Descartes

BiographyofCharacters

Childhood

OnMarch31,1596,RenéDescarteswasborninTouraine-la-Sea,Indre-et-Loire,France.Hecamefromalow-statusaristocraticfamily,andhisfatherJoachimwasamemberoftheBrittanyParliamentinRennesandalsoajudgeoftheDistrictCourt.

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.

HereisaninterestingquoteaboutthephilosopherDescartes'stheoryofthestars.OnceDescarteswassittingonthestepsinfrontofhishouse,gazingatthedimhorizonafterthesettingsun.Apasserbyapproachedhimandasked,"Hey!Smartman,mayIask,howmanystarsareinthesky?"Hereplied,"Fool!Noonecanembracethatboundlessthing..."

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.

OnNovember10,1618,hehappenedtobeontheroadsidebulletinboardandsawamathematicalquestionaskedinFlemish.ThisarousedhisinterestandaskedthepeoplearoundhimtotranslatetheFlemishlanguagehedidn'tunderstandintoLatin.ThemannexttohimisIsaacBeeckman,whoiseightyearsolderthanhim.Beckmanhashighattainmentsinmathematicsandphysics,andsoonbecamehismentor.Fourmonthslater,hewrotetoBeckman:"Youaretheonewhoawakenedmefromindifference..."andtoldhimthathehadmadefourmajordiscoveriesinmathematics.

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.

In1628,hewrote"PrinciplesforGuidingPhilosophy."

In1634,hecompleted"OntheWorld"basedonthetheoryofNicolausCopernicus.Thebooksummarizeshisviewsonphilosophy,mathematicsandmanynaturalscienceissues.

In1637,hewrotethreeessaysinFrench"RefractiveOptics","Meteorology"and"Geometry",andwroteapreface"MethodologyfortheCorrectUseofReasonandthePursuitofTruthinScience"forthispurpose,Referredtoas"Methodology"(Discoursdelaméthode)(1637)inthehistoryofphilosophy.PublishedanonymouslyinLeidenonJune8.

"PrinciplesofPhilosophy"(lesPrincipesdelaphilosophie)(1644).

"Méditationsmétaphysiques"(1641)andsoon,DescartesbecameoneofthemostinfluentialphilosophersinEurope.

Departed

HediedinFebruary1650attheageof54.Unmarriedforlife.Duetothechurch'sobstruction,onlyafewfriendsdiedforhim.Afterhisdeath,hepublished"OntheLight"(1664)andsoon.

In1663,hisworkswereincludedinthebannedbookcatalogissuedbythePopeoftheVaticaninRomeandParis.However,thespreadofhisideaswasnothinderedbythis.DescartesbecameoneofthemostinfluentialmastersinEuropeanphilosophyandscientistsinthe17thcenturyandbeyond.

In1740,Parisliftedtheban,whichwastoprovideanalternativetotheNewtonianworldsystemthatwaspopularinFranceatthattime.

AftertheFrenchRevolutionin1789,Descartes'ashesandrelicsweresenttotheFrenchHistoryMuseum.

In1819,hisashesweremovedtothechurchofSaint-Germain-des-Prés.

Hisphilosophyandmathematicshaveaprofoundimpactonhistory.Peopleinscribedthissentenceonhistombstone:"Descartes,sincetheEuropeanRenaissance,thefirstpersontofightforandguaranteerationalrightsformankind."

Personallife

Descartes'marriage:LikeSpinoza,Newton,andLeibniz,Descartesisunmarriedforlife.Hehadanillegitimatedaughter,butunfortunatelydied,whichwasapityforherlife.

Religiousbeliefs

Descartes’religiousbeliefshavebeenstrictlydebatedinacademiccircles.HeclaimstobeadevoutRomanCatholic,andthepurposeof"meditation"istomaintaintheChristianfaith.Butinhisowntime,Descarteswasaccusedofpreachingsecretdeismandatheism.BlaisePascal,hiscontemporary,said,"Ican’tforgiveDescartes;inallofhisphilosophy,hewantedtoleaveGodalone.Buthecouldn’taskGodtotouchitlightlyinordertomaketheworldmove.;Besides,hedoesn’tneedGodanymore.”

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.

Publishingbooks

Mainachievements

Descartes’contributionstosciencearemultifaceted.Descartesnotonlyopenedupanewpathinthefieldofphilosophy,butatthesametimeDescarteswasascientistwhohadthecouragetoexplore.Hehadcommendableinsightsinthefieldsofphysics,physiology,etc.,especiallyinmathematics,hefoundedanalyticgeometry.Thusopenedthedoorofmodernmathematics,whichhasepoch-makingsignificanceinthehistoryofscience.

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),andthemainideaof​​suspiciondoescontributetoresearch.

