the combinatorics of merge and workspace right-sizing
TRANSCRIPT
TheCombinatoricsofMergeandWorkspaceRight-Sizing*
*SupportedbyJapanSocietyforthePromotionofScienceGrant-in-AidforScientificResearch#16K02769
Sandiway Fong RobertBerwick JasonGinsburgUniversityofArizona MassachusettsInstituteof
TechnologyOsakaKyoiku University
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Being human: our brains• Popularconception,e.g.,Gazzaniga(2008),pg.8:wecongratulateourselvesonourbrainpower:• "I want to begin by simply
recognizing the huge differences between the human mind and brain and other minds and brains […]"
• Weposit:• Themarvelwecallthehumanbrainisactuallytheweaklinkinourcognitiveapparatus.
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SensoryApparatus
• Oursensoryapparatusprovideswaytoomuchinformationforthebraintoprocess.Thereisamplebiologicalevidenceforthis:• Oureyes:
• havesensitivitydowntothesinglephotonlevel(Tinsleyetal.2016)• havepeakacuityof77cycles/degree(Curcioetal.1990)
• Ournose:• sensitivitycanbeoftheorderofpartsperbillion(ppb)(Wackermannová etal.,2016).
• Ourears:• eardrumscandetectvibrationssmallerthanthediameterofahydrogenatom(Fletcher&Munson,1933).
• Allcompletelyunnecessaryforsurvival.• [Dynamicrangeishuge:yetneuronscanfire…]
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Whysuchsensitivity?
• Evolutionarypressureunknown:• couldbeasimplematterofchemistry
• Anyway:• It'sclear,incaseaftercase,thebraindoesnotmakeuseofthefullresolutionofoursensoryinputs.
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Throwingawayinformation
• Sincewecannotcopewiththesensorydeluge,thebraintossesoutmostofthesensoryinformation:• (attentionpuzzle)howtosievethesensoryinformation?• (dynamicrangepuzzle)yetwecanreportonsinglephotons(abovechance)
• Ourhypothesis:• Samegoesforlanguage,thebrain(must)economizewhereitcan:• Chomsky(2005)termsthepressureforcomputationalefficiencyaThirdFactorconsideration.• ThisappliestothereductionofMergetosimplest(binary)Merge(cf.Komachietal.,2019).
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ResolutioninLanguage
• SimplestMergemayfollowdirectlyfromWorkspace(WS)sizingconstraints.• AlthoughsimplestMerge(byitself)hasdemonstrablyundesirablecombinatorics(e.g.fromaninitialWSofjusttwolexicalitems,about8milliondistinctsetscanbeformedinjust8Merges),languagedoesnotmakefulluseofthisresolution.
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WorkspaceSize
• Merge(Chomsky1995,2013,2015,etc.)• Mergeisfree:
• In{α,{β,ɣ}},ɣ canundergointernalSetMergeorPairMergetoform:• {ɣ,{α,{β,ɣ}}}• <ɣ,{α,{β,ɣ}}>
• IfMergeisfree,thenhowdoyoublockaninfinitenumberofMerges?• Intheory,anySOcanundergointernalorexternalSetMergeorPairMergeaninfinitenumberoftimes.• Intheory,whengeneratingaphrase,youhaveaninfinitenumberofpossiblederivations.
*FromFongandGinsburg(2018) 7
Simple example: the book
# of possible Syntactic Objects as # Merges grows
Log-scale graph of possible SOS as # Merges grows
Free Merge must be constrained.
#Merges #SOs
1 3
2 7
3 29
4 161
5 1,423
6 18,144
7 318,480
8 7,396,976
*FromFongandGinsburg(2018)8
WorkspaceRight-Sizing
• Accessibletermsinaworkspace(NoamChomsky,p.c.;Chomsky2017Readinglecture)• WS=Workspace• SO=SyntacticObject• DefineWSSizeas#SOs+#Accessibleterms
• #accessibletermsofaSO=numberofpropersubsetsoftheSO+lexicalitems• SubjecttoMinimalSearch(lowercopiesnotconsideredaccessible)
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WorkspaceRight-Sizing
• {a,{b,c}}isaSyntacticObjectSO• dandeareSOs
Workspace
de
#SOs=3#acc.terms=4WSSize=#SOs+#acc.termsWSSize=3+4WSSize=7
Accessibleterms=4
SOs=3
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• ExternalMerge(EM)ofdand{a,{b,c}}#SOs=2#acc.terms=6WSSize=2+6WSSize=8Accessibleterms=4
WorkspaceRight-Sizing
#SOs=2
ExternalMerge(EM)decreasesthe#ofSOsby1,butincreasesthenumberofaccessibletermsby2.
EMincreasesWSSizeby1
d
ee
#SOs=3#acc.terms=4WSSize=7
#acc.terms=6
SOs=3
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d
• InternalMergeofband{a,{b,c}}
#SOs=3#acc.terms=6WSSize=3+6WSSize=9
#acc.terms=6
SOs=3
InternalMerge(IM)keepsthe#ofSOsthesame,andincreasesthenumberofaccessibletermsby2
IMincreasesWSSizeby2
e d
e
WorkspaceRight-Sizing
#SOs=3#acc terms=4WSSize=7
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Countercyclic MergeJohnhaseatendinner.l AssumePerfectiveMergescounter-cyclicallywithT [{a,{b,c}},d]à [{a,c},{a,{b,c}},d](Huijbregts 2019)
{a,{b,c}}{a,c}
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#SOs=3#acc.terms=4WSSize=3+4WSSize=7
Countercyclic Merge
SOs
d
#SOs=2#acc.terms=4WSSize=6
d
WSSizeincreasesby1WSSizeincreaseisokay
Isthereanywaytoblockthis?
acc.terms
a is 1 acc. Termc is 1 acc term 14
Proposal 1: Merge cannot decrease WS Size.• You canʼt remove anything from the WS.
