Биография на героите
Детство
На 31 март 1596 г. Рене Декарт е роден в Турен-ла-Се, Индре-ет-Лоар, Франция. Той идва от аристократично семейство с ниско положение, а баща му Йоахим е член на парламента на Бретан в Рен, а също и съдия на окръга
Hismotherdiedoftuberculosiswhenhewasmorethanoneyearold,andhewasalsoinfected,whichmadehimfrailandsick.Descarteshadbeensicksincehewasachild,buthisfamilywaswealthysothattheschoolallowedhimtoreadearlyinbed.Afterthedeathofhismother,hisfathermovedtoanothercountryandremarried,andleftDescartestohisgrandmother.Sincethen,fatherandsonhaverarelyseeneachother,buthisfatherhasalwaysprovidedfinancialhelpsothathecanreceiveagoodeducationandpursuehisowncareer.Interestwithoutworryingaboutthesourceofincome.Italsodevelopsthehabitoflifelongcontemplationandawithdrawncharacter.Seeingthathewasquiteaphilosopher,hisfatheraffectionatelycalledhima"littlephilosopher".
In1606or1607,hisfatherhopedthatDescartescouldbecomeatheologianinthefuture,sowhenDescarteswaseightyearsoldhesenthimtothemostfamousaristocraticschoolinEurope—JesusinLaFlecheWillstudyattheRoyalGrandHenryCollege.Inordertotakecareofhisfrailbody,theschoolallowedhimnottoberestrictedbyschoolrules,andhedidnothavetogotoschoolinthemorning,andhecouldreadinbed.Therefore,hehasdevelopedahabitofbeingquietandgoodatthinkingsincehewasachild.Hestudiedattheschoolfor8years,receivedtraditionalculturaleducation,andstudiedclassicalliterature,history,theology,philosophy,law,medicine,mathematicsandothernaturalsciences.Helearnedmathematicsandphysics,includingGalileo'swork.Buthewasquitedisappointedbywhathehadlearned,becauseinhisopinion,thesubtleargumentsinthetextbookswereinfactonlyambiguousorevencontradictorytheories,whichcouldonlymakehimsuspiciousandunabletoobtainconclusiveknowledge.Thecomfortismathematics.
Ето интересен цитат за теорията за звездите на философа Декарт. Веднъж Декарт седеше на стъпалата пред къщата си, гледайки в бездната на хоризонта след залязващото слънце. Минувач се приближи до него и го попита: „Хей! Умнико, може ли да попиташ, колко звезди има в небето?“ Тук отговори: „Глупак!
Youth
AftergraduatinginDecember1616,hefollowedhisfather’swishtobecomealawyerandenteredtheUniversityofPoitierstostudylawandmedicine.Hewasinterestedinallkindsofknowledge,especiallymathematics.,Andobtainedabachelor'sdegreeanddiploma.Aftergraduating,Descarteshasbeenuncertainabouthiscareerchoice,andisdeterminedtotravelalloverEurope,concentratingonseekingthewisdominthe"bigbookoftheworld".
In1618,DescartesjoinedthearmyofMauritzinNassau,Holland.However,anarmisticeagreementwassignedbetweentheNetherlandsandSpain,soDescartesusedthisfreetimetostudymathematics.DuringhismilitaryserviceandtravelinginEurope,hecontinuedtopayattentionto"gatheringallkindsofknowledge"and"tothinkaboutallkindsofthingsheencounteredeverywhere."InDescartes'stime,Latinwasthelanguageofscholars.HealsosignedhisLatinizedname-RenatusCartesius(RenatusCartesius)onhiswritings,aswascustomaryatthetime.Becauseofthis,theCartesiancoordinatesystempioneeredbyhimisalsocalledtheCartesiancoordinatesystem.
Descartes'interestincombiningmathematicsandphysicscameaboutwhenhewasintheDutcharmy.
На 10 ноември 1618 г. той случайно се озова на таблото за обяви отстрани на пътя и видя математически въпрос, зададен на фламандски. Това събуди интереса му и помоли хората около него да преведат фламандския език, той не разбра на латински. или.Четири месеца по-късно той написа на Бекман: „Ти си единственият, който ме събуди от безразличието...“ и му каза, че е направил четири големи открития в математиката.
ItissaidthatDescarteshadthreestrangedreamsinonenight.ThefirstdreamwasthatDescarteswasblownbyastormtoaplacewherethewindcouldnotblow;theseconddreamwasthathegotthekeytoopenthetreasurehouseofnature;thethirddreamwasthatheopenedthewaytotrueknowledge.Thesethreepeculiardreamsstrengthenedhisconfidenceincreatinganewtheory.ThisdaywasaturningpointinDescartes'thoughts,andsomescholarssetthisdayasthebirthdayofanalyticgeometry.
In1621,whenDescartesreturnedfromthearmy,itwasthetimeoftheFrenchcivilstrife.Soin1622,attheageof26,Descartessoldtheassetsleftbyhisfatherandspent4yearstravelinginEurope.Amongthem,hewasinItaly.Livedfor2years,thenmovedtoParisin1625.BecausetheFrenchchurchwassopowerfulatthattime,itwasunabletodiscussreligiousissuesfreely.
DescartesmovedtotheNetherlandsin1628,wherehelivedformorethan20years.Duringthisperiod,Descartesconductedin-depthresearchinthefieldsofphilosophy,mathematics,astronomy,physics,chemistryandphysiology,anddevotedhimselftophilosophicalresearch.closerelationship.
AlmostallofhismajorworkswerecompletedintheNetherlands.
През 1628 г. той написа „Принципи за ръководна философия“.
През 1634 г. той завършва „OntheWorld“ въз основа на теорията на Николай Коперник. Книгата обобщава възгледите му за философията, математиката и много въпроси на природните науки.
През 1637 г. той написа три есета на френски „Рефракционна оптика“, „Метеорология“ и „Геометрия“ и написа предговор „Методология за правилното използване на разума и стремежа към истинска наука“ за тази цел, наричана „Методология“ (Discoursdelaméthode)(1637) в lephiedphilosohistory denon8 юни.
