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<p>Dear Lou and All, //failed to fis because of message size so
sending it to FIS alone<br>
</p>
<p>The replication and biology of form is also influenced the
geometry of the cell, in particular its chirality. Thus the
growing embryo is a complex interaction between the two parental
genomes, their interpretation by the cell, cell and multicellular
physics, cell signaling and the chirality of the cell. <br>
</p>
<p>See for example: <a class="moz-txt-link-freetext" href="https://urldefense.com/v3/__https://arxiv.org/abs/1207.3289__;!!D9dNQwwGXtA!SQqzCRSo2Z_EUFA3NXfjwOydbgsFMYrESlCYu0O3dZZFpc54gnclyYoJESWT31k0kgn9JHr2jtMpR9PUC_ATNW0$" moz-do-not-send="true">https://arxiv.org/abs/1207.3289</a>
for how bilateral symmetry develops </p>
<p>and <a class="moz-txt-link-freetext" href="https://urldefense.com/v3/__https://arxiv.org/abs/1212.5439__;!!D9dNQwwGXtA!SQqzCRSo2Z_EUFA3NXfjwOydbgsFMYrESlCYu0O3dZZFpc54gnclyYoJESWT31k0kgn9JHr2jtMpR9PUjRiFR0M$" moz-do-not-send="true">https://arxiv.org/abs/1212.5439</a>
for how parental genomes interact in development. <br>
</p>
<p>Best,</p>
<p>Eric <br>
</p>
<div class="moz-cite-prefix">On 1/17/25 7:54 AM, Louis H Kauffman
wrote:<br>
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cite="mid:C9C9ABAD-DFD3-4BA7-959F-ACD8CEE087B9@gmail.com">
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<div class="">We shall next meet: </div>
<div class=""> </div>
<div class="">
<div class="">
<div class=""> Friday, January 17, 2024 at
noon CDT Chicago time: </div>
<div class=""><br class="">
</div>
<div class="">We’ll continue the discussion.</div>
<div class="">Along with the points of view as
outlined below there were many contributions
from participants.</div>
<div class="">Some of these points are:</div>
<div class="">1. LK talked about the meaning
of “=“ in terms of “Identity” A = B. </div>
<div class="">Jerry Swatez pointed out that </div>
<div class="">A = B can be seen to mean that A
and B represent the same value or that there
is a series of steps that can be taken from
A to B.</div>
<div class="">3. Karl Javorszky began to talk
about natural numbers in his original way.</div>
<div class="">4. Many other threads of
discussion appeared, including a number of
thoughts related to Rudolf Steiner.</div>
<div class="">5. I shall discuss further the
role of topology in biology and in
fundamental epistemology, at the meeting of
percept and concept.</div>
<div class=""><br class="">
</div>
<div class=""><br class="">
</div>
</div>
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<div class="">
<div
style="margin: 0px; font-stretch: normal; line-height: normal;" class="">Biologic
- at the interface between biology,
topology, logic and cybernetics.</div>
<div
style="margin: 0px; font-stretch: normal; line-height: normal;" class="">Louis
H Kauffman, UIC</div>
<div
style="margin: 0px; font-stretch: normal; line-height: normal; min-height: 14px;"
class=""><br class="">
</div>
<div
style="margin: 0px; font-stretch: normal; line-height: normal;" class="">“What
can be shown, cannot be said.”</div>
<div
style="margin: 0px; font-stretch: normal; line-height: normal;" class="">“Was
gezeigt werden kann, kann nicht gesagt
werden.”</div>
<div
style="margin: 0px; font-stretch: normal; line-height: normal;" class="">(Wittgenstein,
Tractatus, 4.1212)</div>
<div
style="margin: 0px; font-stretch: normal; line-height: normal; min-height: 14px;"
class=""><br class="">
</div>
<div
style="margin: 0px; font-stretch: normal; line-height: normal;" class="">“We
take the form of distinction for the form.”</div>
<div
style="margin: 0px; font-stretch: normal; line-height: normal;" class="">(Spencer-Brown,
Laws of Form, Chapter 1)</div>
<div
style="margin: 0px; font-stretch: normal; line-height: normal; min-height: 14px;"
class=""><br class="">
</div>
<div
style="margin: 0px; font-stretch: normal; line-height: normal;" class="">What
is the form of biology?</div>
<div
style="margin: 0px; font-stretch: normal; line-height: normal;" class="">Is
there a biology of form?</div>
<div
style="margin: 0px; font-stretch: normal; line-height: normal;" 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>
