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

[Ionel <***>]

Dear Tim:

I believe it is important to follow those two papers by Robert Rosen on
Dynamic Realizations of (M,R)-systems; No they are not about the sequential
machine form--that's not so 'hot'. They are about the kinetic
representations of (M,R)-systems in molecular terms and steady-state
kinetics , a subject that also recurs in the recent "Essays..." by Robert
Rosen. For example, the f-->phi--->beta system exhibits damped oscillations
according to Robert, when this dynamic realization is pursued as in his
improved realization of his 1973 paper in BMB.

I will get back to you on the rest of the discussion iff necessary,
Regards,

Ionel
On Wed, 2 Jun 2004 10:04:43 -0400, Tim Gwinn <***> wrote:

>> -----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