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<p>Dear Louis and All,</p>
<p>Sorry there is a '1' missing in the genome semantics link. This
should work:</p>
<p><a class="moz-txt-link-freetext" href="https://urldefense.com/v3/__https://febs.onlinelibrary.wiley.com/doi/10.1016/j.febslet.2005.02.011__;!!D9dNQwwGXtA!WEnKRZnHsI3XpOQozGc_5rQy_1S9OrE-jwJLZ0b7TZGpsr2ErXttoMCW8MalIFQE53UbsDxNNV2nTU6ZkdK6T7c$">https://febs.onlinelibrary.wiley.com/doi/10.1016/j.febslet.2005.02.011</a></p>
<p>Eric<br>
</p>
<div class="moz-cite-prefix">On 1/4/25 4:26 PM, Eric Werner wrote:<br>
</div>
<blockquote type="cite"
cite="mid:a3ee4fd9-bbec-45db-8118-f90288819a51@oarf.org">
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<p>Dear Louis,<br>
</p>
<p>Fascinating approach and tremendous effort. Thank you for all
your work! </p>
<p>But a lot to read! But from an initial skimming, we have some
commonalities of interest and concepts. </p>
<p>Since your work is a bit overwhelming, hence my first response
is with a "Back at ya!" Have a look at: <br>
</p>
<p>(1.) A formalization of embryogenesis of cancer which contains
many of the ideas and forms you talk about:</p>
<p> 'Cybernetics' of Cancer: <a class="moz-txt-link-freetext"
href="https:arxiv.org/abs/1110.5865" moz-do-not-send="true">https:arxiv.org/abs/1110.5865</a></p>
<p>(2.) And a wider view of inter-genome interactions versus your
intra-genome copy-cat interactions that may be related to your
'knotty' ideas:</p>
<p> Genome Interactions in Development and Evolution: <a
class="moz-txt-link-freetext"
href="https://urldefense.com/v3/__https://arxiv.org/abs/1212.5439__;!!D9dNQwwGXtA!UYK3U5uPm8X_-PYmhQ2uxvCO7o6Hj3NY7b7EsSRPKK1hbtjJyZOJ8284ZeGmKVdcAgnY0XUyshx3NQQh2Bw_zvM$"
moz-do-not-send="true">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$"
moz-do-not-send="true">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>
</div>
<blockquote type="cite"
cite="mid:9075dcab-cdfc-4484-be40-e77dca0f868e@gmail.com">
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<title>Biologic - at the interface between biology, topology,
logic and cybernetics.</title>
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<th valign="BASELINE" align="RIGHT" nowrap="nowrap">Asunto:
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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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<th valign="BASELINE" align="RIGHT" nowrap="nowrap">Para:
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<td>"Pedro C. Marijuán" <a
class="moz-txt-link-rfc2396E"
href="mailto:pedroc.marijuan@gmail.com"
moz-do-not-send="true"><pedroc.marijuan@gmail.com></a></td>
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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.Aenvietm.x9yAmZwS@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>
<div class=""><a
href="https://urldefense.com/v3/__https://arxiv.org/abs/1512.04325__;!!D9dNQwwGXtA!Xuz20L8dnuTZYF9WFBHOLyZrvHTyVKqbCy4P55woe-bSQswWK6oGtDnIfdh8ErbhHvbI71N24gtkTUTyEMIjViUloF5d$"
class="moz-txt-link-freetext" moz-do-not-send="true">https://arxiv.org/abs/1512.04325</a></div>
<div class="">Here are other papers included in this
email:</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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<div class="moz-signature">-- <br>
<i> Dr. Eric Werner, FLS <br>
Oxford Advanced Research Foundation <br>
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<pre wrap="" class="moz-quote-pre">_______________________________________________
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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.
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