"Принципи на философията" (lesPrincipesdelaphilosophie) (1644).
"Méditationsmétaphysiques" (1641) и скоро Декарт става един от най-влиятелните философи в Европа.
Напусна
Умира през февруари 1650 г. на възраст от 54 години. Неженен за цял живот. Поради възпрепятстването на църквата само няколко приятели умират за него. След смъртта му той публикува „OntheLight“ (1664) и скоро.
In1663,hisworkswereincludedinthebannedbookcatalogissuedbythePopeoftheVaticaninRomeandParis.However,thespreadofhisideaswasnothinderedbythis.DescartesbecameoneofthemostinfluentialmastersinEuropeanphilosophyandscientistsinthe17thcenturyandbeyond.
In1740,Parisliftedtheban,whichwastoprovideanalternativetotheNewtonianworldsystemthatwaspopularinFranceatthattime.
AftertheFrenchRevolutionin1789,Descartes'ashesandrelicsweresenttotheFrenchHistoryMuseum.
През 1819 г. прашът му е преместен в църквата Saint-Germain-des-Pres.
Hisphilosophyandmathematicshaveaprofoundimpactonhistory.Peopleinscribedthissentenceonhistombstone:"Descartes,sincetheEuropeanRenaissance,thefirstpersontofightforandguaranteerationalrightsformankind."
Личен живот
Бракът на Декарт: Подобно на Спиноза, Нютон и Лайбниц, Декарт е неженен за цял живот. Той имаше незаконна дъщеря, но за съжаление почина, което беше жалко за живота й.
Религиозни вярвания
Религиозните вярвания на Декарт са били стриктно обсъждани в академичните кръгове. Той твърди, че е римокатолик, а целта на „медитацията“ е да поддържа християнската вяра. tes;във цялата си философия той искаше да напусне Годалон. Но не можеше да възложи на Бог да го докосне леко, за да накара света да се движи.;Освен това той не го прави „Нуждая се от Бог повече“.
StephenGokrog’sbiographyofDescarteswrote,“HehasadeepreligiousbeliefasaCatholic.Andkeptituntilthedayofhisdeath,withafirmandpassionatedesiretoexplorethetruth."AfterDescartesdiedinSweden,QueenChristinagaveupherthroneandconvertedtoRomanCatholicism(SwedishlawrequirestherulerIsaProtestant).TheonlyCatholicshehasbeenincontactwithisDescartes,whowasherpersonaltutor.
Descartes'mainmathematicalachievementsareconcentratedinhis"geometry".Atthattime,algebrawasstillanewscience,andgeometricthinkingstilloccupiesadominantpositioninthemindsofmathematicians.BeforeDescartes,geometryandalgebraweretwodifferentresearchfieldsinmathematics.Standingattheheightofmethodologyofnaturalphilosophy,DescartesbelievedthattheGreeks'geometrywastoodependentonfigures,whichconstrainedpeople'simagination.Regardingthepopularalgebraatthetime,hefeltthatitwascompletelysubordinatetolawsandformulas,andcouldnotbeasciencetoimproveintelligence.Therefore,heproposedthattheadvantagesofgeometryandalgebramustbecombinedtoestablishakindof"truemathematics".ThecoreofDescartes'thoughtis:toreducegeometryproblemstoalgebraicproblems,usealgebraicmethodstocalculateandprove,soastoachievetheultimategoalofsolvinggeometricproblems.Basedonthisidea,hefounded"AnalyticGeometry".
In1637,Descartespublished"Geometry"andcreatedaplanerectangularcoordinatesystem.Heusesthedistancefromapointontheplanetotwofixedstraightlinestodeterminethepositionofthepoint,andusescoordinatestodescribethepointinspace.Hethencreatedanalyticgeometry.TheemergenceofanalyticgeometrychangedthetrendofseparationofalgebraandgeometrysinceancientGreece.Heunifiedtheopposite"number"and"shape",andcombinedgeometriccurveswithalgebraicequations..ThisgeniuscreationofDescarteslaidthefoundationforthecreationofcalculus,thusopeningupabroadfieldofvariablemathematics.ThemostvaluablethingisthatDescartesusedthepointofviewofmotiontoregardthecurveasthetrajectoryofthemovementofapoint.Henotonlyestablishedthecorrespondingrelationshipbetweenthepointandtherealnumber,butalsoopposedtheshape(includingpoint,line,surface)and"number".Theobjectsofareunified,andthecorrespondingrelationshipbetweenthecurveandtheequationisestablished.Theestablishmentofthiscorrespondingrelationshipnotonlymarkedthegerminationoftheconceptoffunction,butalsomarkedtheentryofvariablesintomathematics,whichmadeagreattransitioninthewayofthinkinginmathematics-theperiodfromconstantmathematicstovariablemathematics.Dialecticsenteredmathematics,andwithvariables,differentiationandintegrationbecamenecessaryimmediately.TheseachievementsofDescartespavedthewayforthelaterdiscoveryofcalculusbyNewtonandLeibniz,andopenedthewayforalargenumberofnewdiscoveriesbymathematicians.
Издаване на книги
Основни постижения
Приносът на Декарт към науката е многостранен. особено в математиката, той основа аналитичната геометрия. Така отвори вратата на съвременната математика, която има революционно значение в историята на науката.
Buthisphilosophicalthoughtsandmethodologyoccupiesamoreimportantpositioninhislifeactivities.Hisphilosophicalthoughtshadagreatinfluenceonthesubsequentdevelopmentofphilosophyandscience.
Philosophicalaspects
Descartesiswidelyregardedasoneofthefoundersofmodernwesternphilosophy.Hewasthefirsttocreateacompletesetofphilosophicalsystems.Philosophically,Descartesisadualistandrationalist.Descartesbelievedthathumansshouldbeabletousemathematicalmethods—thatis,rationality—forphilosophicalthinking.Hebelievesthatreasonismorereliablethansense.(Hegaveanexample:whenwedream,wethinkweareinarealworld,butinfactthisisjustanillusion,seeZhuangZhouMengdie).Hefound4rulesfromlogic,geometryandalgebra:
Thefirstoneis:AnythingthatIhavenotclearlyrecognized,Iwillneveracceptitastrue.Inotherwords,becarefultoavoidindiscreetjudgmentsandpreconceivedopinions.Exceptforthethingsthatareclearlypresentedinmyheartandmakemeunabletodoubtatall,don'tputalittlemoreintomyjudgment.
