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From: Didier PH Martin [mailto:martind@netfolder.com]
Hi Didier:
>>That's not quite right. The Butterfly Effect is that given a
>>sensitive dependence on initial conditions, two similar systems
>>will evolve to very disimilar states in a short period of time.
>>It is the effect of amplification that occurs when conditions
>>are coupled by non-linear equations that determine unpredictable
>>or uncertain future states.
Didier replies:
>I do not see what you found not right in what I said Len.
I meant the precise definition is the effect is that produced
by sensitive dependence on initial conditions. You are right
about the association to attractors in the modeling context.
In other words, I am discriminating among systems that exhibit
the effect and systems that model it. That's all.
The crucial piece of information I've been after is the
descriptions of non-linear equations that couple systems.
Too many descriptions and derivations of chaos theories
tend to treat it as mysterious and it isn't. It isn't
even a novel observation although good work has been
done on the math since Poincare.
>There is also another way to study networked systems based on stochastic
>models.
As in Markov?
>In these models the attractors could potentially be at each step
>of a network path and look like a random walk (polynomial with
>probabilities for each node).
As in Brownian motion?
>These systems are non continuous, cannot
>be modeled with Riemannian integrals but more with Lebesgue integrals.
>This is why I said that it is easier to model these phenomenons with
>percolation models than with classic chaotic system dynamics involving
>different mathematics.
Agreed. Last time I dipped into this, the percolation models were
more informative when studying a communication network. Hmm. Maybe
information theory is more appropriate for non-linear systems, but
I'm punting without thought or research with that comment.
>This said, a lot of people are actually studying
>stochastic phenomenons through the perspective of attractors.
References? I have intuitions but no references for that.
>So this is why I said modestly that I
>do not know if the VHS/beta phenomenon maps well with chaotic system
>models but I know that they map better or are better modeled with
>percolation models involving stochastic calculus. Utilitarian? Maybe,
>practical? Yes indeed.
VHS/Beta: I understand it as the case study for a slightly inferior
technology beating a better technology in the market place where the
winning quality was form factor and possibly cost. I'm not sure
how to apply non-linear dynamics to that one because it isn't a case
of not being predictable, but a case of not picking the right features
to make the prediction with.
Anyway, if we want to drive this thread back to the topic, we must
examine the role of ontologies.
What relates non-linear dynamic systems to ontologies? Do ontologies
make semantics more or less predictable? Are ontologies simply the
agreement about meaning expressed in a form that enables some community
of users to control the evolution of the agreement? We cannot get
beyond ontologies. There is no there there.
len
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