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Dynamical Systems

Approach

(Teoria Sistemelor Dinamice)


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Netwon (Galilei), Poincare, Landau (44)

Ecological approach (Gibson 66, 79)

Ecological psychologists (Turvey et al. 81)

Turvey Kluger Kelso (80s)-Motor coordinatio

Thelen & Smith (90s) for cognition

Embodied cognition (Gibson, Agre and

Chapman, Hutchins)

Situated action (Gibson Barwise and

Perry 81, 83 Pfeifer and Scheier, Glenberg,

Brooks)

Extended mind (Clark 01, 08)


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van Gelder & Port(95)

Dynamical and computational approaches

to cognition are fundamentally different

Dynamical approach = Kuhnian revolution

Brain (inner, encapsulated) vs. Nervous

system + body + environment

Discrete static Rs vs. Mutually +

simultaneously influencing changes


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Geometrical Rs To conceptualizehow system change!

A plot of states traversed by a systemthrough time = Systems trajectorythroughstate space

TrajectoryContinuous (real time) ordiscrete (sequence of points)

a dimension = a variable of a system

a point = a state

Ex: Height-weight; 2 neurons; 4 or 60neurons = High dimensional state space


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Dynamic systems theory (DST) - Physics

Dynamical system: Set of state variables +

dynamical law (governs how values ofstate variables change with time)

The set of all possible values of state

variables =phase space of system (statespace)

All possible trajectories =phase portrait

Parameters Dimensions of space The sequence of states represents

trajectoryof system


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Dynamical Systems Terminology

1. The state space of a system = space defined by set of all possible statessystem could ever be in.

2. A trajectoryor path = set of positions in state space through which systemmight pass successively. Behavior is described by trajectories through state

space.3. An attractor= point of state space - system will tend when in surroundingregion

4. A repeller= point of state space away from which system will tend when insurrounding region

5. The topologyof a state space = layout of attractors and repellors in state

space6. A control parameter= parameter whose continuous quantitative change

leads to a noncontinuous, qualitative change in topology of a state space

7. Systems - modeled with linear differential equations = linearsystems

Systems - modeled with nonlinear differential equatio-s = nonlinearsystems

8. Only linear systems are decomposable = modeled as collections of

separable components. Nonlinear systems = nondecomposable9. Nondecomposable, nonlinear systems - characterized - collective variables

and/or order parameters, variables/parameters of system that summarizebehavior of systems components (Chemero 09, p. 36)


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Goal: Changes over time (and change in

rate of change over time) of a system

(Clark 2001) DST- Understanding cognition

Cognitive systems = Dynamical systems

Cognitive agents are dynamical systemsand can be scientifically understood as

such. (van Gelder 99)

Change vs. state

Geometry vs. structure (van Gelder 98)


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Behavior of system (changes over time):Sequence of points = Phase space(Numerical space described by differentialequations)

Geometric images Trajectory of evolution

Collective variables (relations bet. variables)

Control parameters= Factors affect evolut.

Ex: Solar system - Position + Momentum ofplanets - Mathematical laws relate changes

over time A math-ical dynamical model Rates of change: Differential equations

(van Gelder 1995, + Port 1995)


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DST: Cognition - in motion

No distinction between mind-body

Mind-body-environment:

Dynamical-coupled systems

Interact continuously, exchanging

information + influencing each other

Processes - in real continuous time


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Quantities(scientific explanation) vs.qualities(Newell & Simon law of

qualitative structure, van Gelder 98)

What makes a system dynamical, in

relevant sense? dynamical systems arequantitative. they are systems in whichdistance matters.

Distances between states of system/times

that are relevant to behavior of system Rate of change (t) (Van Gelder 1998)


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DST: Timeinvolved

Geometric view of how structures in state

space generate/ constrain behavior +

emergence of spatiotemporal patterns

Kinds of temporal behavior - translated in

geometric objects of varying topologies

Dynamics = Geometry of behavior

(Abraham & Shaw 1983; Smale 1980 in

Crutchfield, 95)


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The computational governor vs. the Watt

centrifugal governor

Computational governor- Algorithm:(1)Operating internal Rs and symbols,

(2)Computational operations over Rs

(3)Discrete, sequential and cyclic operations

(4)Homuncular in construction,

Homuncularity = Decomposition of

system in components, each - a subtask+ communicating with others (Gelder 95)


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Centrifugalgovernor (G):

Norepresentational + noncomputational

Relationship betw. 2 quantities(arm angle

and engine speed) = Coupled

Continuously reciprocal causation

through mathematical dynamics

Clark (p. 126)


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Constant speed for flywheel of steam engine:

