Dynamical Systems Approach
(Teoria Sistemelor Dinamice)
• 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)
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
• Geometrical Rs → To conceptualize how system change!
• A plot of states traversed by a system through time = System’s trajectory through state space
• Trajectory – Continuous (real time) or discrete (sequence of points)
• a dimension = a variable of a system a point = a state
• Ex: Height-weight; 2 neurons; 4 or 60 neurons = High dimensional state space
• Dynamic systems theory (DST) - Physics• Dynamical system: Set of state variables +
dynamical law (governs how values of state variables change with time)
• The set of all possible values of state variables = phase space of system (state space)
• All possible trajectories = phase portrait• Parameters → Dimensions of space• The sequence of states represents
trajectory of system
Dynamical Systems Terminology1. The state space of a system = space defined by set of all possible states
system could ever be in.2. A trajectory or path = set of positions in state space through which system
might pass successively. Behavior is described by trajectories through state space.
3. An attractor = point of state space - system will tend when in surrounding region
4. A repeller = point of state space away from which system will tend when in surrounding region
5. The topology of a state space = layout of attractors and repellors in state space
6. 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 = linear systems Systems - modeled with nonlinear differential equatio-s = nonlinear systems8. 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 summarize behavior of system’s components (Chemero ’09, p. 36)
• 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 systems
and can be scientifically understood as such.” (van Gelder 99)
• Change vs. state Geometry vs. structure (van Gelder 98)
• Behavior of system (changes over time): Sequence of points = Phase space (Numerical space described by differential equations)
• Geometric images → Trajectory of evolution• Collective variables (relations bet. variables)• Control parameters = Factors affect evolut.• Ex: Solar system - Position + Momentum of
planets - Mathematical laws relate changes over time → A math-ical dynamical model
• Rates of change: Differential equations(van Gelder 1995, + Port 1995)
• 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
• Quantities (scientific explanation) vs. qualities (Newell & Simon “law of qualitative structure”, van Gelder 98)
“What makes a system dynamical, in relevant sense? … dynamical systems are quantitative. … they are systems in which distance matters.
Distances between states of system/times that are relevant to behavior of system” → Rate of change (t) (Van Gelder 1998)
• DST: Time – involved• 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)
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)
Centrifugal governor (G):
• Norepresentational + noncomputational• Relationship betw. 2 quantities (arm angle
and engine speed) = Coupled• Continuously reciprocal causation
through mathematical dynamics
• Clark (p. 126)
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 available to turn flywheel = Slowing it down
• If flywheel - too slowly, arms - drop → Valve – open: More steam = Increase speed of flywheel
• Such mechanisms = “Control systems” – noncomputational, non-R-l
• No Rs or discrete operations • Explanation = Only dynamic analysis• Relationship arm angle-engine speed: no
computational explanation• These 2 quantities - continuously influence
each other = “Coupling”• Relation brain-body-environ. = = Continuous reciprocal causation
DST- 2 directions for R: (1) Radical embodied cognition = No
Rs/computation “Maturana and Varela 80; Skarda and Freeman 87; Brooks 1991; Beer and Gallagher 92; Varela, Thompson, + Rosch 91; Thelen + Smith 94; Beer 95; van Gelder 95; van Gelder + Port 95; Kelso 95; Wheeler 96; Keijzer 98
We 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 and Thompson 04; Gallagher 05; Rockwell 05; Hutto 05, 07; Thompson 07; Chemero + Silberstein 08; Gallagher + Zahavi 08” (Chemero 09)
(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 embodied cognitive science is misplaced. (Chemero, ’09, p. 32)
• 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, state spaces, intrinsic dynamics, forces. These concepts - not reductible to old”
• “We are not building Rs at all! Mind is activity in time… the real time of real physical causes.” (Thelen and Smith ‘94)
• 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 coupled system (composed of two subsystems)
• Its evolution through differential equations (Clark)
• DST rejects Rs, introduces time • Bodily actions (T&S 98, child’s 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
• Globus 92, 95; Kelso 95: Reject Rs + computations
• Globus: Replaces computation with constraints between elements-levels
• “[R]ather than computes, our brain dwells (at least for short times) in metastable states”. (Kelso 95) (See Freeman 87)
• Radical embodied cognition: Explores “minimally cognitive behavior” = Categorical perception, locomotion, etc. (Chemero 09, p. 39)
• Against REC - Clark and Toribio (94): certain tasks cannot be accomplished without Rs
• “Hungry Rs problems” (decision making, counterfactual reasoning) - Decoupling between R-l system and environment = Off-line cognition (not on-line)
• “Cognitive system has to create a certain kind of item, pattern or inner process that stands for a certain state of affairs, in short, a R.” (Clark 97a)
• Compromise: Milner and Goodale (95), Norman (02)
• TDS - Change: a) Interactions betw. (ensembles) neuronsb) Constitutive relations betw. Rs → No prediction but explanation
• Dynamics among Rs (Fisher and Bidell 98; van Geert 94)
• Radical dynamicists: Cognition = Result of evolution of perception + sensoriomotor control systems
• Dynamical models - “having” R-s: Attractors, trajectories, bifurcations, and parameter settings
→ DS store knowledge + Rules defined over numerical states
(van Gelder & Port 95)
• 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 “a stable state of brain in context of body + environ”. (van Gelder and Port 95)
Distinction on-line/off-line processes
• “Off-line cognition = Decision making + contrafactual reasoning
• Subject thinks about Rs in their absence” → Not rejecting computation of brain that presuposses Rs (Clark)
Van Gelder’s in BBS (98)• “Open Peer Commentary”: Many
commentaries - DST can explain only perception + sensoriomotor control systems, not cognitive processes
• Van Gelder & Port: Everything in motion→ No static discrete Rs → “Everything is simultaneously affecting everything else.”
Cognitive processes • Conceptualize in geometric terms• Unfolds over time = How total states
system 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 times scales (van Gelder & Port 95)
Skarda & Freeman’s model of olfactory bulb
• Freeman’s 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 dynamic
process until observer intrudes. It is experimenter who infers what observed activity patterns represents to in a subject, in order to explain his results to himself.” (Werner 88, in Freeman & Skarda 90)
• 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 changes state; trajectory appears random but determined by equations
• Chaotic systems: Sensitivity to initial conditions = Small differences in initial values → Dissimilar trajectories
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
• Late exhalation: no input + behaves chaotically
• Inhalation: Chaos → Basin of one limit cycle attractors (Each attractor is a previously learned response to a particular odor)
• System - recognized an odor when lands in appropriate attractor
• Recognition response is not static!• Odor recognition = Olfactory system
alternates between relatively free-ranging chaotic behavior (exhalation) and odor-specific cyclic behavior (inhalation)
• Freeman’s 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’ movements)
• 2 basic patterns (in phase-antiphase)• Increase oscillation frequency in time:1) People: in antiphase motion → 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)
“coordination - not as masterminded by a digital computer … but as an emergent property of a nonlinear dynamical system self-organizing around instabilities” (van Gelder 98)
Fischer & Bidell (98), van Geert (93)• Continuity + discreteness • Dynamical combinations of R-s → Dynamical structuralism: Variations within
stability + Structure in motion[Ecological, dynamic, interactive, situated,
embodied approaches]
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 no complex information processing or high-level information-related primitives pp. a priori
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)
• 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 functional
modules + no aspect of agent’s state need be interpretable as a R. (Beer 95, p. 144)