path-dependence: a philosophical issue concerning time

I raised a question on Markov processes for which I didn't receive much
help, and so let me approach my concern from a different angle.

Mathematical fields such as Markov process, ergodic theory,
etc. describe or model the successive states of a system as they exist
in time. This represents successive states along a time line that are
all presumed to be real for the observer.

However, today there is serious doubt that there is a time dimension
(Mellor, Real Time II, for example), but rather time is merely an
extrinsic property of systems. At any moment in time (which can only be
the present because the phrase is being indexed in the present), the
past no longer exists and the future has yet to come. So the past and
the future must be represented as aspects of the present and not
hypostatized as real entities. This point may be troubling in physics,
but it's almost a commonplace in historiography, where historians tend
to seek how-explanations (constraints on possibilities conveyed by
narrative) rather than why-explanations (causality).

Assuming for the moment that only the present exists at present is true,
then how can there be a path dependence? Does that imply a determination
by what does not exist? True, if we were to represent a sequence of
states in memory, we can see that each successive state influenced the
next, and so construct a trajectory in thought. But what is the relation
of such a thought object to the world?

In what sense can this trajectory really be a causal force if the past
no longer exists in the present? A sensible conclusion might be that the
effect of that past can only be a net effect or outcome that exists in
the present. In historiography, the past is refered to as "traces" that
exist in the present. Even persistence can be causally explained
(although causal theories of persistence are contentious) and not
the effect of something transcendental.

This would seem to imply that in terms of objective reality (assuming
this notion to be valid) there can be no path dependence. If there's no
path dependence, then it would seem to make no sense (outside
mathematical modeling and human memory) to use the term path
independence either, since all processes would be path independent
because the past is forgotten and there is no real path in relation to
the present, but only as an imagined reconstruction of the past.

I suppose a simple example of path dependence would help, and in fact
the definition of this request is itself interesting. That is, can
anyone offer an example where information concerning a trajectory of
past states well separated from the present informs a present system
_and is not_ already implicit the definition of the present system? Does
this definition of an example show that a presumption of path
dependence to be a kind of idealism?

--

Haines Brown, KB1GRM



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Relevant Pages

  • Re: path-dependence: a philosophical issue concerning time
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  • Re: path-dependence: a philosophical issue concerning time
    ... This represents successive states along a time line that are ... This would seem to imply that in terms of objective reality (assuming ... this notion to be valid) there can be no path dependence. ... of the fact that all objective existence is posited and contingent on ...
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