool:
http://www.adobe.com/products/indesign.html
[12] ThehomepageofBenojt, afractalexplorationtool:
http://benojt.inner-space.de
[13] Thehomepagefor3DAttractors, aMacapplication:
http://amath.colorado.edu/faculty/juanga/3DAttractors.html
79
[14] FourColurTheorem, overviews:
http://en.wikipedia.org/wiki/Four_color_theorem
http://people.math.gatech.edu/∼thomas/FC/
http://mathworld.wolfram.com/Four-ColorTheorem.html
[15] MATLAB,aprogrammingenvironmentforalgorithmdevelopment, dataanalysis, visualization, andnumericalcomputation:
http://www.mathworks.co.uk/products/matlab/
[16] Magma, acomputationalalgebrasystem:
http://magma.maths.usyd.edu.au/magma/
[17] : Maple, mathematicalcomputationengine:
http://www.maplesoft.com/products/Maple/index.aspx
[18] Mathematica, anapplicationforcomputations:
http://www.wolfram.com/mathematica/
[19] ComprehensivetabulatedonlineresourcebyFreekWiedijkofsoftwarerealtedto
mathematicsinsomeway:
http://www.cs.ru.nl/∼freek/digimath/
[20] REDUCE:TheFirstFortyYears:
http://reduce-algebra.com/reduce40.pdf
[21] H.-O.Peitgen, H.Jürgens, D.Saupe, C.Zahlten, Fractals–AnAnimatedDiscussion, Videofilm, Freeman1990
[22] H.vonKoch, Surunecourbecontinuesanstangente, obtenueparuneconstructiongéometriqueélémentaire, ArkivförMatematik1(1904)681-704.AnotherarticleisH.vonKoch, Uneméthodegéométriqueélémentairepourl’étudedecertainesquestionsdelathéoriedescourbesplanes, ActaMathematica30(1906)145174.
[23] D.Hilbert: ÜberdiestetigeAbbildungeinerLinieaufeinFlächenstück. MathematischeAnnalen38(1891), 459–460.
[24] G.Peano: Surunecourbe, quiremplittouteuneaireplane. MathematischeAnnalen36(1890), 157–160.
[25] “IntibetanBuddhismtheKalachakraMandalaisacosmographicrepresentation
oftheinner, outer, andalternativedimensionsofreality.TheBodyMandalais
surroundedbycrescent-shapedareas, whicharetheofferinggrounds.Nextfollow
circleswhichrepresenttheelements: earth(yellow), water(white), fire(pink/red),
wind(gray/black)andspace(green).Theoutermostcircleisthe”GreatProtective
Circle”, ”MountainofFlames”or”CircleofWisdom”whichrepresentsthewisdom
element.ThedifferentlycoloredareasrepresentthefiveWisdomsoftheBuddha
intheformofarainbow.PicturetakefromaKalachakraMandalatankainKathmandu”
http://michel8170.deviantart.com/art/Kalachakra-Mandala-79844211
80
[26] ManRay-InterviewinCamera(Paris; reprintedin”ManRay: Photographer”,
ed.byPhilippeSers, 1981).
[27] GiovannaDiRosario«OntheSurfaceofAlephNull», presentedattheconference
AndNowFestival2012, 6-10June2012, UniversityofLaSorbonne.
[28] “3D MandelbulbRayTracer: Mandelbulbsareanewclassof3D Mandelbrotfractals.Unlikemanyother3D fractalstheMandelbulbcontinuestorevealfinerdetails
thecloseryoulook.”
http://www.subblue.com/projects/mandelbulb
[29] Explanationwhytheterm intellectualpropertyrights mightbeilladvised–GNU
website:
http://www.gnu.org/philosophy/not-ipr.html
[30] VideotalkonHyde’sbookCommonasAir:
http://cyber.law.harvard.edu/interactive/events/2011/hyde
[31] Line54, “Astobuywater, orwind, orwit, orfirethefourth:/ThesefourtheFather
ofHeavenmadetothisfoldincommon:
http://www.ancientgroove.co.uk/books/PiersPlowman.pdf
[32] Whatisfreesoftware?
