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Cognitive Computing 2012 Consciousness and Computation: human and machine intelligence 3. VAN GELDER ON DYNAMIC SYSTEMS THEORY Mark Bishop

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01/04/2014(c) Bishop: Consciousness and Cognition2 What Might Cognition Be, If Not Computation? Tim Van Gelder, (1995), What might cognition be if not computation?, The Journal of Philosophy, 92: 7, pp See also, Robert Port and Tim Van Gelder, Mind in Motion, MIT Press, (1998). The collection was the first comprehensive presentation of the dynamical approach to cognition; it contains a representative sampling of original, current research on topics such as perception, motor control, speech and language, decision making, and development. In this paper Van Gelder first presents an alternative framework to the then standard computational - GOFAI and connectionist - theories of mind. The new core metaphor for cognitive systems that Van Gelder introduces is that of the mechanical Watt Governor…

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01/04/2014(c) Bishop: Consciousness and Cognition3 The Watt governor The Watt governor is a device that endeavours to control the speed of a device [a flywheel] despite fluctuations in power [steam pressure] and demand. Watts governor was adopted from windmill technology: Vertical spindle which rotated at speed of flywheel. Attached to spindle were two arms. At the end of each arm was a ball. As spindle turned centrifugal force pushed the ball outward and upward. This upward motion of the arms controlled a valve controlling steam pressure. As speed increased balls went up and valve was closed. Conversely as speed decreased balls went down and valve opened.

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01/04/2014(c) Bishop: Consciousness and Cognition4 The Watt governor and dynamics Van Gelders central claim is that the mechanical Watt governor was not computational in character as it did not use or process representations. Van Gelder suggests that representations imply a form of homuncularity hence the Watt Governor is inherently non-homuncular in its operation. It was a closely coupled continuous real time system, with no sense of sequential operation as all its components operated simultaneously. It has parts but they are all directly coupled and do not pass representations between themselves. In contrast to the computational governor, Van Gelder suggest that the mechanical Watt governor is best analysed using the mathematical tools of dynamic systems theory. Differential equations etc. Its behaviour is fundamentally temporally constrained by its temporal dynamics.

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01/04/2014(c) Bishop: Consciousness and Cognition5 Comparison with a computational governor With the advent of computer control, engine speed could also be controlled by a suitable algorithm. In contrast to the Watt governor the computational governor: Is fundamentally sequential in its operation; makes explicit use of representations (and hence implies a form homuncularity); [as long as the sampling frequency is fast enough; Nyquist criterion] there is a sense in which time doesnt matter.

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01/04/2014(c) Bishop: Consciousness and Cognition6 Wheeler on Dynamic systems Is a Dynamic System simply any fully state determined system? No as this doesnt leave room for stochastic - contra deterministic - state dependent changes. Hence consider a Dynamical System (DS) to be any system in which there is state dependent change over time. This covers just about any natural system.. To further substantiate the above definition we need to be able to provide a formal analysis of the way these states evolve over time. This can be achieved using the mathematics of dynamic systems theory.

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01/04/2014(c) Bishop: Consciousness and Cognition7 The analysis of dynamic systems The dynamic systems analyst needs to select: (a) a finite set of component state- variables which fully capture theoverall state of the system at a given point in time. Each state of the system in time is represented by a point in this state space. (b) A set of [differential] state-space evolution equations which describe how the values of the systems state-variables evolve over time. The set of values which characterise the differential equations are the parameters of the system. Hence, given initial conditions of the system, the set of differential equations describe its future time evolution.

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01/04/2014(c) Bishop: Consciousness and Cognition8 The trajectory of the system The set of all possible trajectories defines the systems phase portrait. Attractors are states to which the system tends to converge. All states which lead to the attractor define a basin of attraction. Points in the basin which lead to the attractor - but are not part of the attractor - are called transients. Complementary to attractors are repellors; points in state space from which the system tends to move away.

