Time and context

["Tim Gwinn" <***>]

> -----Original Message-----
> From: ROSEN Forum [mailto:*** Behalf Of Tim
> Gwinn
> Sent: Wednesday, October 08, 2003 11:06 AM
> To: ***
> Subject: Re: When does an (M,R) system cease to be alive?
>
---snip----
>
>
> I think that time is basically about labels and their relation to other
> percepts or observables, using relationals such as "simultaneous" and
> "predecessor-successor".  The idea that there should be one set of
> ubiquitous labels for the entire universe goes back to at least
> the days of
> a belief in a clockwork universe.
>
> Einstein showed that in certain kinds of differing frames of reference,
> these labeling schemes are not universally identical.However, there is
> always a way to _translate_ the time labels in frame of reference to those
> in another frame of reference. It gives the appearance that time is still
> one universal linear construct, but it just happens to get "stretched" or
> "contracted" in these relativistic frames of reference.
>
> I do not think this is general enough. To me, the presumption of
> adequacy of
> a single, linear timeframe is very much like the presumption of
> adequacy of
> a single linear algorithmic sequence. Within the confines of both of these
> schemes, only a very limited kind of description can occur.
>
> Biological systems, particularly as anticipatory systems, seem to
> intimately
> use different labelings for different aspects of the organism.
> And, it seems
> (given that it is a complex system) that there are no ways to translate
> these labeling systems between these aspects into one coherent time label
> reference. So that attempting to describe them using a single
> linear set of
> time labels loses the unique labeling for each different aspect. It loses
> that aspect of the complexity.
>
> This would change time from being merely "relative" to being
> context-dependent. Perhaps organisms are just particularly good at
> exploiting that context-dependence in order to carry on morphogenesis and
> other activities within a multitude of internal, context-dependent
> timeframes, and that is part of what makes the orchestration of such
> processes hard to comprehend.
>

I've been fighting an unwanted symbiote (resulting in a cold) the last
couple of days, so my brain is a little more fuzzy than usual. Hopefully,
someone can check me on what follows.

In regards to time and context, I wanted to add that Rosen discussed
something like this in AS (4.5 "Time in General Dynamical Systems"). He did
so in the language of time differentials 'dt' in Hamiltonian systems. As it
turns out, dt is a _result_ of the specific encoding of the dynamics of a
given system, giving each such system an "intrinsic time", rather than dt
being something that is independent of or sits "outside" of those dynamics
and encodings. And generically, there will be no reason why the dt's (or
"intrinsic times") of different systems will be the same.

As for attempting to relate these various dt's to one "common time", Rosen
states:
"We can conclude then that the encoding of time as a general dynamical
parameter cannot be effectively made within a limited dynamical context.
Rather, we must in each case arbitrarily select a scale factor a(x1,....,xn)
which will convert intrinsic time to Hamiltonian time via (4.5.5) [4.5.5:
dt=a(x1,...,xn)dt-sub-H; where "dt-sub-H" is the intrinsic Hamiltonian time
differential for the given system]; only in this way can we use clocks to
define a "common time" in terms of which dynamical predictions can be made.
Even this is not the end of the matter, for we have already pointed out that
Hamiltonian time differentials can be different from one another. Thus, if
we change from one Hamiltonian time differential to another, the resulting
relations (4.5.5) force these Hamiltonian differentials to be related in a
particular way if (4.5.5) is to remain invariant upon this change. A change
of this kind can be looked upon as a change in observer, and thus we impinge
on the kinds of relativistic considerations which are intrinsic to any
discussion of synchronization."

But, beyond being merely relativistic, he then shows how these
considerations can be extended to the activation-inhibition networks, which
can provide a more general encoding of dynamics. In this situation, he
states:
"In order for such an interpretation to be valid for an arbitrary
function... it is necessary and sufficient that the net activations....which
we have defined should be exact differentials....Furthermore, it is only in
this case that we are able to define an intrinsic time differential dt,
through which the concept of rate itself becomes meaningful."

However, the requirement for these net activations to be exact differentials
is a highly nongeneric requirement! When generically perturbed, these
differentials become inexact. [see EL ch. 22] So it would seem that,
generically, the identification of an intrinsic dt of a general dynamical
system will not be possible, and as a result, the concept of "rate" will
then no longer be meaningful for that system. In a simplified view of
dynamics which presumes a priori 1) a valid "common time"; and/or 2) that
the network of differentials will be exact; will allow the satisfying result
that "rate" and "intrinsic time" will have a meaning, but it does so at the
cost of imposing severe restrictions on the kinds of dynamics that can be
encoded.

Regards,
Tim