1/1意識的數(shù)學(xué)模型意識可以由數(shù)學(xué)模型表示,其本質(zhì)是同構(gòu)。

SecondAsiaInternationalConferenceonModellingSimulation

TheMathematicModelofConsciousness

ZhangYinsheng1

n

n

InstituteofScienceTechnologyInformationofChina,

No.15FuxingRoad,Beijing100038nn

e-mail:zhangyinsheng@,zhangyinshengnet@

1

Abstract

ThethoughtreferringhomomorphismofagrouptothemodeloftrasformatiofromphysicalstructurestothepsychologicaloriginatedfromJeanPiaget.However,JeanPiagethasnotgivenamathematicexpressionbywhichthepsychologicalphenomenacanberepresented,andhehasnottakingthemodelasthecommonmodelofconsciousness.Innn

thepaper,thehomomorphicmodelofconsciousnessisgiveninamathematicexpression,bywhichthesomeimportantquestionsrelevanttotheconsciousnessareformalizedandtheanswercanbeacquired,thequestions(withthefollowedanswersolvedbythehomomorphicmodelofconsciousness)areChineseroomargument,Turingmachinequestion,TuringTestquestion,andaboutifanimalshaveconsciousness,inwhatthemeaningofutilizingandmakingtoolslies,ifDNAandproteinsystemhaveconsciousness.Andfinallythepaperconcludesthatconsciousnessexistswhen:(1)theunitsofsystemcertainlymaptheentitiesoutsidethesystem;(2)thesystemoperatebysomerules;and(3)therulescertainlymapsomelawsorrelatiositheetities.Theesseceofcosciousessiscertaicorrespodecebetweesubstancewithsomerulesorlaws.

1.TheSummarizationoftheDefinitionsofConsciousness

Thedefinitionofconsciousnesshasbeendisputedforseveralthousandsyear.Sometimesthedebatesresultfromthedifferentregulationsofdefinition.Toavoidit,thefollowingregulationsofdefinitionareproposed.

Regulationofdefinition1.Definitionofconsciousnessmustbeaccordedwiththeeverydaymeaningoftheword“consciousness”,thatis,defining

consciousnessisnotvoluntary,itisbuttheinterpretationofthewidelyusedforthousandsyearconceptandisonlytheabstractofthecharacteristicsofthematter,tothematterthewidelyusedconceptofconsciousnessrefers.

Regulationofdefinition2.Definitionofconsciousnessmustbeacceptablebothforphilosophyandthescience.Thedefinershouldbeclearthatthedefinitionoftheword“consciousness”isjustoneasboththephilosophersandthescientistsreferto,thereshouldnotbetheseparateinterpretationoftheword“consciousness”fromanotherstudyfields.

Regulationofdefinition3.Theconceptofconsciousnessmustbecommonforanytypeofthemattertobetestedbythedefinition-standard,inotherword,nomatterhuman,animalormachineitis,ifitsatisfiesthedefinition-standardofconsciousness,itshouldberegardedasbeingconscious.

Bytheunderstandingthethoughtsofregulationsofdefinition1,weshouldbeabletoabstractthecommonmeaningsamongthevariousdefinitions.

NormanMalcolmexplainedthecommonmeanings.Hepointedoutthat“beingconscious”isusedinthetwodifferentways.Thefirstuseiscalledtransitive,becausethisformofconsciousnesstakesanobject,thatis,itisconsciousnessofsomething.Theseconduseiscalledintransitive,becausethisformofconsciousnesshasnoobject.[1]

FromtheviewpointofNormanMalcolm,wecanconcludethattheprimarysenseoftheword“consciousness”istransitive.Wecandefineconsciousnessthattheessenceofconsciousnessistransitivityofainformationsystem,andtransitivitycanbedefinedasacertaincorrespondencebetweenthesystemofinformationandtheoutsidematters.Forexample,theword“sun”correspondtheentitysun.Correspondence,astheessenceofconsciousness,canbemodeledinmathematicexpressiondenotingthecorrespondence.

