<div dir="ltr"> Caro Sheri, <div>con i miei commenti telegrafici e propedeutici ho cercato di porre le premesse per introdurre nella discussione</div><div>quella che tu chiami Godelization of Biology<span id="m_5623729582835426197m_-8623461379238275200m_1887035240223484366gmail-:nd" style="display:inline-flex;min-height:28px;vertical-align:bottom;font-family:"Google Sans",Roboto,RobotoDraft,Helvetica,Arial,sans-serif;font-size:22px"><div aria-label="Importante principalmente perché leggi spesso messaggi con questa etichetta." role="img" id="m_5623729582835426197m_-8623461379238275200m_1887035240223484366gmail-:ng" style="font-size:0px;padding:0px;width:20px;height:20px;display:inline-block;margin:0px 0px 0px 8px"><br></div></span>dal punto di vista dell'economia quantistica</div><div>basata proprio sull'indeterminazione o indecidibilità di Godel<span style="color:rgb(31,31,31);font-family:"Google Sans",Roboto,RobotoDraft,Helvetica,Arial,sans-serif;font-size:22px;font-variant-ligatures:no-contextual">, </span>perchè a mio giudizio<span style="color:rgb(31,31,31);font-family:"Google Sans",Roboto,RobotoDraft,Helvetica,Arial,sans-serif;font-size:22px;font-variant-ligatures:no-contextual"> </span>qualunque altra economia bisogna buttarla alle</div><div>ortiche. Altrimenti il mondo dell'uomo e della natura continuerà ad essere distrutto. Preciso inoltre che la quantistica economica è nata prima della quantistica biologica. Comunque, grazie lo stesso.</div><div>Francesco.</div><div>Dear Sheri, with my telegraphic and preparatory comments I have tried to lay the foundations for introducing into the discussion what you call Godelization of Biology<br>from the point of view of quantum economics, based precisely on Godel's uncertainty or undecidability, because in my opinion any other economy must be thrown away. Otherwise the world of man and nature will continue to be destroyed. I also specify that economic quantum was born before biological quantum. Anyway, thanks anyway, Francesco.<div class="gmail-yj6qo gmail-ajU" style="outline:none;padding:10px 0px;width:22px;margin:2px 0px 0px"><br class="gmail-Apple-interchange-newline"></div></div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">Il giorno mar 1 nov 2022 alle ore 07:32 Francesco Rizzo <<a href="mailto:13francesco.rizzo@gmail.com">13francesco.rizzo@gmail.com</a>> ha scritto:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr"><div dir="ltr"><div dir="ltr">Caro Sheri, <div>con i miei commenti telegrafici e propedeutici ho cercato di porre le premesse per introdurre nella discussione</div><div>quella che tu chiami Godelization of Biology<span id="m_-8935722230862570468m_-8623461379238275200m_1887035240223484366gmail-:nd" style="display:inline-flex;min-height:28px;vertical-align:bottom;font-family:"Google Sans",Roboto,RobotoDraft,Helvetica,Arial,sans-serif;font-size:22px"><div aria-label="Importante principalmente perché leggi spesso messaggi con questa etichetta." role="img" id="m_-8935722230862570468m_-8623461379238275200m_1887035240223484366gmail-:ng" style="font-size:0px;padding:0px;width:20px;height:20px;display:inline-block;margin:0px 0px 0px 8px"><br></div></span>dal punto di vista dell'economia quantistica</div><div>basata proprio sull'indeterminazione o indecidibilità di Godel<span style="color:rgb(31,31,31);font-family:"Google Sans",Roboto,RobotoDraft,Helvetica,Arial,sans-serif;font-size:22px;font-variant-ligatures:no-contextual">, </span>perchè a mio giudizio<span style="color:rgb(31,31,31);font-family:"Google Sans",Roboto,RobotoDraft,Helvetica,Arial,sans-serif;font-size:22px;font-variant-ligatures:no-contextual"> </span>qualunque altra economia bisogna buttarla alle</div><div>ortiche. Altrimenti il mondo dell'uomo e della natura continuerà ad essere distrutto. Preciso inoltre che la quantistica economica è nata prima della quantistica biologica. Comunque, grazie lo stesso.