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1科技英语阅读(ESTREADING)课后习题答案20111213183716转载标签杂谈分类英语天堂UNIT1MATHEMATICSPARTIESTREADING1WHOISBERTRANDRUSSELLBERTRANDARTHURWILLIAMRUSSELLB1872D1970WASABRITISHPHILOSOPHER,LOGICIAN,ESSAYISTANDSOCIALCRITICBESTKNOWNFORHISWORKINMATHEMATICALLOGICANDANALYTICPHILOSOPHYHISMOSTINFLUENTIALCONTRIBUTIONSINCLUDEHISDEFENSEOFLOGICISMTHEVIEWTHATMATHEMATICSISINSOMEIMPORTANTSENSEREDUCIBLETOLOGIC,HISREFININGOFTHEPREDICATECALCULUSINTRODUCEDBYGOTTLOBFREGEWHICHSTILLFORMSTHEBASISOFMOSTCONTEMPORARYLOGIC,HISDEFENSEOFNEUTRALMONISMTHEVIEWTHATTHEWORLDCONSISTSOFJUSTONETYPEOFSUBSTANCETHATISNEITHEREXCLUSIVELYMENTALNOREXCLUSIVELYPHYSICAL,ANDHISTHEORIESOFDEFINITEDESCRIPTIONSANDLOGICALATOMISMRUSSELLISGENERALLYRECOGNIZEDASONEOFTHEFOUNDERSOFMODERNANALYTICPHILOSOPHY,ANDISREGULARLYCREDITEDWITHBEINGONEOFTHEMOSTIMPORTANTLOGICIANSOFTHETWENTIETHCENTURY2WHATISRUSSELLSPARADOXRUSSELLDISCOVEREDTHEPARADOXTHATBEARSHISNAMEIN1901,WHILEWORKINGONHISPRINCIPLESOFMATHEMATICS1903THEPARADOXARISESINCONNECTIONWITHTHESETOFALLSETSTHATARENOTMEMBERSOFTHEMSELVESSUCHASET,IFITEXISTS,WILLBEAMEMBEROFITSELFIFANDONLYIFITISNOTAMEMBEROFITSELFTHEPARADOXISSIGNIFICANTSINCE,USINGCLASSICALLOGIC,ALLSENTENCESAREENTAILEDBYACONTRADICTIONRUSSELLSDISCOVERYTHUSPROMPTEDALARGEAMOUNTOFWORKINLOGIC,SETTHEORY,ANDTHEPHILOSOPHYANDFOUNDATIONSOFMATHEMATICSSECTIONCPOSTREADINGTASKREADINGCOMPREHENSION1DIRECTIONSWORKONYOUROWNANDFILLINTHEBLANKSWITHTHEMAINIDEAPART1PARA1BRIEFINTRODUCTIONTORUSSELLSPARADOXPART2PARAS25THEEFFECTOFRUSSELLSPARADOXONGOTTLOBFREGESSYSTEMPARA2RUSSELLSPARADOXDEALTAHEAVYBLOWTOFREGESATTEMPTSTODEVELOPAFOUNDATIONFORALLOFMATHEMATICSUSINGSYMBOLICLOGICPARA3ANILLUSTRATIONOFRUSSELLSPARADOXINTERMSOFSETSPARA4CONTRADICTIONFOUNDINTHESETPARA5FREGENOTICEDTHEDEVASTATINGEFFECTOFRUSSELLSPARADOXONHISSYSTEMANDINABILITYTOSOLVEITPART3PARAS68SOLUTIONSOFFEREDBYMATHEMATICIANSTORUSSELSPARADOXPARA6RUSSELLSOWNRESPONSETOTHEPARADOXWITHHIS“THEORYOFTYPES“PARA7ZERMELOSSOLUTIONTORUSSELLSPARADOXPARA8WHATBECAMEOFTHEEFFORTTODEVELOPALOGICALFOUNDATIONFORALLOFMATHEMATICSPART4PARA9CORRESPONDENCEBETWEENRUSSELLANDFREGEONTHEPARADOXVOCABULARYANDSTRUCTURE2DIRECTIONSCOMPLETETHESENTENCESWITHTHEWORDSGIVENINTHEBRACKETSCHANGETHEFORMIFNECESSARY1THEKEYTOUNRAVELINGSUCHAPPARENTPARADOXESISTOCHARACTERIZETHEINITIALSETOFPOSSIBILITIES2“INITIAL“MEANINGBEFOREYOURECEIVEANYEXTRAINFORMATIONANDTHENTOELIMINATEPOSSIBILITIESBASEDONTHATEXTRAINFORMATIONBASE2INDEED,THISSEPARATIONOFMEANINGISREFLECTEDBYTHEDEFINITIONOF“WEAK“INTHEOALD,WITHADISTINCTSENSERESERVEDFORITSUSEWHENPERTAININGTOTHATOFSOLUTIONSDEFINITION3THERESULTINGRADICALPOLLUTIONCONTROLPROGRAMMEOUTLINEDBYNIXON,CALLINGFORA90PERCENTREDUCTIONINVEHICLEEMISSIONSBY1980,NOTONLYLEDTOHIMBEINGCREDITEDALBEITBRIEFLYASPOLICYINITIATOROFANENVIRONMENTALCLEANUPBUTALSOPROVIDEDHIMWITHTHECHANCETODEALABLOWTOONEOFHISMOSTIMPORTANTOPPONENTSINTHE1972ELECTIONS,EDMUNDMUSKIEBLOW4SINGAPORESCONTINUINGINVESTMENTSINEDUCATIONANDTRAININGHASBROUGHTATENFOLDINCREASEINOURPOOLOFINFORMATIONTECHNOLOGYPROFESSIONALSANDTHESINGAPOREWORKERHASBEENCONSISTENTLYRATEDBYBERIASTHEWORLDSBESTINTERMSOFTECHNICALSKILLS,ATTITUDEANDPRODUCTIVITYTERM5INTHISWORKHEWASLEDTOTOPOLOGY,ASTILLNEWKINDOFMATHEMATICSRELATEDTOGEOMETRY,ANDTOTHESTUDYOFSHAPESCOMPACTMANIFOLDSOFALLDIMENSIONSLEAD6IFTHEREISNOALLOWABLESTRINGWHICHSPANSTHEWHOLEGRAPH,THENWECANSEARCHINTHESAMEWAYASDESCRIBEDABOVE,BUTWHEREVERTHEREQUIREDPATHDOESNOTEXISTINTHETREE,CHECKIFTHATPOSITIONINTHETREEISFLAGGEDFORENDOFWORDWAY7DURINGTHEPASTCENTURY,STEPSFORWARDINPHYSICSHAVEOFTENCOMEINTHEFORMOFNEWLYFOUNDPARTICLESINENGINEERING,MORECOMPLEXDEVICESINASTRONOMY,FARTHERPLANETSANDSTARSINBIOLOGY,RARERGENESANDINCHEMISTRY,MOREUSEFULMATERIALSANDMEDICATIONSFORM8ASECONDREASONFORMEASUREMENTSISTHEMORETHEORETICAL,PUTBYLOVEAS“THEDISCOVERYOFNUMERICALRELATIONSBETWEENTHEQUANTITIESTHATCANBEMEASUREDTOSERVEASABASISFORTHEINDUCTIVEDETERMINATIONOFTHEFORMOFTHEINTRINSICENERGYFUNCTION“SERVE9THUSTHEOPTIMUMCONDITIONSFORCOASTALTERRACEDEVELOPMENTWOULDSEEMTOBEAREASWITHSMALLTIDALRANGESFINALLY,TIDALRANGEISANIMPORTANTFACTORINTHEGENERATIONOFTIDALCURRENTSWHICHMAYLOCALLYBECOMEOFGEOMORPHOLOGICALIMPORTANCEBECOME10THEORIGINALDOUBLEENTRANCEDOORSTOTHEBOOKINGHALLHADBEENREPLACEDBYANUTTERLYINCONGRUOUSPICTUREWINDOWASHADADJACENTBOOKINGHALLANDWAITINGROOMWINDOWSREPLACE3DIRECTIONSREORDERTHEDISORDEREDPARTSOFASENTENCETOMAKEACOMPLETESENTENCE1ASIMPLEWAYTODESCRIBETOPOLOGYISASARUBBERSHEETGEOMETRYTOPOLOGISTSSTUDYTHOSEPROPERTIESOFSHAPESTHATREMAINTHESAMEWHENTHESHAPESARESTRETCHEDORCOMPRESSED2SINCETHEMID1990SSCIENTISTSHAVEFLOATEDTHEIDEATHATREPRESENTATIONSOFNUMERICQUANTITIES,WHETHEREXPRESSEDASDIGITSORASWRITTENWORDS,ARECODIFIEDBYTHEPARIETALCORTEX,AHIGHERPROCESSINGREGIONINTHEBRAINLOCATEDJUSTABOVETHEFOREHEAD3ASACTIVITYWASMONITORED,LOCATEDJUSTABOVETHEFOREHEAD,RESEARCHERSNOTEDCHANGESUNDERTHEASSUMPTIONTHATTHEBRAINREDUCESACTIVITYASITBECOMESACCUSTOMEDTOASTIMULUSANDTHENREACTIVATESWHENANOVELSTIMULUSISPRESENTED4THATHASNOTSTOPPEDPHYSICISTSFROMDEVISINGNEWALGORITHMSFORTHEDEVICES,WHICHCANCALCULATEALOTFASTERTHANORDINARYCOMPUTERSINFACT,EXPONENTIALLYFASTER,INQUITEALITERALSENSE5SUCHADEVICEWOULDBEMADEOFMETAMATERIAL,ATHICKETOFMETALRINGSOROTHERSHAPESTHATBENDSLIGHTINFUNNYWAYS4DIRECTIONSCHANGETHEFOLLOWINGSENTENCESINTONOMINALIZEDONES1THEPASSAGEOFNIGHTCOULDBEMARKEDBYTHEAPPEARANCEOF18OFTHESESTARS32THEFULLPROOFOFFERMATSLASTTHEOREMISCONTAINEDINTHESETWOPAPERS3THECONCEPTOFFIXEDLENGTHHOURS,HOWEVER,DIDNOTORIGINATEUNTILTHEHELLENISTICPERIOD4THEREISAPROBABILITYTHATMYFIRSTSOCKISREDBECAUSEONLYONEOFTHEREMAININGTHREESOCKSISRED5THEIMPORTANCEOFACCURATEDATAINQUANTITATIVEMODELINGISCENTRALTOUSINGBAYESSTHEOREMTOCALCULATETHEPROBABILITYOFTHEEXISTENCEOFGODDISCOURSEUNDERSTANDING1CA“3PERCENTMARGINOFERROR“MEANSTHATTHEREISA95PERCENTCHANCETHATTHESURVEYRESULTWILLBEWITHIN3PERCENTOFTHEPOPULATIONVALUE2EHOWISITTHATASURVEYOFONLY1,000PEOPLECANREACHTHISLEVELOFACCURACY3GTHEMARGINOFERRORDEPENDSINVERSELYONTHESQUAREROOTOFTHESAMPLESIZE4ATHEMARGINOFERRORISAMATHEMATICALABSTRACTION,ANDTHEREAREANUMBEROFREASONSWHYACTUALERRORSINSURVEYSARELARGER5FFINALLY,THE3PERCENTMARGINOFERRORISANUNDERSTATEMENTBECAUSEOPINIONSCHANGESECTIONAPREREADINGTASK1WHODISCOVEREDTHEMANDELBROTSETTHISISNOTATRICKQUESTION,NOTEASYTOANSWERMANYPEOPLEINCLUDINGMANDELBROTHAVELAIDCLAIMTOTHEDISCOVERY2WHYWASTHESETNAMEDAFTERBENOITBMANDELBROTTHESETISNAMEDAFTERBENOITBMANDELBROT,AMATHEMATICIANATTHEIBMTHOMASJWATSONRESEARCHCENTERBECAUSEHECOINEDTHETERMFRACTALTODESCRIBEPHENOMENASUCHASCOASTLINES,SNOWFLAKES,MOUNTAINSANDTREESWHOSEPATTERNSREPEATTHEMSELVESATSMALLERANDSMALLERSCALES3WHYHASTHEREBEENSOMUCHCONTROVERSYABOUTWHODISCOVEREDTHEMANDELBROTSETMANDELBROTCLAIMSTHATHEANDHEALONEDISCOVEREDTHEMANDELBROTSET,BUTTHEREAREOTHERMATHEMATICIANSWHOHAVECHALLENGEDHISCLAIM4WHATDIDTHECHALLENGERSSAYABOUTMANDELBROTSCLAIMOFDISCOVERYTWOMATHEMATICIANSSAIDTHATTHEYINDEPENDENTLYDISCOVEREDANDDESCRIBEDTHESETATABOUTTHESAMETIMEASMANDELBROTDIDANDANOTHERMATHEMATICIANALSOASSERTEDTHATHISWORKONTHESETNOTONLYPREDATEDMANDELBROTSEFFORTSBUTALSOHELPEDTOGUIDETHEM5WHYDIDSOMEPROFESSORSSUPPORTMANDELBROTSCLAIMMANDELBROTDESERVESTOHAVETHESETNAMEDAFTERHIM,BECAUSEHISEFFORTSBROUGHTTHESETTOTHEATTENTIONOFBOTHTHEPUBLICANDOFTHEPUREMATHEMATICSCOMMUNITYSECTIONCPOSTREADINGTASKLANGUAGEINUSE1MATCHTHECHINESEINTHELEFTCOLUMNWITHTHEENGLISHINTHERIGHTCOLUMN迭代函数ITERATIVEFUNCTION优先权之争PRIORITYBATTLE分形特征FRACTALPROPERTIES有意义MAKESENSE以越来越小的规模重复同一模式PATTERNSREPEATTHEMSELVESATSMALLERANDSMALLERSCALES混沌理论CHAOSTHEORY季刊AQUARTERLYJOURNAL数学界THEMATHEMATICSCOMMUNITY4波纹线CRISPLINES会议公报PROCEEDINGSOFACONFERENCE2JOINTHEFOLLOWINGSHORTSENTENCESINTOLONGERONESEGAAFRACTALISGENERALLYAROUGHORFRAGMENTEDGEOMETRICSHAPEBTHESHAPECANBESUBDIVIDEDINPARTSCEACHPARTISATLEASTAPPROXIMATELYAREDUCEDSIZECOPYOFTHEWHOLE,APROPERTYCALLEDDEACHPARTHASAPROPERTYOFSELFSIMILARITYEGAFRACTALISGENERALLY“AROUGHORFRAGMENTEDGEOMETRICSHAPETHATCANBESUBDIVIDEDINPARTS,EACHOFWHICHISATLEASTAPPROXIMATELYAREDUCEDSIZECOPYOFTHEWHOLE“,APROPERTYCALLEDSELFSIMILARITY1INADDITIONTOCOININGTHETERM“FRACTAL“TODESCRIBEOBJECTSANDSURFACESWHICHAREIRREGULARATVARIOUSDIMENSIONSOFSCALE,HEALSOINTRODUCEDSUCHCONCEPTSAS“FRACTALDIMENSIONS“ANDTHEPARTICULARFRACTALKNOWNASTHEMANDELBROTSET,FREQUENTLYREPRESENTEDWITHTHEMATHEMATICALFORMULAZZ2C2ITAPPEAREDTHATTHINGSWERESETTLINGINTOAPLEASANTANDFRUITFULROUTINE,WITHHISSCHOOLLESSONSSUPPLEMENTEDBYLONGTALKSWITHHISUNCLEABOUTCLASSICALANALYSIS,THEITERATIVEWORKOFPIERREFATOUANDTHEEQUALLYFASCINATINGJULIASETSGENERATEDBYGASTONJULIA3JUSTASTHEYOUTHFULMANDELBROTHADPASSEDHISCOLLEGEENTRANCEEXAMSBYTRANSLATINGALGEBRAICPROBLEMSINTOGEOMETRICALPROBLEMS,ANDSOLVINGTHEMBYINTUITIVELYDEDUCINGTHE“PERFECTED“SHAPE,HEHEREREALIZEDTHEREWASSOMETHINGDEEPER,SOMETHINGMATHEMATICAL,BEHINDTHESESTRANGEPATTERNS4BUTTHEBEAUTYINMANDELBROTSMODELSWASNOTTHATTHEYGENERATEDADECEITFULRANDOMNESS,BUTTHATTHEYCOULDGENERATEGRAPHEDDATAWHOSEVISUALPATTERNACCURATELYMIMICKEDTHEVISUALPATTERNSCREATEDBYREALPHENOMENA。