„Algebraic Mind“, Marcus

(1)

Where does the Machinery of Symbol Manipulation come from

[Seminar: Cognitive Architectures]

Chapter 6 „Algebraic Mind“, Marcus

Anne Lämmel, Jiayong Liu, Michael Elbers

14.05.2003

(2)

Overview

Is the Machinery of Symbol Manipulation (MSM) innate ?

Is Symbol Manipulation (SM) adaptive ?

(evolutionary aspects)

How can SM grow ?

(developmental aspects)

(3)

Innateness Hypothesis

• MSM belongs to the set of things available to children prior to experience

• MSM consists of innately given representational formats for:

– allowing OPOVARs

• set of operations computable over variables

• apparatus for combining operations – structured combinations

– the distinction of individuals from kinds

(4)

The Learnability Argument

• Mostly in context of language acquisition

• Plural Compounds (Gordon, 1985)

• Infant Concept of Object (Spelke, 1994)

• Something has to be innate

• No absolute proof for innateness yet,

but a challenge to theories of learning

that depend on much experience

(5)

Overview

Is the Machinery of Symbol Manipulation (MSM) innate ?

Is Symbol Manipulation (SM) adaptive ?

(evolutionary aspects)

How can SM grow ?

(developmental aspects)

(6)

Evolutionary Aspects

• Has Natural Selection shaped the mind and thus the MSM ?

• Many conflicting views on Natural Selection

• Marcus expects evidence from genetics (Phylogenetic History)

• Marcus discusses evidence for SM in animals

– How pervasive is the MSM in the animal kingdom ?

– How may SM have been advantageous in evolution ?

(7)

Symbols

• No consensus on a definition for „symbol“

• Marcus focusses on Equivalence Classes

– Frog Example (Lettvin et al., 1959) – Three kinds of Equivalence Classes :

• perceptual features

• non-perceptual features

(e.g. convention, organism‘s goals, knowledge of physical world) – Sea Lion (Schusterman & Kastak, 1998)

(8)

Rules

• “Presumably, the ability to learn new rules depends on prior

selection for mechanisms for representing and generalizing rules.“

• Two aspects to rules:

– representation & generalization (pervasive) – learning new rules (not so pervasive)

• Supporting experiments:

– Match-to-Sample Tasks (primates, parrots, sea lions)

– (Solar) Azimuth Function (desert ants & honey bees)

(9)

Rules: Azimuth Experiments

• Azimuth Function (for Navigation) :

calculating the sun‘s position depending on latitude and season – implausibility of look-up table of values

• Limited Exposure (Lindauer, 1959)

– implausibility of extensive sampling/experience

• Learning Azimuth with MLP (Dickinson & Dyer, 1996)

– MLP only operates/generalizes correctly on trained data – Assumption: animals estimate the azimuth by using

recent position data and the time elapsed

=> rule operating over numeric variables

(10)

Rules (concluded)

• Is the ability to manipulate numeric variables

more pervasive than to manipulate non-numeric variables ?

– maybe the non-numerics only evolved with social exchange (exception: mimicking songbirds ?)

• Maybe only humans can adapt domain-specific machinery

for many more general purposes ?

(11)

Structured Representations

• Probably unique to humans to have structured (hierarchical) representations (SR)

– some animals may learn to some extent, but no

evidence for representation of hierarchical structure (basic word-order, temporal orderings)

• Two theories of the origin of SR :

– Communication / Language

– other aspects like Motor control / Planning

– But: we need to better understand the neural substrate

and the role of genes first

(12)

Structured Representations

• Marcus‘ speculative account of evolutionary advantage of using SR in Language

– before language: unique internal identifiers

– then: combining sound elements (words) unstructuredly

(e.g. if the thing referred to is not in plain sight)

– then: simple structured combinations

(e.g. „Johnny give“ vs. „give Johnny“)

– finally: application to nonlinguistic cognition

(13)

Individuals

• Adaptive Advantages of Tracking Individuals :

– hunting

– food sources (object permanence) – family members

– social exchange

• Chicks (Regolin et al., 1995)

– innate object permanence ?

(14)

Overview

Is the Machinery of Symbol Manipulation (MSM) innate ?

Is Symbol Manipulation (SM) adaptive ?

(evolutionary aspects)

How can SM grow ?

(developmental aspects)

(15)

Developmental Aspects

• DNA as Blueprint

– probably works for simple brains, but not for the

complex structure of human brain

(16)

• the Brain is more complex than the Genome

• Variability of the Brain

• Flexibility of the Brain (Elman, 1996):

– size dependence – rewiring

– transplants

– recovery from damage

(17)

Experiments by Elman et al.

• Argument against Nativism (Brain Flexibility)

• Learning is the major Factor

– „attention grabbers“ for fast learning

• architectual and timing differences play a minor

role

(18)

MLP-Models by Elman et al.

• Counterarguments by Marcus:

– input nodes serve as innate representations – can not escape the DNA as Blueprint View

model relies on a lot of prespecification

– can not capture all aspects of Human Cognition

! How we generalize new items

! How we represent structured knowledge

! How we represent and track individual over time

(19)

Strength of Evidence for Flexibility

• Limits on Size Dependence

• Limits on Rewiring

• Limits on Transplants

• Limits on Recovery from Brain Damage

• Constrained Flexibility rather than cortical

Equipotentiality

(20)

Is Learning essential for Brain Development?

• important Aspects of Brain Structure are organized prior to experience

– Ocular dominance columns (Katz & Shatz, 1996)

(21)

Resolving an Apparent Paradox

• Learning vs Blueprint

– (Elman et al. vs. Katz & Shatz)

• DNA as recipe: Structure=Cascade+Signaling

(22)

Proposal:

– The conjunction of cell-to-cell signaling and

cascading genes provides a good account of how

nonmental aspects of embryos develop, and Marcus argues that comparable mechanisms plan an

important role in the development of the brain – MSM could be constructed by genetically driven