意識可以由數(shù)學(xué)模型表示,其本質(zhì)是同構(gòu)。

2.TheMathematicModelofConsciousness

Modelingconsciousnesshasbeenstartedforalongterm.ThecleardeclarationthatconsciousnesscanbemodeledashomomorphismofagroupwasmadebyJeanPiagetwhichprovedthethoughtofNormanMalcolmabouttransitivityofconsciousness

JeanPiagetbelievedthattherearesomephysicalstructuresindependentonhuman,andthestructuresisinaccordancewiththeoperationstructuresofourmind.Transformationofthephysicalandpsychologicalstructurescanbeexpressedbyamodeloftransformationofgroup.However,JeanPiagethasnotgivenamathematicexpression,andhehasnottakingthemodelforthecommonmodelconsciousness.

Weareherebytryingtogivethemathematicmodelofhomeomorphismofgroupforexpressingthephysicalstructuresindependentonhuman,thestructuresisinaccordancewiththeoperationstructuresofourmind,andwetakethemodelasoneofconsciousnessintransitiveessence,themeaningofconsciousnessisdefinedbyNormanMalcolm.

Wefirstgivethedefinitionofhomeomorphismofgroup.Thedefineiswidelyacceptedinmathematics.

LetX,gY,*bethetwogroups,f:XYisamapping,ifforanyelementabX,theremustbe

f(agb)=f(a)*f(b)

(1)

Theessenceofconsciousnessisthetransitivity,thatiscorrespondencebetweeninformationandentity,i.e.,forthesystem,informationx1x2……xncorrespondthemappedentitiesf1(x1)f1(x2)……f1(xn).Besidestheprimarycorrespondence,thereisahigherfunction,thatis,informationofthesystemcanbeprocessed(operated,theresultsasx1gx2……xn),however,theoperationisnotmeaninglessorlawless,theresultofoperationf(x1gx2……xn)isrestrictbyf(x1)*f(x2)……f(xn)whichismovementorrelationsofthemappedentities.Here,movementofthemappedentitiesisgenerallyconsideredaspermutationinatimeserial,relationsofthemappedentitiesisgenerallyconsideredasanewstateofactionofthemappedentities.

Mappingfiscorresponding,itisarepresentationinessenceratherthananobjectiveexistence.ThesymbolFisareflectionorcognitionofthesetoff,justFisconsciousness.Inthissense,consciousnessFisthecharacteristicsofthethirdperson.

AsthehomomorphicmodelofconsciousnessisthepsychologicalmodelbasedontheexperimentmethodsandthetheoreticalabstractbasedonphilosophyofmanyviewpointsofNormanMalcolmandtheothers,soitmeettheregulationsofdefinition2.Forthemodelisbasedonanyinformationsystem,soitmeetstheregulationofdefinition3.

then,f:XYisdefinedashomomorphismfromX,gtoY,*.

Therefore,inreferencetotheabovedefineofhomomorphismofgroup,wedefineconsciousness.

LetX,gbeaninformationsystemF’,Xisinformation,gbeanoperatorofinformation,Y,*isthesystemofentity,Yisthesetoftheentitiesoutsideoftheinformationsuchasthesubstance,*isthetypeofmovementorrelationoftheentities,thereisasetF,amongF,thereiselementf:XYisamapping,ifthereistheelementsx1x2……xnX|n0,sothat

f(x1gx2……xn)=f(x1)*f(x2)……f(xn)

(2)

3.TheExamplesofAnalysisUsingtheModel

Example1.Theanalysisofthesentenceof“thecupisonthetable”bythemodel.

Answer.

x1:“thecup”(asthewords)x2:“thetable”(asthewords)x3:“on”(asaword)x4:“be”(asaword)

f(x1):thecup(astheentity)f(x2):thetable”(astheentity)

f(x3):therelationofthespacestructurethatanentityexistonthelevelorsurfaceofanotherentityf(x4):null

g:permutationofthewordsaccordingtogrammar*:spaceconstructionoftheentitiesofthecupandthetable

WetakethesystemF’cognizingthesetFasthe

f(the,cup,table,on,is,g)iscousciousforthatconsciousnesssystem,i.e.,wesayF’isconsciousorF’(3)f(thecupisonthetable)hasconsciousness.=f(thecup)*f(thetable)*f(on)*f(be)Theinterpretationisasfollowing.