</div><div>Francesco.</div><div>Dear Sheri, with my telegraphic and preparatory comments I have tried to lay the foundations for introducing into the discussion what you call Godelization of Biology<br>from the point of view of quantum economics, based precisely on Godel's uncertainty or undecidability, because in my opinion any other economy must be thrown away. Otherwise the world of man and nature will continue to be destroyed. I also specify that economic quantum was born before biological quantum. Anyway, thanks anyway, Francesco.<span style="color:rgb(31,31,31);font-family:"Google Sans",Roboto,RobotoDraft,Helvetica,Arial,sans-serif;font-size:22px;font-variant-ligatures:no-contextual"><br></span></div><div><span style="color:rgb(31,31,31);font-family:"Google Sans",Roboto,RobotoDraft,Helvetica,Arial,sans-serif;font-size:22px;font-variant-ligatures:no-contextual"><br></span></div><div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">---------- Forwarded message ---------<br>Da: <strong class="gmail_sendername" dir="auto">Markose, Sheri</strong> <span dir="auto"><<a href="mailto:scher@essex.ac.uk" target="_blank">scher@essex.ac.uk</a>></span><br>Date: lun 31 ott 2022 alle ore 18:47<br>Subject: RE: [Fis] New Discussion on Complex Self-Other Interactions and Gödelization of Biology<br>To: Francesco Rizzo <<a href="mailto:13francesco.rizzo@gmail.com" target="_blank">13francesco.rizzo@gmail.com</a>><br></div><br><br><div>
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<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial,sans-serif;color:rgb(31,73,125)">Hello Francesco - I am not familiar with Quantum Economics and so may have little to say in that regard.<u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial,sans-serif;color:rgb(31,73,125)"><u></u> <u></u></span></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial,sans-serif;color:rgb(31,73,125)">You can put your comment in the discussion trail about how Quantum Physics/Economics deals with self-non self.<u></u><u></u></span></p>
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<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial,sans-serif;color:rgb(31,73,125)">Many thanks
<u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial,sans-serif;color:rgb(31,73,125)"><u></u> <u></u></span></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial,sans-serif;color:rgb(31,73,125)">Sheri
<u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial,sans-serif;color:rgb(31,73,125)"><u></u> <u></u></span></p>
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<p class="MsoNormal"><b><span lang="EN-US">From:</span></b><span lang="EN-US"> Francesco Rizzo <<a href="mailto:13francesco.rizzo@gmail.com" target="_blank">13francesco.rizzo@gmail.com</a>>
<br>
<b>Sent:</b> 31 October 2022 16:59<br>
<b>To:</b> Markose, Sheri <<a href="mailto:scher@essex.ac.uk" target="_blank">scher@essex.ac.uk</a>><br>
<b>Subject:</b> Re: [Fis] New Discussion on Complex Self-Other Interactions and Gödelization of Biology<u></u><u></u></span></p>
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<p class="MsoNormal"><u></u> <u></u></p>
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<p class="MsoNormal">Dear Sheri, Did my messages reach you or not?<u></u><u></u></p>
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<p class="MsoNormal">Francis<u></u><u></u></p>
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<p class="MsoNormal">caro Sheri, Ti sono arrivati o no i miei messaggi?<u></u><u></u></p>
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<p class="MsoNormal">Francesco<u></u><u></u></p>
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<p class="MsoNormal">Il giorno gio 27 ott 2022 alle ore 07:57 Francesco Rizzo <<a href="mailto:13francesco.rizzo@gmail.com" target="_blank">13francesco.rizzo@gmail.com</a>> ha scritto:<u></u><u></u></p>