5BUTDESPITEBEINGTHEINSPIRATIONFORSUCHMETAPHYSICS,MANDELBROT,WHENASKEDIFFRACTALSDONTPOINTTOASINGLERULEUNDERLYINGREALITY,HASSIMPLYSTATED,“THEREISNOSINGLERULETHATGOVERNSTHEUSEOFGEOMETRYIDONTTHINKONEEXISTS“3TRANSLATETHESENTENCESINTOCHINESE1HEISBESTKNOWNFORCOININGTHETERMFRACTALTODESCRIBEPHENOMENASUCHASCOASTLINES,SNOWFLAKES,MOUNTAINSANDTREESWHOSEPATTERNSREPEATTHEMSELVESATSMALLERANDSMALLERSCALES他主要是因为用分形这个概念来描述(海岸线,雪花,山脉和树木)等不规则形状等现象而闻名于世,这些不规则形状在越来越小的规模上不断重复同一模式。2ACLOSERLOOKREVEALSTHATTHEBORDERSOFTHESETDONOTFORMCRISPLINESBUTSEEMTOSHIMMERLIKEFLAMES如果再仔细观察,就可以发现集的边界并没有呈波纹线,而是像火焰一样闪光。3KRANTZINTRODUCEDANEWELEMENTINTOTHEDEBATE,HOWEVER,BYSTATINGTHATTHEMANDELBROTSET“WASNOTINVENTEDBYMANDELBROTBUTOCCURSEXPLICITLYINTHELITERATUREACOUPLEOFYEARSBEFORETHETERMMANDELBROTSETWASCOINED“但是,克朗兹在这场辩论中引入了一个新东西,他说曼德布洛特集不是曼德布洛特发明的,而是早在“曼德布洛特集”这个术语出现几年以前就已经明确地在数学文献中出现了。4MANDELBROTALSOSUGGESTEDTHATEVENIFBROOKSANDMATELSKISPUBLICATIONHADPRECEDEDHIS,THEYSTILLCOULDNOTBECONSIDEREDDISCOVERERSOFTHESET,BECAUSETHEYDIDNOTAPPRECIATEITSSIGNIFICANCE5曼德布洛特同时也暗示即使布鲁克斯和马特尔斯基的论文先于他发表,但因为他们没有领会到其价值,仍然不能将他们看作是曼德布洛特集的发现者。5INRESPONSETOHUBBARDANDDOUADYSCHARGETHATHEISSTINGYINGRANTINGCREDIT,MANDELBROTSAYSHEHASALSOBEENACCUSEDOFOVERCITATION对胡巴德和杜阿迪指责他对论文中材料来源的说明上做得非常少,曼德布洛特回应说也有人也指责过他过分引用别人的成果。4TRANSLATETHESENTENCESINTOENGLISH1他的生活和工作过程正如使他成名的几何学一样,既不是线性的,也不具备简单的形状。LIKETHEGEOMETRYTHATMADEHIMFAMOUS,NEITHERHISLIFENORTHECOURSEOFHISWORKWASLINEARORSIMPLISTICINSHAPEANDFORM2曼德布洛特说在随后的的两年里他在多个领域中摸索,却没有明显的相联系的线索。MANDELBROTSAYSHESPENTTHENEXTTWOYEARSGROPING,EXPLORINGFIRSTONEFIELDANDTHENANOTHER,WITHOUTANYCLEARSENSEOFTHECONNECTINGTHREAD3更奇怪的是,他发现噪音周期与清晰传送周期的比率是恒定的,与用于绘制这个现象的时间大小无关。STRANGERSTILL,HEFOUNDTHATTHERATIOOFPERIODSOFNOISETOPERIODSOFCLEANTRANSMISSIONREMAINEDCONSTANT,REGARDLESSOFTHESCALEOFTIMEUSEDTOPLOTTHEPHENOMENON4通过查询一直到1900年的记录,他开始发现了一个令人惊异的模式,这个模式使他明白了他10年前有关线路噪声的研究工作。USINGRECORDSDATINGBACKTO1900,HEBEGANTOPERCEIVEANASTONISHINGPATTERNONETHATHEARKENEDBACKTOHISWORKONLINENOISEADECADEEARLIER5尽管就正常销售而言,价格变化是无序的,而且没有人能够预测价格变化的准确数值,但变化本身却遵循着与变化幅度相关的对称模式。