=therealcircumstancethatthecupisonthetable

意識可以由數(shù)學(xué)模型表示,其本質(zhì)是同構(gòu)。

Thebrainofhumancognizefsatisfyingf(g)=*f,sothebrainisconscious.Here,cognitionisnotonlyusedforhuman,itisaphysicalprocessjustascognitionofapatternbyacomputer.

Thesampleshowsthattheessenceoflanguageofhumanisabilityofprocessingsymbols,thelawsofprocessingcorrespondthenaturallaws.

Example2.Chineseroomargument.Thequestionis:isthecomputerwhichacceptstheChinesewordsorsentencesandtranslatesthemtothecorrespondingEnglishwordsorsentencesonlybythetranslationregulationsinaclosedroom(namedChineseroom)conscious?

Answer.ThecomputerinChineseroomperformsa1ga2……an=b1*b2……bn,butitdoesnotsetupthecorrespondencefsatisfyingf(a1),f(a2)……,f(an),fa1ga2……anandf(a1)*f(a2)……*f(an),i.e.,thecomputerdoesnotsetupthemappingbetweenthesymbolsandtheentitiesoutsidethesymbols.SothecomputerintheChineseroomisnotconscious.Inthissense,mostcomputersinmostcircumstancesarenotconsciousunlesstheysetupfsatisfyingf(g)=*fandcognizeit.

Example3.Turingmachine.Thequestionis:isTuringmachineconscious?

Answer.TuringmachineissimilarwiththecomputerinChineseroom,ithasonlytheregulationsofprocessingthesymbolsbutnotbuildsthecorrespondenceFsoTuringmachineisnotconsciousunlessTuringmachinesetsupfsatisfyingf(g)=*fandcognizeit.

Example4.Turingtest.Thequestionis:isthecomputerpassedTuringtestconscious?

Answer.ThecomputerpassedTuringtestissimilarwiththecomputerinChineseroom,ithasonlytheregulationsofprocessingthesymbolsbutnotbuildsthecorrespondenceFsoitisnotconsciousunlessitsetsupfsatisfyingf(g)=*fandcognizeit.

Example5.Doanimalshaveconsciousness?

Answer.Birds,insects,mammaletc.canremember,itmeanstheinformationissaved.Soanimalscansetupthecorrespondencebetweeninformationintheirnervoussystemandtheentitiesremembered,i.e.,thecorrespondenceFinf(x1),f(x2),……f(xn)exists.Animalshavefewoperationsforinformationx1,x2,……xnbuttheoperationexistsindeedinthenervoussystemofanimals.Itcanbeprovedbyaninstanceofbirdconstructingnests.Theinstancecanbeanalyzedbythemodelasfollowing.

f(informationofbranchesforconstructingnestinthenervoussystemofbirds):thebranchesforconstructingnest(astheentities)

f(informationoftreeforthenest):thetreeforthenest(astheentities)

g:conjunctionofinformation*:conjunctionofentities

f(informationofbranchesforconstructingnest,

(4)

informationoftreeforthenestg)iscousciousforthat

f(informationofbranchesforconstructingnestginformationoftreeforthenest)=thenestmadeofthebranchesinthetree

=f(informationofbranchesforconstructingnestinthenervoussystemofbirds)*f(informationoftreeforthenest)