http://www.gnu.org/philosophy/free-sw.html
[33] Codecannotbestolen, areviewbyZDNet:
http://www.zdnet.com/blog/btl/code-not-physical-property-court-rules-ingoldman-sachs-espionage-case/73984
[34] Original link: http://www.suntimes.com/output/tech/cst-fin-micro01.html unretrievable.QuotebySteveBallmer, CEO ofMicrosoftCorporationfrom2001in
theChicagoSunTimes–unsurprisingasMicrosoftis the leadingproprietarysoftwarecompanywiththemosttoloseasfreesoftwaregains:
http://www.linuxjournal.com/article/5007
[35] WebsiteaddressoftheSagemathpresskit:
http://www.sagemath.org/library-press.html
[36] OnlinehelpvideoforSage:
http://www.sagemath.org/help-video.html
[37] OnlineresourceofSagelibrarypublications:
http://www.sagemath.org/library-publications.html#books
[38] (PARI) Wikipediapage:
http://en.wikipedia.org/wiki/PARI/GP
[39] (GAP) Wikipediapage:
http://en.wikipedia.org/wiki/GAP_computer_algebra_system
81
[40] ThesesoftwarepackagesareusedbySage:
http://www.sagemath.org/links-components.html
[41] OnlineresourcefordevelopersnewtoSage:
http://www.sagemath.org/doc/developer/
[42] Switching from Word Perfect to Word 2000 – Microsoft Corporation online
help:
http://office.microsoft.com/en-us/office-2000-resource-kit/migration-guides-foroffice-2000-HA001138391.aspx
[43] OscasNSF whitepaper(PDF) onlineresource:
http://sage.math.washington.edu/home/wdj/.../oscas-nsf-white-paper12.pdf
[44] OscasNSF whitepaper(TEX) onlineresource:
http://wdjoyner.com/writing/research/oscas-nsf-white-paper12.tex
82
Citations
[Enc, 1982a] (1982a). Art, theory of. In New Encyclopædia Britannica, volume 2.
Chicago, 15thedition.
[Enc, 1982b] (1982b). Tragedy.
Chicago, 15thedition.
In New Encyclopædia Britannica, volume 18.
[Enc, 1982c] (1982c). Wasillykandinsky. InNewEncyclopædiaBritannica, volume 2.
Chicago, 15thedition.
[Aarseth, 1997] Aarseth, E. J.(1997). Cybertext: PerspectivesonErgodicLiterature.
TheJohnsHopkinsUniversityPress.
[Benkler, 2006] Benkler, Y.(2006). WealthofNetworks: HowSocialProduction
TransformsMarketsandFreedomContract: FreedomintheCommons. YaleUniversityPress, NewHaven, CT,USA.
[Bodner, 2011] Bodner, B. L.(2011). A nine-andtwelve-pointedstarpolygondesign
ofthetashkentscrolls. InSarhangi, R.andSéquin, C. H., editors, Proceedings
of Bridges 2011: Mathematics, Music, Art, Architecture, Culture, pages 147–154.
TessellationsPublishing.
[Brooks, 1995] Brooks, F. P.(1995). Themythicalman-month: essaysonsoftwareengineering. Addison-Wesley, Reading, Mass., anniversaryedition.
[Burns, 2011] Burns, A.(2011). Theartofcomplexflowdiagrams. InSarhangi, R.
andSéquin, C. H., editors, ProceedingsofBridges2011: Mathematics, Music, Art,
Architecture, Culture, pages51–58.TessellationsPublishing.
[Calude, 2000] Calude, A. S.(2000). Thejourneyofthefourcolourtheoremthrough
time.
[DenzinandLincoln, 2005] Denzin, N. K. and Lincoln, Y. S., editors (2005). The
Sagehandbookofqualitativeresearch. Sage, ThousandOaks, Calif., thirdedition.
editors: NormanK.Denzin, YvonnaS.Lincoln.
[Foucault, 2002] Foucault, M.(2002). TheOrderofThings: AnArchaeologyofthe
HumanSciences.
[Gammaet al., 1994] Gamma, E., Helm, R., Johnson, R., andVlissides, J.(1994). DesignPatterns: ElementsofReusableObject-orientedSoftware.
[Gere, 2002] Gere, C.(2002). DigitalCulture. ReaktionBooks.
[Ghezziet al., 2002] Ghezzi, C., Jazayeri, M., andMandrioli, D.(2002). FundamentalsofSoftwareEngineering. PrenticeHall, EnglewoodCliffs, N.J., secondedition.
[Guba, 1990] Guba, E. G., editor(1990). TheParadigmDialog. SagePublications,
Inc.
83
[Hardy, 1940] Hardy, G. H.(1940). A mathematician’sapology. attheUniversity
Press, Cambridge. byG.H.Hardy.
[Hayles, 1999] Hayles, N. K.(1999). HowWeBecamePosthuman: VirtualBodiesin
Cybernetics, Literature, andInformatics. UniversityOfChicagoPress, firstedition.
[Hockney, 2006] Hockney, D.(2006). Secretknowledge: rediscoveringthelosttechniquesoftheoldmasters. Thames&Hudson, London, newaexpedition. David
Hockney.
[Hyde, 2011] Hyde, L.(2011). CommonasAir: Revolution, Art, andOwnership. Farrar, StrausandGiroux, firsteditionedition.
[Knuth, 2009] Knuth, D. E.(2009). TheArtofComputerProgramming. AddisonWesley, Boston, Mass.London.
[Koestler, 1959] Koestler, A.(1959). TheSleepwalkers. Hutchinson, London. IntroductionbyHerbertButterfield.
[Kurzweil, 2005] Kurzweil, R.(2005). Thesingularityisnear: whenhumanstranscend
biology. Viking, NewYork. RayKurzweil.
