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1、THEROADTOREALITYBYROGERPENROSETheEmperor’sNewMind:ConcerningComputers,Minds,andtheLawsofPhysicsShadowsoftheMind:ASearchfortheMissingScienceofConsciousnessRogerPenroseTHEROADTOREALITYACompleteGuidetotheLawsoftheUniverseJONATHANCAPELONDONPublishedbyJonathanCape200424681097531CopyrightßRog
2、erPenrose2004RogerPenrosehasassertedhisrightundertheCopyright,DesignsandPatentsAct1988tobeidentifiedastheauthorofthisworkThisbookissoldsubjecttotheconditionthatitshallnot,bywayoftradeorotherwise,belent,resold,hiredout,orotherwisecirculatedwithoutthepublisher’spriorconsentinanyformofbind
3、ingorcoverotherthanthatinwhichitispublishedandwithoutasimilarconditionincludingthisconditionbeingimposedonthesubsequentpurchaserFirstpublishedinGreatBritainin2004byJonathanCapeRandomHouse,20VauxhallBridgeRoad,LondonSW1V2SARandomHouseAustralia(Pty)Limited20AlfredStreet,MilsonsPoint,Sydne
4、y,NewSouthWales2061,AustraliaRandomHouseNewZealandLimited18PolandRoad,Glenfield,Auckland10,NewZealandRandomHouseSouthAfrica(Pty)LimitedEndulini,5AJubileeRoad,Parktown2193,SouthAfricaTheRandomHouseGroupLimitedReg.No.954009www.randomhouse.co.ukACIPcataloguerecordforthisbookisavailablefrom
5、theBritishLibraryISBN0–224–04447–8PapersusedbyTheRandomHouseGroupLimitedarenatural,recyclableproductsmadefromwoodgrowninsustainableforests;themanufacturingprocessesconformtotheenvironmentalregulationsofthecountryoforiginPrintedandboundinGreatBritainbyWilliamClowes,Beccles,SuffolkContent
6、sPrefacexvAcknowledgementsxxiiiNotationxxviPrologue11Therootsofscience71.1Thequestfortheforcesthatshapetheworld71.2Mathematicaltruth91.3IsPlato’smathematicalworld‘real’?121.4Threeworldsandthreedeepmysteries171.5TheGood,theTrue,andtheBeautiful222Anancienttheoremandamodernquestion252.1The
7、Pythagoreantheorem252.2Euclid’spostulates282.3Similar-areasproofofthePythagoreantheorem312.4Hyperbolicgeometry:conformalpicture332.5Otherrepresentationsofhyperbolicgeometry372.6Historicalaspectsofhyperbolicgeometry422.7Relationtophysicalspace463Kindsofnumberinthephysicalworld51
