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<div class="moz-cite-prefix">Dear All,</div>
<div class="moz-cite-prefix">Let me, first of all, announce an
interesting e-conference organized by the journal <b><i>Information</i></b>
(one of the official sponsors of the past IS4SI meeting). <br>
</div>
<div class="moz-cite-prefix">-----------------------------------------------------------------------------------------<br>
</div>
<div class="moz-cite-prefix">It is the 1st International
Electronic Conference on Information (IECI2021),</div>
<div class="moz-cite-prefix">the deadline of which
is approaching<b>: </b><b class="moz-txt-star"><span
class="moz-txt-tag">*</span>October 8th<span
class="moz-txt-tag">*</span></b>. <br>
We are kindly invited to submit an abstract:
<a class="moz-txt-link-freetext"
href="https://sciforum.net/user/submission/create/503">https://sciforum.net/user/submission/create/503</a></div>
<div class="moz-cite-prefix">In any case, they deserve our support:
let us help promote their 1st International Electronic Conference
on Information. <br>
</div>
<div class="moz-cite-prefix">----------------------------------------------------------------------------------------<br>
</div>
<div class="moz-cite-prefix"><br>
</div>
<div class="moz-cite-prefix">Then, answering to Lou (and
acknowledging other philosophical arguments), there is an
additional point that could be relevant: heterogeneity.</div>
<div class="moz-cite-prefix">Maybe I am wrong, but when I read the
mssg below, my impression is that we are only considering a kind
of homogeneous alphabets, that can grow via recursion, but that
cannot go beyond the formal confines of that alphabet-world.</div>
<div class="moz-cite-prefix"><br>
</div>
<div class="moz-cite-prefix">Machine codes in computers (and the
cascade of codes built upon them) are ultimately due to the
physical heterogeneity of their processing architectures. I mean,
CPU, ALU, Central memory, peripherics, etc. are structurally
different and the strings of 0s and 1s circulating within the
system do need codes (*addresses*) so that they can circulate via
the central bus towards the specific component-architecture. This
is the final meaning of computer codes: matching between
heterogeneous processing architectures--and ascending upon
multiple levels so that languages, etc. can be designed.</div>
<div class="moz-cite-prefix"><br>
</div>
<div class="moz-cite-prefix">In the biological world something
similar occurs: we have sequential architectures (DNA & RNA)
based on complementarity, structural architectures (membranes,
cytoskeletons) based on identity, and a general "diluted"
processing architecture (enzymes and proteins) based on
supplementarity. Whatever function we may observe implies multiple
ups and downs, back and forth, among these architectures and they
need the recognition of quite specific motives arranged in well
organized sets. Once the biological genetic code was in place,
some complexity addicts (eukaryotes) progressively developed more
and more codes & complex functions----and finally here we are.
The final meaning of biological codes, like in computers, would be
matching between heterogeneous architectures. About what agents
helped in the code multiplication of eukaryotes, the response
nowadays looks clear and clear: viruses and their complex retinue
in the now internalized RNA world. See Luis Villarroel:<i> ex
virus omnia.</i><br>
</div>
<div class="moz-cite-prefix"><br>
</div>
<div class="moz-cite-prefix">So, there are formal, logical,
philosophical, semiotic arguments to make about codes--OK, but if
they do not consider this real world aspect of heterogeneity of
processing architectures am afraid they will be of limited
usefulness to approach the reliance of computers and living beings
on codes.</div>
<div class="moz-cite-prefix"><br>
</div>
<div class="moz-cite-prefix">Best regards,</div>
<div class="moz-cite-prefix">--Pedro<br>
</div>
<div class="moz-cite-prefix"><br>
</div>
<div class="moz-cite-prefix">El 22/09/2021 a las 19:29, Louis
Kauffman escribió:<br>
</div>
<blockquote type="cite"
cite="mid:E3E263C3-6FB6-415D-9413-AF8E624E33F9@gmail.com">
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Dear Joseph,
<div class=""><br class="">
</div>
<div class="">(I am sending this again without graphics so it can
end up on fis.) </div>
<div class=""><br class="">