<p
style="margin: 0px; font-stretch: normal; line-height: normal;" class=""> </p>
<div
style="margin: 0px; font-stretch: normal; line-height: normal;" 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
style="margin: 0px; font-stretch: normal; line-height: normal; min-height: 14px;"
class=""><br class="">
</div>
<div
style="margin: 0px; font-stretch: normal; line-height: normal;" 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
style="margin: 0px; font-stretch: normal; line-height: normal;" class="">DNA
= <W|C> -----> <W| E |C>
-----> <W|C> <W|C> = DNA
DNA.</div>
<div
style="margin: 0px; font-stretch: normal; line-height: normal;" 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
style="margin: 0px; font-stretch: normal; line-height: normal; min-height: 14px;"
class=""><br class="">
</div>
<div
style="margin: 0px; font-stretch: normal; line-height: normal;" 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
style="margin: 0px; font-stretch: normal; line-height: normal; min-height: 14px;"
class=""><br class="">
</div>
<div
style="margin: 0px; font-stretch: normal; line-height: normal;" 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
style="margin: 0px; font-stretch: normal; line-height: normal;" class="">B,
x —> B,x , X,x</div>
<div
style="margin: 0px; font-stretch: normal; line-height: normal;" 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
style="margin: 0px; font-stretch: normal; line-height: normal;" class="">Let
b be the blueprint for B itself. Then</div>
<div
style="margin: 0px; font-stretch: normal; line-height: normal;" class="">B,b
—> B,b , B,b.</div>
<div
style="margin: 0px; font-stretch: normal; line-height: normal;" class="">The
Von Neumann Machine replicates itself. </div>
<div
style="margin: 0px; font-stretch: normal; line-height: normal;" class="">In
the comparison, we see that The DNA contains
(in its strands) the blueprint for its own
replication.</div>
<div
style="margin: 0px; font-stretch: normal; line-height: normal; min-height: 14px;"
class=""><br class="">
</div>
<div
style="margin: 0px; font-stretch: normal; line-height: normal;" 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
style="margin: 0px; font-stretch: normal; line-height: normal; min-height: 14px;"
class=""><br class="">
</div>
<div
style="margin: 0px; font-stretch: normal; line-height: normal;" 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
style="margin: 0px; font-stretch: normal; line-height: normal;" class=""><br>
</div>
<div
style="margin: 0px; font-stretch: normal; line-height: normal; min-height: 14px;"
class=""><br class="">
</div>
<div
style="margin: 0px; font-stretch: normal; line-height: normal;" 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
style="margin: 0px; font-stretch: normal; line-height: normal;" class="">One
wants to know how far a world-view can be
extended before it disintegrates.</div>
<div
style="margin: 0px; font-stretch: normal; line-height: normal;" class="">What
we see in the electron micrograph is deeply
shaped by the complex story of biological
experiment that surrounds it.</div>
<p
style="margin: 0px; font-stretch: normal; line-height: normal;" class=""> </p>
<div
style="margin: 0px; font-stretch: normal; line-height: normal;" 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
style="margin: 0px; font-stretch: normal; line-height: normal;" class="">Temporality
may look like a tragedy for the classical
mathematics, but it is exactly what
interests us when studying biology. </div>
<div
style="margin: 0px; font-stretch: normal; line-height: normal;" class="">Mathematical
biology is concerned with those structures
leading to recursive generation of
structures from themselves and from their
environments. </div>
<div
style="margin: 0px; font-stretch: normal; line-height: normal;" class=""><br
class="">
</div>
<br class="">
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</blockquote>
<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!SQqzCRSo2Z_EUFA3NXfjwOydbgsFMYrESlCYu0O3dZZFpc54gnclyYoJESWT31k0kgn9JHr2jtMpR9PU1bBOXVE$" moz-do-not-send="true">https://oarf.org</a> <br>
<br>
<br>
</i></div>
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