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<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Arial",sans-serif;color:#002060;mso-fareast-language:EN-US">Dear Andrei and dear Colleagues
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Arial",sans-serif;color:#002060;mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Arial",sans-serif;color:#002060;mso-fareast-language:EN-US">Again, many thanks for the lively discussions that have followed from my post on Self-other Interactions and G</span><span class="contentpasted0"><span style="font-size:12.0pt;color:#002060">ö</span></span><span style="font-size:10.0pt;font-family:"Arial",sans-serif;color:#002060;mso-fareast-language:EN-US">delizaton
of Biology. I apologize for the delay in responding. But be assured that while attending to routine tasks like setting exam papers (took most of last week), I’m mulling things over prompted by comments being posted and responding to them as soon as I can.
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Arial",sans-serif;color:#002060;mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Arial",sans-serif;color:#002060;mso-fareast-language:EN-US">I agree with Andrei that Barbieri’s notion of
</span><span class="contentpasted0"><span style="font-size:12.0pt;color:#002060">codepoiesis may help refocus efforts toward code based explanations rather than solely bio-physical explanations, often thermodynamic ones such as minimizing entropy, for genomic
information processing. </span></span><span class="contentpasted0"><span style="font-size:12.0pt"><o:p></o:p></span></span></p>
<p class="MsoNormal"><span class="contentpasted0"><span style="font-size:12.0pt;color:#002060"><o:p> </o:p></span></span></p>
<p class="MsoNormal"><span class="contentpasted0"><b><span style="font-size:12.0pt;color:#002060">(i)So why Gödel ?
<o:p></o:p></span></b></span></p>
<p class="MsoNormal"><span class="contentpasted0"><span style="font-size:12.0pt;color:#002060"><o:p> </o:p></span></span></p>
<p class="MsoNormal"><span class="contentpasted0"><span style="font-size:12.0pt;color:#002060">Andrei and I seem to think that Gödel Incompleteness Results may have some bearing on how code based systems can endogenously produce novelty in the form of syntactic
objects (code based again) that lie outside listable sets. Why this and not random shocks qualify to be the model for novelty in biology ?
<o:p></o:p></span></span></p>
<p class="MsoNormal"><span class="contentpasted0"><span style="font-size:12.0pt;color:#002060"><o:p> </o:p></span></span></p>
<p class="MsoNormal"><span class="contentpasted0"><span style="font-size:12.0pt;color:#002060">As recently pointed out by Mikhail Prokopenko et. al (2019) if one wants to utilize such an explanation for novelty, then we need to demonstrate that the system
in question has embedded the necessary conditions that Gödel used to constructively produce such a syntactic object. Gödel numbering
</span></span><span style="font-size:10.0pt;font-family:"Arial",sans-serif;color:#002060;mso-fareast-language:EN-US">is the first feature as a means of giving unique (integer) identifiers to finite strings based on a fixed and finite set of alphabets.
</span><span class="contentpasted0"><span style="font-size:12.0pt;color:#002060"> Self-reference and negation operators are the two others that Prokopenko et.al. identify.<o:p></o:p></span></span></p>
<p class="MsoNormal"><span class="contentpasted0"><span style="font-size:12.0pt;color:#002060"><o:p> </o:p></span></span></p>
<p class="MsoNormal"><span class="contentpasted0"><span style="font-size:12.0pt;color:#002060">We need to rewind to the humble antecedents for the classic steps involved in Gödel Incompleteness Results that may throw light on both the above noted ingredients
(self-reference and negation operator) and more importantly the idea that there is always something novel in that it will exceed enumeration. In the so called Cantor Diagonal Lemma there is a sure fire way of showing that no listing is complete and there
is something that has been left out. <o:p></o:p></span></span></p>
<p class="MsoNormal"><span class="contentpasted0"><span style="font-size:12.0pt;color:#002060"><o:p> </o:p></span></span></p>
<p class="MsoNormal"><span style="font-size:12.0pt;color:black">The (informal ) proof of finding a set that is left out of any enumeration of sets
<i>W<sub>1 </sub>, W<sub>2 …… </sub>W<sub>y </sub>, ….. ,</i> given along the rows of a matrix indexed by integers
<i>y </i>= 1,2,3, … , which are also listed along the columns. The membership of each set
<i>W<sub>x</sub></i> is given as 0 or 1s indicating if an integer belongs to the set in row x ,
<i>y</i> </span><span style="font-size:12.0pt;color:black"><i>W<sub>x</sub></i> or otherwise. In order to identify a set that cannot be in the list
<i>W<sub>1 </sub>, W<sub>2 …… </sub>W<sub>x </sub>, ….. , </i>consider the set along the diagonal.
<span style="background:aqua;mso-highlight:aqua">The self-referential predicate </span>
</span><span style="font-size:12.0pt;font-family:Symbol;color:black;background:aqua;mso-highlight:aqua">s</span><span style="font-size:12.0pt;color:black;background:aqua;mso-highlight:aqua">
<i>(x,x) = <b>Diag(x)</b></i> follows as it refers to <i>x </i></span><i><span style="font-size:12.0pt;background:aqua;mso-highlight:aqua"><span style="color:black">W<sub>x</sub></span></span></i><span style="font-size:12.0pt;color:black;background:aqua;mso-highlight:aqua">
</span><span style="font-size:12.0pt;color:black;background:aqua;mso-highlight:aqua"> or whether
<i>W<sub>x</sub></i> contains its own index <i>x</i>.</span><span style="font-size:12.0pt;color:black"> On applying
<span style="background:aqua;mso-highlight:aqua">a negation operator</span> along the diagonal array, changes 0’s to 1’s and 1’s to 0’s, we now have a set (the anti-diagonal set denoted as
<i>D<sup>¬</sup></i>) that is different from all listed sets <i>W<sub>x </sub></i> by at least one element along the diagonal. The steps given here for the set
<i>D<sup>¬ </sup></i> that cannot belong to any enumeration of sets are informal.</span><span class="contentpasted0"><span style="font-size:12.0pt;color:#002060">
<o:p></o:p></span></span></p>
<p class="MsoNormal"><span class="contentpasted0"><span style="font-size:12.0pt;color:#002060"><o:p> </o:p></span></span></p>
<p class="MsoNormal"><span class="contentpasted0"><span style="font-size:12.0pt;color:#002060">The genius of Gödel (1931) is to ‘mechanize’ these ingredients to produce a syntactic object which typically takes the form of the undecidable proposition, aka Gödel
Sentence, along the lines that Louis Kauffman has expertly shown.<o:p></o:p></span></span></p>
<p class="MsoNormal"><span class="contentpasted0"><span style="font-size:12.0pt;color:#002060"><o:p> </o:p></span></span></p>
<p class="MsoNormal"><span class="contentpasted0"><span style="font-size:12.0pt;color:#002060">The typical rendering of the first Gödel (1931) result is as follows<o:p></o:p></span></span></p>
<p class="MsoNormal"><span class="contentpasted0"><span style="font-size:12.0pt;color:#002060"><o:p> </o:p></span></span></p>
<p class="MsoFootnoteText"><span class="contentpasted0"><span style="font-size:12.0pt;color:#002060">
</span></span><span style="font-size:12.0pt;color:#222222;background:white">PA ͰA </span><tt><span style="font-size:12.0pt;color:#222222;background:white">↔</span></tt><span style="font-size:12.0pt;color:#222222;background:white"> ¬Prov(A). Here, A effectively
says of itself that it is not provable (¬Prov(A)), with this undecidable <br>
proposition being a theorem (Ͱ) in the formal system of Peano Arithmetic (PA). </span>
<o:p></o:p></p>
<p class="MsoNormal"><span class="contentpasted0"><span style="font-size:12.0pt;color:#002060"> <o:p></o:p></span></span></p>
<p class="MsoNormal"><span class="contentpasted0"><span style="font-size:12.0pt;color:#002060">As things stand - it is very hard to show how this relates to Biology. I call it a funky, esoteric construction in the foundations of maths, to date of little relevance
