Imagine Math 2: Between Culture and Mathematics

248 Pages·2013·3.215 MB·English

by  Michele Emmer (auth.), Michele Emmer (eds.)

Michele Emmer
Editor
Imagine
Math 2
Between Culture and Mathematics
ImagineMath2
Michele Emmer Editor
Imagine Math 2
Between Culture and Mathematics
MicheleEmmer
DepartmentofMathematics
SapienzaUniversityofRome
ISBN978-88-470-2888-3 ISBN978-88-470-2889-0(eBook)
DOI10.1007/978-88–470-2889-0
LibraryofCongressControlNumber:2013930610
SpringerMilanDordrechtHeidelbergLondonNewYork
(cid:2)c Springer-VerlagItalia2013
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Translations:KimWilliamsforthecontributionsbyC.Ambrosini,D.Amodio,G.P.Brunetta,S.
Cacaceetal.,M.Scroccaro,G.LolliandM.Emmer;SylvieDuvernoyforthecontributionbyA.
Mondot
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Contents
Introduction................................................... 1
Mathematics,NumbersandMusic
TheFascinationofNumbers,betweenMusicandPoetry
MicheleEmmer................................................. 5
TheSolitudeofLastWords
ClaudioAmbrosini .............................................. 11
Mathematics,PoetryandLiterature
Go¨del’sChildhoodandOtherAlgorithms
VincenzoDellaMea ............................................. 23
TheWildNumberProblem:MathorFiction?
PhilibertSchogt ................................................ 31
APlayatDusk.MathematicsinLiterature
CarloToffalori ................................................. 39
MathematicsaccordingtoItaloCalvino
GabrieleLolli .................................................. 49
TheMathematicalMind-IconographyofaTension
PaoloPagli .................................................... 57
MathematicsandFilm
Spatial Rhythms in Cinema between the Avant-Garde and
Entertainment
GianPieroBrunetta ............................................. 69
vi Contents
LessonsinMathematics,attheCinema
MicheleEmmer................................................. 83
Mathematics,Love,andTattoos
EdwardFrenkel................................................. 93
Arithme´tique
GiovanniMunari................................................101
MathematicsandArt
L’artduTraitestl’attraitdel’Art
SophieSkaf ....................................................107
MathematicsandMorphology
MorphogenesisandDynamicalSystems.AViewInstantiatedbya
PerformativeDesignApproach
SaraFranceschelli ..............................................117
EmpiricalEvidencethattheWorldIsNotaComputer
JamesW.McAllister .............................................127
Mathematics,ArtandMusic
NumeriMalefici(EvilNumbers):HomagetoFabioMauri
MicheleEmmer.................................................139
FromPollock’sSummertimetoJacksontime
DavideAmodio .................................................151
MathematicsasaToolfortheCompositionofJacksontime
ChiaradeFabritiis ..............................................161
MathematicsandApplications
Extracting Information from Chaos: a Case in Climatological
Analysis
FrancescoBonghi,RobertoFerretti ................................173
OntheTangibleBoundarybetweenRealandVirtual
AndrienMondot ................................................181
Contents vii
FortMargheraandtheFrenchandAustrianPlansofDefence
MauroScroccaro................................................185
MathematicsandAnts
Myrmedrome:SimulatingtheLifeofanAntColony
SimoneCacace,EmilianoCristiani,DarioD’Eustacchio ..............201
AntsSearchingforaMinimum
MaurizioFalcone ...............................................211
MathematicsandMarco
ExoticSpheresandJohnMilnor
MarcoAbate ...................................................221
CellularAutomata:theGameofLife
GianMarcoTodesco.............................................231
HomagetoAlanTuring
AlanM.Turing(1912-1954)
GabrieleLolli ..................................................247
AlanTuringandthePoisonedApple
MassimoVincenzi ...............................................255
Introduction
Imagineallthepeople
Sharingalltheworld...
