Emerging frameworks for understanding cognitive and sensorimotor abilities: embodied cognition and dynamical

systems theory.

Dr. Mark Ashton Smith

What will be covered in the talk

� Dynamical Systems Theory (DST) and embodied cognition in historical context

� Overview of key concepts of DST and embodied cognition through seminal mathematical models

� A new and possibly fruitful way of conceptualising human cognition in general terms

� Meta-cognitive science / philosophy� What are representations? Information processing?

� What is the ‘computational/symbolic’ paradigm?

� How is DST and embodied cognition a challenge to this paradigm?

Cognitive Science: Historical Context

� 1940s/50s

� Roots of neural networks (McCulloch & Pitts, Hebb)

� Cybernetics (Wiener)

� 1960s

� Symbolic / computational models of cognition (Chomsky, Newell & Simon)

� 1980s

� Connectionism gained prominence (Rummelhart & McClelland), and increasingly in partnership with cognitive neuroscience (e.g. CNBC).

� Symbolic approaches (ACT-R)

� 1990s

� Embodied cognition (Varela et al, Clark)

� 17th Century

� Calculus devised to describe

dynamics of complex physical

systems (Newton)

� 19th Century

� Geometrical approach to

dynamics (Poincare)

� 20th Century

� Dynamical Systems Theory

(DST) –

� 1940s: eddies in stream

1980s: motor coordination

(Turvey et al, Kelso)

� 1990s: cognition (Thelen &

Smith)

Traditional Cog Sci: Computational

� Cognitive science –established as successor to behaviourism in 70s.

� Reasoning, memory, language, perception, motor control.

� cognition involves the transformation of discrete symbols by rules� Symbol configurations are

representations

� Symbols refer to external phenomenon = semantics

� Cognition is computational

� executing information processing programs

� Cognition can be understood independently of the brain and biology: in terms of formal representations and programs

� The mind is the software, the brain the hardware machine. Symbols are physical states in the brain (or computer).

Connectionist models are typically

also computational

1. Computational systems are representational.

2. Computational systems execute programs:� “Programs are assemblies of simple information-

processing units – tiny circuits that can add, match a pattern, turn on some other circuit, or do other elementary logical and mathematical operations”(Pinker, 1997)

� This applies to both traditional (computer language-like) and connectionist models (with static input > output representations)

Dynamical Systems Theory

The basic concepts

� 1. Nonlinearity� The effect of some variable differs across different

parts of its range (e.g. step function, threshold effects)

� Interactions

� Example: Developmental changes in infants

� 2. Trajectories in state space: Phase Portraits� Use of geometrical representations to conceptualise how

systems change.

� 2D state space: predator prey relationships

� Key terms: (a) state space dimensions, trajectory (periodic),

oscillate, periodicity, control parameters, phase portrait (and

conventions) (b) point attractor, damped oscillator, basin of

attraction (c) cyclic attractor =limit cycle, point repeller.

yDCxt

yxByA

t

x)(,)( −=

∂

∂−=

∂

∂(Lotka-Volterra equations)

Minima, maxima & energy landscapes

from Carver & Scheier, 2001

� 3. Chaos and bifurcations

� Systems with complex behaviour/topologies.

� Unstable trajectories which never repeat themselves and appear chaotic (although deterministic from any given point).

� Chaotic attractors � Sensitive dependence on initial conditions for state

space trajectories: trajectories that begin near each other near the attractor tend to diverge (while those starting from the basin of attraction converge). ‘Butterfly effect’.

� Bifurcation � the rapid transition from one phase portrait to another

when the value of one or more control parameters changes slightly.

� A single difference equation might produce a point attractor, a cyclic attractor or a chaotic attractor depending on the value of one control parameter A.