ALTHOUGHPRICECHANGESWEREERRATICINTERMSOFNORMALDISTRIBUTIONANDNOONECOULDPREDICTTHEEXACTAMOUNTOFANYPARTICULARPRICECHANGE,THECHANGESTHEMSELVESFOLLOWEDASYMMETRICALPATTERNWITHREGARDSTOSCALINGUNIT2PHYSICSSECTIONAPREREADINGTASKWARMUPQUESTIONSWORKINPAIRSANDDISCUSSTHEFOLLOWINGQUESTIONS1WHATISQUANTUMPHYSICSQUANTUMPHYSICSISTHESTUDYOFTHEBEHAVIOROFMATTERANDENERGYATTHEMOLECULAR,ATOMIC,NUCLEAR,ANDEVENSMALLERMICROSCOPICLEVELSINTHEEARLY20THCENTURY,ITWASDISCOVEREDTHATTHELAWSTHATGOVERNMACROSCOPICOBJECTSDONOTFUNCTIONTHESAMEINSUCHSMALLREALMSHTTP/PHYSICSABOUTCOM/OD/QUANTUMPHYSICS/P/QUANTUMPHYSICSHTM2DOYOUKNOWANYTHINGABOUTDARKMATTERDARKMATTERISAHYPOTHESIZEDFORMOFMATTERPARTICLETHATDOESNOTREFLECTOREMITELECTROMAGNETICRADIATIONTHEEXISTENCEOFDARKMATTERISINFERREDFROMGRAVITATIONALEFFECTSONVISIBLEMATTER,SUCHASSTARSANDGALAXIESASMALLPERCENTAGEOFTHEGRAVITATIONALEFFECTSOBSERVEDAREFROMVISIBLEMATTERSOMEESTIMATESAREASLOWAS4OFTOTALGRAVITATIONALEFFECTSTHEREMAINING96ISPRESUMEDTORESULTFROMDARKMATTERORDARKENERGY,THOUGHTHESETERMSARESOMEWHATINDICATIVEOFOURIGNORANCEOFTHE6EXACTNATUREOFTHESEUNKNOWNQUANTITIES,ASTHEYHAVENEVERBEENDIRECTLYOBSERVEDONEPOSSIBLECANDIDATEFORDARKMATTERARETHEORETICALPARTICLESKNOWNASWEAKLYINTERACTINGMASSIVEPARTICLESWIMPS,WHICHAREBEINGSEARCHEDFORBYTHECRYOGENICDARKMATTERSEARCHCDMSEXPERIMENT3WHATISDARKENERGYDARKENERGYISAHYPOTHETICALFORMOFENERGYTHATPERMEATESSPACEANDEXERTSANEGATIVEPRESSURE,WHICHWOULDHAVEGRAVITATIONALEFFECTSTOACCOUNTFORTHEDIFFERENCESBETWEENTHETHEORETICALANDOBSERVATIONALRESULTSOFGRAVITATIONALEFFECTSONVISIBLEMATTERDARKENERGYISNOTDIRECTLYOBSERVED,BUTRATHERINFERREDFROMOBSERVATIONSOFGRAVITATIONALINTERACTIONSBETWEENASTRONOMICALOBJECTS,ALONGWITHDARKMATTERTHETERM“DARKENERGY“WASCOINEDBYTHETHEORETICALCOSMOLOGISTMICHAELSTURNER4HAVEYOUEVERHEARDOFTHEBIGBANGTHEORYCANYOUGIVEANACCOUNTOFITTHEBIGBANGISTHEDOMINANTANDHIGHLYSUPPORTEDTHEORYOFTHEORIGINOFTHEUNIVERSEINESSENCE,THISTHEORYSTATESTHATTHEUNIVERSEBEGANFROMANINITIALPOINTORSINGULARITYWHICHHASEXPANDEDOVERBILLIONSOFYEARSTOFORMTHEUNIVERSEASWENOWKNOWITIN1927,ROMANCATHOLICPRIESTANDPHYSICISTGEORGESLEMAITREINDEPENDENTLYCALCULATEDTHEFRIEDMANSOLUTIONANDAGAINSUGGESTEDTHATTHEUNIVERSEMUSTBEEXPANDINGTHISTHEORYWASSUPPORTEDBYHUBBLEWHEN,IN1929