“Tobesure！hanghimandwelcome。But，onceuponatime，acertainrichmiserconceivedthedesignofspunginguponthisAbernethyforamedicalopinion。Gettingup，forthispurpose，anordinaryconversationinaprivatecompany，heinsinuatedhiscasetothephysician，asthatofanimaginaryindividual。
　　“’Wewillsuppose，’saidthemiser，’thathissymptomsaresuchandsuch；now，doctor，whatwouldyouhavedirectedhimtotake？’
　　“’Take！’saidAbernethy，’why，takeadvice，tobesure。’“
　　“But。”saidthePrefect，alittlediscomposed，“Iamperfectlywillingtotakeadvice，andtopayforit。Iwouldreallygivefiftythousandfrancstoanyonewhowouldaidmeinthematter。”
　　“Inthatcase。”repliedDupin，openingadrawer，andproducingacheck-book，“youmayaswellfillmeupacheckfortheamountmentioned。Whenyouhavesignedit，Iwillhandyoutheletter。”
　　Iwasastounded。ThePrefectappearedabsolutelythunder-stricken。
　　Forsomeminutesheremainedspeechlessandmotionless，lookingincredulouslyatmyfriendwithopenmouth，andeyesthatseemedstartingfromtheirsockets；then，apparentlyrecoveringhimselfinsomemeasure，heseizedapen，andafterseveralpausesandvacantstares，finallyfilledupandsignedacheckforfiftythousandfrancs，andhandeditacrossthetabletoDupin。Thelatterexamineditcarefullyanddepositeditinhispocket-book；then，unlockinganescritoire，tookthencealetterandgaveittothePrefect。Thisfunctionarygraspeditinaperfectagonyofjoy，openeditwithatremblinghand，castarapidglanceatitscontents，andthen，scramblingandstrugglingtothedoor，rushedatlengthunceremoniouslyfromtheroomandfromthehouse，withouthavingutteredasyllablesinceDupinhadrequestedhimtofillupthecheck。
　　Whenhehadgone，myfriendenteredintosomeexplanations。
　　“TheParisianpolice。”hesaid，“areexceedinglyableintheirway。
　　Theyarepersevering，ingenious，cunning，andthoroughlyversedintheknowledgewhichtheirdutiesseemchieflytodemand。Thus，whenGdetailedtoushismadeofsearchingthepremisesattheHotelD，Ifeltentireconfidenceinhishavingmadeasatisfactoryinvestigation-sofarashislaborsextended。”
　　“Sofarashislaborsextended？”saidI。
　　“Yes。”saidDupin。“Themeasuresadoptedwerenotonlythebestoftheirkind，butcarriedouttoabsoluteperfection。Hadtheletterbeendepositedwithintherangeoftheirsearch，thesefellowswould，beyondaquestion，havefoundit。”
　　Imerelylaughed-butheseemedquiteseriousinallthathesaid。
　　“Themeasures，then。”hecontinued，“weregoodintheirkind，andwellexecuted；theirdefectlayintheirbeinginapplicabletothecase，andtotheman。Acertainsetofhighlyingeniousresourcesare，withthePrefect，asortofProcrusteanbed，towhichheforciblyadaptshisdesigns。Butheperpetuallyerrsbybeingtoodeeportooshallow，forthematterinhand；andmanyaschoolboyisabetterreasonerthanhe。Iknewoneabouteightyearsofage，whosesuccessatguessinginthegameof’evenandodd’attracteduniversaladmiration。Thisgameissimple，andisplayedwithmarbles。Oneplayerholdsinhishandanumberofthesetoys，anddemandsofanotherwhetherthatnumberisevenorodd。Iftheguessisright，theguesserwinsone；ifwrong，helosesone。TheboytowhomI