)1(11 tt xAxx −=+

X0 = 0.5, A = 3X1= 3 x 0.5 x 0.5 = 0.75 X2= 3 x 0.75 x 0.25 = 0.5625X3= 3 x 0.5625 x 0.4375 = 0.7383X4= 3 x 0.7383 x 0.2617 = 0.5796

Damped oscillator: Converges to point attractor:0.6667

Bifurcation point: just past A = 3: new periodic attractor (periodicity =2)

A > 3.6: chaotic attractors. X takes non-repeating values

� 4. Coupled Dynamical Systems� Autonomous dynamical system

� Control parameters (e.g. A) remain constant). Unaffected by any other system.

� Non-autonomous dynamical system

� System influenced by factors outside its boundaries and values of one or more parameters vary due to the external influences.

� Coupled dynamical systems

� The states of each system influencing the values of the parameters or variables in the other system across time.

� Embodied/Situated Cognition

� One dynamical system (the CNS) coupled with other dynamical systems involving the body and environment – e.g. tapping a pencil: reciprocal relationship between firing neurons (brain), movements of fingers (body) and the tapping of the pencil on the desk (environment).

� This approach goes well beyond symbolic and connectionist ‘boxes in the head’ models with static inputs and discrete processing modules cut off from body and environment.

Semantic pathway modellingHinton & Shallice, 1991

� Feedforward connectionist

network with interactivity.

� Given that connectionist

networks develop weights

mapping similar inputs to

similar outputs, how are

visually similar words mapped

onto dissimilar meanings?

� Lateral inhibition among

‘sememes’ create basins of

attraction to pull initial

semantic patterns to desired

point attractors.

� 40 basins guide network into

appropriate meanings.

Network controllers for robotic insectsBeer (1995, 1997)

� Applied DST tools to activation of units in connectionist network.

� Processing = trajectory through activation space.

� Each leg - 5 interconnected units: 3 output units (motor neurons), 2 ‘inter-neurons’, each receives input from leg sensor (joint angle).

� Through a genetic algorithm, evolved 3 networks:

� 1. Autonomous: sensors off

� 2. Coupled: joint angle input –network and body thus receive input from each other.

� 3. Mixed: evolved with sensors sometimes on, sometimes off.

� All produced the ‘tripod gait’

� Autonomous > stereotypical gait even with sensors on.

� Coupled > fine tuned, but poor if sensors off.

� Mixed > fine tuned and able to function autonomously.

� Further DST analysis� Beer simplified the network to a 5 unit sub-network

controlling a ‘single legged’ insect.

� Autonomous network: The 5-D state space for this control system > limit cycle (projected into 3-D motor space)

� Coupled network: Different dynamics: two point attractors at which trajectories terminate. At these points, forward motion > changing leg angle > switch between attractors. Sensor turned off > network gets stuck at point attractor.

� Mixed network: Trajectories based on limit cycle attractors not point attractors > so no problem. Also it dynamically adjusts to changing sensory feedback to stay in phase.

� Much better (more robust and flexible) robot design than would be possible through ‘modular’ engineering.

� Without DST analysis (and just standard connectionist network analysis), no explanation of the difference in performance of the coupled and mixed networks.

� Beer, like Hinton & Shallice, design and test connectionist models in usual way, then use DST to get better understanding of them. But Beer’s model is embodied.

� Most connectionist models: input > output devices: once the activation trajectory reaches an attractor nothing else happens unless external agent clears activation values (or weights) and provides another input.

� There is a more radical, non-connectionist, DST approach that is biased towards non-stationary dynamics: intrinsic ability to move between attractors rather than get stuck in one.

Putting chaos to work…

� Skarda & Freeman (1987) claim: Background activity of NS not ‘noise’ but deterministic chaos, keeping overall state space active and ready for targeted action.

� Modelled conditioned responses to odours in (rabbit) olfactory system.

� Different neuron types modelled by non linear differential equations, and coupled by – and + connections in interactive networks.

� Model: exhalation: chaotic trajectories; inhalation: odour sends system from chaos to one of several limit cycle attractors (each a previously learned response) = ‘recognition’ of odour.

Free rangingchaotic

behaviour

Odour specific cyclic

behaviour

� Problem: How to stop responding to one odour before responding to another?