to anything in the real world… </span></span><span class="contentpasted0"><span style="color:#002060"><o:p></o:p></span></span></p>
<p class="MsoNormal"><span class="contentpasted0"><span style="font-size:12.0pt;color:#002060"> <b><o:p></o:p></b></span></span></p>
<p class="MsoNormal"><span class="contentpasted0"><b><span style="font-size:12.0pt;color:#002060"> (ii) We need far more machinery than Gödel (1931) to show how Diag, Negation & Theoremhood relate to Biology
<o:p></o:p></span></b></span></p>
<p class="MsoNormal"><span class="contentpasted0"><b><span style="font-size:12.0pt;color:#002060"><o:p> </o:p></span></b></span></p>
<p class="MsoNormal"><span class="contentpasted0"><span style="font-size:12.0pt;color:#002060">In my opinion as Gödel (1931) predates the full developments of what is called Recursive Function Theory, the notion of Church Turing thesis of an algorithm, hence
of codes/programs of self-assembly machines. <o:p></o:p></span></span></p>
<p class="MsoNormal"><span class="contentpasted0"><span style="font-size:12.0pt;color:#002060">We need (Roger’s) Second Recursion Theorem to identify the fixed point of a negation software that will alter the codes of the self-assembly machines. <o:p></o:p></span></span></p>
<p class="MsoNormal"><span class="contentpasted0"><span style="font-size:12.0pt;color:#002060"><o:p> </o:p></span></span></p>
<p class="MsoNormal"><span class="contentpasted0"><span style="font-size:12.0pt;color:#002060">Most of all we need the Emil Post (1944) set theoretic proof of Gödel Incompleteness result which
<o:p></o:p></span></span></p>
<p class="MsoNormal"><span style="color:#333333;background:white">Smullyan (1961, p.58) has noted plays a fundamental role in modern approaches to incompleteness and undecidability. I quote Fefferman of saying the same in my 2017 (AIMS paper). But I do
not know of anybody who has used the Emil Post (1944) proof with creative and productive sets in any application. The sets of theorems and non-theorems, which is implicit in G</span><span class="contentpasted0"><span style="font-size:12.0pt;color:#002060">ö</span></span><span style="color:#333333;background:white">del(1931)
becomes explicit in Post rendering of the problem. </span><span class="contentpasted0"><span style="font-size:12.0pt;color:#002060"><o:p></o:p></span></span></p>
<p class="MsoNormal"><span class="contentpasted0"><span style="font-size:12.0pt;color:#002060"><o:p> </o:p></span></span></p>
<p class="MsoNormal"><span class="contentpasted0"><span style="font-size:12.0pt;color:#002060">It is only when things are laid out in Hartley Roger format of Gödel Meta Representation Theorem in his proof for his Fixed Point Theorem does one see direct evidence
such as the mirror structures in the immune system and in the brain. <o:p></o:p></span></span></p>
<p class="MsoNormal"><span class="contentpasted0"><span style="font-size:12.0pt;color:#002060">I will elaborate more on this in my response to Louis Kauffman. <o:p></o:p></span></span></p>
<p class="MsoNormal"><span class="contentpasted0"><span style="font-size:12.0pt;color:#002060"><o:p> </o:p></span></span></p>
<p class="MsoNormal"><span class="contentpasted0"><b><span style="font-size:12.0pt;color:#002060">(iii) Evidence
<o:p></o:p></span></b></span></p>
<p class="MsoNormal"><span class="contentpasted0"><span style="font-size:12.0pt;color:#002060">My quibble with Andrei is that unless we produce evidence such as even for Gödel numbering in Biology, things are still up in the air. My first inkling for this
is from the work of Gunter Blobel discovery of peptide ‘zip codes’ in proteins which even tell them where to go !! I believe transcription factors in gene expression, which require a number of genomic components to be turned on together, are identified by
having a common identifier (class mark) etc.<o:p></o:p></span></span></p>
<p class="MsoNormal"><span class="contentpasted0"><span style="font-size:12.0pt;color:#002060"><o:p> </o:p></span></span></p>
<p class="MsoNormal"><span class="contentpasted0"><span style="font-size:12.0pt;color:#002060">My idea of what is entailed in Godel numbering is quite prosaic. Say we have a string of alphabets – mapped to an integer m. Now apply another software operation
<i>f </i>on it (some strings from elsewhere via copy paste) – this this composite
<i>f (m) </i> string has g.n q etc. This is called S-M-N theorem in RFT, no clue as to how biology does it…
<o:p></o:p></span></span></p>
<p class="MsoNormal"><span class="contentpasted0"><span style="font-size:12.0pt;color:#002060"><o:p> </o:p></span></span></p>
<p class="MsoNormal"><span class="contentpasted0"><span style="font-size:12.0pt;color:#002060">Best Regards<o:p></o:p></span></span></p>
<p class="MsoNormal"><span class="contentpasted0"><span style="font-size:12.0pt;color:#002060"><o:p> </o:p></span></span></p>
<p class="MsoNormal"><span class="contentpasted0"><span style="font-size:12.0pt;color:#002060">Sheri <o:p></o:p></span></span></p>
<p class="MsoNormal"><span class="contentpasted0"><span style="font-size:12.0pt;color:#002060"><o:p> </o:p></span></span></p>
<p class="MsoNormal"><span class="contentpasted0"><span style="font-size:12.0pt;color:#002060"><o:p> </o:p></span></span></p>
<p class="MsoNormal"><span class="contentpasted0"><span style="font-size:12.0pt;color:#002060"><o:p> </o:p></span></span></p>
<p class="MsoNormal"><span class="contentpasted0"><span style="font-size:12.0pt;color:#002060"><o:p> </o:p></span></span></p>
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<p class="MsoNormal"><b><span lang="EN-US">From:</span></b><span lang="EN-US"> Andrei Igamberdiev <a_igamberdiev@hotmail.com>
<br>
<b>Sent:</b> 31 October 2022 17:07<br>
<b>To:</b> Markose, Sheri <scher@essex.ac.uk>; fis@listas.unizar.es<br>
<b>Subject:</b> Re: New Discussion on Complex Self-Other Interactions and Gödelization of Biology<o:p></o:p></span></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p><strong><span style="font-size:10.0pt;font-family:"Calibri",sans-serif">CAUTION:</span></strong><span style="font-size:10.0pt;font-family:"Times New Roman",serif;color:black"> This email was sent from outside the University of Essex. Please do not click
any links or open any attachments unless you recognise and trust the sender. If you are unsure whether the content of the email is safe or have any other queries, please contact the IT Helpdesk.</span><span style="font-size:10.0pt;font-family:"Times New Roman",serif"><o:p></o:p></span></p>
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<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black">Dear Sheri and Colleagues,<o:p></o:p></span></p>
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<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"><o:p> </o:p></span></p>
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<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black">we are discussing the central and most fundamental issue of generation of novelty and complexification in biological world. The main point here is the generation of
<span class="contentpasted0">Gödel numbers, i.e. the assignment of previously undefined statements in the natural computing system of the cell by meanings. To understand progressive biological evolution, we need to make a move from the description of biological
system as self-sustaining (autopoiesis) to its understanding as generating evolutionary novelty (codepoiesis). While the term autopoiesis arises to Maturana and Varela (although first the autopoietic structure was suggested by Tibor
</span><span class="contentpasted1">Gánti</span><span class="contentpasted0"> in 1971 or even earlier - he conceived the basic idea in 1952), the concept of codepoiesis was introduced by Marcello Barbieri (in detail in his book of 2015 and earlier in his papers).