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<p class="MsoNormal">Dear Sheri, I would like to send you again the email I wrote you and strangely you did not receive. Thanks Francesco<u></u><u></u></p>
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<p class="MsoNormal">Caro Sheri,<u></u><u></u></p>
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<p class="MsoNormal">mi permetto d'inviarti nuovamente l'email che Ti ho scritto e stranamente non hai ricevuto.<u></u><u></u></p>
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<p class="MsoNormal">grazie.<u></u><u></u></p>
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<p class="MsoNormal">Francesco<u></u><u></u></p>
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<p class="MsoNormal" style="text-align:justify;text-indent:14.2pt"><span style="font-size:10pt;font-family:"Times New Roman",serif">Dear Pedro,Louis and Sheri,</span><u></u><u></u></p>
<p class="MsoNormal" style="text-align:justify;text-indent:14.2pt"><span style="font-size:10pt;font-family:"Times New Roman",serif">as an economist who invented the concept of the good-money in 1975, I am very much context of the topic that will be discussed
in the session that is about to begin, because the distinction between self and non-self is typical of physics or of (my) quantum economics. In fact, between being a living cat or a dying cat (probabilistic, non-deterministic is analogous: to being a commodity
(material) and being a sign or coin (immaterial); between being production eing speculation; between being price and being value; etc. In short, everything is the opposite of everything.</span><u></u><u></u></p>
<p class="MsoNormal" style="text-align:justify;text-indent:14.2pt"><span style="font-size:10pt;font-family:"Times New Roman",serif">A warm greeting.</span><u></u><u></u></p>
<p class="MsoNormal" style="text-align:justify;text-indent:14.2pt"><span style="font-size:10pt;font-family:"Times New Roman",serif">Francesco Rizzo, ore 18.29, 21 ottobre 2022.</span><u></u><u></u></p>
<p class="MsoNormal" style="text-align:justify;text-indent:14.2pt"><span style="font-size:10pt;font-family:"Times New Roman",serif"> </span><u></u><u></u></p>
<p class="MsoNormal" style="text-align:justify;text-indent:14.2pt"><span style="font-size:10pt;font-family:"Times New Roman",serif">Dear Pedro, Louis and Sheri,</span><u></u><u></u></p>
<p class="MsoNormal" style="text-align:justify;text-indent:14.2pt"><span style="font-size:10pt;font-family:"Times New Roman",serif">da economista che ha inventato nel 1975 il concetto del bene-moneta, sono molto contesto del tema che si discuterà nella sessione
che sta per iniziare, perché la distinzione tra sé e non sé è tipica della fisica o della (mia)economia quantistica. Difatti tra l’essere gatto che vive o il gatto che muore (probabilistico, non deterministico è analogo: all’essere merce (materiale) e l’essere
segno o moneta (immateriale); tra l’essere produzione e l’essere speculazione, tra l’essere prezzo e l’essere valore; etc. Insomma. Tutto e il contrario di tutto</span><u></u><u></u></p>
<p class="MsoNormal" style="text-align:justify;text-indent:14.2pt"><span style="font-size:10pt;font-family:"Times New Roman",serif">Un caro saluto augurale.</span><u></u><u></u></p>
<p class="MsoNormal" style="text-align:justify;text-indent:14.2pt"><span style="font-size:10pt;font-family:"Times New Roman",serif">Francesco Rizzo, ore 18.40, 21ottobre 2022.</span><u></u><u></u></p>
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<p class="MsoNormal">Il giorno gio 27 ott 2022 alle ore 00:43 Markose, Sheri <<a href="mailto:scher@essex.ac.uk" target="_blank">scher@essex.ac.uk</a>> ha scritto:<u></u><u></u></p>
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<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial,sans-serif;color:rgb(31,73,125)">Hello Francesco - I do not believe I received an email from your on 21 October.