� 1. Organised phase portrait for inhalation includes low energy ‘chaotic well’ (chaotic attractor) which the system goes to if new stimuli is supplied (and from which new limit cycles can form)

� 2. Exhalation > new phase portrait (limit cycle disappears)

Hypothetical phase portraits of the olfactory system (Freeman, 87)

� Snapshots of possible phases.

� X,Y: overall activity of (+) and (–) neurons. Z: amount of ‘energy’.

� Anesthesia: very low energy point attractor.

� Waking: point repellerwith chaotic well (attractor)

� Exhalation (motivated): deepening chaotic attractor with latent limit cycles.

� Inhalation: limit cycles (chaotic dynamics become more organised and stable): Bifurcations

� Seizure: low dimensional chaos.

Experience dynamical systems

yourself!

2. Ambiguous figures (van Leeuwen et al, 97)

1. Finger wagging (Kelso, 1995)

In phase or out of phase at increasing rate

Qualitative applications of DST…(Carver & Scheier, 2001)

� 1. Goals as chaotic attractors for behaviour

� DST can be used to explain how we shift among multiple goals over time.

� 2. Attentional vs Automatized

� ‘Deeper’ attractor basins = more habitual, better learned and automatised behaviours.

� ‘Shallow’ attractor basin: easy to transition away from, less predictable trajectory into it.

� Attention (and consciousness) could be most implicated in behaviour surrounding shallow attractor basins – more need for conscious, effortful processing and decision making.

3. DST and ‘psychological growth’

� Basin depth = relative optimality of

functioning / adaptiveness

(summing over multiple

dimensions in life).

� Stability = proportion of your

thoughts/actions that are adaptive

with respect to your constellation

of goals. More stable > less

tendency to change.

� We may typically be living in a

local minimum, not a global

minimum. The pattern is not ideal!

� But change (internal & external) is

always a reality.

� Growth embraces new dimensions

of experience for reconfigurations

of the landscape.

The Dynamical Challenge

�1995: ‘Mind as Motion: Explorations in the Dynamics of Cognition’. Editors: Port and van Gelder.

� ‘DST has revolutionary implications’� “Dynamical and computational systems are fundamentally

different kinds of systems and hence the dynamical and computational approaches to cognition are fundamentally different in their deepest foundation.” (p. 10)

� The emergence of the dynamical approach is a Kuhnian revolution – a new research paradigm in Kuhn’s classic sense.

Cognitive Science: Computational

� Cognitive science –established as successor to behaviourism in 70s.

� Reasoning, memory, language, perception, motor control.

� cognition involves the transformation of discrete symbols by rules� Symbol configurations are

representations

� Symbols refer to external phenomenon = semantics

� Cognition is computational

� executing information processing programs

� Cognition can be understood independently of the brain and biology: in terms of formal representations and programs

� The mind is the software, the brain the hardware machine. Symbols are physical states in the brain (or computer).

DST Idea: Cognition Not Representational Freeman & Skarda (1990)

� Each bulb burst seems to represent the odour it is correlated with.

� But the pattern of activity for a given odour changes if the reinforcement contingency is changed or new odours added

� The neural activity is correlated not with external things, but reliable interactionsthat are environmentally and behaviourally co-defined

� This dynamic process is not intrinsically representational.

� The observer imposes the idea of representation.

� Representations are not

needed by physiologists

for describing brain

dynamics.

� They can positively detract

from our understanding.

‘Embodied’ Cognitive Science

� Thach et al’s (1992) dart throwing experiment with sideways shifting lenses.

� In time adaptation occurred and subjects were able to aim as well as before.

� BUT when subjects threw with non-dominant hand or underhand > no adaptation!

� Perception geared to action routines; no ‘central’, output independ-ent representation.

� Varela et al (1991): enactive

cognitive science. Cognition

is not ‘action-neutral’ internal

mirroring of an objective

external world. It is based on

sensori-motor interactions.

� Heidegger (1927): Dasein

(‘being there’) – we are not

detached, passive observers

but have skilled, practical

engagement with it (enabling

us to cope and succeed) –

and this is the basis of all

thought and intentionality.

