About the Banach & Tarski theorem

In other words, the Banach & Tarski theorem describes a process that implies a physical model which is different (and incompatible) with LCME (a currently accepted description of our world). An instance of a process that is possible and entirely compatible with a physical model implied by the Banach & Tarski theorem could be judged to be similar or analogous to an instance of a process that is compatible with LCME. A process that is analogous to a Banach & Tarski process could indeed be observed in our world, depending on the exact definition of analogy. In order to complete your argument, you would need at least to provide a definition of 'analogy' or 'similarity'. Now, maybe you think you've done that, by presenting the LCME physical model and how it is mathematically inconsistent with a physical model implied by Banach and Tarski. The problem is that of analogy. Your unstated premise is that no 2 instances of a processes described by incompatible physical descriptions can ever be 'analogous' or 'similar'.

Fundamental creativity

Creativity all the way related to the free will. So the question arises: Can machine have the appearance of free will, if its circuitry is based on chaos dynamics? This could be discussed in materialistic point of view. Chaotic systems are determined, but they are extremely sensitive to initial conditions; since these initial conditions cannot be determined very accurately, the errors multiply and make it impossible to predict the behavior of chaotic systems over long periods of time. Thus being determined is not the same thing as being predictable. If the behavior is not predictable, it could easily be assumed to have free will. But that would be unnecessary carriage. Once again, can chaos dynamics give the robot access to fundamental creativity? It is a fact that chaotic systems stuck in a given pattern (technically called an attractor) can bifurcate to a different attractor if some system guidelines are changed. Could this dynamical change of attractors not simulate fundamental creativity? No again. Chaos-machine computers, if they are to be of any use, must operate within the contexts that the programmer gives them. All computer systems act as trial-and-error systems quite appropriate for situational creativity, but not fundamental creativity, not for the purposeful discovery of a new context. The programmer alone has the purposive ness and the freedom to bring about new contexts.

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