Monday, 29 April 2013

Chaotic machines...

There are a few things I would like to ponder on and let the thoughts develop to whatever end. It is mentioned in page 48 of James Gleick “Chaos, making a new science” that

A letter from a colleague informed him that many systems were not so well-behaved as he had imagined, and it described a counterexample, a system with chaos and stability, together. This system was robust. If you perturbed slightly, as any natural system is constantly perturbed by noise, the strangeness would not go away. Robust and strange - Smale studied the letter with disbelief that melted away slowly.”

And further

Chaos and instability, concepts only beginning to acquire formal definitions, were not the same at all. A chaotic system could be stable if its particular brand of irregularity persisted in the face of small disturbances.”

Irregularities persisting in the face of small disturbances? How can this be used? Irregularities that do not go away? Appearing time and time again? Could that be all that chaos is? Just a curiosity? What about your claim about chaos being creative? The way that nature, and not only, seeks out solutions to problems presented? Any problems? The idea of stable chaos embodied in the persistent presence of irregularities, does not conform with the idea that immersing in chaos what comes out would be a novel way to deal with a problem. A new way of thinking about it.

Or is it that the difference is what a chaotic system is fed with. A chaotic machine, all-in-one, along with its persistent irregularities, an ensemble that acts upon its input to produce a certain output, and in-between the input is treated in various ways characteristic of the particular chaotic machine. The persistent irregularities the hallmark of its bearer, the particular chaotic machine.

 Chaotic machines being widespread and ubiquitous, operating under the principles of self-similarity and universality, for each activity natural or man-made, with their own particular range of parameters representing the input that feeds into them, which as it is mentioned in the same page

The chaos Lorenz discovered, with all its unpredictability, was as stable as a marble in a bowl. You could add noise to this system, jiggle it, stir it up, interfere with its motion, and then when everything settled down, the transients dying away like echoes in a canyon, the system would return to the same peculiar pattern of irregularity as before. It was locally unpredictable, globally stable. Real dynamical systems played by a more complicated set of rules than anyone had imagined.”

Chaotic machines fractally connected, where their inputs being the outputs of other chaotic machines residing in activity levels below, hierarchically arranged in an intricate web that surpasses all reality. The range of parameters in chaotic machines in a particular level, being crucial, to the range of parameters in chaotic machines immediately below.

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