Chapter2TheShapeandMotionoftheHeavensNothingwhichconcernstheeternalcan - PDF document

Chapter2TheShapeandMotionoftheHeavensNothingwhichconcernstheeternalcanbeamatterofchanceorspontaneity.—Aristotle2.1IntroductionAttheoutsetofBookIofOntheHeavens,Aristotlearguedthatthecelestialbodiescannotbecomprisedofoneofthefourcommonlyknownelements—earth,water,airandre.Thisisbecausethesefourelements,whenlefttothemselves,obviouslyexhibitalinearmotioneitherupwardordownward.Witness,forexample,thenaturalmotionofadroppedrockortheascentoftonguesofre.Bycontrast,theheavenlybodiesobviouslyexhibitanaturallycircularmotion.Thesun,moon,planetsandstarsriseandsetdaily.Thisnaturalmotionhaspersistedwithoutalterationordecaythroughoutrecordedhistory—indeedfrometernity,heargues—afactwhichprovesthatthecelestialbodiesarecomprisedofafthelement,whichAristotlecallsThisiswherethepreviousreadingselectionleftoff—attheendofChap.3ofBookI.Inthereadingbelow,wewilljumpintoChap.4ofBookII.Butbeforedoingso,whatdidweskipover?Asitturnsout,quitealot.AttheoutsetofChap.4ofBookI,Aristotleaskswhethertheworld(i.e.theuniverse)isniteorinniteinsize.Afterexploringthedifcultiesthattherotationalmotionofaninnitebodywouldentail,heconcludesthat“itisclearthatthebodyoftheuniverseisnotinnite.”AccordingtoAristotle,theworldisboundedbythesphereofxedstarswhichrotatesonceperdayaroundtheearth.AtthebeginningofChap.8,hethenaskswhethertheremightbenotjustone,butperhapsmanyuniverses.Whilethismayseemabsurd,Aristotleconsiderssuchquestionstobe“all-important”inhissearchfortruth.Indeed,theideathattherearemultipleuniversesisconsideredbysomemoderncosmologiststobeaplausible,orevennecessary,explanationoftheanthropicprinciple—thattheexquisitesuitabilityoftheuniverseinwhichwendourselvescanbebestunderstoodifoursisbutoneofmanyuniverseswhichexist,orhaveexisted.AsforAristotle,heconcludesthatmorethanoneuniverseisimpossible,andmoreoverthattheoneinwhichweliveiseternal.Hisadversaries,however,arguedthattheheavensareeternal,thattheyhadabeginningandmaysomedaysufferdestruction,andthattheirpresentmotionistransientandthusunnatural.SoattheoutsetofBookII,AristotleturnsK.Kuehn,AStudentÕsGuideThroughtheGreatPhysicsTexts,UndergraduateLectureNotesinPhysics,DOI10.1007/978-1-4939-1360-2_2,©SpringerScience+BusinessMedia,LLC2015 2TheShapeandMotionoftheHeavenshisattentiontotheirarguments.Inaddressingthem,Aristotleisledtoconsiderthesource,ororigin,ofmovementitself.Perhapssurprisingly,intherstthreechaptersofBookII,Aristotleclaimsthattheheavenlybodiesareinsomesensetheypossessa“principleofmovement”similartothatwhichallowsanimalstomovefromplacetoplace.Inplantsandanimals,thisprincipleofmovementislinkednotonlytotheirpossessionofasoul,butalsotoacertaininternalasymmetrywhichtheypossess.Forexampleinplants,growthisupward,towardwheretheirshootsaim;andinanimals,locomotionisforward,towardwheretheirsensesaredirected.Lackinganydistinctionoftheirparts,thesewouldbeincapableofinitiatingsuchmovements.Butwhatabouttheperfectsphereswhichcomprisetheheavensandonwhichtheplanetsandstarsride?Lackinganydistinctionofparts,theywouldseemtobeincapableofinitiatingmovement.Theirmovementmustbecaused,then,byaprimemover—animmortalanddivinecelestialspherewhichsurroundsthem,containsthem,andgenerates(orperhapsinspires)theirmovement.ItisinChap.4ofBookIIthatwenowpickupourreadingonceagain.Herein,Aristotleexamineshowthemotionoftheheavensarerelatedto,orperhapsevendictatedby,theirshape.Hebeginsbyrankingtheplanarandsolidguresaccordingtothenumberofedgesandanglestheyhave.Howdoesthisgeometricalclassicationinformhisopinionontheshapeoftheheavens?Arehisargumentsreasonable?Moreover,howishistheoryofheavenlymotioninformedbyhisunderstandingofthegrowthanddecayofanimals?PerhapsmostinterestingareAristotle’sviews,expressedinChap.5,onchance.Inparticular,canchancebethecauseofthemotionoftheheavens?Which(ifany)ofhisargumentspertainingtotheshapeandmotionoftheheavenswouldsufferifheweretoadmitchanceorspontaneityasvalidmodesofexplanation?2.2Reading:Aristotle,OntheHeavensAristotle,OntheHeavens,inAristotle:I,GreatBooksoftheWesternWorld,vol.8,editedbyRobertMaynardHutchins,EncyclopediaBritannica,1952.BookII.2.2.1Chapter4Theshapeoftheheavenisofnecessityspherical;forthatistheshapemostappropriatetoitssubstanceandalsobynatureprimary.First,letusconsidergenerallywhichshapeisprimaryamongplanesandsolidsalike.Everyplaneguremustbeeitherrectilinearorcurvilinear.Nowtherectilinearisboundedbymorethanoneline,thecurvilinearbyoneonly.Butsinceinanykindtheoneisnaturallypriortothemanyandthesimpletothecomplex,thecirclewill 2.2Reading:Aristotle,OntheHeavensbetherstofplanegures.Again,ifbycomplete,aspreviouslydened,wemeanathingoutsidewhichnopartofitselfcanbefound,andifadditionisalwayspossibletothestraightlinebutnevertothecircular,clearlythelinewhichembracesthecircleiscomplete.Ifthenthecompleteispriortotheincomplete,itfollowsonthisgroundalsothatthecircleisprimaryamonggures.Andthesphereholdsthesamepositionamongsolids.Foritaloneisembracedbyasinglesurface,whilerectilinearsolidshaveseveral.Thesphereisamongsolidswhatthecircleisamongplanegures.Further,thosewhodividebodiesintoplanesandgeneratethemoutofplanesseemtobearwitnesstothetruthofthis.Aloneamongsolidstheyleavethesphereundivided,asnotpossessingmorethanonesurface:forthedivisionintosurfacesisnotjustdividingawholebycuttingitintoitsparts,butdivisionofanotherfashionintopartsdifferentinform.Itisclear,then,thatthesphereisrstofsolidgures.If,again,oneordersguresaccordingtotheirnumbers,itismostnaturaltoarrangetheminthisway.Thecirclecorrespondstothenumberone,thetriangle,beingthesumoftworightangles,tothenumbertwo.Butifoneisassignedtothetriangle,thecirclewillnotbeagureatall.Nowtherstgurebelongstotherstbody,andtherstbodyisthatatthefarthestcircumference.Itfollowsthatthebodywhichrevolveswithacircularmovementmustbespherical.Thesamethenwillbetrueofthebodycontinuouswithit:forthatwhichiscontinuouswiththesphericalisspherical.Thesameagainholdsofthebodiesbetweenthoseandthecentre.Bodieswhichareboundedbythesphericalandincontactwithitmustbe,aswholes,spherical;andthebodiesbelowthesphereoftheplanetsarecontiguouswiththesphereabovethem.Thespherethenwillbesphericalthroughout;foreverybodywithinitiscontiguousandcontinuouswithAgain,sincethewholerevolves,palpablyandbyassumption,inacircle,andsinceithasbeenshownthatoutsidethefarthestcircumferencethereisneithervoidnorplace,fromthesegroundsalsoitwillfollownecessarilythattheheavenisspherical.Forifitistoberectilinearinshape,itwillfollowthatthereisplaceandbodyandvoidwithoutit.Forarectilineargureasitrevolvesnevercontinuesinthesameroom,butwhereformerlywasbody,isnownone,andwherenowisnone,bodywillbeinamomentbecauseoftheprojectionatthecorners.Similarly,iftheworldhadsomeothergurewithunequalradii,if,forinstance,itwerelentiform,oroviform,ineverycaseweshouldhavetoadmitspaceandvoidoutsidethemovingbody,becausethewholebodywouldnotalwaysoccupythesameroom.Again,ifthemotionoftheheavenisthemeasureofallmovementswhateverinvirtueofbeingalonecontinuousandregularandeternal,andif,ineachkind,themeasureistheminimum,andtheminimummovementistheswiftest,then,clearly,themovementoftheheavenmustbetheswiftestofallmovements.Nowoflineswhichreturnuponthemselvesthelinewhichboundsthecircleistheshortest;andthatmovementistheswiftestwhichfollowstheshortestline.Therefore,iftheheaven Aristotle’s,III.207 