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Hey again guys,
I don't really know all
the reasons why I'm posting at this time. Maybe it's just an attempt to
keep things moving. I have here in front of me a paper from the procedings
of that conference I attended where Juan-Carlos Letelier spoke about Robert's
work. I wish that I had the patience to type it all in, but I'm also not
sure about copyright stuff. But there is a discusion section at the end of
the paper that I thought might be fair game. So here it is. The paper is
entitled "Metabolic closure in (M,R)-systems". The phrase
'organizational invariance' is the term that Letelier et al. use in place
of replication. They also substitute the word 'replacement' for repair in
the paper.
Discussion
The main objective of this paper
has been to clarify some central aspects of Rosen's ideas. His central
result refers to something most biologists will find extremely esoteric: an
attempt to prove (from purely logical grounds) the necessity for a circular
organization of metabolic networks. Furthermore the mathematical fact used
to introduce this notion, the invertibility of certain evaluation maps, is
unusaul enough to make it very difficult to explain the context of the result
even to mathematicians. Rosen himself never explained the mathematical
context where his central result would hold true and provided neither
mathematical or biological examples.
As may be surmised, we have
adopted the point of view that Rosen had a powerful intuition on the nature of
metabolic networks and the necessary (but otherwise ignored) requirement of
circularity. However, his intuition is far from being workable and ready
to apply to current network analysis without major efforts, both to clarify the
circumstances in which his central result applies, and to explain it's meaning
in biological terms. An intriguing possiblity could be to combine Rosen's
analysis with the notion of autopoietic systems, another theory that posits
metabolic closure as the core of biological organization (Maturana and Varela,
1980; Letelier et al., 2003) This paper is intended as a step in the right
direction, as we have isolated from Rosen's extensive work what we think is it's
core, and we have clarified concepts like f, f, and b. We have explained the
mathematical intuition behind the idea of organizational invariance as embodied
in the operator b, a crucial
concept as essentially it acts as a generator of the complete formal structure
of an (M,R)-system. In effect it is possible to reformulate the very
definition of an organizational invariant (M,R)-system as the kind of system
where for some b the equation f(b) = f has exactly one
solution f, for any given f,
giving rise to the operator b, which sends any f to its
associated f and implicitly generates the structure
of the whole system.
Well there it is. Make of it what you will or
can.
I hope none of you guys have been drowned by
Katrina!
David
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