Dynamical Systems Approach ( Teoria Sistemelor Dinamice )

1. Dynamical Systems Approach (Teoria Sistemelor Dinamice)

2. 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)

3. 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

4. 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

5. 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

6. Dynamical Systems Terminology 1. 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 systems 8. Only linear systems are decomposable = modeled as collections of separable components. Nonlinear systems = nondecomposable 9. 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)

7. 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)

8. 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)

9. 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

10. 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)

11. 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)

12. The computational governor vs. the Watt centrifugal governor Computational governor - Algorithm: • Operating internal Rs and symbols, • Computational operations over Rs • Discrete, sequential and cyclic operations • “Homuncular in construction”, Homuncularity = Decomposition of system in components, each - a subtask + communicating with others (Gelder 95)

13. Centrifugal governor (G): • Norepresentational + noncomputational • Relationship betw. 2 quantities (arm angle and engine speed) = Coupled • Continuously reciprocal causation through mathematical dynamics • Clark (p. 126)

15. 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

16. 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

17. DST- 2 directions for R: • 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)

18. (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)

19. 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)

20. 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)

21. 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

22. 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)

23. 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)

24. 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)

25. 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)

26. DST manages discrete state transitions • Using discrete states (catastrophe model → Bifurcation) • 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)

27. 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)

28. 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.”

29. 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)

30. 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)

31. 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

32. 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

33. 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)

34. 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)

35. 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)

36. “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]

37. 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

38. 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)

39. 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)