Thesecondarticleis:DivideeachproblemIreviewedintoseveralpartsaccordingtothedegreeofpossibilityandnecessity,sothattheycanbeproperlysolvedonebyone.
Thethirdarticleis:Iwillthinkinorder,startingwiththesimplestandeasiestobjects,andgraduallyincreasinggradually,untilIknowthemostcomplicatedobjects;eventhosethatarenotinorderRelatedthingsalsosetanorderforthem.
Thelastoneis:Underanycircumstances,wemustconductathoroughinvestigationasmuchaspossibleandre-examineaswidelyaspossibletomakesurethattherearenoomissions.
Descartesappliedthismethodnotonlytophilosophicalthinking,butalsotogeometry,andcreatedanalyticgeometry.
Therefore,Descartes'firststepisthatdoubtisthestartingpoint.Theknowledgeofsensoryperceptioncanbedoubted,andwecannottrustoursenses.Descartesemphasizedthatthepurposeofscienceistobenefitmankindandmakemanthemasterandrulerofnature.Heopposedscholasticphilosophyandtheology,andproposeda"systematicmethodofdoubt"todoubteverything.Sohewouldnotsay"Isee,thereforeIam","Ilisten,thereforeIam".Fromhereherealizedatruth:whatwecannotdoubtis"ourdoubt."Meaning:Whatwecannotdoubtisthe"doubtitself"whenweare"doubt".Onlyinthiswaycanwebesurethatour"doubt"isauthenticandnotafalseproduct.Hewaspuzzledbythethingsthatpeopletookforgrantedorwereaccustomedto,andhecameupwiththefamousphilosophicalproposition-"Ithink,thereforeIam"(Cogitoergosum).Emphasizesthattheexistenceofindependentspiritualentitieswiththinkingasitsattributecannotbedoubted,anddemonstratestheexistenceofindependentphysicalentitieswithextensionasitsattribute.
Hebelievesthattheabovetwoentitiesarefiniteentities,andputthemtogether,whichshowsthatheisatypicaldualistinmetaphysicsorontology.Descartestookthisasthemostbasicstartingpointinmetaphysics,fromwhichheconcludedthat"I"mustbeathingindependentofthebodyandthinking.DescartesalsotriedtoprovetheexistenceofGodfromthisstartingpoint.Descartesbelievesthatweallhavetheconceptofaperfectentity.Sincewecannotgetaperfectconceptfromanimperfectentity,theremustbeaperfectentity—thatis,God—toallowustogetthisconcept.Thatis,Godisthecreatorandultimatecauseoffiniteentities.Fromthetwopointsobtained,Descartescontinuedtoinferthatsincetheperfectthing(god)exists,thenwecanbesurethatthepreviousdemonhypothesiscannotbeestablished,becauseaperfectthingcannotallowsuchademontodeceivepeople,soThroughconstantdoubt,wecanbesurethat"thisworldreallyexists",andthemathematicallogicaftertheproofshouldbecorrect.Therearemanycharacteristicsintherealworldthatcanbedetectedbyreason,thatis,theirmathematicalcharacteristics(suchaslength,width,height,etc.).Whenourreasoncanclearlyrecognizeathing,thenthethingmustnotbeillusory,Mustbeasweknowit.Thatis,Descartesappliedthegeometricreasoningmethodanddeductivemethodtophilosophy,believedthatclearandclearconceptsweretruth,andputforwardthe"innateconcept".
Descartes'viewofnaturalphilosophyiscompletelyopposedtoAristotle'stheory.Hebelievesthatallmaterialthingsaremachinesgovernedbythesamemechanicallaw,eventhehumanbody.Atthesametime,hebelievedthatinadditiontothemechanicalworld,therewasalsoaspiritualworld.ThisdualisticviewlaterbecamethefundamentalwayofthinkingforEuropeans.
AlthoughDescartesprovedtheexistenceoftherealworld,hebelievedthattherearetwodifferententitiesintheuniverse,namelythinking(mind)andtheexternalworld(material),bothofwhichcomefromGod,andGodexistsindependently.Hebelievesthatonlyhumanshavesouls,andthathumansareadualisticexistence,capableofthinkingandtakingupspace.Animalsbelongonlytothematerialworld.
Descartesemphasizedthestartingpointthatthoughtisunquestionable,whichhadanimportantinfluenceonEuropeanphilosophyafterthis.IthinkthatthecontroversythatIhavegeneratedliesintheso-calledexistenceofGodandanimalmonism(chimpanzees,octopuses,parrots,dolphins,elephants,etc.areallproventohaveintelligence),andthemainideaofsuspiciondoescontributetoresearch.
Methodology
Descarteswantedtointroducehisscientificresearchresultsinabookentitled"TheWorld",butwhenthebookwasabouttobecompletedin1633,helearnedthattheItalianchurchTheauthorityGalileowasguiltybecausehesupportedCopernicus'heliocentrictheory.AlthoughDescarteswasnotpersecutedbytheCatholicauthorityintheNetherlands,hedecidedtoproceedcautiouslyandcollectthemanuscriptsintothebox,becausehedefendedthedoctrineofCopernicusinthebook.Butin1637hepublishedhismostfamouswork"MethodologyforCorrectThinkingandDiscoveryofScientificTruths",usuallyreferredtoas"Methodology"forshort.
Декарт посочи в "Методология", че има четири стъпки за изследване на проблема:
1.NeveracceptanytruththatIdon’tknowclearly,thatis,trytoavoidit.Recklessnessandprejudicecanonlybeveryclearandcertainbasedonone'sownjudgment,andthereisnodoubtaboutthetruth.Thatistosay,aslongasyouhavenotexperiencedtheproblemsyouhavepersonallyexperienced,nomatterwhatauthoritativeconclusionsyouhave,youcandoubtit.Thisisthefamous"doubteverything"theory.Forexample,Aristotleonceconcludedthatwomenhavetwofewerteeththanmen.butitisnotthetruth.