Vertical spindle to flywheel - Rotate at a speed

proportionate to speed of flywheel 2 arms metal balls - free to rise + fall

Centrifugal force-in proportion to speed of G

Mechanical linkage: Angle of arms - change

opening of valve Controlling amount of steam

driving flywheel

If flywheel - turning too fast, arms - rise Valve

partly close: Reduce amount of steam availableto turn flywheel = Slowing it down

If flywheel - too slowly, arms - drop Valve

open: More steam = Increase speed of flywheel


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Such mechanisms = Control systems

noncomputational, non-R-l

No Rs or discrete operations

Explanation = Only dynamic analysis

Relationship arm angle-engine speed: nocomputational explanation

These 2 quantities - continuously influence

each other = Coupling

Relation brain-body-environ. =

= Continuous reciprocal causation

DST 2 di ti f R


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DST- 2 directions for R:

(1) Radical embodied cognition= NoRs/computation

Maturana and Varela 80; Skarda and Freeman 87;Brooks 1991; Beer and Gallagher 92; Varela,Thompson, + Rosch 91; Thelen + Smith 94; Beer95; van Gelder 95; van Gelder + Port 95; Kelso 95;

Wheeler 96; Keijzer 98We might also add Kugler, Kelso, + Turvey 1980;

Turvey et al. 81; Kugler + Turvey 1987; Harvey,Husbands, + Cliff 94; Husbands, Harvey, + Cliff 95;

Reed 96; Chemero 00, 08; Lloyd 00; Keijzer 01;Thompson + Varela 01; Beer 03; Noe andThompson 04; Gallagher 05; Rockwell 05; Hutto05, 07; Thompson 07; Chemero + Silberstein 08;Gallagher + Zahavi 08 (Chemero 09)


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(2) Moderate = Replace vehicle of Rs or R

in a weaker sense

(Bechtel 98, 02; Clark 97a,b; Wheeler &

Clark 97; Wheeler 05)

Clark has argued several times (97, 01,

08; Clark and Toribio 94 (Miner & Goodale

95, ventral vs. dorsal); Clark and Grush

1999) that anti-R-ism of radical embodiedcognitive science is misplaced. (Chemero,

09, p. 32)


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Radicals: R, computation, symbols, and

structures - Useless in explanation cognition

(van Gelder, Thelen & Smith, Skarda, etc.)

Explanation in terms of structure in the head-

beliefs, rules, concepts, and schemata -not

acceptable. Our theory - new concepts

coupling attractors, momentum, statespaces, intrinsic dynamics, forces. These

concepts - not reductible to old

We are not building Rs at all! Mind is activity intime the real time of real physical causes.

(Thelen and Smith 94)


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Notions: Pattern+ self-organization +

coupling+ circular causation(Clark 97b;

Kelso 95; Varela et al. 91) Patterns - emerge from interactions

between organism and environment

Organism-Environment = Single coupledsystem (composed of two subsystems)

Its evolution through differential equations

(Clark)


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DST rejects Rs, introduces time

Bodily actions (T&S 98, childs walking)

Movement of fingers (HKB 87, Kelso 95)

Extrapolate from sensoriomotor

processes to cognition processes!

No decision making/contrafactual reason

Replace static, discrete Rs with attractors

= Continuous movement At conceptual level attractors seem static

and discrete


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Globus 92, 95; Kelso 95: Reject Rs +

computations

Globus: Replaces computation withconstraints between elements-levels

[R]ather than computes, our brain dwells

(at least for short times) in metastablestates. (Kelso 95) (See Freeman 87)

Radical embodied cognition: Explores

minimally cognitive behavior =Categorical perception, locomotion, etc.

(Chemero 09, p. 39)


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Against REC - Clark and Toribio (94):certain tasks cannot be accomplished

without Rs Hungry Rs problems (decision making,

counterfactual reasoning) - Decouplingbetween R-l system and environment =Off-line cognition (not on-line)

Cognitive system has to create a certainkind of item, pattern or inner process that

stands for a certain state of affairs, inshort, a R. (Clark 97a)

Compromise: Milner and Goodale (95),Norman (02)


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TDS - Change:

a) Interactions betw. (ensembles) neurons

b) Constitutive relations betw. Rs

No prediction but explanation

Dynamics among Rs

(Fisher and Bidell 98; van Geert 94)


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Radical dynamicists: Cognition = Result of

evolution of perception + sensoriomotor

control systems

Dynamical models - having R-s:

Attractors, trajectories, bifurcations, andparameter settings

DS store knowledge + Rules defined overnumerical states

(van Gelder & Port 95)


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DST manages discrete state transitions

(a)Using discrete states (catastrophe model

Bifurcation)

(b)Discreteness: How a continuous system

can undergo changes that look discrete

from a distance

If cognition = particular structure in space

and time, mission - discover how astable state of brain in context of body +

environ. (van Gelder and Port 95)


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Distinction on-line/off-lineprocesses

Off-line cognition = Decision making +

contrafactual reasoning

Subject thinks about Rs in their absence

Not rejecting computation of brain that

presuposses Rs (Clark)


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Van Gelders in BBS (98)

Open Peer Commentary: Many

commentaries - DST can explain onlyperception + sensoriomotor control

systems, not cognitive processes

Van Gelder & Port: Everything in motion

No static discrete Rs Everything is

simultaneously affecting everything else.