� The temporal dimension of real world adaptive response is crucial.

� e.g. navigating, communicating, playing sports, etc.

� Internal processes with intrinsic temporal features figure in many adaptive behaviours.

� Models for timing developed using ‘adaptive oscillators’ (with periodicities). Their rhythms can be entrained when coupled with external signals. (e.g. Torras, 1985)

� When couplings result in continuous and mutually modulatory exchange > can be more useful to model coupled overarching dynamics.

� Beer’s mixed network dynamically adjusts to changing timing.

� If sensory input changes more slowly (as when legs longer) then network is entrained, slowing its own cycle to remain in phase

� Note the ‘brain-body’interaction

DST Idea: Cognition is Inherently Dynamic

Different ways of doing ‘timing’

� Computational systems that act in the world require transducersthat turn physical effects into discrete inputs and computational outputs into action.

� Computers process inputs or data; they do not interact as open systems with their environments.

� Successful interaction with the environment requires timing (not just speed). There is no timing in computational formalisms for computers. They do not have intrinsic temporal dynamics.

� The internal clocks of computers (where the timing circuitry is separate from the information processing circuitry) are not biologically realistic.

� The intrinsic dynamics of neurons and their interactions is essential to cognition.

� “The brain solves the timing problem in a very different way. Putclocks everywhere. …neurons and neural circuits are oscillatory, involving baseline levels of oscillation which are modulated by influences from other neurons and neural circuits” (Bickhard)

What Type of System are We?

� Computational systems require discrete inputs and outputs and its processing can be characterised as functions on natural numbers.

� Computational systems can be understood formally and independently from their physical realizations.

� But physical systems (like the system of planets) are generally dynamical systems and not computational systems. Computers are a special, artificially designed case of being both.

� We would not be able to do physics (e.g. predicting the trajectory of a rocket) if we confined our models to computational functions on natural numbers. Physical variables, to take one example, are continuous, not discrete.

� Since we ourselves are physical systems, it would be surprising if we could model our own cognitive capacities adequately computationally rather than by virtue of the kind of dynamical system we are. (Glymour, 1997)

� “In my childhood we were always assured that the brain was a

telephone switchboard. (‘What else could it be?’). I was amused

to see that Sherrington, the great British neuroscientist, thought

that the brain worked like a telegraph system. Freud often

compared the brain to hydraulic and electro-magnetic systems.

Leibniz compared it to a mill, and I am told that some of the

ancient Greeks thought the brain functions like a catapult. At

present, obviously, the metaphor is the digital computer.”

(Searle, Minds Brains and Science, 1984)

Searle’s ‘Latest Technology’ Argument!

DST vs Computational Approaches.

Cognitive processes involve

dynamics in real time.

Cognitive processes do not

occur in arbitrary, discrete

time.

Cognition may typically be

non-discrete & non

representational.

The cognitive system is not

fundamentally symbolic or

representational

The CS is the coupled NS,

body and environment; it is

embodied / situated

The CS is not a ‘black box’ –

inner & encapsulated with an

input > IP > output form

The cognitive system is a

dynamical system

The cognitive system (CS) is

not a computational system

• Embodied cognition is the idea that the mind cannot be

understood by modelling only internal activity but inquiry must

extend outwards to the mind's interactions with the body and

environment.

• Dynamical approaches to cognition - unlike symbolic,

computational approaches - give priority to the dimension of

time and use the mathematical and visualization techniques of

dynamical systems theory.

• This talk will show how these approaches give us an intriguing

challenge to the standard symbolic framework in psychology.

What is the significance of DST and the

embodied cognition approach?

� Are we witnessing a Kuhnian revolution in psychology?