=constructionofnest

Forbirdscognizef(informationofbranchesforconstructingnestinthenervoussystemofbirds)(i.e.f(x1)),itmeansthatthenervoussystemofbirdscognizeorbuildthecorrespondencebetweentheinformationsavedinnervoussystemforactionandthebranchesastheobjects.Similarly,birdscognizef(informationoftreeforthenest)(i.e.f(x2)),thusbirdshavetheprimaryconsciousfunction.Besides,thebirdshavethehigherfunctiontoprocess(operate)theinformation,i.e.,birdscognizef(informationofbranchesforconstructingnestginformationoftreeforthenest)(i.e.f(x1gx2)),itprovedbycognitionofnest(nestistheresultoff(x1gx2)),meanwhile,birdscognizef(informationofbranchesforconstructingnestinthenervoussystemofbirds)*f(informationoftreeforthenest)),italsoprovedbycognitionofnest(nestistheresultoftheoperationofthetwoentitiesofthebranchesforconstructionandthetree(i.e.f1(x1)*f(x2)),infact,f(x1gx2)=f(x1)*f(x2)intheinstance.So,thenervoussystemofbirdsisF’whichisconscious.

Thedisputemightbeifanimalhavetheexpectedorspeculatedandintegratedview(suchasthenest)oftheunitsorsegmentstheysaw(suchasthebranchesforconstructionandthetreeforthenest),i.e.,ifanimalshaveabilitytoperformx1gx2andexpectorspeculatef(x1gx2).KarlMarxassertedthattheremustnotbetheexpectedorspeculatedandintegratedviewoftheunitsorsegmentstheysaw.Hesaidthattheworstconstructorbetterthebestbeeforthereexistsanexpectedorspeculatedbuildinginthebrainbeforebuildingyetbeesdonot.[3]Hereweintroducethetwosamplestoprovethatthebeesdohaveinformationoftheexpectedorspeculatedandintegratedviewof

意識可以由數(shù)學(xué)模型表示,其本質(zhì)是同構(gòu)。

theunitsorsegments,i.e.,thereexistsinformationmappingf(x1gx2)inthenervoussystemofthebees.

AsampleistheresultofThomasSeeley’sexperimentscitedbyMarianStampDawkins.[4]Theexperimentsshowedthatthenestsofbeesismainlycharacterizedbythefollowingitems:15-80litercapacity;enteropentothesouth;themouseofcavelessthen75squarecentimeters;severalmetershightotheground.Beforebuildingthenewnest,beesasthecollectivecarryoutanoptimizedselectionofthecharactersandcommunicatethecharacterstheysawwitheachothers.Itshowedthatwithoutthesavedinformationoftheview(theviewasthenon-existentialwhentheystartbuildingshouldbecalledexpectedorspeculatedone)selectionmustnotbepossible.

AnothersampleistheexperimentmadebyJulieNeiworkandMarkRillingcitedbyMarianStampDawkins.[5]Theexperimentstestedifthepigeonscanjudgewherewouldbeappearanceofthedisappearedpointoftheparticularlymadeclockinaregularcircle,theresultshowedyes.Itprovedthatpigeonscanintegratetheinformationofthepointandtheinformationoftimei.e.,x1gx2,here,theintegrationofinformationofthepointandtheinformationoftimex1gx2mustexistinthenervousofpigeonsbeforethemappedobjectf(x1gx2)thepointappearsinacertainpositionandinatimefortheyarecapableofjudgingwherethepointshouldappears.

Example6.Mostanimalscan’tutilizeandmakethetoolsbutsomeanimalscan.Humancandoit.Whichrelationwithconsciousnessdoesithas?

Answer.Utilizingthetoolsistheactionwithconsciousness.

x1:informationofthetool

x2:informationoftheobjectoperatedbythetoolf(x1):thetool

f(x2):theobjectoperatedbythetool

f(x1gx2):theresultofspeculationorintentionutilizingthetoolupontheobject

f1(x1)*f1(x2):theresultofoperationutilizingthetoolupontheobject

g:conjunctionoftheinformationofthetoolandtheobject

*:actionoroperationbythetoolupontheobject

Infact,f(x1gx2)=f1(x1)*f1(x2),soutilizingthetoolsistheactionwithconsciousness.