Methodology

Descarteswantedtointroducehisscientificresearchresultsinabookentitled"TheWorld",butwhenthebookwasabouttobecompletedin1633,helearnedthattheItalianchurchTheauthorityGalileowasguiltybecausehesupportedCopernicus'heliocentrictheory.AlthoughDescarteswasnotpersecutedbytheCatholicauthorityintheNetherlands,hedecidedtoproceedcautiouslyandcollectthemanuscriptsintothebox,becausehedefendedthedoctrineofCopernicusinthebook.Butin1637hepublishedhismostfamouswork"MethodologyforCorrectThinkingandDiscoveryofScientificTruths",usuallyreferredtoas"Methodology"forshort.

Descartespointedoutin"Methodology"thattherearefourstepstostudytheproblem:

1.NeveracceptanytruththatIdon’tknowclearly,thatis,trytoavoidit.Recklessnessandprejudicecanonlybeveryclearandcertainbasedonone'sownjudgment,andthereisnodoubtaboutthetruth.Thatistosay,aslongasyouhavenotexperiencedtheproblemsyouhavepersonallyexperienced,nomatterwhatauthoritativeconclusionsyouhave,youcandoubtit.Thisisthefamous"doubteverything"theory.Forexample,Aristotleonceconcludedthatwomenhavetwofewerteeththanmen.butitisnotthetruth.

2.Thecomplexproblemtobestudiedcanbebrokendownintoanumberofrelativelysimplesmallproblemsasmuchaspossibleandsolvedonebyone.

3.Arrangethesesmallproblemsfromsimpletocomplex,startingwiththeeasy-to-solveproblems.

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.

"Ithink,thereforeIam"

Descartes’mostfamousthought.From"Methodology".Latin:Cogitoergosum.English:Ithink,thereforeIam.French:Jepense,doncjesuis.

Literalmeaning:Latinoriginalmeaning:Ithink,SoIexist.

In-depthmeaning:Descartes’sphilosophicalpropositionsusetheso-called"doubtmethod"toverifywhetherthesourceof"knowledge"isreliable.Wecandoubteverythingaroundus,thereisonlyonethingwecannotdoubt,andthatis:doubttheexistenceofthe"I"thatisbeingdoubted.Inotherwords,wecannotdoubt"ourdoubt",becauseonlyinthiswaycanour"doubt"beaffirmed.Descartesproved"theexistenceofGod"fromhis"Ithink,thereforeIam".Becausethesubjectofthethoughtof"I"cannotbe"doubt",thenthereisahigher"being"thatenablesthe"I"toexist.Inotherwords,becauseIexist,theremustbean"exist"thatmakesmeexist,andthe"exist"thatmakesmeexistmustalsobethe"exist"thatmakesallthingsexist.Therefore,the"exist"whocanmakeallthingsexistmustbepossibleonlywithGod.

Thisfamousquote,whichDescartestookasthestartingpointofhisphilosophicalsystem,wasregardedasthegeneralrepresentativeofextremesubjectiveidealisminEasternEuropebeforethe17thcenturyandtheChineseacademiccirclesinthe21stcentury.Severecriticism.Manypeopleevenuse"existencemustprecedeconsciousness"and"withoutthebodytherecanbenothought"asarguments,thinkingthatDescartesis"puttingthecartbeforethehorse"and"ridiculous".Descartes’suspicionisnotasuspicionofcertainspecificthingsorspecificprinciples,butanabsolutesuspicionofmankind,theworld,andGod.Fromthisabsolutesuspicion,Descarteswantedtoleadtounquestionablephilosophicalprinciples.

Inphysics

Descarteshasmadeusefulcontributionstophysicsbyrelyingongeniusintuitionandstrictmathematicalreasoning.

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.

Inaddition,manymathematicalsymbolsusednowarethefirstusedbyDescartes,whichincludesknownnumbersa,b,candunknownnumbersx,y,z,etc.,aswellasexponentialexpressions.Healsodiscoveredtherelationshipbetweentheedges,vertices,andfacesofaconvexpolyhedron,laterknownastheEuler-Descartesformula.HealsodiscoveredthecommonCartesianfractallineincalculus.

Cartesiancoordinatesystem

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.

Anecdote:Thecreationofspiderwebsandtheplanerectangularcoordinatesystem

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.

TheLawofDescartesSigns

TheLawofDescartesSignswasfirstdescribedbyDescartesinhiswork"LaGéométrie",Isamethodfordeterminingthenumberofpositiveornegativerootsofapolynomial.

Iftheone-variablerealcoefficientpolynomialisarrangedindescendingpower,thenumberofpositiverootsofthepolynomialiseitherequaltothenumberofchangesinthesignsofadjacentnon-zerocoefficients,oramultipleof2lessthanit.Suchas5,3,1or4,2,0.Thenumberofnegativerootsisthenumberofchangesinthesignofthepolynomialobtainedafterthecoefficientsofallodd-ordertermsarechanged,oramultipleof2lessthanit.

