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Jack,
Thanks for those
links to the papers by Leguizamon/Zaretzky and Zaretzky/Letelier. I will add
those to my Web Resources page.
The
Zaretzky/Letelier paper introduces the notion of physical and
functional "boundaries" to an (M,R)-system. They base this on their idea
that autopoietic systems are a subset of the class of (M,R)-systems, and
that (M,R)-system models ought to have such boundaries since that is part
of the definition of an autopoietic system.
They
take metabolism ("f: A -> B") and consider that "A" must consist
of elements which either come from inside or outside of a physical
boundary. Separately, they define a "functional boundary" as one which
encompasses the (M,R)-system itself along with the input
elements which arise from outside the physical boundary. So, a "complete"
(M,R)-system in their view is a model which has this functional
boundary.
In
Life Itself, Rosen's relational modeling does not
contain the notion of environment, so there is no need for an
explicit formal representation of boundaries. Moreover, as I see it a
physical boundary qua physical boundary is a structural thing, not a
functional one, and so there would not be necessity to represent it in a
functional relational model. But certainly it seems that physical boundaries do
perform some kind of functional role, and physical boundary qua
function(s) would seem to be worth considering the possibility of adding to
the model. Whether or not physical boundaries must always
encompass a realized (M,R)-system is another question
altogether.
The Leguizamon/Zaretzky cancer paper is unique. It is not based
around relational functional organization of a cell, but around energy
characteristics of cells.
Regards,
Tim
<note>had to re craft this
becasue there was a gif image magically added on sending, which does not
exist. Looking at it closer, I notice that the gif came from a copy&paste
which included hidden gif images</note>
In some sense, it is
gratifying to see that "relational biology" at google gets some 97,000 hits,
though a lot of those just have the word relational (as in database) and
biology in the same context. Anticipatory Systems got around 69,000 hits.
Perhaps I am wrong.
While roaming about the space of Deep Ecology, I
see that to be a kind of thought and behavior process, along the lines of the
Gaia hypothesis, which does, indeed, involve wholistic thinking. Moving to
google software of the kind that would facilitate the kinds of analysis that
were included in Ionel's paper, I stumbled (a long way from here) over this
URL
http://www.geometrygames.org/TorusGames/index.html
in
which you are allowed to play games like tic tac toe (noughts and crosses)
laying on a torus. You really have to think topologically if you wish to win
such a game.
Meanwhile, back to the google search on relational
biology, I stumbled (closer to home now) on this URL
http://www.worldscinet.com/jbs/08/0803/S0218339000000213.html
which
Tim reviewed here: http://www.panmere.com/rosen/mhout/msg00296.html
Regrettably,
that paper is at a pay per view paper. I would much prefer that our papers be
published at http://www.plos.org/
Another paper
at the same site
http://www.worldscinet.com/jbs/05/0501/S0218339097000084.html
is
The
Algebraic Relational Theory Suggesting how to Deviate a Cancer Process
by
Leguizamon and Zaretzky 1995
<quote>
It is shown how the biological reality
correlates with an algebraic modification from a pseudo-Boolean structure for
watering processes in normal cells up to a non-modular structure assigned to
water interactions in malignant cells. A set of mathematical propositions
suggests how to deviate this type of cancer process to new structures mainly
maintaining those water structures resulting from the cooperativity between
water molecules generated by a surface. A set of disquisitions is made: about
the meaning of the change of algebra; on the dual Heyting arrow operations
acting for the algebraic triggering of the cancer process; on the loss of
energy in the cancer process and about the enhanced value of energy as
becoming from the new structures to deviate
cancer.
</quote>
and
http://www.worldscinet.com/jbs/10/1003/S0218339002000573.html
Metabolic
Networks from (M,R) Systens and Autopoiesis Perspective
by Zaretzky and
Letelier
<quote>
This paper is the first one of a
series devoted to the analysis of metabolic networks. Its aim is to establish
the theoretical framework for this analysis.
Two different lines of
research are considered: the one about metabolism-repair systems ((M, R),
introduced by Robert Rosen as an abstract representation of cell metabolic
activity, and the concept of autopoiesis developed by Humberto Maturana and
Francisco Varela.
Both concepts have been recently connected by Letelier
et al., determining that the set of autopoietic systems is a subset of
the set of general abstract (M, R) systems. In fact, every specific (M, R) system
is an autopoietic one, being the boundary, which specifies each system as a
unity, the main element of autopoietic systems which is not formalized in
Rosen's representation.
This paper introduces the definition of
boundary - a physical boundary and a functional one - for
(M, R)
systems in the context of a representation using category theory.
The
concept of complete (M, R) system is also introduced by means of a
process of completion in categories which is functorial, natural and
universal.
</quote>
Jesper Hoffmeyer (1997) argues for a
new synthesis in biology at
http://www.gypsymoth.ento.vt.edu/~sharov/biosem/hoffmeyr.html
in
which he makes one reference to Rosen.
Enough for
now.
Jack
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