Job:loaderSheet:1Page:1(September16,2003)[loader]UnreasonableEffective - PDF document

Job:loaderSheet:1Page:1(September16,2003)[loader]UnreasonableEffectivenessbyAlexKasmanAmandaBirnbaumbegantohavesecondthoughts.Couldshereallygothroughwiththis?Hereshewas,pacingbackandforthinthedrysandonatinyislandshehadneverevenheardofjustafewweeksago.Thoughithadasmallpopulationofpeoplelivinginmodesthouses,theislandwasunclaimedbyanycountry.Asfarasanyonecouldtell,itwasjustsoinsignicantthatnocountrywasinterestedinit.And,hereshewas,staringthroughthewroughtirongateoftheonlyreallylargehouseontheislandwithoutanyideaofwhomightberesidingthere.But,sheknewshewasintherightplace.Everymajorscienticpublisherhadgivenherthesamedescriptionofhowtondit.Theyallhadstoriesaboutthisstrangeaddresswhich,foraslongasanyonecouldremember,hadbeenwillingtopayanypricetosubscribetoallofthemajorresearchjournals.Well,evenifhercrazyideaswerewrong,therewassomethinginterestinghere.Perhapsshecouldjustndoutwhoitwasinthisplacethatfeltcompelledtokeepuponthelatestpublishedresearch!So,shewalkedupthelongpathwindingbetweentheweedsandwildowerstothefrontdoorandsherangthebell.Faintly,throughthethickwoodendoor,shecouldhearthesoundofthechimesplayingafamiliartunetoannounceherarrival.Shefeltasuddenurgetorunaway,buthercuriositywonoutandshestayedtoseewhosefeetshecouldhearscufingslowlytowardsthedoor;toseewhatsortofpersonlivedhere.Thedooropenedtorevealashort,veryordinarylookingmiddle­agedmanwithblotchy,darkskinandthewhitesthairshehadeverseen.Whenhelookedupatherface,hewasclearlyverysurprisedandtookastepback.“Ohmy,”shethought,alreadycomfortedbythefactthatthemandidnotlookthreatening,“hewasexpectingsomeoneelse...I'vefrightenedhim.I'lltrytoexplain.IsurehopehespeaksEnglish!”“Dr.Birnbaum!”hesaid,nowgesturingherin,“Iwasnotexpectingtoseeyouhere.Please,please,comein.Please,comein.”“YouknowwhoIam?!?”sheaskedincredulously.“Ofcourse,”heansweredshyly,indicatingachoiceofcomfortableseatingoptionsfromastuffedsofatoacaptain'schair.“Andwhywouldn'tIknowwhoyouare?Why,everyoneistalkingaboutyou.YourPh.D.thesiswaspublishedlessthanoneyearagoinMemoirsoftheAmericanMathematicalSocietyandalreadyhashadaprofoundimpactintheoreticalbiologyaswellasinyourown UnreasonableEffectivenessbyA.KasmanPage2Job:loaderSheet:2Page:2(September16,2003)[loader]areaofhigh­dimensionaltopology.Itwasbrilliant,trulybrilliant.Ireaditmyself!Letmegetyousometea.”Hedisappearedthroughaslender,archeddoorwayatthebackoftheroominwhichshewassitting,givingheramomenttothink.Iftherehadbeenanylingeringdoubtthatshewasintherightplace,hisbehaviorhadeliminatedit.Shewasalsogladthathehadleaptrightintothistopicofconversation,sinceshewasneversurehowshecouldbringitupwithoutsoundingcrazy.“Yes,”shecalledtotheotherroom,“thatiswhatIhadcomeheretotalktoyouabout.”Therewasnoreply,andsoshesupposedthathecouldnothearher.Whenhereturnedafewminuteslater,hewascarryingasilverteaset.“Ah,camelia,”hesaid,snifngatthefragrantaromaoftheteaasheserved.“But,Idon'tunderstand,whywouldyoucomeallofthiswaytotalktomeaboutyourwork?Youcan'tpossiblyknowwhoIam!”“It'snotjustmyresearchthatIwanttotalktoyouabout,itismathresearchingeneral.”Amandastirredhertea,butdidnotevenliftthecupoffofthesaucer.Shehadnointerestintheteajustnow.