Re: Nature of Counting and FIS

From: John Collier <[email protected]>
Date: Mon 07 Oct 2002 - 08:30:29 CEST

At 11:43 PM 06/10/2002, Jerry wrote:

>One issue is the concept of "optimization" in biology. Generally
>speaking, I fail to find a substantial basis for the concept of
>"optimization" in biology or medicine. While local behaviors may appear
>to be quite desirable, the mathematics of optimization require a maximum
>or minimum. But how is a concept of maximum or minimum to be applied to
>a living system where the flow relationships between internal and external
>processes are continuous? It seems that one or the other must be held
>constant in order to invoke an optimum. But in biological systems, both
>internal values and external values are variable - this is the very
>concept adaptability of which we speak! Any suggestions on how to address
>this dilemma? (Such dilemmas are avoided by the Herbert Simon's concept
>of "satisfactory and sufficient".)

Jerry makes a good point. Oster and Wilson, in a paper reprinted in Sober's
collection on evolution, argue that even in cases in which optimality is
relatively well defined the evidence for it is poor. Extremal principles
play a central role in Netwonina physics as it developed in the Laplacean
and Hamiltonian formulations. The latter applies only to conservative
systems, which biological organisms most certainly are not, not even
approximately, however some extremal principles like the principle of
action (PLA) apply to all contemporary dynamics including Quantum
Mechanics. No exceptions are known to PLA, and they are analytically
impossible on current theory (exceptions due to quantum fluctuations have
no dynamical significance).

There are a coupe of extremal principles that have been proposed in
thermodynamics that could apply to biological systems. One is a
generalization of PLA that Prigogine proposed for near to equilibrium
systems (it also applies to network systems in steady state, or near to
steady state, and in general when the Onsager reciprocity relations hold --
this is basically a reciprocity between forces and flows). It is of
interest to this group, since when it holds, local information plays no
role that is independent of overall system constraints (i.e., it is
reducible to dynamical constraints). This principle is that of minimal
entropy production (MinEntPro). It is a local principle, and its integral
is possible in all the cases in which Onsager Reciprocity holds, giving a
global principle. Interstingly, the cases in which Onsager reciprocity
holds are all approximately Hamiltonian, and behave like conservative
systems. This should make us suspicious of any extension to organisms, and
indeed Prigogine pointed out that it does not hold for far from equilibrium
systems. He proposed that entropy production is minimized in the
generalized direction of any applied generalized force. There are no known
exceptions to this hypothesis, but it is hard to test. Nonetheless, it
seems to me that it follows naturally from PLA -- a system will respond to
a force by trying to minimize its direct effects -- this gloss is too
clumsy to use analytically, however. In any case, given the failure of
reciprocity of forces and flows in these cases, details of local structure
matter a lot, and small deviations can lead to large scale system
reorganization -- these two conditions are characteristic of situations
in which small amounts of energy can control large amounts, raising the
possible relevance of control theory, and therefore information theory.
Note that the systems involved are extremely non-Hamiltonian (at least on
the surface -- current Quantum Mechanics is all Hamiltonian -- one might
reflect on how non-Hamiltonian behavior can arise from a Hamiltonian
mechanics, but I will not do this here). There is more on these ideas an
their implications in my four paper series on autonomy for CASYS, available
on my web page at the KLI, so I will drop the issue here.

A second way that extremal principles have been suggested for living
systems is the principle of entropy production maximization (MaxEntPro).
This is a global principle proposed first, I think, by Rod Swenson, though
one can read a version of it back into Jaynes. It seems to violate PLA very
seriously. Anyway, Schneider and Kay have proposed an extension to
thermodynamics according to which systems use every means at their
disposal, including reorganization, to approach as closely as possible to
equilibrium. They claim to have evidence for this from ecology, though I
find the evidence ambiguous. The important point for this group is that,
like MinEntPro, it allows information to be reduced out. Schneider is quite
clear about this implication in his recent writing. MaxEntPro systems are
obviously highly non-Hamiltonian (highly non-conservative), but there is a
sense in which they are very mechanical like, because of their extremal
behavior. One system that approaches MaxEntPro is the Earth's atmosphere,
and fluid vortices in general. it is precisely their lack of stable
structure that allows this. (Recent empirical work suggests that the
Kolmogorov hypothesis of self-similarity of vortices at all scales except
the larges is actually false at small scales, so perhaps event the
atmosphere case does not really fit the MaxEntPro model.)

Anyway, these are two approaches that might support optimality arguments in
a general way. I think that both are flawed, but it is interesting that
both reduce out (eliminative reduction) the need for information. I think
this is a general property of extremal approaches in general, and of
optimality in particular.

There is another approach to organisms that supports optimality. This it
the autopoietic approach. On this approach the organization of the organism
is functionally independent (operationally closed), and works pretty much
like a Hamiltonian system. Maturana and Varella refer to autopoietic
mechanisms. Optimality can be defined with respect to autopoietic
operation. Rosen also makes operational closure a central part of living
systems, but explicitly denies mechanism. A close look at his work, though,
shows that he really denies only one side of traditional mechanism, and has
little to say about the other side, which is more important for a system
being treatable by Hamiltonian methods (Don Mickulecky, a noted Rsoenite,
specifically champions network methods, for example, despite the original
authors on network approaches explicitly excluding their applicability to
general biological systems on the grounds of far from equilibrium
conditions). Personally, I don't find Rosen's writings on these issues very
clear, partly because of his idiosyncratic view of mechanism. I am not sure
he is wrong, but I am not sure he is right either. In any case, the
autopoiesis approach does support optimality approaches, and it does allow
the elimination of information (Maturana and Varela, for example, carefully
point out that information accounts are external to the autopoietic system,
and that there is no need for information accounts internally -- they are
quite correct in this, but I think that this shows that autopoiesis,
strictly understood in their terms, cannot be the basis of the organization
of organisms -- but that is just my opinion -- for the arguments for this
opinion, see the papers on autonomy and self-organization on my web site.)

So, in answer to Jerry, there are at least three approaches in the current
literature that are not reductionist in the traditional microreductionist
(Newtonian atomism is an example) sense that nonetheless have the following
properties: 1) they do not require information accounts (eliminativist with
respect to information), 2) they support extremal principles,and hence some
version of optimality, 3) they have elements of mechanism, and 4) they are
basically extensions of Hamiltonian models.

I think they are all seriously flawed, but I can't go into the details of
my reasons now.

John
Received on Mon Oct 7 08:30:42 2002

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