For many years generation of novelty was considered as a random process, while it can be described as a continuous realization of the proof of Gödel's theorems. Why this happens - it is an inevitable consequence of natural computation, in other words, it is
the consequence of the incompleteness of a sufficiently rich formal system, i.e., of the presence of undecidable statements within the system. The simple prokaryotic system can be insufficiently rich for advanced complexification (although at certain stage
the process of complexification generated the eukaryotic cell), while in eukaryotes the capacity for complexification significantly increases.
</span><o:p></o:p></span></p>
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<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"><o:p> </o:p></span></p>
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<p class="MsoNormal"><span class="contentpasted0"><span style="font-size:12.0pt">The process of Gödel numbering introduces a new code to the system
</span></span><span class="contentpasted6"><span style="font-size:12.0pt">which proves that certain statements are undecidable</span></span> within the system. This code can be externally applied but it can be<span class="contentpasted6"><span style="font-size:12.0pt">
efficiently internalized in the system itself. The resulting hierarchical</span></span><span class="contentpasted0"><span style="font-size:12.0pt"> structure, consisting of the formal system and its reflection in the course of the proof of undecidability,
corresponds to a new organization where</span></span> <span class="contentpasted0">
<span style="font-size:12.0pt">Gödel </span></span>numbers represent a new information system that emerged from the original system by assigning codes to it. The undecidable statements become the basis of the evolutionary<span class="contentpasted0"><span style="font-size:12.0pt">
unfolding of the system by assigning certain values to them. The details can be found in my paper published in BioSystems 207 (2021) 104454,
</span></span><a href="https://urldefense.com/v3/__https://linkprotect.cudasvc.com/url?a=https*3a*2f*2fdoi.org*2f10.1016*2fj.biosystems.2021.104454&c=E,1,EahD_AZmPoOx690SC8rsCzcPdE7d1D96ZEy32L2jizRYPlUhBsh9jq_8YaaoEkrBSmJwdzckQLb6klSv94sqUziYLX1k_E6IzS-vGxB5_d5H&typo=1__;JSUlJSU!!D9dNQwwGXtA!UyCtjIKq6bLofcL6dBQ6z-6R4kA6nftw0YH6vVFZUKODBcUEs1j7q0VcLQrp00gchhkHyXZ3YnrejIttHi0$"><span style="font-size:12.0pt">https://doi.org/10.1016/j.biosystems.2021.104454</span></a><span class="contentpasted0"><span style="font-size:12.0pt">,
although the original idea arises to my early paper published in 1986. More detailed metamathematical analysis of this process of assigning codes is presented in Shelah, S., Strüngmann, L., 2021. Infinite combinatorics in mathematical biology. Biosystems 204,
104392. </span></span><a href="https://urldefense.com/v3/__https://linkprotect.cudasvc.com/url?a=https*3a*2f*2fdoi.org*2f10.1016*2fj.biosystems.2021.104392&c=E,1,r32d1oKsRGye-9Ya_4O662cEGxP0muGCKCPPj1DTtUKAc2hVYM07MXG1f4DI-MGZR7R7lT5Or1dBWj2fEJsBO2V-x9oZyFwyoIo-bwJBia0sJehAzqDqd_CYt0Y,&typo=1__;JSUlJSU!!D9dNQwwGXtA!UyCtjIKq6bLofcL6dBQ6z-6R4kA6nftw0YH6vVFZUKODBcUEs1j7q0VcLQrp00gchhkHyXZ3Ynrete8XQ2w$"><span style="font-size:12.0pt">https://doi.org/10.1016/j.biosystems.2021.104392</span></a><span class="contentpasted0"><span style="font-size:12.0pt">.</span></span><o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal"><span class="contentpasted0"><span style="font-size:12.0pt">It is definitely true that the immune system has a great capacity for generation of Gödel numbers. The significant increase of capacity for complexification occurs at certain level
of organization, corresponding to eukaryotic cell. The prokaryotic progressive evolution is limited by the size of formal coding system, and most likely most living structures in the Universe do not overcome this limit, so the chance of finding the eukaryotic
life outside the Earth is extremely low. </span></span><o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal"><span class="contentpasted0"><span style="font-size:12.0pt">The simplest way of generating new codes (especially at early stages of evolution) is the activity similar t</span></span><span class="contentpasted15"><span style="font-size:12.0pt">o
the enzyme polynucleotide phosphorylase (EC 2.7.7.8), which can catalyze the casual rearrangement of nucleotides and operates without energy cost. It realizes the RNA-based multiplication of generativity and thus can serve as an elementary tool for codepoiesis.
A new rearranged sequences generated via such polynucleotide phosphorylase equilibrium can potentially acquire biological functions and correspond to the evolution of autopoietic systems.
</span></span><span class="contentpasted0"><span style="font-size:12.0pt"> </span>
</span><span class="contentpasted16"><span style="font-size:12.0pt">At higher evolutionary levels, combinatorial rearrangements represent a powerful tool for evolutionary changes; they can be realized at the level of meiotic crossover and lead to the expansion
of the genome.</span></span><o:p></o:p></p>
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<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"><o:p> </o:p></span></p>
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<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black">Sheri has suggested certain concrete examples of
<span class="contentpasted0">Gödel</span>ization of code-based information such as bio-peptide unique identifiers, e.g., signal peptide sequences, antibody production in response to non-self antigens, etc. We can discuss the particular cases and outline possible
ways of generation of such new information. Comparing bacteria-phage arms race with antibody production will clarify the complexification of the eukaryotic system in comparison with the prokaryotic.
