Sunday, 11 January 2009

Chaos traces in Ed Fredkin's digital philosophy?

Exciting aspects, in what I have read in Cellular automaton models in Digital Philosophy website which compels me to write them down, raw as they are.

The following extract from Chapter 1 Cellular automaton models

"Our thesis is that some CA model may be, in effect, programmed to act like physics. We call such models digital mechanics (DM). In short, DM is a discrete and deterministic modelling system which we propose to use (instead of differential equations, for example) for modelling phe­nomena in physics. We are driven in this direc­tion by many heuristics; primarily by the concept, borrowed (and extended) from automata theory, of the universal machine [3] Any ordinary com­mercial computer would be a universal machine, except for the fact that it does not have an infi­nite memory. In this paper, we shall extend the meaning of the term "universal machine" to in­clude the universal cellular automaton (UCA) or other kinds of general purpose computers that have large but finite memories; this would include any commercial computer. A universal machine can exactly mimic the behavior of any other finite computer, provided its memory is just a very little bit larger than the target machine."

referring to the universal cellular automaton model, as being based on the concept of the universal machine, which can exactly mimic 'behaviours' applicable to wider and varied settings?

Is it directly related with the universality principle prevalent in chaos, or is it a simple circumstantial connection? Intended or unintended? It is worth pursuing that line of thinking.

And further

"By "complexity" we mean some combination of: a large number of states per cell, a complex CA rule, neighborhood (spatial connectivity and dimensionality), boundary condition or initial con­dition."

the mention of 'boundary condition or initial condition', brings into mind chaos's 'sensitive dependence on initial conditions', and that notion combined with the statement

" RUCA also exhibit unusual and counterintuitive behavior that is a consequence of perfect reversibility combined with extreme quantization."

where the 'unusual and counterintuitive behavior', being the hallmark of chaos developing states, as well as from the phrase 'a consequence of perfect reversibility combined with extreme quantization', the mention of 'extreme quantization', strengthening the ties of the RUCA model with chaos via its sensitive dependence on the minutiae of changes in initial conditions.

Which is further exacerbated in the paragraph

"RUCA reversibility is very different than the intuitive notion of microscopic reversibility that relies on continuity to ensure that no effect gets lost no matter how infinites­imal it becomes."

initial conditions preserved no matter how 'infinites­imal' they become.

Remarks that sink deeper into my mind the chaotic origins of reality.

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