2.Thecomplexproblemtobestudiedcanbebrokendownintoanumberofrelativelysimplesmallproblemsasmuchaspossibleandsolvedonebyone.
3. Подредете тези малки проблеми от прости до сложни, като започнете с лесните за решаване проблеми.
4.Afteralltheproblemsaresolved,theywillbetestedtogethertoseeifitiscompleteandwhethertheproblemiscompletelysolved.
Beforethe1960s,Westernscientificresearchmethods,frommechanicaltohumananatomy,werebasicallycarriedoutinaccordancewithDescartes’"TalkingaboutMethods",whichgaverisetotherapiddevelopmentofmodernWesternscience.Considerablepromotion.Buttherearealsocertainflaws,suchasthefunctionofthehumanbody,whichisonlyamechanicalsynthesisofvariousparts,andtheinteractionbetweenthemisnotthoroughlystudied.ItwasnotuntiltheemergenceoftheApollo1moonlandingprojectthatscientistsdiscoveredthatsomecomplexproblemscouldnotbedecomposedandmustbetreatedinacomplexway.Thisledtotheemergenceofsystemsengineering,andthemethodologicalapproachwasthefirsttimethatacomprehensiveapproachwasadopted.replace.Theemergenceofsystemsengineeringhasgreatlypromotedmanylarge-scaleWesterntraditionalsciences,suchasenvironmentalscience,meteorology,biology,artificialintelligence,andsoon.
"Мисля, следователно"
Най-известната мисъл на Декарт. От „Методология“. Латински: Cogitoergosum. Английски: Мисля, следователно съм. Френски: Jepense,doncjesuis.
Буквално значение: Латинско оригинално значение: Мисля, SoLexist.
По-задълбочено значение:Философските предложения на Декарт използват така наречения „метод на съмнението“, за да проверят дали източникът на „знание“ е надежден. canour"съмнение "потвърдено. Декарт доказва" съществуването на Бог "от своето" Мисля, следователно съм ". Тъй като субектът на мисълта за "аз" не може да се "съмнява", тогава има по-висше" същество, което позволява "аз" да съществува. "което кара всички неща да съществуват. Следователно "съществуването", което може да накара всички неща да съществуват, трябва да е възможно само с Бог.
Thisfamousquote,whichDescartestookasthestartingpointofhisphilosophicalsystem,wasregardedasthegeneralrepresentativeofextremesubjectiveidealisminEasternEuropebeforethe17thcenturyandtheChineseacademiccirclesinthe21stcentury.Severecriticism.Manypeopleevenuse"existencemustprecedeconsciousness"and"withoutthebodytherecanbenothought"asarguments,thinkingthatDescartesis"puttingthecartbeforethehorse"and"ridiculous".Descartes’suspicionisnotasuspicionofcertainspecificthingsorspecificprinciples,butanabsolutesuspicionofmankind,theworld,andGod.Fromthisabsolutesuspicion,Descarteswantedtoleadtounquestionablephilosophicalprinciples.
Във физиката
Декарт има полезен принос за физиката, като се осланя на гениална интуиция и строго математическо разсъждение.
SincereadingJohannesKepler’sopticalworksin1619,Descarteshasbeenpayingattentiontolenstheory;hehasparticipatedinthenatureoflight,reflectionandrefractiveindexfromboththeoreticalandpracticalaspects.Andthestudyofgrindinglenses.Heregardedthetheoryoflightasthemostimportantpartoftheentireknowledgesystem.Descartesfirmlybelievedthatlightspreads"immediately".Inhisworks"OnMan"and"PrinciplesofPhilosophy",hefullyexplainedtheconceptofthenatureoflight.Descartesusedhiscoordinategeometrytoengageinopticalresearch,andforthefirsttimein"RefractiveOptics",heputforwardatheoreticalargumentforthelawofrefractionoflight.SharethehonorofdiscoveringthelawofrefractionoflightwithSnelloftheNetherlands.Hebelievesthatlightisthepropagationofpressureintheether.Fromtheperspectiveoflightemissiontheory,heusesthemodelofatennisballontheclothtocalculatethereflection,refractionandtotalreflectionoflightattheinterfaceoftwomedia.ThisisthefirsttimeThelawofrefractionisderivedundertheassumptionthatthevelocitycomponentparalleltotheinterfaceisconstant;however,hisassumptioniswrong,andhisdeductionleadstothewrongconclusionthatthespeedoflightincreaseswhenthelightenterstheopticallydensemediumfromtheopticallythinmedium.Healsoperformedanopticalanalysisofthehumaneye,explainedthatthecauseoftheabnormalvisionisthedeformationofthelens,anddesignedalenstocorrectvision.
Healsousesthelawoflightrefractiontoexplaintherainbowphenomenon,andanalyzescolorsthroughtherotationspeedofelementparticles.
Inmechanics,DescartesdevelopedthetheoryoftherelativityofGalileomotion.Forexample,inthebook"PrinciplesofPhilosophy",therearevividexamplessuchasthewatchwheelsofseamen'spocketwatchesonseagoingshipsinvoyage,toillustratetheprincipleofchoosingareferenceframeformotionandstatic.
Inthesecondchapterof"PrinciplesofPhilosophy",Descartesdescribedthelawofinertiarelativelycompletelyintheformofthefirstandsecondlawsofnature:aslongastheobjectstartstomove,itwillcontinuetomoveatthesamespeed.Andmovealongthesamestraightlineuntilitencountersobstaclesordeviationscausedbysomeexternalcause.HereheemphasizedthelinearityofinertialmotionthatGalileodidnotexpressclearly.
Inthischapter,healsoclearlyproposedthelawofconservationofmomentumforthefirsttime:thetotalamountofmatterandmotionwillalwaysremainthesame.Laidthefoundationforthelawofconservationofenergy.