<o:p></o:p></span></p>
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<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"><o:p> </o:p></span></p>
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<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black">In conclusion, the understanding of
<span class="contentpasted0">Gödelization of code-based information will represent an overall fundamental principle of evolving natural-computing systems operating towards the appearance of the structures with maximum power efficiency, and the well-known principles
(and their limitations) such as natural selection, variability, adaptability, etc. will represent a consequence of the basic phenomenon of the codepoietic nature of the evolutionary biological phenomena. It is worth to consider and discuss the particular examples
of codepoiesis as well as the "codification" of the codepoietic events in the individual development of multicellular organisms during cell differentiation. This could be a very valuable discussion.</span><o:p></o:p></span></p>
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<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"><o:p> </o:p></span></p>
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<p class="MsoNormal" style="background:white"><span class="contentpasted0"><span style="font-size:12.0pt;color:black">All the best,</span></span><span style="font-size:12.0pt;color:black"><o:p></o:p></span></p>
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<p class="MsoNormal" style="background:white"><span class="contentpasted0"><span style="font-size:12.0pt;color:black">Andrei Igamberdiev
</span></span><span style="font-size:12.0pt;color:black"><o:p></o:p></span></p>
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<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"><o:p> </o:p></span></p>
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<p class="MsoNormal"><b><span style="color:black">From:</span></b><span style="color:black"> Fis <</span><a href="mailto:fis-bounces@listas.unizar.es">fis-bounces@listas.unizar.es</a><span style="color:black">> on behalf of Markose, Sheri <</span><a href="mailto:scher@essex.ac.uk">scher@essex.ac.uk</a><span style="color:black">></span><o:p></o:p></p>
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<p class="MsoNormal"><b><span style="color:black">Sent:</span></b><span style="color:black"> October 25, 2022 6:42 PM<br>
<b>To:</b> </span><a href="mailto:fis@listas.unizar.es">fis@listas.unizar.es</a><span style="color:black"> <</span><a href="mailto:fis@listas.unizar.es">fis@listas.unizar.es</a><span style="color:black">><br>
<b>Subject:</b> [Fis] New Discussion on Complex Self-Other Interactions and Gödelization of Biology</span>
<o:p></o:p></p>
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<p class="MsoNormal"> <o:p></o:p></p>
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<p class="xmsonormal"><span style="font-family:"Arial",sans-serif">Dear Colleagues - I look forward to your valuable comments.</span><o:p></o:p></p>
<p class="xmsonormal"><span style="font-family:"Arial",sans-serif"> </span><o:p></o:p></p>
<p align="center" style="text-align:center;background:white"><a name="x__Hlk116426332"><b><span style="color:black;border:none windowtext 1.0pt;padding:0cm">G</span></b></a><span style="color:black">ö<b><span style="border:none windowtext 1.0pt;padding:0cm">delian
Self-Referential Genomic Information Processing: Complex Self-Other Interactions and Novelty Production</span></b></span><o:p></o:p></p>
<p style="background:white"><b><span style="color:black;border:none windowtext 1.0pt;padding:0cm"> </span></b><o:p></o:p></p>
<p style="background:white"><b><i><span style="color:black;border:none windowtext 1.0pt;padding:0cm">Overview for Foundations of Information Science Discussion –
</span></i></b><o:p></o:p></p>
<p style="background:white"><b><i><span style="color:black;border:none windowtext 1.0pt;padding:0cm">Sheri Markose 25-10-2022</span></i></b><o:p></o:p></p>
<ol style="margin-top:0cm" start="1" type="1">
<li class="MsoNormal" style="color:black;mso-list:l2 level1 lfo3;background:white">
<b><span style="border:none windowtext 1.0pt;padding:0cm">Background </span></b><o:p></o:p></li></ol>
<p style="background:white"><span style="color:black;border:none windowtext 1.0pt;padding:0cm">Complexity, evolvability, novelty production and ‘thinking outside the box’ in biology and humans have for most part relied on models of randomness or on statistical
white noise error terms. </span><o:p></o:p></p>
<p style="background:white"><span style="color:black;border:none windowtext 1.0pt;padding:0cm"> The digitization of inheritable information in the genome encoded in a near universal alphabet (A,T,C,G/U) has been called the ‘algorithmic takeover
of biology’ by Walker and Davis (2013). The Faustian pact at the genesis of life colourfully portrayed by Freeman Dyson as ‘ the takeover of a replicative digital virus of an analogue metabolism’ accords with the perspective of Forterre, Zimmer, Villareal,
Koonin and others. </span><span style="color:black">This underpins the remarkable fact that in nature only life and biology as we know it and the artifacts of genomic intelligence (GI) thereof are explicitly code based digital systems.
</span><o:p></o:p></p>
<p class="xmsobodytext2"><span style="font-family:"Times New Roman",serif"> Genomic intelligence is a concept introduced in
</span><a href="https://urldefense.com/v3/__https:/doi.org/10.3390/e23040405__;!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqV3O-kDY$"><span style="font-family:"Times New Roman",serif">Markose (2021)</span></a><span style="font-family:"Times New Roman",serif">
specifically to characterize the Gödelization of code-based information processing in genomic systems with the distinctive self-referential conditions of Gödel Incompleteness results that appear to have been acquired for complexification over the course of
evolution of multicellular eukaryote life, </span><a href="https://urldefense.com/v3/__https:/doi.org/10.1016/j.biosystems.2022.104718__;!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqPn2Rp5k$"><span style="font-family:"Times New Roman",serif">Markose
(2022)</span></a><span style="font-family:"Times New Roman",serif">. <a name="x_bbib59">
To explain the latter in contrast to the relative stasis of prokaryotes, which has remain unchanged since inception,
</a></span><span style="mso-bookmark:x_bbib59"></span><a href="https://urldefense.com/v3/__https:/www.sciencedirect.com/science/article/pii/S0303264722001022*bib10__;Iw!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqdTKw3lg$"><span style="font-family:"Times New Roman",serif;color:#0C7DBB">Barbieri
(2012</span></a><span style="font-family:"Times New Roman",serif;color:#2E2E2E">; </span><a href="https://urldefense.com/v3/__https:/www.sciencedirect.com/science/article/pii/S0303264722001022*bib13__;Iw!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSq0lIhVMs$"><span style="font-family:"Times New Roman",serif;color:#0C7DBB">2018)</span></a><span style="font-family:"Times New Roman",serif">,for
instance, has resorted to Code Biology and Codeopoiesis, viz. biotic code based explanations to complement the more popular thermodynamic explanations of self-organization and
</span><a href="https://urldefense.com/v3/__https:/www.sciencedirect.com/topics/mathematics/autopoiesis__;!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqDFaksjk$" title="Learn more about autopoiesis from ScienceDirect's AI-generated Topic Pages"><span style="font-family:"Times New Roman",serif;color:#2E2E2E">autopoiesis</span></a><span style="font-family:"Times New Roman",serif;color:#2E2E2E">.
</span><a href="https://urldefense.com/v3/__https:/www.sciencedirect.com/science/article/pii/S0303264722001022*bib59__;Iw!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqIQhnjCw$"><span style="font-family:"Times New Roman",serif;color:#0C7DBB">Igamberdiev
(2021)</span></a><span style="font-family:"Times New Roman",serif;color:#2E2E2E"> gives general principles, but no concrete evidence, for why “living systems during evolution continuously realize the proof of Gödel's theorems (1931).” </span><span style="font-size:12.0pt;font-family:"Times New Roman",serif"><o:p></o:p></span></p>
<p style="background:white"><span style="color:black;border:none windowtext 1.0pt;padding:0cm"> Significantly, while debunking the idea that the primary source of evolutionary changes arise from random transcription/replication errors, t</span><span style="color:black;background:white">he
epochal discovery by Nobel Laureate <a name="x_bbib88">Barbara </a></span><span style="mso-bookmark:x_bbib88"></span><span style="color:black"><a href="https://urldefense.com/v3/__https:/www.sciencedirect.com/science/article/pii/S0303264722001022*bib88__;Iw!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqajIC2C4$"><span style="color:#0C7DBB">McClintock
(1984)</span></a><span style="background:white"> of viral transposable elements that conduct cut-paste (transposons) and copy-paste (retrotransposon) gives a code based explanation for genomic evolvability, brain plasticity and novel phenotype primarily in
eukaryotes. This underscores the truism that primarily only software can change software and also that viral hacking by such internal and external biotic malware is the Achilles heel of genomic digital systems.</span><span style="background:yellow">
</span><span style="background:white"> </span></span><o:p></o:p></p>
<ol style="margin-top:0cm" start="2" type="1">
<li class="MsoNormal" style="mso-list:l5 level1 lfo6;background:white"><b><span style="color:black;border:none windowtext 1.0pt;padding:0cm">Unpacking the Evidence</span></b><span style="color:black;border:none windowtext 1.0pt;padding:0cm">
<b>for </b></span><b><span style="color:black">Gödelization of Biology</span></b><span style="color:black">
</span><o:p></o:p></li></ol>
<p style="background:white"><span style="color:black;border:none windowtext 1.0pt;padding:0cm"> While operations on encoded information fall under the purview of Computation Theory and Recursion Function Theory (<b>RFT</b>), till recently
there was no evidence for how this and </span><span style="color:#2E2E2E">Gödel's theorems apply to</span><span style="color:black;border:none windowtext 1.0pt;padding:0cm"> biology. Markose (</span><span style="color:black"><a href="https://urldefense.com/v3/__https:/www.sciencedirect.com/science/article/pii/S0303264722001022*bib61__;Iw!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSq6qlj9z0$"><span style="border:none windowtext 1.0pt;padding:0cm">2022</span></a><span style="border:none windowtext 1.0pt;padding:0cm">)
unpacks the recent breakthroughs here. </span></span><o:p></o:p></p>
<p class="xmsofootnotetext"><span style="font-family:"Times New Roman",serif"> Gödelization of information processing starts, firstly, with unique identifiers or Gödel numbers for digital entities well known in the digital economy and taking
the form of bio-peptide unique identifiers including ‘zip codes’ in organisms as discovered in the Nobel prize winning work of Blobel (2009). It appears all signalling in bio-ICT relies on peptide identifiers from transcription factors to neuron-neuron links.
