Richard,

>  Question:  "How many systems do you know of in which the system elements
> are governed by a mechanism that has all four of these, AND where the system
> as a whole has a large-scale behavior that has been shown (by any method of
> "showing" except detailed simulation of the system) to arise from the
> behaviors of the elements of the system?  I would like an example of any
> case of a complex system in which there are large numbers of individual
> elements where each element has (a) memory for recent events, (b) adaptation
> and development of its character over long periods of time, where that
> adaptation is sensitive to influences from other elements, (c) an identity,
> so that what one element does to another will depend crucially on which
> element it is, and (d) nonlinearity in the mechanisms that determine how the
> elements relate and adapt."

I don't really understand your definition of "identity" in the above, could you
clarify, preferably with examples?

>  Show me any non-trivial system, whatsoever, in which there is general
> agreement that all four of these characteristics are present in the
> interacting elements, and where someone figured out ahead of time what the
> overall behavior of the system was going to be, given only knowledge of the
> element mechanisms, and without simulating the whole system and looking at
> the simulation.
>
>  There does not have to be a mathematical proof, just some derivation that
> allows me to see an example of someone predicting the behavior from the
> mechanisms.

I'm not sure what you mean by "predicting the behavior."

With the Pet Brain, which does seem to fulfill the criteria you mention above
(pending my new confusion about your meaning of "identity") (with the Atoms
in the Novamente AtomTable as the "elements" in your description), one cannot
predict the precise course of development of the system ... we can't predict
what any one pet will do in response to it's environment ... but we do
understand
what sorts of behaviors the pets are capable of... based on general
understanding
of how the system and its dynamics work...

ben

-------------------------------------------
agi
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