2TheShapeandMotionoftheHeavensmovesinacircleandmovesmoreswiftlythananythingelse,itmustnecessarilybeCorroborativeevidencemaybedrawnfromthebodieswhosepositionisaboutthecentre.Ifearthisenclosedbywater,waterbyair,airbyre,andthesesimilarlybytheupperbodies—whichwhilenotcontinuousareyetcontiguouswiththem—andifthesurfaceofwaterisspherical,andthatwhichiscontinuouswithorembracesthesphericalmustitselfbespherical,thenonthesegroundsalsoitisclearthattheheavensarespherical.Butthesurfaceofwaterisseentobesphericalifwetakeasourstarting-pointthefactthatwaternaturallytendstocollectinahollowplace—‘hollow’meaning‘nearerthecentre’.Drawfromthecentrethelines,andlettheirextremitiesbejoinedbythestraightline.Theline,drawntothebaseofthetriangle,willbeshorterthaneitheroftheradii.Thereforetheplaceinwhichitterminateswillbeahollowplace.Thewaterthenwillcollectthereuntilequalityisestablished,thatisuntilthelineisequaltothetworadii.Thuswaterforcesitswaytotheendsoftheradii,andthereonlywillitrest:butthelinewhichconnectstheextremitiesoftheradiiiscircular:thereforethesurfaceofthewaterBECisspherical.Itisplainfromtheforegoingthattheuniverseisspherical.Itisplain,further,thatitisturned(sotospeak)withanishwhichnomanufacturedthingnoranythingelsewithintherangeofourobservationcanevenapproach.Forthematterofwhichthesearecomposeddoesnotadmitofanythinglikethesameregularityandnishasthesubstanceoftheenvelopingbody;sincewitheachstepawayfromearththemattermanifestlybecomesnerinthesameproportionaswaterisnerthanearth.2.2.2Chapter5Nowtherearetwowaysofmovingalongacircle,fromorfrom,andwehavealreadyexplainedthatthesemovementsarenotcontrarytooneanother.Butnothingwhichconcernstheeternalcanbeamatterofchanceorspontaneity,andtheheavenanditscircularmotionareeternal.Wemustthereforeaskwhythismotiontakesonedirectionandnottheother.Eitherthisisitselfanultimatefactorthereisanultimatefactbehindit.Itmayseemevidenceofexcessivefollyorexcessivezealtotrytoprovideanexplanationofsomethings,orofeverything,admittingnoexception.Thecriticism,however,isnotalwaysjust:oneshouldrstconsiderwhatreasonthereisforspeaking,andalsowhatkindofcertaintyislookedfor,whetherhumanmerelyorofamorecogentkind.Whenanyoneshallsucceedinndingproofsofgreaterprecision,gratitudewillbeduetohimforthediscovery,butatpresentwemustbecontentwithaprobablesolution.Ifnaturealwaysfollowsthebestcoursepossible,and,justasupwardmovementisthesuperiorformofrectilinearmovement,sincetheupperregionismoredivinethanthelower,soforwardmovementissuperiorto Aristotle’sOntheHeavens,BookI.4. 2.2Reading:Aristotle,OntheHeavensbackward,thenfrontandbackexhibits,likerightandleft,aswesaidbeforeandasthedifcultyjuststateditselfsuggests,thedistinctionofpriorandposterior,whichprovidesareasonandsosolvesourdifculty.Supposingthatnatureisorderedinthebestwaypossible,thismaystandasthereasonofthefactmentioned.Foritisbesttomovewithamovementsimpleandunceasing,and,further,inthesuperioroftwopossibledirections.2.2.3Chapter6Wehavenexttoshowthatthemovementoftheheavenisregularandnotirregular.Thisappliesonlytotherstheavenandtherstmovement;forthelowerspheresexhibitacompositionofseveralmovementsintoone.Ifthemovementisuneven,clearlytherewillbeacceleration,maximumspeed,andretardation,sincetheseappearinallirregularmotions.Themaximummayoccureitheratthestarting-pointoratthegoalorbetweenthetwo;andweexpectnaturalmotiontoreachitsmaximumatthegoal,unnaturalmotionatthestarting-point,andmissilesmidwaybetweenthetwo.Butcircularmovement,havingnobeginningorlimitormiddleinthedirectsenseofthewords,hasneitherwhencenorwhithernormiddle:forintimeitiseternal,andinlengthitreturnsuponitselfwithoutabreak.Ifthenitsmovementhasnomaximum,itcanhavenoirregularity,sinceirregularityisproducedbyretardationandacceleration.Further,sinceeverythingthatismovedismovedbysomething,thecauseoftheirregularityofmovementmustlieeitherinthemoverorinthemovedorboth.Forifthemovermovednotalwayswiththesameforce,orifthemovedwerealteredanddidnotremainthesame,orifbothweretochange,theresultmightwellbeanirregularmovementinthemoved.Butnoneofthesepossibilitiescanbeconceivedasactualinthecaseoftheheavens.Astothatwhichismoved,wehaveshownthatitisprimaryandsimpleandungeneratedandindestructibleandgenerallyunchanging;andthemoverhasanevenbetterrighttotheseattributes.Itistheprimarythatmovestheprimary,thesimplethesimple,theindestructibleandungeneratedthatwhichisindestructibleandungenerated.Sincethenthatwhichismoved,beingabody,isneverthelessunchanging,howshouldthemover,whichisincorporeal,bechanged?Itfollowsthen,further,thatthemotioncannotbeirregular.Forifirregularityoccurs,theremustbechangeeitherinthemovementasawhole,fromfasttoslowandslowtofast,orinitsparts.Thatthereisnoirregularityinthepartsisobvious,since,iftherewere,somedivergenceofthestarswouldhavetakenplacebeforenowintheinnityoftime,asonemovedslowerandanotherfaster:butnoalterationoftheirintervalsiseverobserved.Noragainisachangeinthemovementasawholeadmissible.Retardationisalwaysduetoincapacity,andincapacityisunnatural.Theincapacitiesofanimals,age,decay,andthelike,areallunnatural,due,itseems,tothefactthatthewholeanimalcomplexismadeupofmaterialswhichdifferinrespectoftheirproperplaces,andnosinglepartoccupiesitsownplace.Ifthereforethatwhichisprimarycontainsnothingunnatural,beingsimpleandunmixedandinitsproper 2TheShapeandMotionoftheHeavensplaceandhavingnocontrary,thenithasnoplaceforincapacity,nor,consequently,forretardationor(sinceaccelerationinvolvesretardation)foracceleration.Again,itisinconceivablethatthemovershouldrstshowincapacityforaninnitetime,andcapacityafterwardsforanotherinnity.Forclearlynothingwhich,likeincapacity,isunnaturalevercontinuesforaninnityoftime;nordoestheunnaturalendureaslongasthenatural,oranyformofincapacityaslongasthecapacity.Butifthemovementisretardeditmustnecessarilyberetardedforaninnitetime.Equallyimpossibleisperpetualaccelerationorperpetualretardation.Forsuchmovementwouldbeinniteandindenite,buteverymovement,inourview,proceedsfromonepointtoanotherandisdeniteincharacter.Again,supposeoneassumesaminimumtimeinlessthanwhichtheheavencouldnotcompleteitsmovement.For,asagivenwalkoragivenexerciseontheharpcannottakeanyandeverytime,buteveryperformancehasitsdeniteminimumtimewhichisunsurpassable,so,onemightsuppose,themovementoftheheavencouldnotbecompletedinanyandeverytime.Butinthatcaseperpetualaccelerationisimpossible(and,equally,perpetualretardation:fortheargumentholdsofbothandeach),ifwemaytakeaccelerationtoproceedbyidenticalorincreasingadditionsofspeedandforaninnitetime.Theremainingalternativeistosaythatthemovementexhibitsanalternationofslowerandfaster:butthisisamerectionandquiteinconceivable.Further,irregularityofthiskindwouldbeparticularlyunlikelytopassunobserved,sincecontrastmakesobservationeasy.Thatthereisoneheaven,then,only,andthatitisungeneratedandeternal,andfurtherthatitsmovementisregular,hasnowbeensufcientlyexplained.2.3StudyQuestions2.1Whatistheshapeoftheheavens?a)HowdoesAristotleclassifyplanegures?Whatshapedoesherankastherst,orofthehighestpriority?Andhowdothenotionsofcompleteness,divisibilityandnumbergureintohisranking?b)Whatdoesallthishavetodowiththeshapeoftheheavens?IsAristotlejustiedinrelatingguresandbodiesinthisway?c)Whatdoesthecircularmotionoftheheavensimplyaboutitsshape?Inparticular,whydoeshesaytheheavenscannotbeegg-shapedorlens-shaped?Doesheconsidertheheavenstobeabody,oravoid?Andwhatconceptualdifcultyisheencounteringhere?d)Whatdoesthespeedoftheheavensimplyaboutitsshape?Ishisargumentconvincing?Whatcorroboratingevidencedoeshecitepertainingtotheshapeoftheheavens?2.2Whatisthemotionoftheheavens?a)IsAristotlecorrectthat“nothingwhichconcernstheeternalcanbeamatterofchanceorspontaneity?”Howdoesthistintohisargument?b)Arethemotionsoftheheavensregularirregular?Whatdoesthismean? 2.5Vocabularyc)Whatevidencedoesheprovidethattheheavensareunchangeable?Andwhy,accordingtoAristotle,doanimalsdecay,buttheheavensdonot?2.4Exercises(Causalityandchance).chanceavalidmodeofexplanationforob-servedphenomena?Consider:dowelearnanythingfrompositingchanceastheofsomething?Whatdoesyouranswertothisquestionimply?2.5Vocabulary1.Rectilinear9.Posterior2.Curvilinear10.Acceleration3.Contiguous11.Incorporeal4.Palpably12.Divergence5.Void13.Admissible6.Corroborative14.Perpetual7.Folly15.Fiction8.Cogent