,HEFOUNDTHATTHEREWASACORRELATIONBETWEENTHEDISTANCEOFTHEGALAXIESANDTHEAMOUNTOFREDSHIFTINTHATGALAXYSLIGHTTHEDISTANTGALAXIESWEREMOVINGAWAYFASTER,WHICHWASEXACTLYWHATWASPREDICTEDBYLEMAITRESSOLUTIONSIN1931,LEMAITREWENTFURTHERWITHHISPREDICTIONS,EXTRAPOLATINGBACKWARDSINTIMEFINDTHATTHEMATTEROFTHEUNIVERSEWOULDREACHANINFINITEDENSITYANDTEMPERATUREATAFINITETIMEINTHEPASTTHISMEANSTHEUNIVERSEMUSTHAVEBEGUNINANINCREDIBLYSMALL,DENSEPOINTOFMATTERA“PRIMEVALATOM“5HOWDOYOUUNDERSTANDSTRINGTHEORYSTRINGTHEORYISAMATHEMATICALTHEORYTHATTRIESTOEXPLAINCERTAINPHENOMENAWHICHISNOTCURRENTLYEXPLAINABLEUNDERTHESTANDARDMODELOFQUANTUMPHYSICSSTRINGTHEORYWASINITIALLYDEVELOPEDINTHE1970SINANATTEMPTTOEXPLAINSOMEINCONSISTENCIESWITHTHEENERGYBEHAVIOROFHADRONSANDOTHERFUNDAMENTALPARTICLESOFPHYSICSASWITHMUCHOFQUANTUMPHYSICS,THEMATHEMATICSTHATAPPLIESTOSTRINGTHEORYCANNOTBEUNIQUELYSOLVEDPHYSICISTSMUSTAPPLYPERTURBATIONTHEORYTOOBTAINASERIESOFAPPROXIMATEDSOLUTIONSSUCHSOLUTIONS,OFCOURSE,INCLUDEASSUMPTIONSWHICHMAYORMAYNOTBETRUETHEDRIVINGHOPEBEHINDTHISWORKISTHATITWILLRESULTINA“THEORYOFEVERYTHING,“INCLUDINGASOLUTIONTOTHEPROBLEMOFQUANTUMGRAVITY,TORECONCILEQUANTUMPHYSICSWITHGENERALRELATIVITY,THUSRECONCILINGTHEFUNDAMENTALFORCESOFPHYSICSSECTIONCPOSTREADINGTASKREADINGCOMPREHENSION1DIRECTIONSWORKONYOUROWNANDFILLINTHEBLANKSWITHTHEMAINIDEAPART1PARAS13BRIEFINTRODUCTIONTODARKENERGYPARA1DARKENERGYISANUNEXPLAINEDFORCEWHICHTUGSGALAXIESAWAYFROMEACHOTHERPARA2DARKENERGYISSOMEWHATLIKEANTIGRAVITYPARA3DARKENERGYISSCIENTISTSHYPOTHETICFORMOFENERGYTOEXPLAINTHEUNIVERSESEXPANSIONPART2PARAS49THEDISCOVERYOFDARKENERGYCONFOUNDINGEXPECTATIONSPARA4THEDISCOVERYOFDARKENERGYISACASEOFSCIENCECONFOUNDINGEXPECTATIONS7PARA5EXPERTSEXPECTEDTHATGRAVITYHADSLOWEDDOWNTHEUNIVERSESRATEOFEXPANSIONPARA6THEUNIVERSESRATEOFEXPANSIONWASSPEEDINGUPPARA7THERESULTWASBEYONDEXPERTSEXPECTATIONSWHICHCAUSEDMUCHNERVOUSLAUGHTERPARA8THEMEASUREMENTSOFSUPERNOVAEPROVIDEDTHEEVIDENCETHATTHEUNIVERSESRATEOFBALLOONINGWASSPEEDINGUPPARA9THESCIENTISTSOBSERVEDMANYSUPERNOVAEATDIFFERENTDISTANCESTODETERMINEHOWFASTTHEYARESPEEDINGAWAYFROMUSPART3PARAS1013THERATEOFTHEEXPANSIONOFTHEUNIVERSESHOCKINGRESULTSPAR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