<div class="">The RD construction is very general, but we have
articulated it with particular models. </div>
<div class=""><br class="">
</div>
<div class="">One starts with a domain where distinctions can be
made and there is a notion of locality.</div>
<div class="">In that domain one makes distinctions about given
entities </div>
<div class="">and replaces the entities by the corresponding
signs of distinction. </div>
<div class="">These signs amalgamate to become new entities to
be distinguished at the next round. </div>
<div class=""><br class="">
</div>
<div class="">Lest this seem abstract, look again at the model.</div>
<div class=""><img apple-inline="yes"
id="76CE295D-901D-4180-8A16-241547BC1538" apple-width="yes"
apple-height="yes" class=""
src="cid:part2.5BDA5A74.0CD1748B@aragon.es" width="339"
height="72"></div>
<div class="">The sign = is an amalgamation of empty word on
left and empty word on rght.</div>
<div class="">The sign ] is amalgamation of empty word on left
and vertical bar | on rght.</div>
<div class="">The sign [] is amalgamation of vertical bar | on
left and empty word on rght.</div>
<div class="">The sign O is meant to be a box and so is an
amalgamation of vertical bar on left and right.</div>
<div class=""><br class="">
</div>
<div class="">The point is that the alphabet arises by the
amalgamations of previous distinctions and so new symbolic
entities arise from the process of distinguishing by these
rules.</div>
<div class="">After the body of this email, I will show you how
the two dimensional RD alphabet arises.</div>
<div class=""><br class="">
</div>
<div class="">This level of model includes notions of language
and description in a very elementary formal framework. </div>
<div class="">I have not included a logical language or a
language that even begins to</div>
<div class="">have self-reference and ordinary reference. Thus
meta-levels and thinking about thinking are not fully
reflected in this small model. </div>
<div class="">But the action of the model gives one the
opportunity to reflect on these</div>
<div class="">larger issues. I am in the business of finding
significant minimal models. </div>
<div class="">These models are not going to be complete
articulations of the whole situation of thinking about
thinking or</div>
<div class="">reflecting on reflecting. They are intended as
ways to help thinking about that. </div>
<div class=""><br class="">
</div>
<div class="">Note also that the RD above engages in “mitosis”
or “self-replication”. It does so without a reflective level.
This is of interest</div>
<div class="">for thinking about coding in biology and in
thinking about what coding would mean in physical situations
“below” biology.</div>
<div class=""><br class="">
</div>
<div class="">Let me give here another example: the audio-active
sequences studied by John Horton Conway.</div>
<div class="">1</div>
<div class="">11 - read “one one” and it describes the line
above.</div>
<div class="">21- read “two ones” and it describes the line
above.</div>
<div class="">1211- read “one two, one one” and it describes the
line above.</div>
<div class="">111221- read “three ones, two two’s, one one” and
it describes the line above.</div>
<div class="">312211- read “one three, two two’s, one one” and
it describes the line above.</div>
<div class="">…</div>
<div class="">This recursion is an example of "describing
describing" and the coding issues are somewhat different from
the RD.</div>
<div class="">We retain locality of interaction and have a fixed
alphabet that is less iconic. Counting is needed at the
descriptive level.</div>
<div class="">This recursion requires more structure to run, but
it is very very interesting.</div>
<div class="">Note that 22 is the only self-referential
sequence.</div>
<div class=""><br class="">
</div>
<div class="">Note also that we could write nx —> xx…x (n
x’s) meaning that nx describes xx…x. </div>
<div class="">In the audio active line we would have</div>
<div class="">xxxx…x</div>
<div class="">nx</div>
<div class=""><br class="">
</div>
<div class="">as in</div>
<div class="">777</div>
<div class="">37.</div>
<div class=""><br class="">
</div>
<div class="">So we have nx —> xx…x</div>
<div class="">and 2x —> xx</div>
<div class="">and so</div>
<div class="">22 —> 22.</div>
<div class=""><br class="">
</div>
<div class="">This pattern fits into the whole of 20th century
