|
I would dispute the claim that, as Howard put it:
Relational models as described by Rosen are timeless forms. They do not
imply a dynamics.
The model my father (aka RR) referred to as his diagram
of an (M,R)-System is a relational model. One of the things that relational
models of this type do best is "imply a dynamics". They imply "ongoing time" as
well. These implications are innate, because metabolism and repair are not
static entities, not structural entities, and not singular functional entities
either. The only exist in time, as opposed to "timelessness". The usual
criticism of this kind of formalism is that relational models don't specify
exact times-- or exact ANYTHING, for that matter. To model a functional
capability is to model the effects of relations within complex organization. But
in modeling the aspects of a living organism that differentiate it from a
rock, say... or from a dead organism... these are the sorts of things it becomes
necessary to model.
Judith
----- Original Message -----
Sent: Friday, December 03, 2004 1:06
AM
Subject: Re: [ROSEN] Form
Steve,
I normally use "form" in the sense of shape or
configuration. However, the essential aspect of form as used in physics,
mathematics, and much philosophy is that it can be conceived of as synchronic
or timeless, and consequently independent of any dynamics that maybe imposed
on form. Technically, physicists speak of "configuration space" in which forms
are defined independent of the dynamical laws. Logical and mathematical forms
are also considered as timeless structures. That is why they are called
"formal." This is somewhat like the Platonic concept of forms that were
considered as timeless or eternal.
Synchronic and diachronic models are
complementary. Physical laws can be described by state-determined models that
change in time, or equivalently by synchronic forms like symmetry principles
or extremum principles (least action). In quantum theory there is the "sum
over histories" approach that is somewhere in between. The Ghorbanzadeh paper
is interesting because his model is also somewhere in between. I think he is
chunking normal state descriptions into "short-timeless" forms that he defines
as a new kind of state. (I haven't followed the math.)
Relational
models as described by Rosen are timeless forms. They do not imply a dynamics.
Rosen was well aware of the complementary nature of formal and dynamical
models. Here is a short discussion from the 70s when he was using automata
models. We were discussing von Neumann's point that formal timeless systems
can produce paradoxes whereas real systems that depend on time cannot.
Rosen: In physics you [usually] take the state description as
primitive, and what you are interested in is the way the system changes state.
. . In automata theory one of the things you can do is to define states in
terms of equivalence classes of histories. The state becomes an equivalence
class of all possible histories going back to minus infinity, as it were,
which put the system into the same state.
Pattee: It eliminates time,
the order in time of the system.
Rosen: That's right. So you have an
alternative way of describing what's going on, either in terms of equivalence
classes of histories . . . or the state description which physics takes as
primitive. Also, the fact that we are dealing with complex systems which admit
many descriptions, each of which is only partially true, gets rid of many of
the logical difficulties that have been raised here, while at the same time
raising still others.
[A Question of Physics: Conversations in Physics and
Biology, Paul Buckley and David Peat, eds. Univ. of Toronto Press, 1979, p.
106]
Howard
|