GuillermoLorenzo(UniversidaddeOviedo)glorenzo@uniovi.es

Workshop:AdvancesinBiolinguis@cs

SergioBalari(UniversitatAutònomadeBarcelona)Sergi.Balari@uab.cat

COMPUTATIONAL HOMOLOGY

Sergio Balari Guillermo Lorenzo

SocietasLinguis@caEuropaea44Logroño,September2011

“Homologyisthecentralconceptofallbiology.[…]Itissufficientto‘know’thathomology,liketruth,exists.”

(Wake1994:268)

HOMOLOGY •  OWEN’SHOMOLOGY•  DARWIN’SHOMOLOGY

OWEN

’SHOMOLO

GY

DARW

IN’SH

OMOLO

GY

Owen’shomology

Darwin’shomology

AP1

D1P1

D2P1

Archetype1

H

H

H

D1P1 D2P1H

AP1

“Simpson’s[i.e.Darwin’s]defini@onimpliesanotherextensionoftheoriginalmeaningof‘homology;’itappliestofunc@onsaswellasstructures.”

(Atz1970:53)

Behavioral/func@onalhomology?

“Morphologicalcharacteris@csofaspeciesmaybeunderstoodasaspecializedformofthegeneral(abstracted)typecharacteris@cofthegenus;eachgenusrepresentsaspecialmodifica@onfromthegeneralstructuralpajernofthesuperordinatefamily;eachfamilyrepresentsspecialdevia@onsfromthemoregeneralstructuralpajernoftheorder,etc.Ontheotherhand,thesystema*csofbehaviordonothavethesamehierarchicalrela*onships.Discon*nui*esanduniquetraitsarecommon:specializa*onsofbehaviorseemtodeviatemoremarkedlyfromgeneralpa>erns,andinmanycasesthespecializa*onsaresopronouncedthattheabstrac*onofgeneralbehaviortypesisimpossibleorhazardous.”

(Lenneberg,1967:27)

Computational homology!

Activity Use (‘What S does/How S works’) (‘What S is for’)

S’ dynamics (mere activity) Ecological viability Selected effects

Computing Speaking Nest building (…)

Natural kinds subject to evolutionary diversification ✓ ✗

(see Wouter 2003 and Love 2007)

(1) The ‘same’ computational activity can serve to disparate uses in different organisms—like speaking or building nests;

(2) The underlying ‘sameness’ at this level can legitimately be referred to as a form of homology—computational homology—with relevant evolutionary import.

The same organ of computation in different animals under every

variety of function

Type 3

Type 2

Type 1

Type 0

Unrestricted languages Computational power: Turing Machine (unlimited memory resources)

Context-sensitive languages Computational power: Enhanced Push-down Automaton (a set of memory stacks)

Context-free languages Computational power: Push-down Automaton (a memory stack)

Regular languages Computational power: Finite State Automaton (no memory)

The Chomsky Hierarchy

(see Chomsky 1956, 1957, 1963, Joshi 1985; Khabbaz 1974, for a summary)

(1) Computational complexity is a function of the memory regime that each type of language has access to;

(2) ‘Memory’, in the sense of automata theory, has a plausible psychological correlate in the cognitive function usually referred to as ‘procedural’ or ‘working memory’;

(3) The Chomsky Hierarchy can be interpreted from a naturalistic point of view: Natural systems of computation vary along lines similar to that of the hierarchy, gaining access to higher levels of complexity as a result of evolutionarily significant modifications affecting its working memory component.

x

CompType 3

CompType 2 CompType 1

y

(continuous variation)

bifurcation point (discontinuous variation)

(continuous variation)

(continuous variation)

developmental factors (posible phenotypes)

Theoretical computational morphospace

CompType 0

Com

pType 0

(see Alberch 1989, 1991; see also Rasskin-Gutman 2005)

(impossible phenotypes)

(1) Natural systems of computation can safely been deemed ‘homologous’ in exactly the sense of the modern ‘biological concept of homology’ (Wagner 1989a, 1989b), according to which organic systems are homologues in as much as they share a common ground of developmental constraining factors;

(2) Homologues ‘as computational systems’ ultimately break down into different homological subfamilies—‘homologues as a Type 3/Type 2/Type 1 systems’, with the former category corresponding to a form of ‘deep homology’ (Shubin, Tabin and Carroll 1997, 2009) and the latter to a highly constrained pattern of diversification within such a shared developmental background.

Some conceptual advantages:

(3) The ‘problem of continuity’ (Chomsky 1968, Bickerton 1990)—i.e., that the closest counterparts of FL in terms of computational complexity should be found within our closest evolutionary relatives—vanishes. That there should exist a match between ancestry relations—as reflected in evolutionary trees—and types and degrees of computational complexity is nothing to really be expected under the present framework.

(Chomsky 2000: 4)

A1

A2 A3

…

…

…

T3 T3 T1 T1 T3 T3

…