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<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial,sans-serif;color:rgb(31,73,125)"> </span><u></u><u></u></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial,sans-serif;color:rgb(31,73,125)">I tried to Goggle your work but could not find it – so I’m unable to comment.
</span><u></u><u></u></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial,sans-serif;color:rgb(31,73,125)"> </span><u></u><u></u></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial,sans-serif;color:rgb(31,73,125)">Best Regards</span><u></u><u></u></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial,sans-serif;color:rgb(31,73,125)"> </span><u></u><u></u></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial,sans-serif;color:rgb(31,73,125)">Sheri
</span><u></u><u></u></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial,sans-serif;color:rgb(31,73,125)"> </span><u></u><u></u></p>
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<p class="MsoNormal"><b><span lang="EN-US">From:</span></b><span lang="EN-US"> Francesco Rizzo <<a href="mailto:13francesco.rizzo@gmail.com" target="_blank">13francesco.rizzo@gmail.com</a>>
<br>
<b>Sent:</b> 26 October 2022 15:31<br>
<b>To:</b> Markose, Sheri <<a href="mailto:scher@essex.ac.uk" target="_blank">scher@essex.ac.uk</a>><br>
<b>Subject:</b> Re: [Fis] New Discussion on Complex Self-Other Interactions and Gödelization of Biology</span><u></u><u></u></p>
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<p><strong><span style="font-size:10pt;font-family:Calibri,sans-serif">CAUTION:</span></strong><span style="font-size:10pt;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><u></u><u></u></p>
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<p class="MsoNormal">Dear Sheri,<br>
last October 21 I sent you an email revealing that I am as happy with your being an economist as I am. On October 25, you stated, among much more: Discussion points and areas in which I would like collaborators and from which I can learn since in my daily work
I am an economist. I expected you to dwell on the relationship between genomic biology and the genetic economy underlying physics or quantum reality: a problem that I have modestly dealt with at least in the last twenty years of my research. Why didn't you
do it? Anyway thanks.<u></u><u></u></p>
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<p class="MsoNormal">Francis<u></u><u></u></p>
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<p class="MsoNormal"><span style="font-size:10.5pt;font-family:"Times New Roman",serif;color:rgb(51,51,51)">Caro Sheri,</span><u></u><u></u></p>
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<span style="font-size:10.5pt;font-family:"Times New Roman",serif;color:rgb(51,51,51)">il 21 ottobre scorso Ti ho mandato un’email rivelandomi contento del tuo essere economista come lo sono io. Il 25 ottobre Tu hai affermato, tra tanto altro:
</span><span style="font-family:"Times New Roman",serif">Spunti di discussione e aree in cui vorrei collaboratori e da cui posso imparare visto che nel mio lavoro quotidiano sono un economista (</span><span style="font-size:12pt;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 economis)</span><span style="font-family:"Times New Roman",serif">. Mi aspettavo che Tu ti soffermarsi sul rapporto che passa tra la biologia genomica
e l’economia genetica sottese dalla fisica o realtà quantistica: problematica di cui mi sono modestamente occupato almeno negli ultimi vent’anni della mia ricerca. Perché non l’hai fatto? Comunque, grazie.</span><u></u><u></u></p>
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<p class="MsoNormal"><span style="font-family:"Times New Roman",serif">Cari saluti Francesco</span><u></u><u></u></p>
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<p class="MsoNormal">Il giorno mar 25 ott 2022 alle ore 20:43 Markose, Sheri <<a href="mailto:scher@essex.ac.uk" target="_blank">scher@essex.ac.uk</a>> ha scritto:<u></u><u></u></p>
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<p class="MsoNormal"><span style="font-family:Arial,sans-serif">Dear Colleagues - I look forward to your valuable comments.</span><u></u><u></u></p>