[Lessig, 2001] Lessig, L. (2001). Future of Ideas : The Fate of the Commons in a
ConnectedWorld. RandomHouse, Incorporated, Westminster, MD,USA. ID:
10005111.
[Lessig, 2005] Lessig, L.(2005). FreeCulture: TheNatureandFutureofCreativity.
Penguin, NY,USA.
[Lessig, 2006] Lessig, L. (2006).
Code 2.0.
http://creativecommons.org/licenses/by-sa/2.5/.
Basic Books, New York.
[Luhmann, 1982] Luhmann, N.(1982). TheDifferentiationofSociety. translatedby
StephenHolmesandCharlesLarmore.
[Lyotard, 1984] Lyotard, J.-F.(1984). ThePostmodernCondition. UniversityofMinnesotaPress, Minneapolis. translationfromtheFrenchbyGeoffBenningtonand
BrianMassumi; forewordbyFredericJameson.
[Mandelbrot, 1983] Mandelbrot, B. B.(1983). TheFractalGeometryofNature. W.
H.FreemanandCompany, NewYork, updatedandaugmentededition.
[Manovich, 2002] Manovich, L.(2002). TheLanguageofNewMedia. TheMIT
Press.
[Peitgenet al., 1992] Peitgen, H.-O., Saupe, D., andJürgens, H.(1992). Chaosand
Fractals: NewFrontiersofScience. Springer-Verlag, NewYork, Berlin, Heidelberg, London, Paris, Tokyo, HongKong, Barcelona, Budapest.
[Raymond, 2001] Raymond, E. S.(2001). TheCathedral&theBazaar. O’ReillyMedia, Sebastapol, CA,USA,revised&expandedsoftcover, january2001edition.
84
[Rosenberg, 2008] Rosenberg, S.(2008). DreaminginCode. ThreeRiversPress,
RandomHouse, Inc., NewYork, firstpaperbackedition.
[Snow, 1993] Snow, C. P.(1993). TheTwoCultures(Canto). CambridgeUniversity
Press. Redelecture: 1959.
[Steadman, 2001] Steadman, P.(2001). Vermeer’scamera: uncoveringthetruthbehindthemasterpieces. OxfordUniversityPress, Oxford. PhilipSteadman.
[Steinet al., 2011] Stein, W.et al.(2011). SageMathematicsSoftware(Version4.7.x).
TheSageDevelopmentTeam. http://www.sagemath.org.
[TorvaldsandDiamond, 2002] Torvalds, L.andDiamond, D.(2002). JustforFun:
TheStoryofanAccidentalRevolutionary. HarperBusiness: AnImprintofHarperCollinsPublishers, firstpaperbackedition.
[Tufte, 2001] Tufte, E. R. (2001). The visual display of quantitative information.
GraphicsPress, Cheshire, Conneticut, secondedition.
[Turkle, 2011] Turkle, S.(2011). AloneTogether: whyweexpectmorefromtechnology
andlessfromeachother. BasicBooks, NewYork. Hardcover.
[Vattimo, 1988] Vattimo, G.(1988). TheEndofModernity: NihilismandHermeneuticsinPostmodernCultures. PolityPress, London. GianniVattimo; translatedand
withanintroductionbyJonR.Snyder.
[Williams, 2009] Williams, S. (2009). Free as in Freedom. SoHo Books, Lexington, KY, USA, paperback edition reprint edition. reprint, 07 February 2011,
http://www.gnu.org/licenses/fdl-1.1.html.
[Wu, 2011] Wu, T.(2011). TheMasterSwitch: TheRiseandFallofInformationEmpires. AlfredA.Knopf, RandomHouse, NewYork, Toronto, tradepaperbackedition.
TheabovebibliographyiscreatedfromaBibTEX database.
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8
Appendix
Includedwiththisthesisis(1a)acopyoftheOpenDocument(text)formatrevisedquestionnairedeliveredtotheSagemailinglistand(1b)acopyoftheonlinesurveyform
ofthesamedocumentpowered, asyoucanseefromthebottomofthedocument, by
GoogleDocs. Theanswersarriveinspreadsheetformat. I cannotstressenoughthe
sheereleganceandutilityofthismethod. Alsoincludedis(2)acopyoftheslightlymodifiedquestionnairetothegroupofpeopledealingprimarilywithproprietarysoftware
–againthiswasonline. Onepieceofadvice, continuallycheckfornewresponses, new
onesareeasytomiss. I havemadeHTML filesfromtheonlinequestionnairesrather
thansharingincludingthelinksbutthelinksareavailableonrequest.
• (1a)FREE &OPEN SOURCE MATHEMATICAL TOOLS RESEARCH
-SpreadsheetViewForm.zip
containsHTML +CSS files
• (1b)FREE &OPEN SOURCE MATHEMATICAL TOOLS RESEARCH
-RevisedQuestionnaire.odt
• (2)MATHEMATICAL SOFTWARE TOOLS RESEARCH -Spreadsheet
ViewForm.zip
containsHTML +CSS files
86