� “Along with new experimental data, our most important discoveries are of new ways of solving problems, unforeseen links between different subjects, powerful analogies, and new, unsuspected types of problem: collections of new possibilities as well as collections of new facts.” John Barrow, 1995

� “Is that self-control –the voluntary restriction to the task of extending knowledge outwards from the observed to the unobserved instead of imposing imagined universal principles inwards on the world of observation – that is the essential hallmark of the man of science, distinguishing him most fundamentally from the scientific philosopher.”Herbert Dingle (in Barrow, 1995)

� Anderson, J.r. (1983) The Architecture of Cognition. Cambridge, MA: Harvard University Press.

� Barrow, J.D. (1988) The World within the World. Oxford: Oxford University Press.

� Beer, R.D. (1995) A dynamical systems perspective on agent-environment interaction. Artificial Intelligence, 72, 173-215.

� Beer, R.D. (1997) The dynamics of adaptive behavior: A research program. Robotics and Autonomous Systems, 20, 257-89.

� Carver, C.S. and Scheier, F. (1998) On the Self-Regulation of Behavior. Cambridge: Cambridge University Press.

� Clark, A. (1997) Being There. Putting Brain, Body and World Together Again. Cambridge, MA: MIT Press.

� Freeman, W.J. (1987) Simulation of chaotic EEG patterns with a dynamic model of the olfactory system. Biological Cybernetics, 56, 139-50.

� Freeman, W.J. and Skarda, C.A. (1990) Representations: Who needs them? In J.L. McGaugh, N.M. Weinberger, and G. Lynch (eds), Brin Organization and Memory: Cells, Systems and Circuits. Oxford: Oxford University Press, 375-80.

� Glymour, C. (1997). Thinking Things Through. MIT Press.

� Hebb, D.O. (1949) The Organization of Behavior. New York: John Wiley and Sons.

� Heidegger, M. (1927) Being and Time. Harper and Row, 1961.

� Hinton, G.E. and Shallice, T. (1991) Lesioning an attractor network: Investigations of acquired dyslexia. Psychological Review, 98, 74-95.

� Kelso, J.A.S. (1995) Dynamic Patterns: The Self-organization of Brain and Behavior. Cambridge, MA: MIT Press.

References

� Kuhn, T.S. (1970/1962) Structure of Scientific Revolutions. Chicago: University of Chicago Press.

� McCulloch, W.S. and Pitts, W. (1943) A logical calculus of the ideas immanent in nervous activity. Bulletin of Mathematical Biophysics, 5, 115-33.

� Newell, A. and Simon, H.A. (1956) The logic theory machine. IRE Transactions on Information Theory, 3, 61-79.

� Port, R. and van Gelder, T. (Eds) (1995) Mind as Motion: Explorations in the Dynamics of Cognition. Cambridge, MA: MIT Press.

� Pinker, S. (1997) How the Mind Works. Norton.

� Rumelhart, D.E. and McClelland, J.L. (1986) PDP models and general issues in cognitive science. In Rumelhart, McClelland, and the PDP Research Group (1986), Chapter 4, 110-46.

� Searle, J. (1984). Minds, Brains & Science. Penguin Books.

� Skarda, CA. and Freeman, W.J. (1987) How brains make chaos to make sense of the world. Behavioral and Brain Sciences, 10, 161-95.

� Thach, w., Goodkin, H., and Keating, J. (1992) The cerebellum and the adaptive coordination of movement. Annual Review of Neuroscience, 15, 403-42.

� Thelen, E. and Smith, L.B. (1994) A Dynamical systems Approach to the Development of Cognition and Action. Cambridge, MA: MIT Press.

� Torras, C. (1985) Temporal Pattern Learning in Neural Models. Springer-Verlag.

� Turvey, M., Shaw, R., Reed, E. and Mace, W. (1981) Ecological laws of perceiving and acting. Cognition, 9, 237-304.

� Weiner, N. 1965 (1948). Cybernetics. MIT Press.

� van Leeuwen, C., Steyvers, M., and Nooter, M. (1997) Stability and intermittency in large-scale coupled oscillator models for perceptual segmentation. Journal of Mathematical Psychology, 41, 319-44.

� Varela, F., Thompson, E., and Rosch, E. 1991. The Embodied Mind: Cognitive Science and Human Experience. MIT Press.