JohnLennon
Imaginemathematics,imaginewiththehelpofmathematics,imaginenewworlds,
new geometries, new forms. Imagine building mathematical models that make it
possibletomanageourworldbetter,imaginesolvinggreatproblems,imaginenew
problemsneverbeforethoughtof,imaginemusic,art,poetry,literature,architecture,
theatre and cinema with mathematics. Imagine the unpredictable and sometimes
irrationalapplicationsofmathematicsinallareasofhumanendeavour.
Imaginationandmathematics,imaginationandculture,cultureandmathematics.
Forsomeyearsnowtheworldofmathematicshaspenetrateddeeplyintohumancul-
ture,perhapsmoredeeplythaneverbefore,evenmorethanintheRenaissance.In
theatre, stories of mathematicians are staged; in cinema Oscars are won by films
about mathematicians; all over the world museums and science centres dedicated
to mathematics are multiplying. Journals have been founded for relationships be-
tweenmathematicsandcontemporaryartandarchitecture.Exhibitionsaremounted
to present mathematics, art and mathematics, and images related to the world of
mathematics.
Thevolumesintheseries“ImagineMath”areintendedtocontributetograsping
how much that is interesting and new is happening in the relationships between
mathematics,imaginationandculture.
Thissecondvolumeoftheseriesbeginswiththeconnectionsbetweenmathemat-
ics, numbers, poetry and music, with the latest opera by Italian composer Claudio
Ambrosini.Literatureand narrativealsoplayan importantrolehere.There iscin-
ematoo,withthe“erotic”mathematicsfilmsbyEdwardFrenkel,andthenewshort
“Arithmtique”byMunariandRovazzani.Thesectiononapplicationsofmathemat-
icsfeaturesastudyofants,aswellastherefinedformsandsurfacesgeneratedby
algorithmsusedintheperformancesbyAdrienMondotandClaireBardainne.Last
but not least, in honour of the hundredth anniversary of his birth, a mathematical,
literaryandtheatricalhomagetoAlanTuring,oneoftheoutstandingfiguresofthe
twentiethcentury,agreatmathematicianwhowasthevictimoftheprejudicesofhis
day.
Thetopicsaretreatedinawaythatisrigorousbutcaptivating,detailedbutfull
ofevocations.Anall-embracinglookattheworldofmathematicsandculture.
MicheleEmmer
EmmerM.(Ed.):ImagineMath2.BetweenCultureandMathematics
DOI10.1007/978-88-470-2889-0 1,(cid:2)c Springer-VerlagItalia2013
Mathematics, Numbers and Music
The Fascination of Numbers, between Music
and Poetry
MicheleEmmer
Ichoosenumbersbecausetheyaresoconstant,confined,andartistic.
Numbersareprobablytheonlyrealdiscoveryofmankind.Anumberofsomething
issomethingelse.It’snotpurenumberandhasothermeanings.
HanneDarboven,artist[1]
Godmadethenaturalnumbers;allelseistheworkofman.
LeopoldKronecker,mathematician
Mathematicsandnumbers,mathematicsandpoetry
Amathematician,likeapainterorapoet,isamakerofpatterns.Ifhispatternsaremore
permanentthantheirs,itisbecausetheyaremadewithideas.Apaintermakespatternswith
shapesandcolours,apoetwithwords.Apaintingmayembodyan‘idea’,buttheideais
usuallycommonplaceandunimportant.Inpoetry,ideascountforagooddealmore;but,
asHousmaninsisted,theimportanceofideasinpoetryishabituallyexaggerated:‘Icannot
satisfymyselfthatthereareanysuchthingsaspoeticalideas.... Poetryisnotthethingsaid
butawayofsayingit.’
Notallthewaterintheroughrudesea
CanwashthebalmfromananointedKing.1
Couldlinesbebetter,andcouldideasbeatoncemoretriteandmorefalse?Thepoverty
oftheideasseemshardlytoaffectthebeautyoftheverbalpattern.Amathematician,on
theotherhand,hasnomaterialtoworkwithbutideas,andsohispatternsarelikelytolast
longer,sinceideaswearlesswithtimethanwords.Themathematician’spatterns,likethe
painter’sorthepoet’smustbebeautiful;theideas,likethecoloursorthewords,mustfit
togetherinaharmoniousway.Beautyisthefirsttest:thereisnopermanentplaceinthe
worldforuglymathematics.
MicheleEmmer
DepartmentofMathematics“GuidoCastelnuovo”,SapienzaUniversityofRome,Rome(Italy).
1FromShakespeare,RichardII,actIII,sceneII.
EmmerM.(Ed.):ImagineMath2.BetweenCultureandMathematics
DOI10.1007/978-88-470-2889-0 2,(cid:2)c Springer-VerlagItalia2013