　　alludewonallthemarblesoftheschool。Ofcoursehehadsomeprincipleofguessing；andthislayinmereobservationandadmeasurementoftheastutenessofhisopponents。Forexample，anarrantsimpletonishisopponent，and，holdinguphisclosedhand，asks，’aretheyevenorodd？’Ourschoolboyreplies，’odd，’andloses；butuponthesecondtrialhewins，forhethensaystohimself，’thesimpletonhadthemevenuponthefirsttrial，andhisamountofcunningisjustsufficienttomakehimhavethemodduponthesecond；Iwillthereforeguessodd；’-heguessesodd，andwins。
　　Now，withasimpletonadegreeabovethefirst，hewouldhavereasonedthus：’ThisfellowfindsthatinthefirstinstanceI
　　guessedodd，and，inthesecond，hewillproposetohimself，uponthefirstimpulse，asimplevariationfromeventoodd，asdidthefirstsimpleton；butthenasecondthoughtwillsuggestthatthisistoosimpleavariation，andfinallyhewilldecideuponputtingitevenasbefore。Iwillthereforeguesseven；’-heguesseseven，andwins。
　　Nowthismodeofreasoningintheschoolboy，whomhisfellowstermed’lucky，’-what，initslastanalysis，isit？”
　　“Itismerely。”Isaid，“anidentificationofthereasoner’sintellectwiththatofhisopponent。”
　　“Itis。”saidDupin；“and，uponinquiring，oftheboybywhatmeansheeffectedthethoroughidentificationinwhichhissuccessconsisted，Ireceivedanswerasfollows：’WhenIwishtofindouthowwise，orhowstupid，orhowgood，orhowwickedisanyone，orwhatarehisthoughtsatthemoment，Ifashiontheexpressionofmyface，asaccuratelyaspossible，inaccordancewiththeexpressionofhis，andthenwaittoseewhatthoughtsorsentimentsariseinmymindorheart，asiftomatchorcorrespondwiththeexpression。’ThisresponseoftheschoolboyliesatthebottomofallthespuriousprofunditywhichhasbeenattributedtoRochefoucault，toLaBougive，toMachiavelli，andtoCampanella。”
　　“Andtheidentification。”Isaid，“ofthereasoner’sintellectwiththatofhisopponent，depends，ifIunderstandyouaright，upontheaccuracywithwhichtheopponent’sintellectisadmeasured。”
　　“Foritspracticalvalueitdependsuponthis。”repliedDupin；“andthePrefectandhiscohortfailsofrequently，first，bydefaultofthisidentification，and，secondly，byill-admeasurement，orratherthroughnon-admeasurement，oftheintellectwithwhichtheyareengaged。Theyconsideronlytheirownideasofingenuity；and，insearchingforanythinghidden，advertonlytothemodesinwhichtheywouldhavehiddenit。Theyarerightinthismuch-thattheirowningenuityisafaithfulrepresentativeofthatofthemass；butwhenthecunningoftheindividualfelonisdiverseincharacterfromtheirown，thefelonfoilsthem，ofcourse。Thisalwayshappenswhenitisabovetheirown，andveryusuallywhenitisbelow。Theyhavenovariationofprincipleintheirinvestigations；atbest，whenurgedbysomeunusualemergency-bysomeextraordinaryreward-theyextendorexaggeratetheiroldmodesofpractice，withouttouchingtheirprinciples。What，forexample，inthiscaseofD，hasbeendonetovarytheprincipleofaction？Whatisallthisboring，andprobing，andsounding，andscrutinizingwiththemicroscopeanddividingthesurfaceofthebuildingintoregisteredsquareinches-
　　whatisitallbutanexaggerationoftheapplicationoftheoneprincipleorsetofprinciplesofsearch，whicharebasedupontheonesetofnotionsregardinghumaningenuity，towhichthePrefect，inthelongroutineofhisduty，hasbeenaccustomed？Doyounotseehehastakenitforgrantedthatallmenproceedtoconcealaletter，-notexactlyinagimletholeboredinachair-leg-but，atleast，insomeout-of-the-wayholeorcornersuggestedbythesametenorofthoughtwhichwouldurgeamantosecretealetterinagimlet-holeboredinachair-leg？Anddoyounotseealso，thatsuchrecherch閟
