Complexity, information loss, and model building: from neuro- to cognitive dynamics
Year: 2007
Authors: Arecchi F.T.
Autors Affiliation: Università di Firenze
Abstract: A scientific problem described within a given code is mapped by a corresponding computational problem, We call complexity (algorithmic) the bit length of the shortest instruction which solves the problem. Deterministic chaos in general affects a dynamical systems making the corresponding problem experimentally and computationally heavy, since one must reset the initial conditions at a rate higher than that of information loss (Kolmogorov entropy). One can control chaos by adding to the system new degrees of freedom (information swapping: information lost by chaos is replaced by that arising from the new degrees of freedom). This implies a change of code, or a new augmented model. Within a single code, changing hypotheses is equivalent to fixing different sets of control parameters, each with a different a-priori probability, to be then confirmed and transformed to an a-posteriori probability via Bayes theorem. Sequential application of Bayes rule is nothing else than the Darwinian strategy in evolutionary biology. The sequence is a steepest ascent algorithm, which stops once maximum probability has been reached. At this point the hypothesis exploration stops. By changing code (and hence the set of relevant variables) one can start again to formulate new classes of hypotheses . We call semantic complexity the number of accessible scientific codes, or models, that describe a situation. It is however a fuzzy concept, in so far as this number changes due to interaction of the operator with the system under investigation. These considerations are illustrated with reference to a cognitive task, starting from synchronization of neuron arrays in a perceptual area and tracing the putative path toward a model building.
Journal/Review: PROCEEDINGS OF SPIE
Volume: 6602 Pages from: 660214-1 to: 660214-14
KeyWords: complexity