<p class="MsoNormal"><span style="font-family:Arial,sans-serif"> </span><u></u><u></u></p>
<p align="center" style="margin:0cm;text-align:center;background:white"><b><span style="color:black;border:1pt none windowtext;padding:0cm">G</span></b><span style="color:black">ö<b><span style="border:1pt none windowtext;padding:0cm">delian Self-Referential
Genomic Information Processing: Complex Self-Other Interactions and Novelty Production</span></b></span><u></u><u></u></p>
<p style="margin:0cm;background:white"><b><span style="color:black;border:1pt none windowtext;padding:0cm"> </span></b><u></u><u></u></p>
<p style="margin:0cm;background:white"><b><i><span style="color:black;border:1pt none windowtext;padding:0cm">Overview for Foundations of Information Science Discussion –
</span></i></b><u></u><u></u></p>
<p style="margin:0cm;background:white"><b><i><span style="color:black;border:1pt none windowtext;padding:0cm">Sheri Markose 25-10-2022</span></i></b><u></u><u></u></p>
<ol start="1" type="1">
<li class="MsoNormal" style="background:white">
<b><span style="color:black;border:1pt none windowtext;padding:0cm">Background </span>
</b><u></u><u></u></li></ol>
<p style="margin:0cm;background:white"><span style="color:black;border:1pt none windowtext;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><u></u><u></u></p>
<p style="margin:0cm;background:white"><span style="color:black;border:1pt none windowtext;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><u></u><u></u></p>
<p> Genomic intelligence is a concept introduced in <a href="https://urldefense.com/v3/__https:/doi.org/10.3390/e23040405__;!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqV3O-kDY$" target="_blank">
Markose (2021)</a> specifically to characterize the Gödelization of code-based information processing in genomic systems with the distinctive self-referential conditions of Gödel Incompleteness results that appear to have been acquired for complexification
over the course of evolution of multicellular eukaryote life, <a href="https://urldefense.com/v3/__https:/doi.org/10.1016/j.biosystems.2022.104718__;!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqPn2Rp5k$" target="_blank">
Markose (2022)</a>. To explain the latter in contrast to the relative stasis of prokaryotes, which has remain unchanged since inception,
<a href="https://urldefense.com/v3/__https:/www.sciencedirect.com/science/article/pii/S0303264722001022*bib10__;Iw!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqdTKw3lg$" target="_blank">
<span style="color:rgb(12,125,187)">Barbieri (2012</span></a><span style="color:rgb(46,46,46)">; </span><a href="https://urldefense.com/v3/__https:/www.sciencedirect.com/science/article/pii/S0303264722001022*bib13__;Iw!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSq0lIhVMs$" target="_blank"><span style="color:rgb(12,125,187)">2018)</span></a>,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
<a href="https://urldefense.com/v3/__https:/www.sciencedirect.com/topics/mathematics/autopoiesis__;!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqDFaksjk$" title="Learn more about autopoiesis from ScienceDirect's AI-generated Topic Pages" target="_blank">
<span style="color:rgb(46,46,46)">autopoiesis</span></a><span style="color:rgb(46,46,46)">. </span>
<a href="https://urldefense.com/v3/__https:/www.sciencedirect.com/science/article/pii/S0303264722001022*bib59__;Iw!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqIQhnjCw$" target="_blank"><span style="color:rgb(12,125,187)">Igamberdiev
(2021)</span></a><span style="color:rgb(46,46,46)"> gives general principles, but no concrete evidence, for why “living systems during evolution continuously realize the proof of Gödel's theorems (1931).” </span><u></u><u></u></p>
<p style="margin:0cm;background:white"><span style="color:black;border:1pt none windowtext;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 Barbara
</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$" target="_blank"><span style="color:rgb(12,125,187)">McClintock
(1984)</span></a><span style="background:white"> of viral transposable elements that conduct cut-paste (transposons) and copy-paste (retrotransposon) gives a code based explanation for genomic evolvability, brain plasticity and novel phenotype primarily in
