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> A Dynamical System consists of some "variables" and
> some "equations of motion" or "dynamical equations".
> The variables are any things which can vary with time.
> They can be multiple or single, continuous or discrete.
> They must be chosen in such a way that complete knowledge
> of all the variables determines uniquely the "state" of
> the system at one time.
Thanks Sergio. This is very useful information.
Perhaps this is obvious to everyone but ...
Consider the situation of a stylesheet processing an XML document:
XML (input) ---> XSLT ---> XML (output)
An XML document is a "model" of a system. For example, a Fitness Center
XML document is a model of a fitness center. Thus, an input XML document
represent the "current state" of the system, the output XML document
represents the "next state", and the stylesheet is simply a mechanism
for implementing the transition from state (i) to state (i+1). Thus,
the "variables" of the system correspond to elements in an XML document.
Which elements in an XML document represents the system variables? For
example, in the following Fitness Center XML document, which elements
correspond to the "system variables"?
<?xml version="1.0"?>
<FitnessCenter>
<Member level="platinum">
<Name>Jeff</Name>
<Phone type="home">555-1234</Phone>
<Phone type="work">555-4321</Phone>
<FavoriteColor>lightgrey</FavoriteColor>
</Member>
<Member level="gold">
<Name>Stacey</Name>
<Phone type="home">888-1234</Phone>
<Phone type="work">888-4321</Phone>
<FavoriteColor>purple</FavoriteColor>
</Member>
</FitnessCenter>
Are the <Member> elements the "system variables"? Or, are the <Name>,
<Phone>, and <FavoriteColor> elements the "system variables"?
My answer to this question is: the <Member> elements. The <Member>
elements represent a "building block" that is presumably the product of
evolution, i.e., over time a collection of <Name>, <Phone>, and
<FavoriteColor> elements coalesced to create a useful building block
(this is analogous to molecules aggregating together to form a useful
building block - a cell). It is at the building block level that
competition and collaboration occur (and this competition/collaboration
activity is physically implemented by the XSLT stylesheet).
Do you agree with this analysis? If so, can you think of a
competition/collaboration activity that might transpire among Members?
Fascinating stuff! A whole new way of looking at things. /Roger
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