　　nooksforconcealmentareadaptedonlyforordinaryoccasions，andwouldbeadoptedonlybyordinaryintellects；for，inallcasesofconcealment，adisposalofthearticleconcealed-adisposalofitinthisrecherch？manner，-is，intheveryfirstinstance，presumableandpresumed；andthusitsdiscoverydepends，notatallupontheacumen，butaltogetheruponthemerecare，patience，anddeterminationoftheseekers；andwherethecaseisofimportance-
　　or，whatamountstothesamethinginthepolicialeyes，whentherewardisofmagnitude，-thequalitiesinquestionhaveneverbeenknowntofail。YouwillnowunderstandwhatImeantinsuggestingthat，hadthepurloinedletterbeenhiddenanywherewithinthelimitsofthePrefect’sexamination-inotherwords，hadtheprincipleofitsconcealmentbeencomprehendedwithintheprinciplesofthePrefect-itsdiscoverywouldhavebeenamatteraltogetherbeyondquestion。Thisfunctionary，however，hasbeenthoroughlymystified；andtheremotesourceofhisdefeatliesinthesuppositionthattheMinisterisafool，becausehehasacquiredrenownasapoet。Allfoolsarepoets；thisthePrefectfeels；andheismerelyguiltyofanondistributiomediiinthenceinferringthatallpoetsarefools。”
　　“Butisthisreallythepoet？”Iasked。“Therearetwobrothers，I
　　know；andbothhaveattainedreputationinletters。TheMinisterI
　　believehaswrittenlearnedlyontheDifferentialCalculus。Heisamathematician，andnopoet。”
　　“Youaremistaken；Iknowhimwell；heisboth。Aspoetandmathematician，hewouldreasonwell；asmeremathematician，hecouldnothavereasonedatall，andthuswouldhavebeenatthemercyofthePrefect。”
　　“Yousurpriseme。”Isaid，“bytheseopinions，whichhavebeencontradictedbythevoiceoftheworld。Youdonotmeantosetatnaughtthewell-digestedideaofcenturies。Themathematicalreasonhaslongbeenregardedasthereasonparexcellence。”
　　“’Ilya？pari鑢，’“repliedDupin，quotingfromChamfort，“’quetouteid閑publique，touteconventionre鐄eestunesottise，carelleaconvenueauplusgrandnombre。’Themathematicians，Igrantyou，havedonetheirbesttopromulgatethepopularerrortowhichyouallude，andwhichisnonethelessanerrorforitspromulgationastruth。Withanartworthyabettercause，forexample，theyhaveinsinuatedtheterm’analysis’intoapplicationtoalgebra。TheFrencharetheoriginatorsofthisparticulardeception；butifatermisofanyimportance-ifwordsderiveanyvaluefromapplicability-then’analysis’conveys’algebra’aboutasmuchas，inLatin，’ambitus’implies’ambition，’’religio’’religion，’or’homineshonesti，’asetofhonorablemen。”
　　“Youhaveaquarrelonhand，Isee。”saidI，“withsomeofthealgebraistsofParis；butproceed。”
　　“Idisputetheavailability，andthusthevalue，ofthatreasonwhichiscultivatedinanyespecialformotherthantheabstractlylogical。
　　Idispute，inparticular，thereasoneducedbymathematicalstudy。