eukaryotes. This underscores the truism that primarily only software can change software and also that viral hacking by such internal and external biotic malware is the Achilles heel of genomic digital systems.</span><span style="background:yellow">
</span><span style="background:white"> </span></span><u></u><u></u></p>
<ol start="2" type="1">
<li class="MsoNormal" style="background:white">
<b><span style="color:black;border:1pt none windowtext;padding:0cm">Unpacking the Evidence</span></b><span style="color:black;border:1pt none windowtext;padding:0cm">
<b>for </b></span><b><span style="color:black">Gödelization of Biology</span></b><span style="color:black">
</span><u></u><u></u></li></ol>
<p style="margin:0cm;background:white"><span style="color:black;border:1pt none windowtext;padding:0cm"> While operations on encoded information fall under the purview of Computation Theory and Recursion Function Theory (<b>RFT</b>),
till recently there was no evidence for how this and </span><span style="color:rgb(46,46,46)">Gödel's theorems apply to</span><span style="color:black;border:1pt none windowtext;padding:0cm"> biology. Markose (</span><span style="color:black"><a href="https://urldefense.com/v3/__https:/www.sciencedirect.com/science/article/pii/S0303264722001022*bib61__;Iw!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSq6qlj9z0$" target="_blank"><span style="border:1pt none windowtext;padding:0cm">2022</span></a><span style="border:1pt none windowtext;padding:0cm">)
unpacks the recent breakthroughs here. </span></span><u></u><u></u></p>
<p> 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.
<u></u><u></u></p>
<p> Two other <span style="color:black;border:1pt none windowtext;padding:0cm;background:white">
distinctive </span>Gödelian<span style="color:black;border:1pt none windowtext;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 (<a href="https://urldefense.com/v3/__https:/www.sciencedirect.com/science/article/pii/S0303264722001022*bib48__;Iw!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqGSrl56A$" target="_blank"><span style="color:rgb(12,125,187)">2012</span></a><span style="color:rgb(46,46,46)">, </span><a href="https://urldefense.com/v3/__https:/www.sciencedirect.com/science/article/pii/S0303264722001022*bib49__;Iw!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqpGCiPPQ$" target="_blank"><span style="color:rgb(12,125,187)">2017</span></a><span style="color:rgb(46,46,46)"> Chapter
3 p. 109</span><span style="font-family:Georgia,serif;color:rgb(46,46,46)">)</span> as to what the self-referential/Diagonal operator means for biology, where a program
<i>g </i>builds<i> </i>machine <i><span style="font-family:Symbol">f </span></i>to run
<i>g </i>(typically denoted as <i><span style="font-family:Symbol">f</span><sub>g</sub>(g)</i>). Gershenfeld (<a href="https://urldefense.com/v3/__https:/www.sciencedirect.com/science/article/pii/S0303264722001022*bib48__;Iw!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqGSrl56A$" target="_blank"><span style="color:rgb(12,125,187)">2012</span></a>)
says what 21 century digital fabrication is trying to achieve is something biology solved 3.7 billion years ago with the self-assembly programs associated with the ribosome and other transcriptase machinery involved in gene expression for the morphology, somatic
identity and regulatory control of the organism. <u></u><u></u></p>
<p> Despite the central role assigned to self-reference for the sentient self in advanced organisms (<a href="https://urldefense.com/v3/__https:/scholar.google.se/citations?view_op=view_citation&hl=sv&user=ZW8RWdAAAAAJ&citation_for_view=ZW8RWdAAAAAJ:Y0pCki6q_DkC__;!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqclXIy_8$" target="_blank">Gardenfors
2003</a>, <a href="https://urldefense.com/v3/__https:/doi.org/10.1016/j.neuroimage.2005.12.002__;!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqKaUbmro$" target="_blank">
Northoff et. al, 2006</a> , <a href="https://urldefense.com/v3/__https:/www.sciencedirect.com/science/article/pii/S0303264722001022*bib94__;Iw!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqkgZx_Ng$" target="_blank">
