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Mostpeoplearebaffledbyhowcomputersworkandassumethattheywillneverunderstandthem.WhattheydontrealizeandwhatDanielHillissshortbookbrilliantlydemonstratesisthatcomputersseeminglycomplexoperationscanbebrokendownintoafewsimplepartsthatperformthesamesimpleproceduresoverandoveragain.ComputerwizardHillisoffersaneasy-to-followexplanationofhowdataisprocessedthatmakestheoperationsofacomputerseemasstraightforwardasthoseofabicycle.Avoidingtechnobabbleordiscussionsofadvancedhardware,thelucidexplanationsandcolorfulanecdotesinThePatternontheStonegostraighttotheheartofwhatcomputersreallydo.Hillisproceedsfromanoutlineofbasiclogictocleardescriptionsofprogramminglanguages,algorithms,andmemory.Hethentakesreadersinsimplestepsuptothemostexcitingdevelopmentsincomputingtodayquantumcomputing,parallelcomputing,neuralnetworks,andself-organizingsystems.Writtenclearlyandsuccinctlybyoneoftheworldsleadingcomputerscientists,ThePatternontheStoneisanindispensableguidetounderstandingtheworkingsofthatmostubiquitousandimportantofmachines:thecomputer
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DanielHillisisoneoftheworld''shottestcomputerscientists.Hewasco-founderandchiefscientistoftheThinkingMachinesCorporationandprincipalarchitectofthecompany''smajorproduct,theConnectionMachine.HeisanEditorofseveralscientificjournals,includingArtificialLifeandFutureGenerationComputerSystemsandiscurrentlyVicePresidentandDisneyFellowatWaltDisneyImagineering.AdamHart-Davisisafreelancephotographer,writerandbroadcaster.HewonawardsfortheBBC2series,LocalHeroesandhispublicationsincludeEurekaaarh!BornandraisedinHenley-on-Thames,AdamHart-DavisattendedEtonCollegebeforestudyingforanMAinchemistryatOxfordUniversityandlateraDPhilinOrganometallicChemistryattheUniversityofYork.Aftercarryingoutthreeyears''postdoctoralresearchattheUniversityofAlbertainCanada,hetookuparoleattheOxfordUniversityPress,editingsciencetextsandchessmanuals.Hisworkinbroadcastingbeganin1977whenhejoinedYorkshireTelevisionasaresearcherforMagnusPyke,DavidBellamyandArthurC.Clarkeamongothers.Adamhassincefollowedaneclecticcareerpath,butisbestknownasthepresenterofawiderangeofhugelypopulartelevisionseries,suchasLocalHeroes,WhattheRomansDidForUsandScienceShack.Butaswellasbeingtelevision''sfavouritescienceenthusiast,heistheauthorofmanybooksonpopularscience,includingWhyDoesaBallBounce?andWhatthePastDidForUs.Heisalsoakeenphotographerandcyclist,andcurrentlylivesinBristolwithhispartner,SueBlackmore.--Thistextreferstoanoutofprintorunavailableeditionofthistitle.