</span><span style="font-size:10.0pt;font-family:"Times New Roman",serif"><o:p></o:p></span></p>
<p class="xmsofootnotetext"><span style="font-family:"Times New Roman",serif"> Two other
<span style="color:black;border:none windowtext 1.0pt;padding:0cm;background:white">
distinctive </span>Gödelian<span style="color:black;border:none windowtext 1.0pt;padding:0cm;background:white"> features found in genomic intelligence, using epithets from Hofstadter (1999) are self-reference (<b>Self-Ref</b>) or the online machine execution
involving the Diagonal operator and offline virtual self-representation (<b>Self-Rep</b>) of the former.
</span>The breakthrough on the significance of these staples of <b>RFT</b> found in textbooks such as Rogers (1967) and Cutland (1980), starts with the insight from Gershenfeld (</span><a name="x_bbib48"></a><a href="https://urldefense.com/v3/__https:/www.sciencedirect.com/science/article/pii/S0303264722001022*bib48__;Iw!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqGSrl56A$"><span style="font-family:"Times New Roman",serif;color:#0C7DBB">2012</span></a><span style="font-family:"Times New Roman",serif;color:#2E2E2E">, </span><a name="x_bbib49"></a><a href="https://urldefense.com/v3/__https:/www.sciencedirect.com/science/article/pii/S0303264722001022*bib49__;Iw!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqpGCiPPQ$"><span style="font-family:"Times New Roman",serif;color:#0C7DBB">2017</span></a><span style="font-family:"Times New Roman",serif;color:#2E2E2E"> Chapter
3 p. 109</span><span style="font-family:"Georgia",serif;color:#2E2E2E">)</span><span style="font-family:"Times New Roman",serif"> as to what the self-referential/Diagonal operator means for biology, where a program
<i>g </i>builds<i> </i>machine </span><i><span style="font-family:Symbol">f </span>
</i><span style="font-family:"Times New Roman",serif">to run <i>g </i>(typically denoted as
</span><i><span style="font-family:Symbol">f</span></i><i><sub><span style="font-family:"Times New Roman",serif">g</span></sub></i><i><span style="font-family:"Times New Roman",serif">(g)</span></i><span style="font-family:"Times New Roman",serif">). Gershenfeld
(</span><a href="https://urldefense.com/v3/__https:/www.sciencedirect.com/science/article/pii/S0303264722001022*bib48__;Iw!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqGSrl56A$"><span style="font-family:"Times New Roman",serif;color:#0C7DBB">2012</span></a><span style="font-family:"Times New Roman",serif">)
says what 21 century digital fabrication is trying to achieve is something biology solved 3.7 billion years ago with the self-assembly programs associated with the ribosome and other transcriptase machinery involved in gene expression for the morphology, somatic
identity and regulatory control of the organism. </span><span style="font-size:10.0pt;font-family:"Times New Roman",serif"><o:p></o:p></span></p>
<p class="xmsofootnotetext"><span style="font-family:"Times New Roman",serif"> Despite the central role assigned to self-reference for the sentient self in advanced organisms (</span><a href="https://urldefense.com/v3/__https:/scholar.google.se/citations?view_op=view_citation&hl=sv&user=ZW8RWdAAAAAJ&citation_for_view=ZW8RWdAAAAAJ:Y0pCki6q_DkC__;!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqclXIy_8$"><span style="font-family:"Times New Roman",serif">Gardenfors
2003</span></a><span style="font-family:"Times New Roman",serif">, </span><a href="https://urldefense.com/v3/__https:/doi.org/10.1016/j.neuroimage.2005.12.002__;!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqKaUbmro$"><span style="font-family:"Times New Roman",serif">Northoff
et. al, 2006</span></a><span style="font-family:"Times New Roman",serif"> , </span>
<a name="x_bbib94"></a><a href="https://urldefense.com/v3/__https:/www.sciencedirect.com/science/article/pii/S0303264722001022*bib94__;Iw!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqkgZx_Ng$"><span style="font-family:"Times New Roman",serif;color:#0C7DBB">Newen
(2018)</span></a><span style="font-family:"Times New Roman",serif"> , </span><a href="https://urldefense.com/v3/__https:/doi.org/10.1016/j.pbiomolbio.2018.10.002__;!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqM9CMK80$"><span style="font-family:"Times New Roman",serif">Miller
et.al., 2018</span></a><span style="font-family:"Times New Roman",serif"> , etc) only
</span><a name="x_bbib114"></a><a href="https://urldefense.com/v3/__https:/www.sciencedirect.com/science/article/pii/S0303264722001022*bib114__;Iw!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqPf630Ss$"><span style="font-family:"Times New Roman",serif;color:#0C7DBB">Tsuda
(2014)</span></a><span style="font-family:"Times New Roman",serif;color:#2E2E2E"> </span><span style="font-family:"Times New Roman",serif">and Markose (2017, 2021,2022) have noted how the evolutionary development of
<b>Self-Rep</b> mirror structures as in <span style="color:black;border:none windowtext 1.0pt;padding:0cm;background:white">
the</span> Gödel Meta-Representation Theorem (Rogers,1967) is necessary for biotic elements to make statements about themselves, first having self-assembled themselves. This
<i>offline</i> embodied <b>Self-Rep</b>, which contrasts with no such structures in prokaryotes, was a paradigm shift
<span style="color:black;border:none windowtext 1.0pt;padding:0cm;background:white">
in the Adaptive Immune System (AIS) some 500 million years ago in the lineage of jawed fish, called the Big Bang of Immunology, Janeway et. al (2005). This latterly appears as Mirror Neuron System (MNS) mostly in primate brains first discovered by the Parma
Group of neuroscientists. </span></span><span style="font-size:10.0pt;font-family:"Times New Roman",serif"><o:p></o:p></span></p>
<p class="xmsofootnotetext"><span style="font-family:"Times New Roman",serif;color:black;border:none windowtext 1.0pt;padding:0cm;background:white"> </span><span style="font-family:"Times New Roman",serif">The
<b><span style="color:black;border:none windowtext 1.0pt;padding:0cm;background:white">AIS</span></b><span style="color:black;border:none windowtext 1.0pt;padding:0cm;background:white"> demonstrates virtual offline mirrored self-representation (<b>Self-Rep</b>)
in the MHC1 T cell receptors of ~85 % of expressed genes viz. <i>halted </i>machine executions of genomic self-assembly codes that determine the somatic and phenotype identity for the organism. As will be seen, these Self-Repped gene codes in the Thymus,
called the <i>Thymic Self </i> (</span></span><a href="https://urldefense.com/v3/__https:/www.frontiersin.org/articles/10.3389/fpsyt.2020.540676/full__;!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqRtkoQzk$"><span style="font-family:"Times New Roman",serif;border:none windowtext 1.0pt;padding:0cm;background:white">Ramon