Makingthetoolsistheactionwithconsciousness.Let

x-1:informationofthematerialformakingthetoolx0:informationofthetool(i.e.,thehandsinprimary)formakingthetool

f1(x--1gx0):thespeculationorintentionmakingthetool

f1(x--1)*f1(x0):theresultofmakingthetoolutilizingthematerialbythehands

Theactionfrommakingtooltoutilizingthetoolcanbedenotedas

f2f1(x0gx1)gx2……xn

(5)

=f2f1(x0gx1)*f2(x2)

Obviously,utilizingthetoolmadebytheutiliserismoreinmappingthenutilizingthetoolonly.Inessence,makingtoolandutilizingtoolisthesameinthemodelastheexpression(2)and(5).

Example7.Dothesystemofgenomeandproteomehaveconsciousness?

Answer.Genomeistheentitiesy1,y2,…ynratherthantheinformation.Althoughgenomeiscalledasinformation,itisametaphor,andnottheseparatememoryastherealfeaturesofinformationtorestoreorrepresenttheentity,theseparatememorycanbedenoteasthecharacterssuchasAACTTGC…...SothereisnotasystemXtomaptheentitiesy1gy2……yn,thusthereisnotaparallelgroupfortransitioninthesystem,sothesystemofgenomeandproteomeisnotconscious.

4.TheMathematicModelofConsciousnesswiththeParametersoftheNeurons

Anexperimentapprovedthatconsciousnessofhumansatisfyingequation(2).

In2023,H.R.Heekerenetalmadeanexperiment.Theyprovedthatfortheinformationexpressingconceptsandsentences,combinationoftheinformationmatchresponsivecombinationneuronsofbrain.

ThepreviousexperimentsbeforetheexperimentofH.R.Heekerenidentifiedtheregionsinthehumanventraltemporalcortexthataremoreactivatedbyfacesthanbyhouses,andviseversa.Weherebyconsidertheactivatedregiontofacesandhousesastherepresentedregionssavedinformationofthefacesandhouses.TheexperimentofH.R.Heekerenwastoaskthetestedpersonstodecideiftheinputimagesintheshowedscreenwasthefaceorhouse,giventheinputimagesrespectivelyoftheclearfaceandhouseandofthefaceandhousewithnoise(fuzzyvoxels),functionalmagneticresonanceimaging(fMRI)recordedtheresponsiveregionsbybloodoxygenleveldependent(BOLD)whenthetestedpersonssawtheinputimagesandansweredwhethertheimageswasthefaceorhouse.Thedatashowedthattheresponsiveintensitytohigherleveldecisionmaking(answer)dependpositivelyasthedifferenceofresponsiveintensitybetweentheface-responsiveregionandthehouse-responsiveregionto

意識可以由數(shù)學(xué)模型表示,其本質(zhì)是同構(gòu)。

animage.Theyconcludedthatperceptualdecisionsaremadebyintegratingevidencefromsensoryprocessingarea,i.e.,decision-makingareasusetheoutputfromthelowerlevelsensoryregions.Thisusejustindicatesthatcombinationofinformationmappingtheentitiescorrespondcombinationofneuronunits,i.e.,thepatternorprocessoftheneuralcorrelateofconsciousnessofhumanisjusttheinformationmeetingequation(2).Theconsciousnesscanbeanalyzedasfollowing.

Letn1n2……nndenoteneuronsorlessunitsofneurons

:combinationofneuronsortheunitslessneuronsintimeserial

*referstoasimplerelationofstandingsidebyside.f0(n1n2……nn)representcorresponsiveinformationbyn1n2……nn,i.e.,f0(n1n2……nn)=x1gx2……xn

IntheexperimentofHeekeren,f1(face-responsiveregion)=face

Therefore,wehavef1(f0(n1n2……nn)g)=f1(x1)*f1(x2)……f1(xn)

(6)

f1(f0(face-responsiveregionface-responsive

(7)

regionāitā-responsiveregionābeā-responsiveregion))

=f1(faceghousegitgbe)=f1(itistheface,itisthehouse)=f1(face)*f1(house)

=theimageofthefacefortest*theimageofthehousefortest

Equation(6),(7)arethebridgelinkingtheobjectivity,consciousnessandneuronsandjoiningphysicsandmetaphysics.Itinterpretsthemodelinthephysicalsense.

the