“BackwhenIwasanundergraduate,oneofmyprofessorshaddenedmathematicsas`thestudyofnecessarycon­sequencesofarbitraryaxiomsaboutmeaninglessthings.'MyclassmatesandI,allmathmajors,didnotlikethisdescription.Itseemedtoignoretheusefulnessofmathematics.Afterall,mathisusedinengineering,physics,biology,eco­nomics,youknow.Wehadadiscussion,aboutthisparadox.`Ifmathematicsbeginswiththesemeaninglessabstractions,whyisitthatitturnsouttobesousefulintheend?'Therewerelotsofdifferentopinionsonthesubject.”“Ohyes,”hechimedinwithabrightsmile,“I'veheardsuchdebatesbeforemanytimes.`TheUnreasonableEffectivenessofMathematics'!`Whyisitthatresultsinabstractmathematics,constructedwithoutanythoughtgiventotherealworld,sometimelaterturnouttobeusefulafterall?”'“Right!Right.Likenon­Euclideangeometry.Atthetimeitwasrstsuggested,itwasjustasortoftrick.`Lookwhatwecandoifwepretendthatparallellinesmeettoo!'Butthen,afterRiemann,Clifford,HilbertandEinsteinit'snolongerajoke,itisadescriptionoftheuniversewelivein,thoughweneverknewitbefore.”“And,”headded,clearlyenjoyingthisconversation,“whatabouttheuseofnon­commutativeringsandimaginarynumbersinparticlephysics?!?”“Yes,”sheagreed,“whenimaginarynumberswererstdiscussedbymath­ematicianstheywerebarelyevenconsideredtoberealmathematics.Nowphysicistsregularlyconsiderquantumwavefunctionswhicharecomplexvaluedwithnoqualms.”“Andwhenthephysicistsrstfoundnon­commutativityintheirmeasurements, UnreasonableEffectivenessbyA.KasmanPage3Job:loaderSheet:3Page:3(September16,2003)[loader]thesupposedlyuselesstheoryofabstractalgebrawasalreadythere,instanta­neouslytransformedintoabranchof`applied'mathematics!”Helaughedsohardthatshedidbegintogetfrightened.Henoticedherreaction,andtriedtocalmhimselfdown,slowlysippingathisteaandtryingnottolaugh.“I'msorry,”hesaid,“Ihavenothadthisconversationforquitealongtimeand...andIhaveaspecialinterestinit.Oh,butyouhadsomethingtosayandcamesuchalongway.PerhapsIshouldjustletyoutalk.”Therewasanuncomfortablepausewhileshetriedtocollectherthoughtsandhercourage.“So,”shecontinued,“whenmyfriendsandIdiscussedtheseideasincollegethereweretwomainviewpoints.Somearguedthatmathematicsallowsustostudyanystructuredsystem,andthensincetheuniverseseemstohavesomerulestoit,weobviouslywillbeabletousemathtosaythingsaboutitsomehow.”“Hmmm,”hehummedwhilenibblingonasugarcookie.“Andtheothersallthoughtthattheuniverseiswaybeyondourcomprehensionanyway.Accordingtothem,whenwehaveanewmathematicalidea,weapplyittotheuniversebecausewehavenothingbettertouse.”“Ah,”hesaidswallowing,“astheysay:toamanwhoseonlytoolisahammer,everythinglookslikeanail!”Rememberingthathehadpromisedtobesilent,hestoppedsuddenly,`zipping'hismouthshutwithhisthumbandforenger.“Right.But,Ihadanotheridea.Itwassocrazy,Ididn'tevenmentionittomyfriends,butIkeptitinmindasasortofjoke.”Shewaitedforhimtoaskwhatthecrazyideawas,buthejustsmiledandlookeddownatthetable,asifheknewshewastalkingabouthim.“Myidea,”shecontinued,“wasthatanothergoodexplanationforwhy`puremathematical'researchbecomesusefulsometimeafteritsdiscoveryisthattheuniverseitselfchangestotourmathematicaldiscoveries.”“Oh,”hesaid,suddenlyblinkingrapidlywhilestillsmiling.“Andwhyhaveyoucomeallofthiswaytotalktomeaboutit?”“Because,Ithinkyou'retheonewhoisdoingit.”Henoddedslowly,asifadmittingitwastrue.Thissurprisedher,sinceshehadexpectedadenial.Shehadexpectedtobetoldthatshewascrazy.Itwasacrazyidea,afterall...wasn'tit?Therewasanotheruncomfortablesilence.“So,”shesaidsharply,“it'strue?”