Specialcase:Notethatifyouknowthatthepolynomialhasonlyrealroots,youcanusethismethodtocompletelydeterminethenumberofpositiveroots.Sincetherepeatabilityofzerorootsiseasytocalculate,thenumberofnegativerootscanalsobecalculated.Thenthesymbolsofallrootscanbedetermined.

Euler-Descartesformula

TheEuler-Descartesformulaisaformulaingeometry.

Thecontentoftheformulais:inanyconvexpolyhedron,letVbethenumberofvertices,Ebethenumberofedges,andFIsthenumberoffaces,thenV−E+F=2.

ThisformulawasfirstprovedbyFrenchmathematicianDescartesaround1635,butitisnotknown.Thepost-SwissmathematicianLeonhardEulerindependentlyprovedthisformulain1750.In1860,Descartes'workwasdiscovered,andtheformulawasthencalledEuler-Descartesformula.

CartesianFoliage

TheCartesianFoliageisanalgebraiccurve,firstproposedbyDescartesin1638.

TheimplicitequationsoftheCartesianlobedlineare

Theequationsinpolarcoordinatesare

ThenamecomesfromtheLatinwordfolium,whichmeans"leaf".

Characteristicsofcurve:Usingthederivationruleofimplicitfunction,wecanfindy':

Usingthepoint-slopeequationofastraightline,wecanFindthetangentequationatthepoint():

Horizontalandverticaltangent:When,CartesianleavesThetangentoftheshapelineishorizontal.So:

When,thetangentoftheCartesianleafshapelineisvertical.So:

Thiscanbeexplainedbythesymmetryofthecurve.Wecanseethatthecurvehastwohorizontaltangentsandtwoverticaltangents.TheCartesianlobedlineissymmetricalabouty=x,soifthehorizontaltangenthasacoordinate(),theremustbeacorrespondingverticaltangentwiththecoordinate().

Asymptote:Thecurvehasanasymptote:x+y+a=0

Theslopeofthisasymptoteis-1,bothxandyinterceptsYes-a.

ThestoryofDescartesandChristine'sheart-shapedline(thatis,theheartline)

Heartline

ThereisnorigorousevidencethattheheartlinewasinventedbyDescartes.

Theheartlineisanepicycloidwithasharppoint.Inotherwords,whenacirclerollsalonganothercirclewiththesameradius,thetrajectoryofapointonthecircleistheheartline.

Heartlineisakindofepicycloid,anditsnis2.Itcanalsobeexpressedinpolarcoordinates:r=1+cosθ.Theperimeterofsuchaheartlineis8,andtheenclosedareais.

Theheartlineisalsoakindofcocklesline.

ThefigureinthemiddleoftheMandelbrotsetisaheartline.

TheEnglishnameoftheheartline"Cardioid"waspublishedbydeCastillonin"PhilosophicalTransactionsoftheRoyalSociety"in1741;itmeans"likeaheart".

IntheCartesiancoordinatesystem:theparametricequationoftheheartlineis:

whererIstheradiusofthecircle.Thecuspofthecurveislocatedat(r,0)

Theequationinthepolarcoordinatesystemis:

ρ(θ)=2r(1-cosθ)

Area:

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.

AnalyticGeometry

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."

Psychology

Descartes'viewsandmajordiscoveriesinpsychologyhavehadaconsiderableimpactonlaterpsychology.

Heisafamousrepresentativeofmoderndualismandidealismtheories.Hismajordiscoveriesofreflectionandreflectionarcprovidedanimportantbasisforthethesisthat"animalsaremachines".Andputforwardthehypothesisofresponse-stimulus.

ButDescartes’conceptofreflectionismechanical.Heemphasizedthedifferencebetweenhumansandanimals.Animalshavenominds,buthumanshaveminds.Suchinferenceisatypicalmanifestationofdualism.Inaddition,thetheoryofmind-mindsympathyisanothertypicalmanifestationofDescartes'dualismintherelationshipbetweenbodyandmind.Hebelievedthatthehumanbodyiscomposedofmaterialentitiesandthehumanmindiscomposedofspiritualentities.Themindandthehumanbodycaninfluenceeachother,causeandeffecteachother,andinteract.

Hebelievesthattherearesixprimitiveemotionsofpeople:surprise,love,hatred,desire,joy,andsadness.Otheremotionsarebranchesorcombinationsofthesesixprimitiveemotions.

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.

Characteranecdotes

AfterDescartes'death,histombwasexcavatedbyrobbers,andhisskullhaschangedhandsseveraltimes.ItisnowintheMuséedel',PalaisdeChaillot,Paris,France.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.

TwomorepointsareworthnotinginDescartes’methodology.

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".