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<p>Dear Louis,<br>
</p>
<p>Fascinating approach and tremendous effort. Thank you for all
your work! </p>
<p>But a lot to read! But from an initial skimming, we have some
commonalities of interest and concepts. </p>
<p>Since your work is a bit overwhelming, hence my first response is
with a "Back at ya!" Have a look at: <br>
</p>
<p>(1.) A formalization of embryogenesis of cancer which contains
many of the ideas and forms you talk about:</p>
<p> 'Cybernetics' of Cancer: <a class="moz-txt-link-freetext" href="https:arxiv.org/abs/1110.5865">https:arxiv.org/abs/1110.5865</a></p>
<p>(2.) And a wider view of inter-genome interactions versus your
intra-genome copy-cat interactions that may be related to your
'knotty' ideas:</p>
<p> Genome Interactions in Development and Evolution:
<a class="moz-txt-link-freetext" href="https://urldefense.com/v3/__https://arxiv.org/abs/1212.5439__;!!D9dNQwwGXtA!UYK3U5uPm8X_-PYmhQ2uxvCO7o6Hj3NY7b7EsSRPKK1hbtjJyZOJ8284ZeGmKVdcAgnY0XUyshx3NQQh2Bw_zvM$">https://arxiv.org/abs/1212.5439</a></p>
<p>(3.) And a philosophical - semantic view of genomes:<br>
</p>
<p> Genome semantics:
<a class="moz-txt-link-freetext" href="https://urldefense.com/v3/__https://febs.onlinelibrary.wiley.com/doi/10.1016/j.febslet.2005.02.01__;!!D9dNQwwGXtA!UYK3U5uPm8X_-PYmhQ2uxvCO7o6Hj3NY7b7EsSRPKK1hbtjJyZOJ8284ZeGmKVdcAgnY0XUyshx3NQQhD9ODzN8$">https://febs.onlinelibrary.wiley.com/doi/10.1016/j.febslet.2005.02.01</a></p>
<p>There is more of course, but we don't want to get too wordy. 😉</p>
<p>Kind regards,</p>
<p>Eric <br>
</p>
<div class="moz-cite-prefix">On 1/4/25 1:42 PM, Pedro C. Marijuán
wrote:<br>
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<td>Re: Biologic - at the interface between biology,
topology, logic and cybernetics.</td>
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<th valign="BASELINE" align="RIGHT" nowrap="nowrap">Fecha:
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<td>Fri, 3 Jan 2025 12:38:13 -0600</td>
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<th valign="BASELINE" align="RIGHT" nowrap="nowrap">De: </th>
<td>Louis Kauffman <a class="moz-txt-link-rfc2396E"
href="mailto:loukau@gmail.com" moz-do-not-send="true"><loukau@gmail.com></a></td>
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<td>"Pedro C. Marijuán" <a class="moz-txt-link-rfc2396E"
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<div class="" align="center"><font size="4"><b>Biologic -
at the interface between biology, topology, logic
and cybernetics.</b></font></div>
<div class="" align="center"><font size="4"><b><br>
</b></font></div>
<div class="" align="center"><b>Louis H Kauffman, UIC</b></div>
<div class=""><br class="">
</div>
<div class="" align="center">“What can be shown, cannot be
said.”</div>
<div class="" align="center">“Was gezeigt werden kann,
kann nicht gesagt werden.”</div>
<div class="" align="center">(Wittgenstein, Tractatus,
4.1212)</div>
<div class="" align="center"><br class="">
</div>
<div class="" align="center">“We take the form of
distinction for the form.”</div>
<div class="" align="center">(Spencer-Brown, Laws of Form,
Chapter 1)</div>
<div class=""><br class="">
</div>
<div class="">What is the form of biology?</div>
<div class="">Is there a biology of form?</div>
<div class=""><br>
</div>
<div class="">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?</div>
<div class=""> </div>
<div class="">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?</div>
<div class=""><br class="">
</div>
<div class="">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.</div>
<div class="">DNA = <W|C> -----> <W| E |C>
-----> <W|C> <W|C> = DNA DNA.</div>
<div class="">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.</div>
<div class=""><br class="">
</div>
<div class="">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.</div>
<div class=""><br class="">
</div>
<div class="">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 </div>
<div class="">B, x —> B,x , X,x</div>
<div class="">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.</div>
<div class="">Let b be the blueprint for B itself. Then</div>
<div class="">B,b —> B,b , B,b.</div>
<div class="">The Von Neumann Machine replicates itself. </div>
<div class="">In the comparison, we see that The DNA
contains (in its strands) the blueprint for its own
replication.</div>
<div class=""><br class="">
</div>
<div class="">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?</div>
<div class=""><br class="">
</div>
<div class="">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.</div>
<div class=""><img apple-inline="yes"
id="093308C2-C64C-41FE-8115-2651F174960D"
src="cid:part1.QTolAux4.sACJhX9d@oarf.org" class=""></div>
<div class=""><br class="">
</div>
<div class="">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. </div>
<div class="">One wants to know how far a world-view can
be extended before it disintegrates.</div>
<div class="">What we see in the electron micrograph is
deeply shaped by the complex story of biological
experiment that surrounds it.</div>
<div class=""> </div>
<div class="">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. </div>
<div class="">Temporality may look like a tragedy for the
classical mathematics, but it is exactly what interests
us when studying biology. </div>
<div class="">Mathematical biology is concerned with those
structures leading to recursive generation of structures
from themselves and from their environments. </div>
<div class=""> </div>
<div class="">#############################</div>
<div class=""><br class="">
</div>
</div>
<div class="">Here is a related paper:</div>
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<div class="">Very best,</div>
<div class="">Louis H Kauffman</div>
<div class="">Dept Mathematics</div>
<div class="">University of Illinois at Chicago</div>
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<pre wrap="" class="moz-quote-pre">_______________________________________________
Fis mailing list
<a class="moz-txt-link-abbreviated" href="mailto:Fis@listas.unizar.es">Fis@listas.unizar.es</a>
<a class="moz-txt-link-freetext" href="http://listas.unizar.es/cgi-bin/mailman/listinfo/fis">http://listas.unizar.es/cgi-bin/mailman/listinfo/fis</a>
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INFORMACIÓN SOBRE PROTECCIÓN DE DATOS DE CARÁCTER PERSONAL
Ud. recibe este correo por pertenecer a una lista de correo gestionada por la Universidad de Zaragoza.
Puede encontrar toda la información sobre como tratamos sus datos en el siguiente enlace: <a class="moz-txt-link-freetext" href="https://sicuz.unizar.es/informacion-sobre-proteccion-de-datos-de-caracter-personal-en-listas">https://sicuz.unizar.es/informacion-sobre-proteccion-de-datos-de-caracter-personal-en-listas</a>
Recuerde que si está suscrito a una lista voluntaria Ud. puede darse de baja desde la propia aplicación en el momento en que lo desee.
<a class="moz-txt-link-freetext" href="http://listas.unizar.es">http://listas.unizar.es</a>
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<div class="moz-signature">-- <br>
<i>
Dr. Eric Werner, FLS <br>
Oxford Advanced Research Foundation <br>
<a class="moz-txt-link-freetext" href="https://urldefense.com/v3/__https://oarf.org__;!!D9dNQwwGXtA!UYK3U5uPm8X_-PYmhQ2uxvCO7o6Hj3NY7b7EsSRPKK1hbtjJyZOJ8284ZeGmKVdcAgnY0XUyshx3NQQhyu4v2Mw$">https://oarf.org</a> <br>
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