Descartesdiscoveredtheoriginalformoftheprincipleofconservationofmomentum(themomentumdefinedbyDescartesisanabsolutevalue,notavector,sohisprincipleofconservationofmomentumwaslaterprovedtobewrong).
Descartesdidpreliminaryresearchonissuessuchascollisionandcentrifugalforce,whichcreatedtheconditionsforthesuccessofChristianHuygens.
Astronomy
Descartesappliedhismechanisticviewtocelestialbodies,developedthetheoryofcosmicevolution,andformedhistheoryontheoccurrenceandstructureoftheuniverse.Hebelievesthatitiseasiertounderstandthingsfromtheperspectiveofdevelopmentratherthanjustobservingfromexistingforms.Hefoundedthewhirlpooltheory.Hethinksthattherearehugevorticesandstarsaroundthesun.
Hebelievesthatthemovementofcelestialbodiescomesfromtheinertiaandthepressureofacertaincosmicmaterialvortexoncelestialbodies.Theremustbeacertaincelestialbodyinthecenterofvorticesofvarioussizes.Thishypothesisisusedtoexplaintheinter-celestialbodyinteraction.Descartes’smodeloftheethericvortexoftheoriginofthesunreliedonmechanicsinsteadoftheologyforthefirsttimetoexplaintheformationprocessofcelestialbodies,thesun,planets,satellites,comets,etc.ItwasacenturyearlierthanKant’snebula,andwasthemostauthoritativeinthe17thcentury.Cosmology.
Descartes’theoryofcelestialbodyevolution,vortexmodel,andclose-rangeactionviews,justlikehisentireideologicalsystem,ontheonehandfeaturesrichphysicalthoughtsandrigorousscientificmethods,andactsagainstscholasticphilosophyTheroleofinspiringscientificthinkingandpromotingtheadvancementofnaturalscienceatthattimehadaprofoundimpactonthethinkingofmanynaturalscientists;ontheotherhand,theyoftenstayedintheintuitiveandqualitativestageinsteadofstartingfromquantitativeexperimentalfacts,sosomeconcreteconclusionsareoftenThereweremanydefects,whichbecamethemainantithesisofNewtonianphysics,whichledtowidespreadcontroversy.
Hebelievesthattherearehugevorticesaroundthesun,whichdrivestheplanetstocontinuetorevolve.Theparticlesofmatterareinaunifiedvortex,andthethreeelementsofearth,airandfirearedifferentiatedduringthemovement.Theearthformstheplanet,andthefireformsthesunandthestars.
Healsodevelopedtheoreticaltheoriessuchasthetheoryofcosmicevolutionandvortextheory.Althoughthespecifictheorieshavemanyflaws,theystillhaveanimpactonfuturenaturalscientists.
Mathematics
ThemostimportantcontributionofDescartestomathematicsisthecreationofanalyticgeometry.IntheDescartesera,algebrawasstillarelativelynewsubject,andgeometricthinkingstilloccupiesadominantpositioninthemindsofmathematicians.Descartesdevotedhimselftothestudyoftheconnectionbetweenalgebraandgeometry,andsuccessfullyconnectedthealgebraandgeometrythatwerecompletelyseparateatthattime.In1637,afterthecreationofthecoordinatesystem,analyticgeometrywassuccessfullycreated.Hisachievementlaidthefoundationforthecreationofcalculus,whichisanimportantcornerstoneofmodernmathematics.Analyticalgeometryisstilloneoftheimportantmathematicalmethodsuntilnow.
Descartesnotonlyputforwardthemainthinkingmethodofanalyticgeometry,butalsopointedoutitsdevelopmentdirection.Inhisbook"Geometry",Descartescombinedlogic,geometry,andalgebraicmethods.Bydiscussingdrawingproblems,heoutlinedanewmethodofanalyticgeometry.Sincethen,numbersandshapeshavecometogether,andthenumberaxisisnumberandshape.Thefirstcontact.Andtoprovetotheworldthatgeometricproblemscanbereducedtoalgebraicproblems,butalsothroughalgebraictransformationtodiscoverandprovegeometricproperties.Descartesintroducedtheconceptofcoordinatesystemandlinesegmentoperations.Heinnovatively‘translated’geometricfiguresintoalgebraicequationstosolvegeometricproblemsalgebraically.Thisistoday’s"analyticgeometry"or"coordinategeometry".
Thecreationofanalyticgeometryisanepoch-makingturningpointinthehistoryofmathematics.Theestablishmentoftheplanerectangularcoordinatesystemisthebasisfortheestablishmentofanalyticgeometry.ThecreationoftheCartesiancoordinatesystembuiltabridgebetweenalgebraandgeometry.Itenabledgeometricconceptstobeexpressedinalgebraicform,andgeometricfigurescouldalsobeexpressedinalgebraicform,soalgebraandgeometrybecameafamily.
Освен това, много използвани математически символи, които не знаят, че са използвани за първи път от Декарт, което включва известни числа a, b, и неизвестни числа x, y, z и т.н., както и експоненциални изрази. lus.
Декартова координатна система
Inmathematics,Cartesiancoordinatesystem(Cartesiancoordinatesystem),alsoknownasRectangularcoordinatesystemisanorthogonalcoordinatesystem.Thetwo-dimensionalrectangularcoordinatesystemiscomposedoftwonumberaxesthatareperpendiculartoeachotherandcoincidewithzeropoints.Intheplane,thecoordinatesofanypointaresetaccordingtothecoordinatesofthecorrespondingpointonthenumberaxis.Intheplane,thecorrespondencebetweenanypointandcoordinatesissimilartothecorrespondencebetweenpointsandcoordinatesonthenumberaxis.
Usingrectangularcoordinates,geometricshapescanbeclearlyexpressedbyalgebraicformulas.Therectangularcoordinatesofeachpointofthegeometricshapemustcomplywiththisalgebraicformula.
TheCartesiancoordinatesystemwascreatedbytheFrenchmathematicianRenéDescartes.In1637,Descartespublishedhismasterpiece"Methodology".ThisbookdedicatedtothestudyanddiscussionofWesternscholarshipmethodsprovidedmanycorrectinsightsandgoodsuggestions,andmadeagreatcontributiontothelaterdevelopmentofWesternacademics.
