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Life is not a formal system... so far.
Roger, you are seeing ontologies from the view
of the declaration. A dynamic system includes
operators, and operators require selectors.
1. The ontology declares choices (really, the intelligence
that abducts data, inducts relationships, and enables logical
operations to be applied: aka, life). This is the step
that may demonstrate "sensitivity to initial conditions".
2. The operator affects the choices (insert, delete, negate, etc)
3. The selector activates the operators (may be a nested
set of selectors; may require multiple modalities)
4. Output from the process is measured and fed back to
the selectors as new choices.
5. Continuity is determined by the affect of the selections
on the energy budget of the system.
That's the simple model.
Consider the complexity of having multiple word senses
for given terms. How does the selector choose the
appropriate word for a given communication? Context(s).
How does the selector determine context. Measurement.
How does the selector measure uncertainty in the results of a
measurement (what is the measure of the measure)?
From: Danny Ayers [mailto:firstname.lastname@example.org]
> Sorry, I wasn't clear. My point here was to contrast treating semantics
> using graphs (which is used to capture snapshots) vice using the field of
> complex systems to capture dynamically changing relationships. /Roger
Somewhere near your question is the difference between discrete and
continuous systems (of which time is just an example). In terms of (digital)
computer systems this points towards the contrast between
statistical/numeric (may be sampled analogue) and formal logic-based
systems. I don't think it's particularly difficult to bridge the gap (I've
got some things to try ;-), but the payoffs are potentially enormous - as a
simple example, it would put Google on the Semantic Web.