“Betweenyouandme?”helookedbackandforthasifheexpectedtondpeopleeavesdroppingrightthereinhislivingroom.“Betweenyouandme,itis,anditisathanklessjob.” UnreasonableEffectivenessbyA.KasmanPage4Job:loaderSheet:4Page:4(September16,2003)[loader]“So,doesthatmakeyou...youknow...areyou...thecreatoroftheuniverse?”“Ha!”heshoutedsoloudlythatshealmostspilledhertea.“IfIwereoneofthecreators,youthinkI'dbehereonthiscrazylittleplanetinthemiddleofnowhere?Nooffenseintended.No,no,I'vejustbeendoingthishereforafewhundredyearsandaftertwohundredmoreIcanretiretoanicealternaterealityI'vebeendreamingof.”Shewasstilltryingtoprocessallofthis.“So,youmeanwheneverwemakeadiscoverythewholeuniversechanges?”“Well,notquitethewholeuniverse,andnotquiteeverydiscovery.WhenIndaresultthatIndespeciallyinterestingorentertaining,Indsomewaytoincorporateitintotheuniverse...butonlylocally.That'swhyyourcosmologistshavebeensoconfusedintheirtheories.Inotherdistricts,thosewithmyjobmayhavedifferenttastesinmath,differentideasofhow`reality'couldbe.Infact,itisthisdiversityofpossibilitiesthatthecreatorsenjoymost...it'swhyIhaveajob!”Hewasveryhappytohavesomeonetotalktoaboutthisafterbeingsilentforsolong.Asmileofcontentmentshoneonhisfaceandheleanedbackinhisseatasifhehadneverbeensocomfortableinhislife.“Butthen,”shehadsomanyquestions,shefounditdifcultwhichtoaskrst,“if...”“Wait!”heinteruptedsittingupstraightwithaworriedexpression.“Amanda,please,youmusttellmehowyoufoundmeout.Iamnotsupposedtobediscovered,youknow.”“Well,”shesaid,unabletolookhimintheeye,“youremembermythesis?”“Verywell!”Hiseyeslitupinawayshefoundattering.Hehadclearlylikedherwork.“Younoticedthatthecohomologyofacertainclassofhigh­dimensionalmanifoldshadsomebizarrealgebraicproperties.Becausethebehaviorremindedyouofimmunesystemsinbiology,youcalledsuchmanifolds`immunitymanifolds'.Althoughyousayintheintroductionthatyouarenotanexpertinbiology,theideamotivatedyournomenclaturethroughoutthethesis.Someimmunitymanifoldsarehealthy,somearenot.Someevenhaveauto­immunediseases!”“JustnamesIgavethemtohelpmedescribeandunderstandthemathemat­icalstructure.Iwasdoingmath,notbiology.”“Perhaps,butyourscientistswereneverabletomakesenseoutoftheimmunesystembeforeandtherewassomuchroomforrichandbeautifuldiscoveriestogrowoutofyourtheories.Ijustcouldn'twaittogettoworkonit.YoumusthaveseenbynowhowIwasabletobringittoplayonsomequestionsregardingtheimprovementofvaccinationsandinjustafewmonthssomemedicalresearchers UnreasonableEffectivenessbyA.KasmanPage5Job:loaderSheet:5Page:5(September16,2003)[loader]workingonthediseasesclerodermawilldiscoverthattheycanuseSerredualityto...”“But,”sheinterupted,“youmadeamistake.Imean,Imadeamistake.Iwaswrongaboutequation3.6.Themicrochimericsubalgebrasdon'thavetobesimplyconnected,andsodenition3.9justdidn'tmakeanysenseand...”“No,”hisjawfellopenandhedroppedthelastlittlepieceofhiscookie.“Notequation3.6!Butthatwasoneofmyfavoriteparts.Iusedthateverywhere!”“Yes,Iknow.ThatishowIfoundyou.Yousee,IcaughtthemistakejustaftertheMemoirwaspublished.Itwasn'teasy,butIwasabletomakesurethateverycopywiththemistakewascollectedunreadandreplacedwithacorrectedversion...everycopyexcepttheonethatwassentseparatelybyprivatecourierheretoyourhouse.AndthatishowIknew...”“Ohmy,”hesaid,stirringhisteavigorously.“Ohmy,howcarelessofme!Wewillhavetodosomethingaboutthat,won'twe?Yes,somethingwillhavetobedoneaboutthat.”