Inordertoshowtheadvantagesandeffectsofthenewmethod,andtohelphimpersonallyinscientificresearch,headdedanotherbook"Geometry"totheappendixof"Methodology".TheresearchontheCartesiancoordinatesystemappearsinthebook"Geometry".
Descartes’researchonthecoordinatesystemcombinesalgebraandEuclideangeometry,andhasakeyinsightintolaterachievementsinanalyticgeometry,calculus,andcartography.
Анекдот: Създаването на паяжина и равнинната правоъгълна координатна система
ItissaidthatonedayDescartesfellillinbedandwasinaveryseriouscondition.Nevertheless,heIalsothoughtaboutaquestionagainandagain:geometricfiguresareintuitive,andalgebraicequationsarerelativelyabstract.Cangeometricfiguresandalgebraicequationsbecombined,thatistosay,cangeometricfiguresbeusedtoexpressequations?Toachievethisgoal,thekeyishowtohookupthepointsthatmakeupthegeometricfiguresandeachsetof"numbers"thatsatisfytheequation."Connect.Suddenly,hesawaspideronthecorneroftheroof,pullingathreadandhangingdown.Afterawhile,thespiderclimbedupthethreadagain,drawingsilkfromlefttorightontheupperside.Thespider's"performance"madeDescartes'thinkingsuddenlyopen.Hethought,thespidercanberegardedasapoint.Hecanmoveup,down,leftandrightintheroom.Caneachpositionofthespiderbedeterminedbyasetofnumbers?Hethoughtagainthatthetwoadjacentwallsintheroomhadthreelinescrossingtheground.Ifthecornersonthegroundweretakenasthestartingpointandthethreelinesweretakenasthethreenumberaxes,thenthepositionofanypointinthespacecouldbeonthesethreelines.Findthreenumbersinorderonthenumberline.Conversely,anygivensetofthreesequentialnumberscanalsofindapointPcorrespondingtoitinspace.Inthesameway,asetofnumbers(X,Y)canrepresentapointontheplaneandapointontheplane.Itcanalsoberepresentedbyasetoftwosequentialnumbers,whichistheprototypeofthecoordinatesystem.
Законът на знаците на Декарт
Законът за знаците на Декарт е описан за първи път от Декарт в неговата работа "LaGéométrie", е метод за определяне на броя на положителните или отрицателните корени на многочлена.
Iftheone-variablerealcoefficientpolynomialisarrangedindescendingpower,thenumberofpositiverootsofthepolynomialiseitherequaltothenumberofchangesinthesignsofadjacentnon-zerocoefficients,oramultipleof2lessthanit.Suchas5,3,1or4,2,0.Thenumberofnegativerootsisthenumberofchangesinthesignofthepolynomialobtainedafterthecoefficientsofallodd-ordertermsarechanged,oramultipleof2lessthanit.
Specialcase:Notethatifyouknowthatthepolynomialhasonlyrealroots,youcanusethismethodtocompletelydeterminethenumberofpositiveroots.Sincetherepeatabilityofzerorootsiseasytocalculate,thenumberofnegativerootscanalsobecalculated.Thenthesymbolsofallrootscanbedetermined.
Формула на Ойлер-Декарт
Формулата на Ойлер-Декарт е формулна геометрия.
Съдържанието на формулата е: във всеки изпъкнал многостен, некаVе брой върхове,Eе брой ръбове иFе брой лица, след товаV−< i>E+F=2.
ThisformulawasfirstprovedbyFrenchmathematicianDescartesaround1635,butitisnotknown.Thepost-SwissmathematicianLeonhardEulerindependentlyprovedthisformulain1750.In1860,Descartes'workwasdiscovered,andtheformulawasthencalledEuler-Descartesformula.
CartesianFoliage
TheCartesianFoliageisanalgebraiccurve,firstproposedbyDescartesin1638.
Имплицитните уравнения на картезианската лобова линия са
Уравненията в полярни координати са
Името идва от латинската думаfolium, което означава "листа".
Характеристики на кривата: Използвайки правилото за извеждане на неявна функция, можем да намерим':
Използвайки уравнението точка-наклон на бърза права линия, можем да намерим допирателното уравнение в точката():
Хоризонтален и вертикален допирателен: Когато декартовият оставя допирателния на фигурната линия е хоризонтален. Така че:
Когато допирателната на декартовата листова линия е вертикална. Така че:
Thiscanbeexplainedbythesymmetryofthecurve.Wecanseethatthecurvehastwohorizontaltangentsandtwoverticaltangents.TheCartesianlobedlineissymmetricalabouty=x,soifthehorizontaltangenthasacoordinate(),theremustbeacorrespondingverticaltangentwiththecoordinate().
Асимптота: кривата имасанасимптота: x+y+a=0
Наклонът на тази симптотеза е-1, и двете х и пресичат Да-а.
Историята на сърцевидната линия на Декарт и Кристин (това е линията на сърцето)
Сърдечна линия
ThereisnorigorousevidencethattheheartlinewasinventedbyDescartes.
Theheartlineisanepicycloidwithasharppoint.Inotherwords,whenacirclerollsalonganothercirclewiththesameradius,thetrajectoryofapointonthecircleistheheartline.
Сърдечната линия е киндофепициклоид и нейнотоnе 2. Може също да бъде изразено в полярни координати:r=1+cosθ.Периметърът на такава сърдечна линия е 8, а оградената област е.
Линията на сърцето също е нещо като линия на петел.
ThefigureinthemiddleoftheMandelbrotsetisaheartline.
Английското име на линията на сърцето „Cardioid“ е публикувано от de Castillon във „Philosophical TransactionsoftheRoyalSociety“ през 1741 г.; то означава „като сърце“.
IntheCartesiancoordinatesystem:theparametricequationoftheheartlineis:
къдетоrе радиус на окръжността. Куфът на кривата е разположен в(r,0)
Уравнението в полярната координатна система е:
ρ(θ)=2r(1-cosθ)
Площ:
Theequationinpolarcoordinatesistobeinvestigated,hereisforreferenceonly.