and Faure, 2021</span></a><span style="font-family:"Times New Roman",serif;color:black;border:none windowtext 1.0pt;padding:0cm;background:white">) or ‘the science of self’ (</span><a href="https://urldefense.com/v3/__https:/link.springer.com/article/10.1007/s00281-020-00831-y__;!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSq71KRW4U$"><span style="font-family:"Times New Roman",serif;border:none windowtext 1.0pt;padding:0cm;background:white">Greenen,
2021</span></a><span style="font-family:"Times New Roman",serif;color:black;border:none windowtext 1.0pt;padding:0cm;background:white">) are primarily used to identify the hostile other, viz. negation function operators of non-self antigens. In turn, the
Mirror Neuron System (<b>MNS</b>) reuses codes of self-actions from the sensory-motor cortex for social cognition and inference regarding conspecifics via virtual simulations in the
<b>MNS</b> (</span><a href="https://urldefense.com/v3/__https:/www.sciencedirect.com/science/article/pii/S0303264722001022*bib35__;Iw!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqek3WNP4$"><span style="font-family:"Times New Roman",serif;color:#0C7DBB">Fadiga
et al. (1995)</span></a><span style="font-family:"Times New Roman",serif;color:#2E2E2E">; </span><a href="https://urldefense.com/v3/__https:/www.sciencedirect.com/science/article/pii/S0303264722001022*bib46__;Iw!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqHLWVVsM$"><span style="font-family:"Times New Roman",serif;color:#0C7DBB">Gallese
et al. (1996)</span></a><span style="font-family:"Times New Roman",serif;color:#2E2E2E">; </span><a href="https://urldefense.com/v3/__https:/www.sciencedirect.com/science/article/pii/S0303264722001022*bib102__;Iw!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqmxeFzqA$"><span style="font-family:"Times New Roman",serif;color:#0C7DBB">Rizzolatti
et al. (1996)</span></a><span style="font-family:"Times New Roman",serif">). </span>
<span style="font-size:10.0pt;font-family:"Times New Roman",serif"><o:p></o:p></span></p>
<p class="xmsofootnotetext"><span style="font-family:"Times New Roman",serif"> It is conjectured that an identical
<b>RFT</b> machinery is involved in the self-other nexus in both the <b>AIS</b> and
<b>MNS</b>. The graphics for <b>Self-Rep</b> Mirror Mapping in the <b>AIS</b> and
<b>MNS</b> is given in </span><a href="https://urldefense.com/v3/__https:/www.mdpi.com/1099-4300/23/4/405__;!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSq8Rs91D0$"><span style="font-family:"Times New Roman",serif">Figure
1 in Markose (2021)</span></a><span style="font-family:"Times New Roman",serif">.</span><span style="font-size:10.0pt;font-family:"Times New Roman",serif"><o:p></o:p></span></p>
<p class="xmsofootnotetext"><span style="font-family:"Times New Roman",serif;color:black;background:lime"> </span><span style="font-size:10.0pt;font-family:"Times New Roman",serif"><o:p></o:p></span></p>
<ol style="margin-top:0cm" start="3" type="1">
<li class="xmsolistparagraph" style="margin-top:0cm;margin-bottom:0cm;mso-list:l4 level1 lfo9">
<b><span style="font-family:"Times New Roman",serif">Detection of Non-Self Antigen in AIS: New Diversity-Selector Model and Gödel Sentence in Genomic Blockchain Distributed Ledger (BCDL)
</span></b><span style="font-family:"Times New Roman",serif"><o:p></o:p></span></li></ol>
<p class="xmsofootnotetext"><b> </b><span style="font-family:"Times New Roman",serif">The most significant of all breakthroughs here is the one made by the game theorist Binmore (1987) who raised the ‘spectre of Gödel (1931)’ in the form
of Gödel’s Liar who will negate or falsify what can be computed/predicted. Binmore effectively mooted the adversarial digital game which is co-extensive with life itself (Markose, 2017, 2021). This constitutes the
<i>fourth</i> condition of Gödel systems and involves an adversarial agent in the form of a virus or a hacker whose actions cannot be constrained in anyway.
</span><span style="font-size:10.0pt;font-family:"Times New Roman",serif"><o:p></o:p></span></p>
<p class="xmsofootnotetext"><span style="font-family:"Times New Roman",serif"> The Gödel Incompleteness result that generates the Gödel Sentence permits a code qua biotic element to self-report “I’m under attack”, when it has been hacked/negated
by a novel malware. This marks an endogenous exit from listable sets, a necessary condition for novelty and the production of novel antibodies, to avoid the irrational state of logical inconsistency of formal systems (</span><a href="https://urldefense.com/v3/__https:/www.jstor.org/stable/j.ctt1b7x7ww__;!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqtrLoY_E$"><span style="font-family:"Times New Roman",serif">Smullyan,1961</span></a><span style="font-family:"Times New Roman",serif">).
The genomic Gödel Sentence in terms of 21 century nomenclature is a <i>hash</i> that helps demonstrate endogenously that the outputs of expressed genes have been maliciously altered. Note,
</span><span style="font-size:10.0pt;font-family:"Times New Roman",serif">that halting self-assembly gene codes,
<i>g</i> </span><span style="font-size:10.0pt;font-family:Symbol">Î </span><b><span style="font-size:10.0pt;font-family:"Times New Roman",serif">G
</span></b><span style="font-size:10.0pt;font-family:"Times New Roman",serif">that create the organism are theorems of the genomic system
</span><span style="font-family:"Times New Roman",serif">theorems and is disjoint from known non-theorems or what the immunologist Burnett (1958) famously called ‘forbidden codes’ if allowed to run will ‘negate’ the theorems and cause harm.
</span><span style="font-size:10.0pt;font-family:"Times New Roman",serif"><o:p></o:p></span></p>
<p class="xmsofootnotetext"><span style="font-family:"Times New Roman",serif"> Indeed, how the
<b>AIS</b> identifies novel software attacks on own gene codes, <i>g</i> , by malware/parasite negating functions
<i>f<sub>p</sub></i><sup>¬ !</sup> , which belongs to an uncountable infinite set that cannot be mechanically listed, is stupendous case of uber bio-cybersecurity.
</span><span style="font-size:10.0pt;font-family:"Times New Roman",serif"><o:p></o:p></span></p>
<p class="xmsofootnotetext"><span style="font-family:"Times New Roman",serif"> <span style="color:black;border:none windowtext 1.0pt;padding:0cm;background:white">The AIS implements ‘out of the box’ astronomic anticipative search for novel non-self
antigens necessary for </span>novel anti-body production and cognition <span style="color:black;background:white">
in humans manifests unbounded proteanism for novel extended phenotypes, Dawkins (1987), in the form of artifacts outside of ourselves</span>.