Proposal 2: Copies are not accessible terms.
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d
• InternalMergeofband{a,{b,c}}
#SOs=3#acc.terms=4WSSize=3+4WSSize=7
#acc.terms
SOs
IMkeepsthe#ofSOsandaccessibletermsthesame.
IMdoesnotchangeWSSize
e d
e
#SOs=3#acc.terms=4WSSize=7
WorkspaceRight-SizingMinimalSearch:excludelowercopiesfromsetofaccessibleterms• Copyofbisindicatedasb
notaccessible16
Countercyclic MergeJohnhaseatendinner.l AssumePerfectiveMergescounter-cyclicallywithT [{a,{b,c}},d]à [{a,c},{a,{b,c}},d](Huijbregts 2019)
{a,{b,c}}{a,c}
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#SOs=3#acc.terms=2WSSize=#SOs+#Acc.WSSize=5
Countercyclic Merge
#SOs=3
d
acc.terms
#SOs=2#acc.terms=4WSSize=6
d
WSSizedecreasesThisisn’tallowed
notaccessible
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#SOs=3#acc.terms=2WSSize=#SOs+#Acc.WSSize=5
SidewardMovement
#acc.terms=2
#SOs=2#acc.terms=4WSSize=6
WSSizedecreasesThisisn’tallowed
notaccessible
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[{a,b},{c,d}]—>[{a,c},{a,b},{c,d}](Huijbregts 2019)• Notsure if examples likethis exist,butthey stillneed to be blocked.
SidewardMovement• RelativeClauseadjunction(followingNunes 2001)
• WhichclaimthatJohnmadewashewillingtodiscuss?(Chomsky1993:36,Nunes2001:316)
[{a,b},c,d]à [{a,c},{a,b},d](Huijbregts 2019){a,b}
{a,c}
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[CP washewillingtodiscuss[whichclaim]1][CP [whichclaim]1[OP2 thatJohnmadeOp2]]
• SidewardMerge
WorkspaceRight-Sizing
c d
d
#SOs=3#acc.terms=2WSSize=5
#SOs=3#acc.terms=2WSSize=5 NotaccessiblebecauseitisanSO
notaccessible
Give Example phrase
WSSizeremainsthesameSimilartoIM• Notethatthismaybeaproblem• TheWSSizedoesn’tdecrease.• Thisisaproblemifwewanttoban
sidewardmovement
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Conclusion
• UnconstrainedSimplestMergeleadstoanundesirablecombinatorialexplosioninthenumberofpossibleSyntacticObjects.
• ResearchQuestion:whatarethewell-motivatedconstraintsthatdon'tinvolvenewmachinery(aproblemforevolution)?
• PossibleAnswer:thereisnonewmachinery,onlythesimplestpossibleboundonWSSize,i.e.,WSSizemustnotdecreaseandWSSizemustnotexpandbymorethan1.
Furtherconsequences(notdiscussedhere):
• Canreplaceotherconstraintssuchasonvacuousmovement(e.g.iteratedIM)– nowcanbeblockedbyWSSizenarrowlimits– normallywouldrequireloopdetectionmachinery.
• CanalsoexplainwhylanguagecannotcountdespitethefreeavailabilityofIM,i.e.thesuccessorfunctionissimplyaloop
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ReferencesChomsky,Noam.(1993).AMinimalistprogram for linguistic theory.InTheview from Building20:Essaysinlinguistics inhonor of SylvainBromberger,ed.By KennethHaleand SamuelJayKeyser,1-52.Cambradige:MA:MITPress.
Chomsky,Noam.(2005).Three Factors inLanguageDesign.Linguistic Inquiry,36,1–22
Chomsky,Noam.(2017)Lecture atUniversityof Reading.
Curcio,C.A.,Sloan,K.R.,Kalina,R.E.,&Hendrickson,A.E.(1990).HumanPhotoreceptor Topography.TheJournalof Comparative Neurology,292,497–523.
Fong,Sandiwary,&Ginsburg,Jason(2018).Onconstraining FreeMerge.The43rdMeetingof the Kansai Linguistics Society.KonanUniversity:Kobe,Japan.
Fletcher,H.and Munson,W.A.(1933).Loudness,its definition,measurement and calculation.TheJournalof the Acoustical Societyof America,5,82–108.
Gazzaniga,M.(2008).Human:TheScienceBehindWhat Makes Us Unique.NewYork,HarperCollins.
Huijbregts,Riny.(2019)Specialand general theory of Merge with special and general thanks to Noam.SyntaxInterfaceLectures2019,Utrecht.
Komachi,M.,Kitahara,H.,Uchibori,A.,&Takita,K.(2019).Generativeprocedure revisited.Reportsof the Keio Instituteof Culturaland Linguistic Studies,50,269–283.
Nunes,Jairo.(2001).SidewardMovement.LinguisticInquiry,32,303-344.
Tinsley,J.N.,Molodstov,M.U.,Prevedel,R.,Wartmann,D.,Espigulé-Pons,J.,Lauwers,M.,&Vaziri,A.(2016).Direct detection of asingle photon by humans.NatureCommunications, 7,12172.
Wackermannová,M.,Pinc,L.,&Jebavý,L.(2016).Olfactory sensitivity inmammalian species.PhysiologicalResearch,65,369-390.
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