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01/04/2014(c) Bishop: Consciousness and Cognition9 Representation and reasoning Van Gelders insight was to realise that various systems can appear to demand they represent and reason about their environment but which in practise do not. Historically this fallacy has arisen as people have not considered the alternative dynamicist approach. Nonetheless if required - say to escape problems earlier identified with behaviourism - representational significance can be assigned to some or all of the state variables or parameters. Or particular points in phase space, (e.g. attractors; repellors; specific trajectories etc).

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01/04/2014(c) Bishop: Consciousness and Cognition10 So in a sense the Watt governor is representational after all! For example, we might correlate arm angles with speed. But arm angles are correlate with speed only when at equilibrium. In dynamic operation there is a complex coupled relationship; at perturbation the speed of the flywheel may change quickly yet the balls only fall relatively slowly under gravitational acceleration. Representation is simply the wrong conceptual tool to link arm angle and engine speed: Arm angle and engine speed are coupled. I.e. They are determined by and both determine each others behaviour. We analyse Watt governors using the mathematics of dynamic systems not computations on internal representations.

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01/04/2014(c) Bishop: Consciousness and Cognition11 In a sense the Watt governor does have a computational description A Watt governor is only describable by computations in mere simulation. Otherwise we have a computational governor. Fundamentally the operation of any physical Watt governor is: continuous; temporal; non-representational. Hence a real Watt governor cannot be genuinely computational in character.

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01/04/2014(c) Bishop: Consciousness and Cognition12 The link between computational and dynamic systems, (Wheeler) Computational systems are themselves a particular class of dynamic systems that have been carefully designed, when used appropriately, to: Realise well defined I/O functions, (by using and manipulating representations). Planets realise a specific function, defined by Keplers laws, but dont explicitly utilise representations. Be temporally austere, (lack temporal phenomena): No specification of the time of each processing step; No specification of the time interval between steps; States dont persist for any length of time.

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01/04/2014(c) Bishop: Consciousness and Cognition13 Dynamic system theory of cognition (DSC) DSC: Cognitive systems are best conceived as continuous dynamical systems not discrete computational systems. I.e. Cognition is more similar to the Watt governor than to the Turing Machine. In the last decade there has been considerable research activity involving dynamic systems theories of cognition. Cf. The 1995 collection edited by Port & Van Gelder, Mind as Motion.

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01/04/2014(c) Bishop: Consciousness and Cognition14 Example: language processing (Elman, 1991, 1995) Elman has done work with a simple three layer recurrent neural network: A network where the output of hidden nodes is fed back after one time step. Elmans network was able to predict whether a verb ought to be plural or singular. Activation space is space defined by all the network node activation values. Given the initial conditions, the network defines a trajectory in this (70D) space as it operates. Elman used PCA to reduce this to a 2D space where grammatical features (e.g. number etc.) became evident.

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01/04/2014(c) Bishop: Consciousness and Cognition15 The analysis of property If a cognitive dynamic system is counted as possessing some property, (e.g. intentionality), by virtue of achieving a particular state-dependent change over time; a specific phase trajectory. Then the mathematical analysis of the system constitutes a set of sufficient conditions for the presence of the property.

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01/04/2014(c) Bishop: Consciousness and Cognition16 Radical dynamic systems theory Hence for radical dynamic systems theorists a cognitive system is any system that instantiates appropriate real valued state transitions. Such a system thus encompasses: Real valued state transitions; Is fundamentally temporal The state transitions embedded in time; Does not use explicit representations; Is fundamentally non-homuncular (as no representations).

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01/04/2014(c) Bishop: Consciousness and Cognition17 Summary of DSC DSC provide a post-Cartesian conception of cognition that rejects the model of mind as an a-temporal representer, and emphasizes instead the ongoing, real-time dynamics of complex systems. Such a post-Cartesian cognitive agent manages to cope with the world without [necessarily] representing it. Dynamic systems theory provides a mathematical framework to study both embodied and non embodied theories of cognition. Radical DSC abstracts the dynamics from agent / environment interactions. Get the dynamics right and appropriate cognition must follow.

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