<span style="color:black;background:white">This facility found only in the <b>AIS</b> relying on the Recombination Activator genes (<b>RAG</b> 1 and 2) and in the human brain for neural receptor diversity runs into orders of magnitude of 10<sup>20</sup> – 10<sup>30</sup> that
exceed the pre-scripted germline genome size many times over. </span></span><span style="font-size:10.0pt;font-family:"Times New Roman",serif"><o:p></o:p></span></p>
<p class="xmsofootnotetext"><span style="font-family:"Times New Roman",serif;color:#555555;background:white"> </span><span style="font-family:"Times New Roman",serif"> The Rogers (1967) fixed point indexes for yet to happen
<i>f<sub>p</sub></i><sup>¬ !</sup> attacks by the non-self antigens are generated in the
<b>AIS</b> in most ingenious fashion: a large number of codes/indexes purported to be of different
<a name="x__Hlk117013984"><i>f<sub>p</sub></i><sup>¬ !</sup> </a>on each <b>self-repped</b>
<i> g </i>are generated in the T-Cell Receptors. This is the most spectacular case of predictive coding. Suppose that the g.n for the specific tuple {<i> f<sub>p</sub></i><sup>¬
</sup>, <i>g<sub>n</sub></i> } denoted by <i>g<sup>¬</sup></i>. When the attack by
<i>f<sub>p</sub></i><sup>¬ !</sup> takes place in real time in the periphery involving the said pair {<i> f<sub>p</sub></i><sup>¬
</sup>, <i>g<sub>n</sub></i> }, the experientially driven peripheral MHC1 receptor must record this and if this ‘syncs’ with the one that was speculatively generated in the thymic MHC1 receptors, two parts of the fixed point come together to construct a genomic
Gödel Sentence. <i> </i></span><span style="font-size:10.0pt;font-family:"Times New Roman",serif"><o:p></o:p></span></p>
<p class="xmsofootnotetext"><span style="font-family:"Times New Roman",serif"> This molecular genomic diversity-selector model follows a unique self-referential blockchain distributed ledger that is different, in terms of the self-referential
design, from man-made <b>BCDLs</b> first invented circa 2009. <span style="color:black;border:none windowtext 1.0pt;padding:0cm">
The genomic </span><b>BCDL </b><span style="color:black;border:none windowtext 1.0pt;padding:0cm">manifests secure digital and decentralized record keeping where no internal or external bio-malware can compromise the immutability of the life’s building blocks
and no novel blocks can be added that is not consistent with extant blocks. </span>
</span><span style="font-size:10.0pt;font-family:"Times New Roman",serif"><o:p></o:p></span></p>
<p class="xmsofootnotetext"><span style="font-family:"Times New Roman",serif;color:black;border:none windowtext 1.0pt;padding:0cm"> There are no doubt
</span><span style="font-family:"Times New Roman",serif;color:black;background:white">macroscopic environmental and population level pressures of the Neo-Darwinian style natural selection arising from conspecific or multi-species competition for survival in
terms of those which reproduce more and those which die out. There is growing evidence that at level of bio-digital smart controls of the eukaryote genome and homeostasis, selective pressures are based on the principles of a unique self-referential
</span><b><span style="font-family:"Times New Roman",serif;color:black;border:none windowtext 1.0pt;padding:0cm">BCDL</span></b><span style="font-family:"Times New Roman",serif;color:black;background:white">
</span><span style="font-size:10.0pt;font-family:"Times New Roman",serif"><o:p></o:p></span></p>
<p class="xmsofootnotetext"><span style="font-family:"Times New Roman",serif;color:black;background:white"> In conclusion, genomic intelligence in vertebrates that has reached its apogee in humans is highly empathic as the conspecific/other
is the projection of self; greatly Machiavellian having co-evolved with adversarial viral agents; geared toward unbounded proteanism from the get-go starting with transposon based diversity of
<b>RAG</b> genes in the immune system and stringently self-regulated by a <b>BCD</b>L driven by the principle of autonomy of the life of the organism and an agenda to be hack-free.
</span><span style="font-size:10.0pt;font-family:"Times New Roman",serif"><o:p></o:p></span></p>
<p class="xmsonormal"><span style="font-family:"Arial",sans-serif"> </span><o:p></o:p></p>
<p class="xmsofootnotetext"><b><span style="font-family:"Times New Roman",serif">Points for discussion and areas where I would like collaborators and those I can learn from as in my day job I’m an economist
</span></b><span style="font-size:10.0pt;font-family:"Times New Roman",serif"><o:p></o:p></span></p>
<p class="xmsofootnotetext"><b><span style="font-family:"Times New Roman",serif">#1</span></b><span style="font-family:"Times New Roman",serif"> I fully concur with the latter part of
</span><a href="https://urldefense.com/v3/__https:/doi.org/10.1016/j.pbiomolbio.2018.10.002__;!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqM9CMK80$"><span style="font-family:"Times New Roman",serif">Miller/Torday
(2018)</span></a><span style="font-family:"Times New Roman",serif"> statement : </span>
<span style="font-size:10.0pt;font-family:"Times New Roman",serif"><o:p></o:p></span></p>
<p style="background:white"><span style="color:#2E2E2E">“As self-referential cognition is demonstrated by all living organisms, life can be equated with the sustenance of cellular </span><span style="color:black"><a href="https://urldefense.com/v3/__https:/www.sciencedirect.com/topics/biochemistry-genetics-and-molecular-biology/homeostasis__;!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSq8F9h1Jc$" title="Learn more about homeostasis from ScienceDirect's AI-generated Topic Pages"><span style="color:#2E2E2E">homeostasis</span></a></span><span style="color:#2E2E2E"> in
the continuous defence of 'self'.” </span><span style="color:black">However, Miller/Torday do not use any of the code based
<b>RFT</b> Gödel style <b>Self-Ref</b> mirror structures for genomic information processing.</span><o:p></o:p></p>
<p class="xmsofootnotetext"><span style="font-family:"Times New Roman",serif"> No doubt prokaryote CRISPR based identification of non-self antigens is highly sophisticated and so are the innate immune system strategies which primarily entail
analog defences of setting up barriers, toxicity, raising temperature by inflammation and ingestion by phagocytes. Prokaryotes distinctively do not have the mirror
<b>Self-Rep </b>offline structures of self as in the Rogers (1967) <b>RFT</b> fixed point theorems which permit bio-molecules to self-report changes to their own codes. My take on homeostasis in eukaryotes post jawed fish is that bio software data security
and hence the autonomy of self was taken to the next level: the design of how codes can self-report they have been changed by bio malware by utilizing hashes like the Gödel Sentence.
</span><span style="font-size:10.0pt;font-family:"Times New Roman",serif"><o:p></o:p></span></p>
<p class="xmsofootnotetext"><span style="font-family:"Times New Roman",serif"> It will be interesting to compare the bacteria-phage arms race in prokaryotes with the one in the
<b>AIS</b> antibody production outlined above. I have reached out to John Mattick and Silvia Sanchez Ramon on these issues.
