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1、SpaceandTimeWarpsThislectureistheintellectualpropertyofProfessorS.W.Hawking.Youmaynotreproduce,editordistributethisdocumentinanywayformonetaryadvantage.Insciencefiction,spaceandtimewarpsareacommonplace.Theyareusedforrapidjourneysaroundthegalaxy,orfortravelthroughtime.Buttoday'ssciencefiction,is
2、oftentomorrow'ssciencefact.Sowhatarethechancesforspaceandtimewarps.Theideathatspaceandtimecanbecurved,orwarped,isfairlyrecent.Formorethantwothousandyears,theaxiomsofEuclideangeometry,wereconsideredtobeselfevident.AsthoseofyouthatwereforcedtolearnEuclideangeometryatschoolmayremember,oneofthecons
3、equencesoftheseaxiomsis,thattheanglesofatriangle,adduptoahundredand80degrees.However,inthelastcentury,peoplebegantorealizethatotherformsofgeometrywerepossible,inwhichtheanglesofatriangle,neednotadduptoahundredand80degrees.Consider,forexample,thesurfaceoftheEarth.Thenearestthingtoastraightlineon
4、thesurfaceoftheEarth,iswhatiscalled,agreatcircle.Thesearetheshortestpathsbetweentwopoints,sotheyaretherootsthatairlinesuse.ConsidernowthetriangleonthesurfaceoftheEarth,madeupoftheequator,thelineof0degreeslongitudethroughLondon,andthelineof90degreeslongtitudeeast,throughBangladesh.Thetwolinesofl
5、ongitude,meettheequatoratarightangle,90degrees.Thetwolinesoflongitudealsomeeteachotheratthenorthpole,atarightangle,or90degrees.Thusonehasatrianglewiththreerightangles.Theanglesofthistriangleadduptotwohundredandseventydegrees.Thisisgreaterthanthehundredandeightydegrees,foratriangleonaflatsurface
6、.Ifonedrewatriangleonasaddleshapedsurface,onewouldfindthattheanglesaddeduptolessthanahundredandeightydegrees.ThesurfaceoftheEarth,iswhatiscalledatwodimensionalspace.Thatis,youcanmoveonthesurfaceoftheEarth,intwodirectionsatrightanglestoeachother:youcanmovenorthsouth,oreastwest.Butofcourse,therei
7、sathirddirectionatrightanglestothesetwo,andthatisupordown.Thatistosay,thesurfaceoftheEarthexistsinthree-dimensionalspace.Thethreedimensionalspaceisflat.Thatistosay,itobeysEuclideangeometry.Theanglesofatriangle,adduptoahundredandei