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*Preface:TheMagicintheStone*NutsandBolts*UniversalBuildingBlocks*Programming*HowUniversalAreTuringMachines?*AlgorithmsandHeuristics*Memory:InformationandSecretCodes*Speed:ParallelComputers*ComputersThatLearnandAda
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Chapter4:HowUniversalAreTuringMachines?...QuantumComputingAsnotedearlier,thepseudorandomnumbersequencesproducedbycomputerslookrandom,butthereisanunderlyingalgorithmthatgeneratesthem.Ifyouknowhowasequenceisgenerated,itisnecessarilypredictableandnotrandom.Ifeverweneededaninherentlyunpredictablerandom-numbersequence,wewouldhavetoaugmentouruniversalmachinewithanondeterministicdeviceforgeneratingrandomness.Onemightimaginesucharandomness-generatingdeviceasbeingakindofelectronicroulettewheel,but,aswehaveseen,suchadeviceisnottrulyrandombecauseofthelawsofphysics.Theonlywayweknowhowtoachievegenuinelyunpredictableeffectsistorelyonquantummechanics.Unliketheclassicalphysicsoftheroulettewheel,inwhicheffectsaredeterminedbycauses,quantummechanicsproduceseffectsthatarepurelyprobabilistic.Thereisnowayofpredicting,forexample,whenagivenuraniumatomwilldecayintolead.ThereforeonecoulduseaGeigercountertogeneratetrulyrandomdatasequences-somethingimpossibleinprincipleforauniversalcomputertodo.Thelawsofquantummechanicsraiseanumberofquestionsaboutuniversalcomputersthatnoonehasyetanswered.Atfirstglance,itwouldseemthatquantummechanicsfitsnicelywithdigitalcomputers,sincetheword"quantum"conveysessentiallythesamenotionastheword"digital."Likedigitalphenomena,quantumphenomenaexistonlyindiscretestates.Fromthequantumpointofview,theapparentlycontinuous,analognatureofthephysicalworld-theflowofelectricity,forexample-isanillusioncausedbyourseeingthingsonalargescaleratherthananatomicscale.Thegoodnewsofquantummechanicsisthatattheatomicscaleeverythingisdiscrete,everythingisdigital.Anelectricchargecontainsacertainnumberofelectrons,andthereisnosuchthingashalfanelectron.Thebadnewsisthattherulesgoverninghowobjectsinteractatthisscalearecounterintuitive.Forinstance,ourcommonsensenotionstellusthatonethingcannotbeintwoplacesatthesametime.Inthequantummechanicalworldthisisnotexactlytrue,becauseinquantummechanicsnothingcanbeexactlyinanyplaceatall.Asinglesubatomicparticleexistseverywhereatonce,andwearejustmorelikelytoobservesuchaparticleatoneplacethanatanother.Formostpurposes,wecanthinkofaparticleasbeingwhereweobserveittobe,buttoexplainallobservedeffectswehavetoacknowledgethattheparticleisinmorethanoneplace.Almosteveryone,includingmanyphysicists,findthisconceptdifficulttocomprehend.Mightwetakeadvantageofquantumeffectstobuildamorepowerfultypeofcomputer?Asofnow,thisquestionremainsunanswered,buttherearesuggestionsthatsuchathingispossible.Atomsseemabletocomputecertainproblemseasily,suchashowtheysticktogether-problemsthatareverydifficulttocomputeonaconventionalcomputer.Forinstance,whentwohydrogenatomsbindtoanoxygenatomtoformawatermolecule,theseatomssomehow"compute"thattheanglebetweenthetwobondsshouldbe107degrees.Itispossibletoapproximatelycalculatethisanglefromquantummechanicalprinciplesusingadigitalcomputer,butittakesalongtime,andthemoreaccuratethecalculationthelongerittakes.Yeteverymoleculeinaglassofwaterisabletoperformthiscalculationalmostinstantly.Howcanasinglemoleculebesomuchfasterthanadigitalcomputer?Thereasonittakesthecomputersolongtocalculatethisquantummechanicalproblemisthatthecomputerwouldhavetotakeintoaccountaninfinitenumberofpossibleconfigurationsofthewatermoleculetoproduceanexactanswer.Thecalculationmustallowforthefactthattheatomscomprisingthemoleculecanbeinallconfigurationsatonce.Thisiswhythecomputercanonlyapproximatetheanswerinafiniteamountoftime.Onewayofexplaininghowthewatermoleculecanmakethesamecalculationistoimagineittryingouteverypossibleconfigurationsimultaneously--inotherwords,usingparallelprocessing.Couldweharnessthissimultaneouscomputingcapabilityofquantummechanicalobjectstoproduceamorepowerfulcomputer?Nobodyknowsforsure.Recentlytherehavebeensomeintriguinghintsthatwemaybeabletobuildaquantumcomputerthattakesadvantageofaphenomenonknownasentanglement.Inaquantummechanicalsystem,whentwoparticlesinteract,theirfatescanbecomelinkedinawayutterlyunlikeanythingweseeintheclassicalphysicalworld:whenwemeasuresomecharacteristicofoneofthem,itaffectswhatwemeasureintheother,eveniftheparticlesarephysicallyseparated.Einsteincalledthiseffect,whichinvolvesnotimedelay,"spookyactionatadistance,"andhewasfamouslyunhappywiththenotionthattheworldcouldworkthatway.Aquantumcomputerwouldtakeadvantageofentanglement:aone-bitquantummechanicalmemoryregisterwouldstorenotjusta1ora0;itwouldstoreasuperpositionofmanyi''sandmany0''s.Thisisanalagoustoanatombeinginmanyplacesatonce:abitthatitisinmanystates1or0atonce.Thisisdifferentfrombeinginanintermediatestatebetweena1anda0,becauseeachofthesuperposed1''sand0''scanbeentangledwithotherbitswithinthequantumcomputer.Whentwosuchquantumbitsarecombinedinaquantumlogicblock,eachoftheirsuperposedstatescaninteractindifferentways,producinganevenrichersetofentanglements.Theamountofcomputationthatcanbeaccomplishedbyasinglequantumlogicblockisverylarge,perhapseveninfinite.Thetheorybehindquantumcomputingiswellestablished,buttherearestillproblemsinputtingittouse.Foronething,howcanweuseallthiscomputationtocomputeanythinguseful?ThephysicistPeterShorrecentlydiscoveredawaytousethesequantumeffects-atleast,inprinciple--todocertainimportantanddifficultcalculationslikefactoringlargenumbers,andhisworkhasrenewedinterestinquantumcomputers.Butmanydifficultiesarestillthere.Oneproblemisthatthebitsinaquantumcomputermustremainentangledinorderforthecomputationtowork,butthesmallestofdisturbances--apassingcosmicray,say,orpossiblyeventheinherentnoisinessofthevacuumitselfcandestroytheentanglement.Yes,inquantummechanicsevenavacuumdoesstrangethings.Thislossofentanglement,calleddecoherence,couldturnouttobetheAchillesheelofquantummechanicalcomputers.Moreover,Shor''smethodsseemtoworkonlyonaspecificclassofcomputationswhichcantakeadvantageofafastoperationcalledageneralizedFouriertransform.TheproblemsthatfitintothiscategorymaywellturnouttobeeasytocomputeonaclassicalTuringmachine;ifso,Shor''squantumideaswouldbeequivalenttosomeprogramonaconventionalcomputer.Ifitdoesbecomepossibleforquantumcomputerstosearchaninfinitenumberofpossibilitiesatonce,thentheywouldbequalitatively,fundamentallymorepowerfulthanconventionalcomputingmachines.MostscientistswouldbesurprisedifquantummechanicssucceedsinprovidingakindofcomputermorepowerfulthanaTuringmachine,butsciencemakesprogressthroughaseriesofsurprises.Ifyou''rehopingtobesurprisedbyanewsortofcomputer,quantummechanicsisagoodareatokeepaneyeon.Thisleadsusbacktothephilosophicalissuestouchedonatthebeginningofthechapter-thatis,therelationshipbetweenthecomputerandthehumanbrain.Itiscertainlyconceivable,asatleastonewell-knownphysicisthasspeculatedtohootsfrommostofhiscolleagues,thatthehumanbraintakesadvantageofquantummechanicaleffects.Yetthereisnoevidencewhatsoeverthatthisisthecase.Certainly,thephysicsofaneurondependsonquantummechanics,justasthephysicsofatransistordoes,butthereisnoevidencethatneuralprocessingtakesplaceatthequantummechanicallevelasopposedtotheclassicallevel;thatis,there
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