Monday, May 14, 2007

Chaos related musings

     So the chaos situation or state refers to the behaviour of systems and that behaviour depends so sensitively to the system's precise initial conditions, and because of that, it is unpredictable and appears as a random process, but it is deterministic, approached from a mathematical viewpoint. Additionally, should point out, that even a very small perturbation can have a very large effect on a system. The system is geared up, amplifying minute changes in values of parameters and variables connected with its initial conditions, to very large values in other dependent variables and parameters in the system, which give rise to the intense behaviour of chaos. The amplification is exponential and it appears as a result of nonlinear functions between the variables involved in a system.

     P. S. de Laplace's statement, "We ought then to regard the present state of the universe as the effect of its preceding state and the cause of its succeeding state", brings out clearly the situations governing all chaotic systems the cause and effect relationships and the importance of pre-existing conditions in determining its current state.

     In general deterministic systems can evolve to unpredictably random behaviour, chaotic behaviour. Though, actually, it appears to us as random, primarily as a limitation of our sensory apparatus, as well as, of the limitations of our cognitive abilities. So despite our inability to discern the determinism of the chaotic processes, deterministic chaos exists and is responsible for complexity and finally emergence.

Misplaced character of deterministic

     Is it correct to regard determinism as defunct, when it comes to consider the nature's workings? It is suggested, that human evolution is not deterministic, by invoking the argument that the laws of evolution should have built into them anticipation of all events possible. One of many assumptions possible stemming from our inability to discern the underlying causes of changes in nature. The laws of evolution do not require to have all outomes possible, the multitude of all configurations of states possible, to account for state configurations, with far removed possibilities to be adapted by a system. It is more economical to account for states with a greater chance of being adapted, an attracting range of state configurations, a chaotic attractor, as deterministic chaos dictates. And this is the anticipation built, in the laws of evolution.

     The anticipation, so described, can be similar to the anticipation John Holland invokes, for neural networks. "Elements in a stimulus sequence not yet seen, are anticipated by the corresponding extrasensitive assemblies". Stimulus sequences are of similar nature, as of John Holland's reverberating cell assemblies. What about the corresponding extrasensitive assemblies? What would their equivalent be, in human evolution? Certainly, these should be the procceses most prevalent at any time in the course of human evolution. The ones, that once they have been selected, multiplied, became dominant, reinforced in the agent populations. Reinforced processes,(practises customs), become extrasensitive, by virtue of their sheer numbers in the agent populations, for the system. They provide the response to presented stimulus sequences and determine the succeding states. Anticipation is inherent, as the chaotic attractor set of states, is an attracrting set and even if it is preturbed off the attractor, it eventually ends up in the set.

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