Approaching the linguistic complexity

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aApproachingthelinguisticcomplexityStanis lawDro˙zd˙z1,2,Jaros lawKwapie´n1,andAdamOrczyk11PolishAcademyofScience,InstituteofNuclearPhysics,31-342Krak´ow,Poland,Stanislaw.Drozdz@ifj.edu.pl2UniversityofRzesz´ow,FacultyofMathematicsandNaturalSciences,35-310Rzesz´ow,PolandAbstract.Weanalyzetherank-frequencydistributionsofwordsinse-lectedEnglishandPolishtexts.Wecomparescalingpropertiesofthesedistributionsinbothlanguages.WealsostudyafewsmallcorporaofPolishliterarytextsand ndthatforacorpusconsistingoftextswrit-tenbydi erentauthorsthebasicscalingregimeisbrokenmorestronglythaninthecaseofcomparablecorpusconsistingoftextswrittenbythesameauthor.Similarly,foracorpusconsistingoftextstranslatedintoPolishfromotherlanguagesthescalingregimeisbrokenmorestronglythanforacomparablecorpusofnativePolishtexts.Moreover,basedontheBritishNationalCorpus,weconsidertherank-frequencydistribu-tionsofthegrammaticallybasicformsofwords(lemmas)taggedwiththeirproperpartofspeech.We ndthatthesedistributionsdonotscaleifeachpartofspeechisanalyzedseparately.Theonlypartofspeechthatindependentlydevelopsatraceofscalingisverbs.Keywords:Complexity,naturallanguage,Zipflaw,wordclasses1IntroductionEventhoughcentraltothecontemporarysciencetheconceptofcomplexity-byitsverynature-stillleavesitsprecisede nitionasomewhatopenissue.Inintuitiveandqualitativetermsthisconceptreferstopersityofforms,toemergenceofcoherentandorderlypatternsoutofrandomness,butalsotoasigni cant exibilitythatallowsswitchingamongsuchpatternsonawaytowardssearchingfortheonesthatareoptimalinrelationtoenvironment.Physicso ersthemethodologyandconceptsthatseempromisingforformalizingcomplexity.Oneofthoseconceptsiscriticalityimplyingalackofcharacteristicscalewhich

indeed ndsevidenceinabundanceofpowerlawsandfractalsinNature.Whateverde nitionofcomplexityonehoweveradopts,thehumanlanguagedeservesaspecialstatusintherelatedinvestigations.Itnotonlyledhumanstodevelopcivilizationbutitalsoconstitutes-fromascienti cperspective-anextremelyfascinatingandcomplexdynamicalstructure[1].Likemanynaturalsystems,languageduringitsevolutiondevelopedremarkablecomplexpatternsofbehavioursuchashierarchicalstructure,syntacticorganization,long-rangecorrelations,and-whatisparticularlyrelevanthere-alackofcharacteristicscale.Thislatterphenomenon-inquantitativelinguisticscommonlyreferred

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2Stanis lawDro˙zd˙zetal.

toastheZipflaw-describestherank-frequencydistributionofwordsina(su cientlylarge)pieceoftext.Thiswell-known,quantitativelyformulatedin1949byG.K.Zipfobservation[2],basedoriginallyon“Ulysses”andlatteroncon rmedformanyotherliterarytexts,statesthatfrequencyoftherank-orderedwordsisinverselyproportionaltothewords’rank.Itneedstobeaddedherethatthislawconstitutesaprincipalreferenceinquantitativelinguisticsandinspirationforideasanddevelopmentinmanydi erentareasofscience.

Zipfsuggestedinterpretationofthislawintermsoftheso-calledprincipleofleast-e ort[2,5].ThisinterpretationwashoweversoonquestionedafterithadbeenshownthattheZip anrelationappliesalsotoa“typewritingmonkey”example[6],i.e.anessentiallypurelyrandomprocess.ThispointedtotheZipflawastooindiscriminatetore ectthecomplexorganizationoflanguages.2Resultsanddiscussion

OurrecentstudiesbasedonEnglishaswellasonPolishtextsopenanewperspectivetocomprehendthelinguisticcomplexityandshedsanewlightonaninvolvedmessageencodedintheZipflaw.First,referringtotheclassicanalysisof“Ulysses”byJamesJoyce,carriedoutbyG.K.Zipf[2],wecomparepropertiesoftherank-frequencydistributionsofwordsintheEnglishandthePolishtext[7]ofthisnovel.ResultsareshowninFigure1(a)andFigure1(b).Bothversionsofthetextshowscalingbehaviouroverthreedecadesbetweentheranks10and10,000.However,thescalingexponentforthePolishtext(α 0.90)issigni cantlysmallerthanfortheEnglishoriginal(α 1.05).Thisdi erencemightoriginatefromafarmorein ectablecharacterofthePolishlanguage,whichdemandsalargersetofwords(understoodasparticularsequencesofletters)toreproducethecourseofnarrationin“Ulysses”.Thisobservationmaybeconsideredaregularity,sincetypicalPolishtextshavesmallerαthantypicalEnglishtexts.Thereare,however,PolishtextswhichhaveavalueofαthatissimilartoEnglishstandardsasitisdocumentedinFigure1(c).Itisnoteworthythateachofthethreetextsarewellapproximatedbypower-lawdistributionsalmostoverthewholerangeofranks.

Anytext,asapieceofhumansyntacticcommunication,isnotaseriesofgrammaticallyequivalentwords,butratheraconvolutedmixtureofwordsbe-longingtodi erentpartsofspeech(classes).Taggingallthewordswiththeirproperpartsofspeechallowsustocomparestatisticalpropertiesofwordswithineachclassseparately.Figure2showstherank-frequencydistributionsofthemostfrequentnouns,verbs,adjectives,andadverbsintheBritishNationalCorpus[3]whichisarepresentativesampleofthecontemporarywrittenandspokenEn-glish.Thedatacomesfrom[4].Asitcanbeseen,despitethefactthatthewholecorpusexhibitsaZipf-typescalingforranksuptoseveralthousands[9],thecorrespondingdistributionsmaynotnecessarilyshowanyscalingifonlywordsrepresentingasinglepartofspeechareconsidered.Verbsaretheonlyclassofwordsthatdevelopsometraceofscalingbehaviourwiththescalingindexα≈1.

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Linguisticcomplexity3

Lookingfromthisperspectiveattheglobaldistributionofallthewordsbelong-ingtoalltheclassestogetheritisextremelyinterestingtoreiteratethattheentirerank-frequencydistributionisZipf-like.

Thisresultcanre ectahighlyconvolutedsyntacticorganizationofhumanlanguage,whichmaybeconsideredasacomplexsystem.Fromthisangle,thelin-guisticcomplexityprimarilymanifestsitselfthroughthelogicofmutualdressingamongwordsbelongingtodi erentpartsofspeechthattheentireproportionsemergescale-freeeventhoughinmajorityofthesepartssepar …… 此处隐藏：10334字，全部文档内容请下载后查看。喜欢就下载吧 ……