"TheStoryofMathematics"talkedaboutthelovestoryofmathematicianDescartes.DescarteswasborninFrancein1596.WhentheBlackDeathbrokeoutontheEuropeancontinent,hewanderedtoSweden.HemetKristina,an18-year-oldprincessinasmallprincipalityinSweden,andlaterbecamehermathteacher.Theprincess'sfather,theking,becamefuriouswhenhefoundoutabouteachother,andorderedDescartestobeexecuted.Later,becauseofhisdaughter'splea,hewasexiledtoFrance.PrincessChristinewasalsoplacedunderhousearrestbyhisfather.DescartescontractedtheBlackDeathshortlyafterreturningtoFrance.Hewrotetotheprincesseveryday,butbecausehewasinterceptedbytheking,ChristineneverreceivedaletterfromDescartes.DescartesdiedaftersendingthethirteenthlettertoChristine.Thethirteenthlettercontainedonlyashortformula:r=a(1-sinθ).Thekingcouldn’tunderstandandfeltthatthetwoofthemdidn’talwaystalkaboutlove,sohehandedthislettertoChristine,whowasalwaysglum,andwhentheprincesssawit,sheimmediatelyunderstoodthelover’sintentions,andsheimmediatelysetaboutThegraphoftheequationwasdrawnandshewasveryhappyseeingthegraph.Sheknewthattheloverstilllovedher.Thegraphoftheequationwasintheshapeofaheart.Theprincessestablishedapolarcoordinatesystemonpaper,tracedthepointsoftheequationwithapen,sawtheheartlinerepresentedbytheequation,andunderstoodDescartes'deeploveforherself.Thisisthefamous"heart-shapedline".
Afterthedeathoftheking,ChristinabecameenthronedandimmediatelysentpeopletolookforhersweethearteverywhereinEurope.Thehelplesspersonwasdeceased,shetookastepfirst,leavingheraloneintheworld...
Itissaidthatthisworld-renownedalternativeloveletterisstillpreservedinthememorialhallofDescartesinEurope.
Inhistory,DescartesandChristinadidhavefriendships.ButDescartescametoSwedenonOctober4,1649attheinvitationofChristina,whoatthattimehadbecometheQueenofSweden.DescartesandChristinatalkaboutphilosophicalissuesratherthanmathematics.ItisdocumentedthatduetothetightscheduleofQueenChristina,Descartescouldonlydiscussphilosophywithheratfiveo'clockinthemorning.TherealcauseofDescartes'deathwaspneumoniacausedbycoldweatherandoverwork,nottheBlackDeath.
Аналитична геометрия
TheRenaissanceenabledEuropeanscholarstoinheritthegeometryofancientGreeceandalsoacceptthealgebraintroducedfromtheEast.Thedevelopmentofthescienceofscienceandtechnologyhasmadetheuseofmathematicalmethodstodescribesportsacentralissueofconcern.Descartesanalyzedtheadvantagesanddisadvantagesofgeometryandalgebra,sayingthathewould"seeforanothermethodthatincludestheadvantagesofthesetwoscienceswithouttheirdisadvantages."
InVolume1of"Geometry"(apartof"Methodology"),heusesthedistancefromapointontheplanetotwofixedstraightlinestodeterminethedistanceofapoint,andusescoordinatestodescribethespacePoint.HethenfoundedAnalyticGeometry,showingthatgeometricproblemscannotonlybereducedtoalgebraicforms,butalsocanberealizedthroughalgebraictransformationstodiscovergeometricpropertiesandprovegeometricproperties.
Descartestransformedgeometryproblemsintoalgebraicproblemsandproposedaunifieddrawingmethodforgeometricproblems.Tothisend,heintroducedunitlinesegments,aswellastheconceptsofaddition,subtraction,multiplication,division,andsquarerootingoflinesegments,soastoconnectlinesegmentswithquantities,andthroughtherelationshipbetweenlinesegments,"findtwowaystoexpressthesamequantity.,Thiswillformanequation",andthendrawagraphbasedontherelationshipbetweenthelinesegmentsrepresentedbythesolutionoftheequation.
Inthesecondvolume,whenDescartesusedthisnewmethodtosolvethePapsproblem,heusedastraightlineasthebaselineontheplane,specifiedastartingpointforit,andselectedanotherintersectingone.Straightlines,whicharerespectivelyequivalenttothex-axis,origin,andy-axis,formanobliquecoordinatesystem.Thenthepositionofanypointontheplanecanbeuniquelydeterminedwith(x,y).Papps'problemistransformedintoaquadraticindeterminateequationwithtwounknowns.Descartespointedoutthatthedegreeoftheequationhasnothingtodowiththechoiceofthecoordinatesystem,socurvescanbeclassifiedaccordingtothedegreeoftheequation.
Thebook"Geometry"putsforwardthemainideasandmethodsofanalyticgeometry,markingthebirthofanalyticgeometry.Sincethen,humanshaveenteredthestageofvariablemathematics.
InVolume3,Descartespointedoutthatanequationmayhaveasmanyrootsasitsdegree,andhealsoproposedthefamousDescarteslawofnotation:themaximumnumberofpositiverootsofanequationisequaltothesignofitscoefficient.Thenumberoftimes;themaximumnumberofitsnegativeroots(whichhecalledfalseroots)isequaltothenumberoftimesthesigndoesnotchange.DescartesalsoimprovedthesymbolsystemcreatedbyVedic,usinga,b,c,...todenoteknownquantities,andx,y,z,...todenoteunknownquantities.
TheemergenceofanalyticgeometrychangedthetrendofseparationofalgebraandgeometrysinceancientGreece,unifyingtheopposing"number"and"shape",andcombininggeometriccurveswithalgebraicequations.ThisgeniuscreationofDescarteslaidthefoundationforthecreationofcalculus,thusopeningupabroadfieldofvariablemathematics.
AsEngelssaid:"TheturningpointinmathematicsisCartesianvariables.Withvariables,motionentersmathematics,withvariables,dialecticsentersmathematics,andwithvariables,differentiationandintegrationalsoItbecamenecessaryimmediately."