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Cognitive processes

Conceptualize in geometricterms

Unfolds over time = How total statessystem passes through spatial location

Unfold in real time their behaviors - by

continuities and discretenesses

Structures - not present from first moment,

but emerge over time - operate over many

times scales and events at different timesscales

(van Gelder & Port 95)


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Skarda & Freemans model of olfactorybulb

Freemans network (85) (Bechtel, p. 259) Rabbit - Pattern neurons - Smelling A,

then B then again A

Pattern of activity A1 A2 (even similar) No Rs (88, 90)

Nothing intrinsically R-l about dynamicprocess until observer intrudes. It is

experimenterwho infers what observedactivity patterns represents to in a subject,in order to explain his results to himself.(Werner 88, in Freeman & Skarda 90)


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Neural system does not exhibit behavior

that can be modeled with point attractors,

except (anesthesia or death) Instead, nervous system = Dynamical

system, constantly in motion

Chaos - System continuously changesstate; trajectory appears random but

determined by equations

Chaotic systems: Sensitivity to initialconditions = Small differences in initial

values Dissimilar trajectories


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Excitatory + inhibitory neurons (different cell

types) = Separate components:

Second-order nonlinear diff-tial equations

Coupled via excitatory/inhibitory connec-s

Interactive network

Conditioned rabbits respons to odors

EEG recordings:

- Exhalation = Pattern of disorderly- Inhalation = More orderly


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Late exhalation: no input + behaves

chaotically

Inhalation: Chaos Basin of one limit cycleattractors (Each attractor is a previously

learned response to a particular odor)

System - recognized an odor when lands inappropriate attractor

Recognition response is not static!

Odor recognition = Olfactory systemalternates between relatively free-ranging

chaotic behavior (exhalation) and odor-

specific cyclic behavior (inhalation)


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Freemans model - Logistic equation

(figure 8.2, p. 242) = Chaotic dynamics in

a region with values of A beyond 3.6.

Within this region there existed values of A

for which dynamics again became periodic

Moving from chaotic to temporarily stable

(and back to chaotic ones) through small

changes in parameter values

Ability could be extremely useful for a

nervous system (Bechtel 02)

Haken Kelso Bunz model (fingers


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Haken-Kelso-Bunz model (fingers

movements)

2 basic patterns (in phase-antiphase)

Increase oscillation frequency in time:

1) People: in antiphasemotion in-phase (at a

certain frequency of movement critical region)

2) Subjects: in-phase = NO in phase motion

2 stable patterns of low frequencies,

1 pattern = Stable, frequen. beyond critical point 2 stable attractors at low frequencies

bifurcation at a critical point 1 stable attractor

at high frequencies (Kelso in Walmsley 2008)


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coordination - not as masterminded by adigital computer but as an emergentproperty of a nonlinear dynamical system

self-organizing around instabilities (vanGelder 98)

Fischer & Bidell (98), van Geert (93) Continuity + discreteness

Dynamical combinations of R-s

Dynamical structuralism: Variations withinstability + Structure in motion

[Ecological, dynamic, interactive, situated,

embodied approaches]


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Melanie Mitchell (98)

Theory of cognition: both computational and

dynamical notions How functional information-processing

structures emerge in complex dynamical

system DST - Do not explain information-processing

content of states over which change is

occurring because either tasks with nocomplex information processing or high-level

information-related primitives pp. a priori


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Objections

Computers are Dynamical Systems

Dynamical Systems are Computers Dynamical Systems are Computable

Description Not Explanation

(Dynamical models = Descriptions of data,not explain why data takes form it does.Wrong Level (DST operates at micro,lower levels)

Not focus on specifically cognitive aspects

Complexity + Structure (van Gelder 98)


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Both alternatives (computationalism &

DST) = Necessary for explaining cognition

Clark 97, 01

Markman & Dietrich 00, 02

Wheeler 96, 05

Fisher & Bidell 98

van Geert 94

no decomposition into distinct functionalmodules + no aspect of agents state need

be interpretable as a R. (Beer 95, p. 144)

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