8 sisteme dinamice
TRANSCRIPT
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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)