Re: Modern Physics, Newtonian Paradigm, and the notion of State

[Tim Gwinn <***>]

> -----Original Message-----
> From: ROSEN Forum []On Behalf Of Ionel
> Sent: Wednesday, June 02, 2004 5:33 AM
> Subject: Re: Modern Physics, Newtonian Paradigm, and the notion of State
>
>
> Hi, Tim:
>
> I'd go along with most of your comments about (M,R)-systems, but there are
> some important facts that are running contrary to your sentence cited
> below, if I understood your argumentation correctly:
>
> >>These functional relational models are in an entirely different formal
> universe of discourse than a formal universe of discourse built around
> spatiotemporal relations.>> It is, metaphorically speaking, like
> a parallel
> formal universe - a rather alien one to the one in which we are used to
> doing physics in. >>....Of course, the opposite is also true: these
> relational models have abstracted away state information entirely - they
> have "thrown away the physics".) >>
>
> ---------------
> FACTS: Both in 1971 and 1973, Robert published in BMB two substantial
> papers in which he developed dynamic representations of (M,R)-systems that
> appear to be aimed at linking the Abstract (M,R)-systems approach to the
> physical representation of such systems in terms of kinetic or dynamics
> eqs.,etc,  e.g. attempting to avoid to "throw away the physics", such as
> the dynamics in terms of states and state-spaces. It is clear
> that Roberts'
> states are not quantum states.
> -------------


I haven't seen those particular papers, but it had puzzled me for some time
that in his 1971 paper in "Foundations of Mathematical Biology" Rosen
discussed the (M,R)-system in terms of "finite sequential machines", and
talking about things like "operation lag" and "transport lag" as one chases
through the diagram. Yet by 1991 in "Life Itself", he describes his concept
of relational models as "entailment without states" where "our systems are
assigned no states, no environments, and there is no recursion". [p. 109]

These are two quite disparate views of the same model. It was not until I
got hold of "Theoretical Biology and Complexity" that it made some sense to
me. I think his chapter in TB&C, which occurred in 1985 between the 1971 and
1991 views, is a candid account of some of the evolution of his thinking
along the way to "Life Itself". I'll quote a bit more from that chapter:

        "The strategy to be followed in physically realizing an abstract
organizational structure like an (M,R)-system seemed at first to me not too
different from that followed by an engineer in designing a real physical
structure to meet some given initial set of functional specifications. For
here, too, we must reach into a class of physically diverse but functionally
similar systems and pick one out. The usual criterion for this selection
purpose is one of optimality (e.g., least cost). Indeed, I might assert that
optimality is the canonical way of selecting individual elements from
equivalence classes; one may think even of such things as the Jordan
canonical form of ordinary matrices (in which the number of 0 entries is
maximized).
        But the problem did not turn out to be that straightforward after all.
        ....
        Let us begin by reviewing an early attempt of mine (1964) to solve the
realization problem. It seemed to me that a first step would be to transform
mathematically the (M,R)-system to a form in which the various sets and
mappings of the (M,R-system) could be interpreted in terms of the states of
some system and a set of dynamical laws could be superimposed thereon. This
was at least the conventional language in which physical systems were to be
universally described; hence realizing this kind of mathematical object
would be much easier than realizing an (M,R)-system directly.
        The first idea that came to mind was the language of sequential machines,
or finite automata. This is in effect the language of classical dynamical
system theory (or better, of control theory) paraphrased to the constraints
of discrete time and discrete states.
        ....
        At first, this looked extremely promising. Biologically, there were a host
of network realization now available (e.g., operon networks).
Mathematically, there were a number of possibilities for passing from
discrete to continuous time, i.e., to true dynamical and control systems,
and thence to explicit "hardware" realizations, which would comprise "cells"
of perhaps utterly novel kinds.
        ....
        There were indeed many intresting conclusions that could be drawn from just
these possibilities. But the really fundamental problems remained refractory
to this whole approach. In a nutshell, the reason lay in the mathematical
dichotomy between set (object) and mapping in the (M,R)-system. In a network
realization, a "state" of the network is a pattern of activation in the
elements that constitute the network, while the "next-state mapping" is
embodied in the wiring diagram of the network. But intuitively, in the
(M,R)-system, both the metabolic map(s) f and the nuclear or repair maps Phi
should themselves be embodied in (or realized by) physical structures, and
their mapping properties should be consequences of these structures. When we
realize Phi(f(a)), for example, this is abstractly a mapping (f:A -> B) in
the (M,R)-system; it is a pattern of excitation (i.e., a single state) in a
network; but it should be a material structure in the kind of realization we
are actually seeking. Even more, the map Phi itself in the (M,R)-system is a
wiring diagram in a network realization, a pattern of specificities in an
operon network, but, in fact, it should be realized itself as a material
structure, from which all these mapping properties should follow.
        These considerations led to a fundamental rethinking of the whole idea of
how to go about realizing any kind of abstract relational description of a
material system.... I began to entertain the possibility that that our
conventional mathematical descriptions of physical reality, which have
essentially gone unquestioned for three centuries, might themselves be
fundamentally deficient, that it was this deficiency that was responsible
for the problems posed by an attempt to realize physically an abstract
functional organization." [p. 177-178]

That ended up being a longer quote than intended. But it seems to me quite
instructive, both about his evolution of thinking and about the problems of
realization.

Regards,
Tim