Психология
Възгледите и големите открития на Декарт в психологията са оказали значително влияние върху по-късната психология.
Heisafamousrepresentativeofmoderndualismandidealismtheories.Hismajordiscoveriesofreflectionandreflectionarcprovidedanimportantbasisforthethesisthat"animalsaremachines".Andputforwardthehypothesisofresponse-stimulus.
ButDescartes’conceptofreflectionismechanical.Heemphasizedthedifferencebetweenhumansandanimals.Animalshavenominds,buthumanshaveminds.Suchinferenceisatypicalmanifestationofdualism.Inaddition,thetheoryofmind-mindsympathyisanothertypicalmanifestationofDescartes'dualismintherelationshipbetweenbodyandmind.Hebelievedthatthehumanbodyiscomposedofmaterialentitiesandthehumanmindiscomposedofspiritualentities.Themindandthehumanbodycaninfluenceeachother,causeandeffecteachother,andinteract.
Той вярва, че има шест примитивни емоции на хората: изненада, любов, омраза, желание, радост и тъга. Други емоции са разклонения или комбинация от тези шест примитивни емоции.
AlthoughDescartes’dualisticpsychologythoughtistheoreticallywrong,itwasverypropellingandprogressiveunderthesocialbackgroundofthetime.Heuseddualismtogetridoftheabsolutecontrolofsciencebytheology.Leadingpeople'sthoughtstorationalthinkingandspecificresearch,sohiscontributiontopsychologycannotbeignored.
Contributiontothetheoryofinstinct.TheauthorThomasAquinas(1225-1274)proposedtheconceptofinstinctandbelievedthatanimalshaveinstincts,buthumansdonot.Hearguedthathumanbeingshavedualnatures-materialandnon-material,orphysicalandmental(intellectual)-butthelawsgoverningthematerialnatureofhumansaredifferentfromthosegoverninganimals.ThereasonforthisdifferenceItcomesfromtheviewthat"manisaspecialproductcreatedbyGod".Manyearlyscientistsarguedovertheprofoundsimilaritiesbetweenanimalmotivesandhumanmotives.Onthesurface,humansandanimalsarecontrolledbythesamelaws,butthereseemstobeadifference.Descartesproposedanexplanationthatcanreconcilethesetwopointsofview:physicalbehavioratthelevelofvolitionalactioncanbeexplainedmechanically(instinct),butbehaviorrelatedtothingssuchasmoralconductisunderthecontrolofvolition.Descartesarguedthatthebodyandspirit(will,soul)interact,andtheplacewheretheeffectoccursisthepinealgland.Certainphysicalbehaviors,suchassexualbehaviors,occurunderthecontrolofthemindratherthansimpleproductsofsomemachinery.ThisdualviewcanechotheviewsofscientistsandtheCatholicChurchatthesametime.Itwasofpositivesignificanceatthetime.
Характерни анекдоти
След смъртта на Декарт гробницата му е била изкопана от разбойници и черепът му е сменял ръцете си няколко пъти.Това е в музея Muséedel', Palaisde Chaillot, Париж, Франция.Homme).
DescartesfirmlydeniestherelationshipbetweenhimandtheGermanRosicrucian,buttherearemanycoincidencesintherelevantdocumentsheleftbehind.Hedoesnotadmitthatitmaybebecauseofthechurchatthetime.
DescartessharedhisearlierresearchontheintegrationofgeometryandalgebrawithBeckman,andoncesaid:"Ifyouhavetheopportunity,youdon’twanttoabandonmyresearchorideas,youcanexpressthatIt'syourthoughts."It'sjusthisoverlypoliteandhumbleattitude,butBeckmanreallytookitashisowncredit.ThismadeDescartesinsulted,sohecondemnedBeckman's"stupidityandignorance."
SocialEvaluation
DescartesisadualistinphilosophyandregardsGodasthecreator.ButDescarteswasamechanistwithinthescopeofnaturalscience,whichwasofprogressivesignificanceatthetime.
DescartesisoneofthefoundersofmodernEuropeanphilosophy.Hegelcalledhim"thefatherofmodernphilosophy".Heformedhisownsystem,fusingmaterialismandidealismintoone,andhadaprofoundinfluenceinthehistoryofphilosophy.
Descartes'methodologyhasanimportantinfluenceonthelaterdevelopmentofphysics.Hecreatedadeductionmethodbasedonmathematicsonthebasisoftheancientdeductionmethod:basedonrationalism,startingfromself-evidentintuitiveaxioms,usingmathematicallogicaldeductiontodrawconclusions.Thismethod,combinedwiththeexperimentalinductionmethodadvocatedbyBacon,hasbecomeanimportantmethodinphysics,especiallytheoreticalphysics,throughthecomprehensiveapplicationofHuygensandNewton.Asoneofthemostsuccessfulexamplesofhisuniversalmethod,Descartesusedalgebraicmethodstosolvegeometricproblemsandestablishedthebasisofcoordinategeometry,thatis,analyticgeometry.
Още две точки си струва да се отбележат в методологията на Декарт.
First,heisgoodatusingintuitive"models"toillustratephysicalphenomena.Forexample,the"tennis"modelisusedtoillustratetherefractionoflight;the"blindman'scane"isusedtovisualizetheinstantaneoustransmissionoflightinformationalongthematerial;theglassballfilledwithwaterisusedtosimulateandsuccessfullyexplaintherainbowphenomenon.
Secondly,headvocatestheuseofhypothesesandhypotheses,suchasthevortextheoryinthetheoryofthestructureoftheuniverse.Inaddition,healsoputforwardtheprincipleof"generalsuspicion".Thisprincipleplayedagreatroleinopposingchurchrule,advocatingauthority,advocatingrationality,andadvocatingscienceunderthehistoricalconditionsatthattime.
DescartescanberegardedasoneofthemostinfluentialmastersinEuropeanphilosophyandscienceinthe17thcenturyandbeyond,andheisknownasthe"ancestorofmodernscience".