From: Tennessee Leeuwenburg (tennessee@tennessee.id.au)
Date: Thu Sep 08 2005 - 22:45:06 MDT
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Joel Peter William Pitt wrote:
> On 9/8/05, *Tennessee Leeuwenburg* <tennessee@tennessee.id.au
> <mailto:tennessee@tennessee.id.au>> wrote:
>
> I don't think that's a proper description of what chaotic is. Chaos
> doesn't mean "without rules", but rather it means that the
> behaviour of the system is obviously derivable from the rules. The
> states are chaotic in that it would be exceedingly difficult to
> predict from knowledge of the initial conditions of the system what
> the precise state of the system would be sometimes in the future.
> The predictability of a car comes not from a bottom-up
> understanding of all interacting components, but rather from
> grokking what the stable patterns are.
>
>
> The states in a chaotic system *are* able to be predicted with the
> knowledge of initial conditions and the rules they follow. However
> any slight deviation or error in the initial conditions result in
> the system following different trajectories - so, in the real world
> a chaotic system is deterministic, but we can't predict it's
> future because all our measurement will have some degree of error
> and even a slight amount of error results in quick divergence of
> trajectories.
Perhaps I was loose with my language. They are, in principle, able to
be predicted, viz they are deterministic. It is the deviation and
error which makes them difficult to actually predict.
Chaos theory, I thought, was predominantly related to the emergent
patterns, organisation, attractors and repulsors which are
identifiable in many (most?) chaotic systems. I read a book on this
topic, which (as I am a bear of little brain) was right at my level
being primarily qualitative with a smattering of maths.
It was using examples of state change in systems, the patterns of
variables making a random walk, etc etc to describe real systems at
the level of patterns and tendencies.
I really thought that Chaos theory was not about "giving up" on making
predictions, but rather a description of the kinds of claims that we
can make about deterministic but practically indeterminable systems.
As applied to something like AI, for example, or neural network
propagation, or idea propagation, or the presence of any particular
population or identifiable set within a possibility space, this is
basically referring to the patterns that we can expect to find. It is
less concerned with how to move from detail to complete prediction,
and rather offers us a set of tools for analysing things at a higher
level.
For example, if we designed an AI, which was implemented as a complex
system, we could expect to see features within that AI, some of which
will be robust, some which will be fragile etc. We should expect to
see state changes whereby there are critical points at which change
will propagate very rapidly throughout the entire system, even though
it was previously stable.
Cheers,
- -T
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