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<div style="direction: ltr;font-family: Tahoma;color:
#000000;font-size: 10pt;"><big>Dear FIS Colleagues,
</big>
<div><big><br>
</big></div>
<big>
</big>
<div><big>Due to communication problems with Louis (he is
attending a conference) I am attaching here his presentation.
Well, if you have any trouble with it, we have uploaded the
file in fis web pages too:<br>
<br>
<a class="moz-txt-link-freetext" href="http://fis.sciforum.net/fis-discussion-sessions/">http://fis.sciforum.net/fis-discussion-sessions/</a><br>
<br>
By clicking on Louis H. Kaufman session (highlighted in red)
you can immediately obtain it.<br>
Nevertheless, herewith below a selection of more general ideas
from the paper. For those interested in previous FIS
discussions related with the topic: biological information
(19998), molecular recognition (2003), biomolecular networks
(2005</big><big>), chemical information (2011), etc. They can
be found in the same above link.<br>
<br>
Best greetings</big><small><small></small></small><big><big><big><small><small>--Pedro</small></small><br>
<br>
-------------------------------------------------------------<span
style="font-size: 10pt;"><br>
<b><big><big>Biologic - An Introduction<br>
</big></big></b></span></big></big></big><big><big><big><span
style="font-size: 10pt;"><small><small><small><big><big><big><big><big>Louis
H. Kaufman</big></big></big></big></big></small></small></small><i><big><br>
<br>
We explore the boundary shared by biology and formal
systems.<br>
<br>
</big></i><big><font face="Helvetica, Arial,
sans-serif">This essay is an introduction to my
research on the mathematics of self-reference,
self-replication<br>
and its applications to molecular biology. This
introduction is based on my paper [22] and the<br>
reader is encouraged to examine that paper. Other
relevant papers will be found in the bibliography<br>
of this paper.<br>
</font><br>
<font face="Helvetica, Arial, sans-serif">I will
concentrate here on relationships of formal systems
with biology. In particular, this<br>
is a study of different forms and formalisms for
replication. See previous papers by the author<br>
[25, 24, 23]. We concentrate here on formal systems
not only for the sake of showing how there is<br>
a fundamental mathematical structure to biology, but
also to consider and reconsider philosophical<br>
and phenomenological points of view in relation to
natural science and mathematics. The<br>
relationship with phenomenology [37, 35, 36, 9, 1,
39] comes about in the questions that arise<br>
about the nature of the observer in relation to the
observed that arise in philosophy, but also in<br>
science in the very act of determining the context
and models upon which it shall be based. Our<br>
original point of departure was cybernetic
epistemology [44, 43, 41, 34, 12, 13, 14, 15, 16,
17,<br>
18, 24, 23, 25] and it turns out that cybernetic
epistemology has much to say about the relation of<br>
the self to structures that may harbor a self. It
has much to say about the interlacement of selves<br>
and organisms. This study can be regarded as an
initial exploration of this theme of mathematics,<br>
formalities, selves and organisms - presented
primarily from the point of view of cybernetic
epistemology,<br>
but with the intent that these points of view should
be of interest to phenomenologists.<br>
We hope to generate fruitful interdisciplinary
discussion in this way.<br>
<br>
Our point of view is structural. It is not intended
to be reductionistic. There is a distinct<br>
difference between building up structures in terms
of principles and imagining that models of the<br>
world are constructed from some sort of
building-bricks. The author wishes to make this
point<br>
as early as possible because in mathematics one
naturally generates hierarchies, but that does not<br>
make the mathematician a reductionist. We think of
geometry as the consequences of certain axioms<br>
for the purpose of organizing our knowledge, not to
insist that these axioms are in any way<br>
other than logically prior to the theorems of the
system. Just so, we look for fundamental patterns<br>
from which certain complexes of phenomena and ideas
can be organized. This does not entail<br>
any assumption about “the world” or how the world
may be built from parts. Such assumptions<br>
are, for this author, useful only as partial forms
of explanation...<br>
<br>
...In living systems there is an essential
circularity that is the living structure. Living
systems<br>
produce themselves from themselves and the materials
and energy of the environment. There is<br>
a strong contrast in how we avoid circularity in
mathematics and how nature revels in biological<br>
circularity. One meeting point of biology and
mathematics is knot theory and topology. This is<br>
no accident, since topology is indeed a controlled
study of cycles and circularities in primarily<br>
geometrical systems. In the end we arrive at a
summary formalism, a chapter in boundary mathematics<br>
(mathematics using directly the concept and notation
of containers and delimiters of forms)...<br>
</font></big><i><big><br>
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