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[数学类]

题目序号题型归类

第1题段落结构题型

第2题审题定位与引申推导题型

第3题审题定位与细节推导题型

第4题审题定位与关键词语题型

第5题指代词题型

Computerprogrammersoftenremarkthatcomputingmachines,withaperfectlackofdiscrimination,willdoanyfoolishthingtheyaretoldtodo.Thereasonforthislies,ofcourse,inthenarrowfixationofthecomputingmachine’s“intelligence”onthedetailsofitsownperceptions—itsinabilitytobeguidedbyanylargecontext.Inapsychologicaldescriptionofthecomputerintelligence,threerelatedadjectivescometomind:single-minded,literal-minded,andsimple-minded.Recognizingthis,weshouldatthesametimerecognizethatthissingle-mindedness,literal-mindedness,andsimple-mindednessalsocharacterizestheoreticalmathematics,thoughtoalesserextent.

Sincesciencetriestodealwithreality,eventhemostprecisesciencesnormallyworkwithmoreorlessimperfectlyunderstoodapproximationstowardwhichscientistsmustmaintainanappropriateskepticism.Thus,forinstance,itmaycomeasashocktomathematicianstolearnthattheSchrodingerequationforthehydrogenatomisnotaliterallycorrectdescriptionofthisatom,butonlyanapproximationtoasomewhatmorecorrectequationtakingaccountofspin,magneticdipole,andrelativisticeffects;andthatthiscorrectedequationisitselfonlyanimperfectapproximationtoaninfinitesetofquantumfield-theoreticalequations.Physicists,lookingattheoriginalSchrodingerequation,learntosenseinitthepresenceofmanyinvisibletermsinadditiontothedifferentialtermsvisible,andthissenseinspiresanentirelyappropriatedisregardforthepurelytechnicalfeaturesoftheequation.Thisveryhealthyskepticismisforeigntothemathematicalapproach.

Mathematicsmustdealwithwell-definedsituations.Thus,mathematiciansdependonanintellectualeffortoutsideofmathematicsforthecrucialspecificationoftheapproximationthatmathematicsistotakeliterally.Givemathematiciansasituationthatistheleastbitill-defined,andtheywillmakeitwell-defined,perhapsappropriately,butperhapsinappropriately.Insomecases,themathematiciansliteral-mindednessmayhaveunfortunateconsequences.Themathematiciansturnthescientists’theoreticalassumptionsthatis,theirconvenientpointsofanalyticalemphasis,intoaxioms,andthentaketheseaxiomsliterally.Thisbringsthedangerthattheymayalsopersuadethescientiststotaketheseaxiomsliterally.Thequestion,centraltothescientificinvestigationbutintenselydisturbinginthemathematicalcontext—whathappensiftheaxiomsarerelaxed?—istherebyignored.

Thephysicistrightlydreadspreciseargument,sinceanargumentthatisconvincingonlyifitispreciselosesallitsforceiftheassumptionsonwhichitisbasedareslightlychanged,whereasanargumentthatisconvincingthoughimprecisemaywellbestableundersmallperturbationsofitsunderlyingassumptions.

1.Theauthordiscussescomputingmachinesinthefirstparagraphprimarilyinordertodowhichofthefollowing?

[A]Indicatethedangersinherentinrelyingtoagreatextentonmachines.

[B]Illustratehisviewsabouttheapproachofmathematicianstoproblemsolving.

[C]Comparetheworkofmathematicianswiththatofcomputerprogrammers.

[D]Provideonedefinitionofintelligence.

2.Itcanbeinferredformthetextthatscientistsmakewhichofthefollowingassumptionsaboutscientificarguments?

[A]Theliteraltruthoftheargumentscanbemadeclearonlyinamathematicalcontext.

[B]Theargumentsnecessarilyignorethecentralquestionofscientificinvestigation.

[C]Theargumentsprobablywillbeconvincingonlytootherscientists.

[D]Thepremisesonwhichtheargumentsarebasedmaychange.

3.Accordingtothetext,mathematicianspresentarisktoscientistforwhichofthefollowingreasons?

[A]Mathematiciansmayprovidetheoriesthatareincompatiblewiththosealreadydevelopedbyscientists.

[B]Mathematiciansmaydefinesituationsinawaythatisincomprehensibletoscientists.

[C]Mathematiciansmayconvincescientiststhattheoreticalassumptionsarefacts.

[D]Scientistsmaycometobelievethataxiomaticstatementsareuntrue.

4.Theauthorsuggeststhattheapproachofphysiciststosolvingscientificproblemiswhichofthefollowing?

[A]Practicalforscientificpurposes.

[B]Detrimentaltoscientificprogress.

[C]Unimportantinmostsituations.

[D]Expedient,butoflittlelong-termvalue.

5.Theauthorimpliesthatscientistsdevelopahealthyskepticismbecausetheyareawarethat

[A]mathematiciansarebetterabletosolveproblemsthanarescientists.

[B]changesinaxiomaticpropositionswillinevitablyunderminescientificarguments.

[C]well-definedsituationsarenecessaryforthedesignofreliableexperiments.

[D]somefactorsinmostsituationsmustremainunknown.