Re: Metabolic closure in (M,R)-systems

[Judith Rosen <***>]

Hi David,

I found the abstract for that paper quite interesting. On the one hand, I dispute the claim made that Robert Rosen "never explained the mathematical context nor gave any mathematical or biological examples". On the other hand, I find it interesting that the writers still chose to accept the conclusion my father reached, in spite of their dissatisfaction, and then built outward from that; assembling what they considered to be the "missing" mathematical context, etc. I've got to say-- that's a really unusual reaction. Most of the time, it has been a situation like what we recently saw with Franzen and Ostrum, whereby every intelligent shred of evidence is discounted because it does not conform to the usual formalistic "logic", and instead of checking into whether the formalistic logic is as limited as RR claimed it to be, they start cataloguing all the useful things mathematics and science can do with it (as if that constitutes proof that RR was incorrect about those limitations...). That totally misses the salient points. So I really appreciate the fact that Letelier and his associates chose to concentrate on the salient points, even though they felt there wasn't enough evidence to nail those points down.

[Incidentally, I found several references to "naive set theory" while I was researching infinite sums... it refers to Cantor's version, the original Set Theory. I can't remember which one it was who seemed so offended by Aloisius' use of that term, but one who is truly fluent in mathematics ought to know the derivation of that term, it seems to me. They acted as though Aloisius made it up.]

Anyway, back to the subject at hand: I don't know if I would agree that there is "metabolic closure" in living organisms. In the (M,R)-System model, metabolism and repair are both required for a system to be "closed to efficient causation" and THAT is what is required for life. Metabolism, by itself, is not enough. On top of that, I'm not sure where the term "metabolic closure" comes from. To my knowledge, my father never used that phrase. 

I also have a question about which "invertibility" they are referring to in this paper-- I suspect it is the issue of "repair" and "replication" entailing one another, but I don't see the connection to the central argument of this paper.

Anybody?

Judith

Web address: http://www.rosen-enterprises.com
BioTheory: An electronic journal of general science based on the Relational Complexity Paradigm
On Aug 30, 2005, at 6:25 PM, David Macy wrote:

> 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