[Fis] Biologic - at the interface between biology, topology, logic and cybernetics (by Lou Kauffman)
Pedro C. Marijuán
pedroc.marijuan at gmail.com
Sat Jan 4 13:42:58 CET 2025
Asunto: Re: Biologic - at the interface between biology, topology,
logic and cybernetics.
Fecha: Fri, 3 Jan 2025 12:38:13 -0600
De: Louis Kauffman <loukau at gmail.com>
Para: "Pedro C. Marijuán" <pedroc.marijuan at gmail.com>
Download of below articles available until Feb 2, 2025
'Slides Festival' available at: https://urldefense.com/v3/__https://fis.sciforum.net/resources/__;!!D9dNQwwGXtA!Xuz20L8dnuTZYF9WFBHOLyZrvHTyVKqbCy4P55woe-bSQswWK6oGtDnIfdh8ErbhHvbI71N24gtkTUTyEMIjVuWJIXes$
*Biologic - at the interface between biology, topology, logic and
cybernetics.*
*
*
*Louis H Kauffman, UIC*
“What can be shown, cannot be said.”
“Was gezeigt werden kann, kann nicht gesagt werden.”
(Wittgenstein, Tractatus, 4.1212)
“We take the form of distinction for the form.”
(Spencer-Brown, Laws of Form, Chapter 1)
What is the form of biology?
Is there a biology of form?
In particular, this is a study of different forms and formalisms for
replication. We concentrate on diagrammatic formal systems not only for
the sake of showing how there may be fundamental mathematical structure
in biology, but also to consider philosophical and phenomenological
points of view in relation to natural science and mathematics. The
relationship with phenomenology comes about in the questions that arise
about the nature of the observer in relation to the observed that arise
in philosophy, but also in science in the very act of determining the
context and models upon which it shall be based. Our original point of
departure was the idea of distinction and cybernetic epistemology.
Cybernetic epistemology has much to say about the relation of the self
to structures that may harbor a self. What is the interlacement of
selves and organisms?
Our point of view is structural. There is a distinct difference between
building up structures in terms of principles and imagining that models
of the world are constructed from some sort of building-bricks. I want
to make this point as early as possible because in mathematics one
naturally generates hierarchies, but that does not make the
mathematician a reductionist. We think of geometry as the consequences
of certain axioms for the purpose of organizing our knowledge, not to
insist that these axioms are in any way other than logically prior to
the theorems of the system. Just so, we look for fundamental patterns
from which certain complexes of phenomena and ideas can be organized.
This does not entail any assumption about ``the world'' or how the world
may be built from parts. What is a part that a world might be built from it?
We examine the schema behind the reproduction of DNA. The pattern of the
DNA reproduction is very simple. The DNA molecule consists of two
interwound strands, the Watson Strand (W) and the Crick Strand (C). The
two strands are bonded to each other via a backbone of base-pairings and
these bonds can be broken by certain enzymes present in the cell. In
reproduction of DNA the bonds between the two strands are broken and the
two strands then acquire the needed complementary base molecules from
the cellular environment to reconstitute each a separate copy of the
DNA. At this level the situation can be described by a symbolism like this.
DNA = <W|C> -----> <W| E |C> -----> <W|C> <W|C> = DNA DNA.
Here E stands for the environment of the cell. The first arrow denotes
the separation of the DNA into the two strands. The second arrow denotes
the action between the bare strands and the environment (the creation of
new base-pairings) that leads to the production of the two DNA molecules.
Much is left out of this schema. Indeed the DNA molecule is a tight
spiral winding of its two interlocked strands and so the new DNA's would
be linked around one another if it were not for the work of toposomerase
enzymes that manage to unlink the new DNA's in time for cell division to
occur. Nevertheless, this is the large scale description of the
replication of DNA that is fundamental to the division of cells and to
the continuance of living organisms.
This form of replication can be compared with other forms. For example,
John von Neumann suggested a “building machine” B such that when B is
supplied with a “blueprint” x then
B, x —> B,x , X,x
This means that B and the blueprint x will produce X the entity whose
plan is x along with a copy of the blueprint x. The first B,x is the
persistence of the original machine B.
Let b be the blueprint for B itself. Then
B,b —> B,b , B,b.
The Von Neumann Machine replicates itself.
In the comparison, we see that The DNA contains (in its strands) the
blueprint for its own replication.
The comparison made, what questions do you ask? The mathematical roots
of von Neumann’s construction are very deep. What are the
physical/biological roots of the DNA replication?
We invite the reader to examine the form of the science involved in this
well-known description. We speak of the DNA molecules as though we could
see them directly in the phenomenology of our ordinary sight. Science
does involve the direct extension of sight as the experience of looking
through a telescope or a light microscope. But in the case of the DNA
one proceeds by logical consistency and the indirect but vivid images
via the electron microscope and the patterns of gel electrophoresis. In
the case of electron microscope images there is every reason to assume
(it appears consistent to assume) that the objects shown can be taken to
be analogous to the macroscopic objects of our perception. This means
that one has the possibility of observing ``directly" that DNA molecules
can be knotted. I do not say that one can observe directly the coiling
of the Watson and the Crick strands, but the DNA can be observed as
though it were a long rope. This rope can be seen to be coiled and
knotted in electron micrographs. Even this ``showing'' requires a
difficult technique beyond the usual techniques of the electron
microscope. The DNA was coated with protein by the experimenters so that
it became a chain of larger and more robust diameter. Then the electron
microscope revealed the patterns of knotting in an apparent projection
of the coated DNA from three dimensional space to the two dimensional
space of the image.
It is remarkable how consistent is the hypothesis of indirect perception
on which the work is based. Most working biologists would not question
the basis of their biological perceptions direct or indirect. For those
who are philosophically inclined there is a lesson to be learned about
experimental phenomenology.
One wants to know how far a world-view can be extended before it
disintegrates.
What we see in the electron micrograph is deeply shaped by the complex
story of biological experiment that surrounds it.
Along with these forays into experimentation, there are analogous forays
into the limits of logic. Here we meet the replication schema again.
Replication in logic is intimately related to self-reference and to
formalisms that can lead to paradox. The reasons for this are, by now,
apparent. The usual mathematical formalisms for set theory assume that
there is no temporal evolution in the structures.
Temporality may look like a tragedy for the classical mathematics, but
it is exactly what interests us when studying biology.
Mathematical biology is concerned with those structures leading to
recursive generation of structures from themselves and from their
environments.
#############################
Here is a related paper:
https://urldefense.com/v3/__https://arxiv.org/abs/1512.04325__;!!D9dNQwwGXtA!Xuz20L8dnuTZYF9WFBHOLyZrvHTyVKqbCy4P55woe-bSQswWK6oGtDnIfdh8ErbhHvbI71N24gtkTUTyEMIjViUloF5d$
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Autopoiesis and Eigenform -computation-11-00247-v3.pdf
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Very best,
Louis H Kauffman
Dept Mathematics
University of Illinois at Chicago
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