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 that solves the problem. Deterministic chaos in general affects a dynamical system 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 means fixing different sets of control parameters, each with a different a-priori probability, to be then confirmed and transformed into 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 creativity the action of code changing, which is guided by hints not formalized within the previous code, whence not accessible to a computer. We call semantic complexity the number of different 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 context. 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. Since this is a report on work in progress, we skip technicalities in order to stress the gist of the question, and provide references to more detailed work.
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Arecchi, F. Physics of cognition: Complexity and creativity. Eur. Phys. J. Spec. Top. 146, 205–216 (2007). https://doi.org/10.1140/epjst/e2007-00181-0
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DOI: https://doi.org/10.1140/epjst/e2007-00181-0