Dynamical Systems Slides (2) PDF

Dynamical Systems Theory Cognitive science without representations? Basic principles of traditional cognitive science: Cognition is a form of information processing Information-processing involves manipulating representations PSSH and artificial neural networks incorporate different...

Dynamical Systems Theory Cognitive science without representations? Basic principles of traditional cognitive science: Cognition is a form of information processing Information-processing involves manipulating representations PSSH and artificial neural networks incorporate different models of information-processing (mental architectures) Dynamical Systems Hypothesis cognitive scientists should understand cognitive agents as dynamical systems embedded in their environment cognition is a process that evolves through time, but does not necessarily involve computation or representations at least not as standardly understood Sometimes offered as an alternative both to PSSH and to ANN’s The empty brain - Epstein The empty brain - Epstein Dynamical System Any system that evolves over time According to this definition it is trivial to say that cognitive agents are dynamical systems, we need a richer notion Dynamical model: track the evolving relationship between a small number of quantities that change over time A dynamical system is a system that can be studied using the tools of dynamical modeling Dynamical model Typically use calculus to track the evolving relationship between a small number of variables that change over time difference equations (for modeling discrete time series) differential equations (form modeling continuous time series) State Space The state space of a dynamical system is a geometric way of thinking about all the possible states the system can be in As many different dimensions as it has quantities that vary independently of each other The state of a system at a time can be identified with a particular set of coordinates in its state space The evolution of a system is its trajectory through state space from a set of initial conditions  Can we find cognitive systems for which a dynamical systems model works better than a standard, computational account? Doing without representation? Modeling child development with dynamical systems theory Motor skill: Walking Cognitive skill: A not B error Both illustrate dependencies on cognitively irrelevant variables and can be modeled using DST Computational Model of Motor Control Planning movements (e.g. reaching) begins with CNS calculating position of target and position of hand coordinating input from vision and proprioception Planning movement requires (a) calculating trajectory, (b) working out a series of muscle movements that will take the hand along that trajectory Executing movement requires calculating changes in muscle movement to accommodate visual/proprioceptive feedback  A typical computatio nal model DST alternative Walking is not a planned activity involving a specific set of motor commands “programming” limbs to move in certain ways Walking emerges out of complex interactions between muscles, limbs and different environmental features coupled system multiple feedback loops Learning to walk Infants standardly show a U-shaped developmental trajectory Infants capable of making stepping movements during first 2 months of life Ability disappears during non-stepping window [2-8 months] Reappears when walking begins Standard explanation neural – depends upon maturation of areas of cortex responsible for executive control Learning to Walk Cortex Baby Reflexive Cortex control of learns to action control voluntary walk increases movement to increases suppress reflex # of steps Age in months Learning to Walk Thelen and Smith Environmental changes induce stepping motion at all stages of cortex development (e.g. by holding the baby upright in warm water; by putting baby on a treadmill) Learning to walk can be modeled using dynamical systems approach – by mathematically specifying the interactions between a small set of variables (leg fat, muscle strength, gravity, and inertia). Object Permanence Object permanence = infants’ understanding that objects continue to exist when unperceived Important stage in development of child’s naïve physics Studied by Swiss psychologist Jean Piaget in terms of search for hidden objects  Object Permanence : Baillargeon’ s drawbridge experiments  https://youtu.be/4jW668F7H The A not B error dA Occurs between ages of 7 and 12 months Children reach to the original hiding place, even after seeing the object moved from container A to container B The A not B error Cognitive explanations: Insufficient representational capacity Insufficient development in the prefrontal cortex Thelen and Smith’s Dynamical filed model Babies’ performance is variable and easy to manipulate Responsive to changes in the babies’ dynamic field; changing inputs 3 different kinds of inputs: (1) Environmental (distance to containers, salience of target...) (2) Task demands (experimenter drawing attention to target) (3) Memory input (from previous reaching trials)  Thelen and Smith’s model captures some features of infant reaching behavior It does not explicitly appeal to standard CogSci factors representational states emergence of executive control cortical maturation Highly sensitive to initial conditions Doing without representations? Review analogy in textbook, p. 127