</span><span style="font-size:10.0pt;font-family:"Times New Roman",serif"><o:p></o:p></span></p>
<p class="xmsofootnotetext"><span style="font-family:"Times New Roman",serif"> </span><span style="font-size:10.0pt;font-family:"Times New Roman",serif"><o:p></o:p></span></p>
<p class="xmsofootnotetext"><b><span style="font-family:"Times New Roman",serif">#2.</span></b><span style="font-family:"Times New Roman",serif"> In Markose (2021) I indicate that the generation of genomic Gödel Sentences for detection of novel the non-self
antigen is necessary for novel antibody production is a testable hypothesis. Those who died of Covid 19 were found not to be capable of antibody production and instead were subjected by a cytokine storm brought about by the analog defences of toxicity and
inflammation of the innate immune system. </span><span style="font-size:10.0pt;font-family:"Times New Roman",serif"><o:p></o:p></span></p>
<p class="xmsofootnotetext"><span style="font-family:"Times New Roman",serif"> </span><span style="font-size:10.0pt;font-family:"Times New Roman",serif"><o:p></o:p></span></p>
<p class="xmsofootnotetext"><b><span style="font-family:"Times New Roman",serif"># 3</span></b><span style="font-family:"Times New Roman",serif"> A common
<b>Self-Rep</b> mirror <b>RFT</b> machinery for self-other recognition in the <b>
AIS </b>and social cognition following from the Mirror Neuron Systems in primates has been conjectured. Similar conjectures have been made at least since Irun Cohen, but without any
<b>RFT</b> to guide the discussions. </span><a href="https://urldefense.com/v3/__https:/www.mdpi.com/1099-4300/23/4/405__;!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSq8Rs91D0$"><span style="font-family:"Times New Roman",serif">Figure
1 in Markose (2021)</span></a><span style="font-family:"Times New Roman",serif"> shows how a knock-out of the circuitry for self’s updates on non-self activity vis-à-vis self (the RHS entry in the
<i>offline</i> <b>Self-Rep</b> </span><span style="font-family:Symbol">s</span><span style="font-family:"Times New Roman",serif">(g,g) operator ) known to be controlled by interferon gamma as in
</span><a href="https://urldefense.com/v3/__https:/www.nature.com/articles/nature18626__;!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqF1KRYvk$"><span style="font-family:"Times New Roman",serif">Jonathan Kipnis Group
2016</span></a><span style="font-family:"Times New Roman",serif"> experiment on rats, could lead to loss of immune capabilities as well as their sociability. Note, the Markose
<b>RFT</b> machinery for the self-other nexus is a different explanation to the evo-devo one given by Kipnis
</span><a href="https://urldefense.com/v3/__https://linkprotect.cudasvc.com/url?a=https*3a*2f*2fet.al&c=E,1,gM9IH0l2_WyCH4oxGyy4qH5YHFHLfyPWaXVy6cuQ8D9BarKsxnYxmIv85rzwVEYx3t674fcYC9xwPHX9REjolv82s-JTTmjlFPERtC4ZphcjW1Y,&typo=1&ancr_add=1__;JSUl!!D9dNQwwGXtA!UyCtjIKq6bLofcL6dBQ6z-6R4kA6nftw0YH6vVFZUKODBcUEs1j7q0VcLQrp00gchhkHyXZ3YnreRaiVXtM$"><span style="font-family:"Times New Roman",serif">et.al</span></a><span style="font-family:"Times New Roman",serif">
</span><span style="font-size:10.0pt;font-family:"Times New Roman",serif"><o:p></o:p></span></p>
<p class="xmsofootnotetext"><span style="font-family:"Times New Roman",serif"> </span><span style="font-size:10.0pt;font-family:"Times New Roman",serif"><o:p></o:p></span></p>
<p class="xmsofootnotetext"><b><span style="font-family:"Times New Roman",serif">#4</span></b><span style="font-family:"Times New Roman",serif"> Finally, it is a matter of incredulity that over 90 years have passed since Gödel (1931) for evidence to be found
that the staples of <b>Self-Ref</b> and <b>Self-Rep</b> and the Gödel Sentence are ubiquitous in Biology. A number of factors can be adduced. Even those who espouse that code-based operations are relevant in cognition such as in the Computational Theory of
Mind never mention <b>Self-Ref</b> and <b>Self-Rep</b>, let alone that the Gödel Sentence is like a
<i>hash </i>which permits a software document to endogenously self-report it has been hacked. There is a strong anti-machine view which overlooks the encoded basis of the genome and biology and claims that biology is a non-digital natural process that is creative
in some vitalistic way. </span><span style="font-size:10.0pt;font-family:"Times New Roman",serif"><o:p></o:p></span></p>
<p class="xmsofootnotetext"><span style="font-family:"Times New Roman",serif"> </span><span style="font-size:10.0pt;font-family:"Times New Roman",serif"><o:p></o:p></span></p>
<p class="xmsonormal"><b><span style="font-family:"Times New Roman",serif">References
</span></b><o:p></o:p></p>
<p class="xmsonormal"><b><span style="font-family:"Times New Roman",serif">#Blog on University of Essex Website:
<i>How we became smart – a journey of discovery through the world of game theory and genomic intelligence</i>
</span></b><a href="https://urldefense.com/v3/__https:/www.essex.ac.uk/blog/posts/2021/10/26/how-we-became-smart__;!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqVgSsoLo$"><b><span style="font-family:"Times New Roman",serif">https://www.essex.ac.uk/blog/posts/2021/10/26/how-we-became-smart</span></b></a><b><span style="font-family:"Times New Roman",serif">
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#</span></b><span style="font-family:"Times New Roman",serif">Markose, S.M, 2022,
<span style="color:#505050">Complexification of eukaryote phenotype: Adaptive immuno-cognitive systems as unique Gödelian blockchain distributed ledger,
</span><span style="color:#323232">Biosystems, ISSN: 0303-2647, Vol: 220, </span>
</span><a href="https://urldefense.com/v3/__https:/doi.org/10.1016/j.biosystems.2022.104718__;!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqPn2Rp5k$" title="Persistent link using digital object identifier"><span style="font-family:"Times New Roman",serif;color:#0C7DBB">https://doi.org/10.1016/j.biosystems.2022.104718</span></a><span class="xmsohyperlink"><u><span style="font-family:"Times New Roman",serif;color:#0C7DBB">
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<span class="xmsohyperlink">#</span></span></u><span style="font-family:"Times New Roman",serif;color:black;background:white">Markose, S.M, 2021, </span><a href="https://urldefense.com/v3/__https:/doi.org/10.3390/e23040405__;!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqV3O-kDY$"><span style="font-family:"Times New Roman",serif;color:#70B85D;border:none windowtext 1.0pt;padding:0cm;background:white">“Genomic
Intelligence as Über Bio-Cybersecurity: The Gödel Sentence in Immuno-Cognitive Systems”</span></a><span style="font-family:"Times New Roman",serif;color:black;background:white">, </span><em><span style="font-family:"Calibri",sans-serif;color:black;border:none windowtext 1.0pt;padding:0cm;background:white">Entropy. </span></em><span style="font-family:"Times New Roman",serif;color:black;background:white">23(4),
405; ttps://</span><a href="https://urldefense.com/v3/__https://linkprotect.cudasvc.com/url?a=https*3a*2f*2f*2f*2fdoi.org*2f10.3390*2fe23040405*26nbsp*3b*26nbsp*3b&c=E,1,5ljJnDyIM9_72M8MI5wXv03g8R_xcMpRIJlprpoJlE3VxeysqCeuaM5BD03I_cDZuFkptB_foj9qlcTVhWq8_mCu8nrDmJk5UpevoDwqAG-mS9ZcGA,,&typo=1&ancr_add=1__;JSUlJSUlJSUlJSU!!D9dNQwwGXtA!UyCtjIKq6bLofcL6dBQ6z-6R4kA6nftw0YH6vVFZUKODBcUEs1j7q0VcLQrp00gchhkHyXZ3YnreTR3KzjA$"><span style="font-family:"Times New Roman",serif;background:white">//doi.org/10.3390/e23040405 </span></a><span style="font-family:"Times New Roman",serif;color:black;background:white">
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<span class="xinfo">Markose, S.M, 2017, Complex type 4 structure changing dynamics of digital agents: Nash equilibria or a game with arms race in innovations. </span></span><span class="xinfo"><i><span style="font-family:"Times New Roman",serif;color:black;border:none windowtext 1.0pt;padding:0cm">Journal
of Dynamics & Games</span></i></span><span class="xinfo"><span style="font-family:"Times New Roman",serif;color:black;border:none windowtext 1.0pt;padding:0cm;background:white">, 2017, 4 (3) : 255-284. doi: </span></span><a href="https://urldefense.com/v3/__http:/dx.doi.org/10.3934/jdg.2017015__;!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqC_UOvRc$"><span style="font-family:"Times New Roman",serif;color:#70B85D;border:none windowtext 1.0pt;padding:0cm">10.3934/jdg.2017015</span></a><span style="font-family:"Times New Roman",serif;color:black;background:white">
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<p class="xmsonormal"><span style="font-size:10.0pt;font-family:"Arial",sans-serif">-------------------</span><o:p></o:p></p>
<p class="xmsonormal"><span style="font-size:10.0pt;font-family:"Arial",sans-serif">Professor Sheri Markose</span><o:p></o:p></p>
<p class="xmsonormal"><span style="font-size:10.0pt;font-family:"Arial",sans-serif">Economics Department</span><o:p></o:p></p>
<p class="xmsonormal"><span style="font-size:10.0pt;font-family:"Arial",sans-serif">University of Essex</span><o:p></o:p></p>
<p class="xmsonormal"><span style="font-size:10.0pt;font-family:"Arial",sans-serif">UK
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