logic since Russell.</div>
<div class="">Let me tender persuasions.</div>
<div class="">Russell: Rx = ~xx</div>
<div class="">This is the definition of the Russell set if you
take AB to mean “B is a member of A” and ~ is “not”.</div>
<div class="">Then: RR = ~ RR is the Russell paradox.</div>
<div class="">In this formalism, the Russell paradox becomes the
production of a fixed point for negation.</div>
<div class=""><br class="">
</div>
<div class="">Church and Curry generalized this to an abstract
formalism (lambda calculus) where they could write</div>
<div class="">gx = F(xx) for an arbitrary F.</div>
<div class="">Then</div>
<div class="">gg = F(gg) and we produce a fixed point for F.</div>
<div class="">This is exactly how we got to the self reference
of 22 by</div>
<div class="">2x —> xx</div>
<div class="">22 —> 22 </div>
<div class="">where here equality is replaced by reference.</div>
<div class=""><br class="">
</div>
<div class="">The notion of replacement of reference is integral
to Goedelian self-refefrence.</div>
<div class="">g ——> P(x) now interpreted as “g is the Goedel
number of the proposition P(x) with free variable x.</div>
<div class="">Then let #g be the Goedel number of P(g) so that </div>
<div class="">#g —> P(g).</div>
<div class="">Let the language be rich enough so that # is an
operation in the language.</div>
<div class="">h —> P(#x)</div>
<div class="">Then</div>
<div class="">#h—> P(#h)</div>
<div class="">and P(#h) talks about its own Goedel number.</div>
<div class="">Then with Goedel let ~B(x) mean that “there is no
proof of the statement with Goedel number x.</div>
<div class="">Then with </div>
<div class="">h —> ~B(#x)</div>
<div class="">#h —> ~B(#h)</div>
<div class="">and we have produced the proposition ~B(#h) that
asserts its own unprovability!</div>
<div class="">This is the core of Goedel’s incompleteness
Theorem.</div>
<div class=""><br class="">
</div>
<div class="">I hope you see that we have arrived Goedel’s
Theorem on a track leading directly from the self-reference of
22, by way of the Russell Paradox.</div>
<div class="">All this comes from the capacity of language to
speak about language and thinking to think about thinking.</div>
<div class="">Goedel in fact shows us that all formalisms that
we build that are rich enough and are consistent will be
incomplete.</div>
<div class="">So there is no intent here to create complete
formalisms.</div>
<div class="">I want to look at how the simplest non trivial
formalisms behave, and how even very similar ones such as the
RD and the audio activity are related to each other and to </div>
<div class="">the larger issues of reference, self reference
and the generation of such dialogues at all levels.</div>
<div class=""><br class="">
</div>
<div class="">Note also how small formalisms can summarize wide
ideas.</div>
<div class="">The von Neumann Universal Building Machine B acts
as follows.</div>
<div class="">B,x —> X,x.</div>
<div class="">Give B a blueprint x and B will produce X (the
entity described by the blueprint).</div>
<div class="">Hence if b is the blueprint for B, then B can
build itself!</div>
<div class="">B,b —> B,b.</div>
<div class="">This is another variant of 2x —> xx so 22—>
22.</div>
<div class=""><br class="">
</div>
<div class="">Another thing that happened in the 20th century is
that everyone got frightened about Rx =~xx giving RR = ~ RR,</div>
<div class="">and the story I am telling here of the central
role of reference and self-reference is still not fully
appreciated by mathematical practitioners such as</div>
<div class="">economists and even physicists.</div>
<div class="">Very best,</div>
<div class="">Lou</div>
<div class=""><br class="">
</div>
<div class=""><br class="">
</div>
</div>
<br>
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</blockquote>
<p><br>
</p>
<pre class="moz-signature" cols="72">--
-------------------------------------------------
Pedro C. Marijuán
Grupo de Bioinformación / Bioinformation Group
<a class="moz-txt-link-abbreviated" href="mailto:pcmarijuan.iacs@aragon.es">pcmarijuan.iacs@aragon.es</a>
<a class="moz-txt-link-freetext" href="http://sites.google.com/site/pedrocmarijuan/">http://sites.google.com/site/pedrocmarijuan/</a>
-------------------------------------------------</pre>
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