Proceedings Article | 21 June 2007
Proc. SPIE. 6602, Noise and Fluctuations in Biological, Biophysical, and Biomedical Systems
KEYWORDS: Cognitive modeling, Data modeling, Sensors, Control systems, Cognition, Dynamical systems, Motion models, Systems modeling, Neurons, Chaos
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.