　　Themathematicsarethescienceofformandquantity；mathematicalreasoningismerelylogicappliedtoobservationuponformandquantity。Thegreaterrorliesinsupposingthateventhetruthsofwhatiscalledpurealgebra，areabstractorgeneraltruths。AndthiserrorissoegregiousthatIamconfoundedattheuniversalitywithwhichithasbeenreceived。Mathematicalaxiomsarenotaxiomsofgeneraltruth。Whatistrueofrelation-offormandquantity-isoftengrosslyfalseinregardtomorals，forexample。Inthislatterscienceitisveryusuallyuntruethattheaggregatedpartsareequaltothewhole。Inchemistryalsotheaxiomfails。Intheconsiderationofmotiveitfails；fortwomotives，eachofagivenvalue，havenot，necessarily，avaluewhenunited，equaltothesumoftheirvaluesapart。Therearenumerousothermathematicaltruthswhichareonlytruthswithinthelimitsofrelation。Butthemathematicianargues，fromhisfinitetruths，throughhabit，asiftheywereofanabsolutelygeneralapplicability-astheworldindeedimaginesthemtobe。Bryant，inhisverylearned’Mythology，’mentionsananalogoussourceoferror，whenhesaysthat’althoughthePaganfablesarenotbelieved，yetweforgetourselvescontinually，andmakeinferencesfromthemasexistingrealities。’Withthealgebraists，however，whoarePagansthemselves，the’Paganfables’arebelieved，andtheinferencesaremade，notsomuchthroughlapseofmemory，asthroughanunaccountableaddlingofthebrains。Inshort，Ineveryetencounteredthemeremathematicianwhocouldbetrustedoutofequalroots，oronewhodidnotclandestinelyholditasapointofhisfaiththatx2pxwasabsolutelyandunconditionallyequaltoq。Saytooneofthesegentlemen，bywayofexperiment，ifyouplease，thatyoubelieveoccasionsmayoccurwherex2pxisnotaltogetherequaltoq，and，havingmadehimunderstandwhatyoumean，getoutofhisreachasspeedilyasconvenient，for，beyonddoubt，hewillendeavortoknockyoudown。
　　“Imeantosay。”continuedDupin，whileImerelylaughedathislastobservations，“thatiftheMinisterhadbeennomorethanamathematician，thePrefectwouldhavebeenundernonecessityofgivingmethischeck。Iknowhim，however，asbothmathematicianandpoet，andmymeasureswereadaptedtohiscapacity，withreferencetothecircumstancesbywhichhewassurrounded。Iknewhimasacourtier，too，andasaboldintriguant。Suchaman，Iconsidered，couldnotfailtobeawareoftheordinarypolicialmodesofaction。
　　Hecouldnothavefailedtoanticipate-andeventshaveprovedthathedidnotfailtoanticipate-thewaylayingstowhichhewassubjected。Hemusthaveforeseen，Ireflected，thesecretinvestigationsofhispremises。Hisfrequentabsencesfromhomeatnight，whichwerehailedbythePrefectascertainaidstohissuccess，Iregardedonlyasruses，toaffordopportunityforthoroughsearchtothepolice，andthusthesoonertoimpressthemwiththeconvictiontowhichG，infact，didfinallyarrive-theconvictionthattheletterwasnotuponthepremises。Ifelt，also，thatthewholetrainofthought，whichIwasatsomepainsindetailingtoyoujustnow，concerningtheinvariableprincipleofpolicialactioninsearchesforarticlesconcealed-IfeltthatthiswholetrainofthoughtwouldnecessarilypassthroughthemindoftheMinister。Itwouldimperativelyleadhimtodespisealltheordinarynooksofconcealment。Hecouldnot，Ireflected，besoweakasnottoseethatthemostintricateandremoterecessofhishotelwouldbeasopenashiscommonestclosetstotheeyes，totheprobes，tothegimlets，andtothemicroscopesofthePrefect。Isaw，infine，thathewouldbedriven，asamatterofcourse，tosimplicity，ifnotdeliberatelyinducedtoitasamatterofchoice。Youwillremember，perhaps，howdesperatelythePrefectlaughedwhenIsuggested，uponourfirstinterview，thatitwasjustpossiblethismysterytroubledhimsomuchonaccountofitsbeingsoveryself-evident。”
　　“Yes。”saidI，“Irememberhismerrimentwell。Ireallythoughthewouldhavefallenintoconvulsions。”