<span style="color:rgb(12,125,187)">Newen (2018)</span></a> , <a href="https://urldefense.com/v3/__https:/doi.org/10.1016/j.pbiomolbio.2018.10.002__;!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqM9CMK80$" target="_blank">
Miller et.al., 2018</a> , etc) only <a href="https://urldefense.com/v3/__https:/www.sciencedirect.com/science/article/pii/S0303264722001022*bib114__;Iw!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqPf630Ss$" target="_blank">
<span style="color:rgb(12,125,187)">Tsuda (2014)</span></a><span style="color:rgb(46,46,46)"> </span>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:1pt none windowtext;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:1pt none windowtext;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><u></u><u></u></p>
<p><span style="color:black;border:1pt none windowtext;padding:0cm;background:white"> </span>The
<b><span style="color:black;border:1pt none windowtext;padding:0cm;background:white">AIS</span></b><span style="color:black;border:1pt none windowtext;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><a href="https://urldefense.com/v3/__https:/www.frontiersin.org/articles/10.3389/fpsyt.2020.540676/full__;!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqRtkoQzk$" target="_blank"><span style="border:1pt none windowtext;padding:0cm;background:white">Ramon
and Faure, 2021</span></a><span style="color:black;border:1pt none windowtext;padding:0cm;background:white">) or ‘the science of self’ (</span><a href="https://urldefense.com/v3/__https:/link.springer.com/article/10.1007/s00281-020-00831-y__;!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSq71KRW4U$" target="_blank"><span style="border:1pt none windowtext;padding:0cm;background:white">Greenen,
2021</span></a><span style="color:black;border:1pt none windowtext;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$" target="_blank"><span style="color:rgb(12,125,187)">Fadiga
et al. (1995)</span></a><span style="color:rgb(46,46,46)">; </span><a href="https://urldefense.com/v3/__https:/www.sciencedirect.com/science/article/pii/S0303264722001022*bib46__;Iw!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqHLWVVsM$" target="_blank"><span style="color:rgb(12,125,187)">Gallese
et al. (1996)</span></a><span style="color:rgb(46,46,46)">; </span><a href="https://urldefense.com/v3/__https:/www.sciencedirect.com/science/article/pii/S0303264722001022*bib102__;Iw!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqmxeFzqA$" target="_blank"><span style="color:rgb(12,125,187)">Rizzolatti
et al. (1996)</span></a>). <u></u><u></u></p>
<p> It is conjectured that an identical <b>RFT</b> machinery is involved in the self-other nexus in both the
<b>AIS</b> and <b>MNS</b>. The graphics for <b>Self-Rep</b> Mirror Mapping in the
<b>AIS</b> and <b>MNS</b> is given in <a href="https://urldefense.com/v3/__https:/www.mdpi.com/1099-4300/23/4/405__;!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSq8Rs91D0$" target="_blank">
Figure 1 in Markose (2021)</a>.<u></u><u></u></p>
<p><span style="color:black;background:lime"> </span><u></u><u></u></p>
<ol start="3" type="1">
<li class="MsoNormal">
<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><u></u><u></u></li></ol>
<p><b> </b>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.
<u></u><u></u></p>
<p> 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 (<a href="https://urldefense.com/v3/__https:/www.jstor.org/stable/j.ctt1b7x7ww__;!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqtrLoY_E$" target="_blank">Smullyan,1961</a>).
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, that halting self-assembly gene codes,
<i>g</i> <span style="font-family:Symbol">Î </span><b>G </b>that create the organism are theorems of the genomic system 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. <u></u><u></u></p>
<p> 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.
<u></u><u></u></p>
<p> <span style="color:black;border:1pt none windowtext;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><u></u><u></u></p>
<p><span style="color:rgb(85,85,85);background:white"> </span> 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="m_-8935722230862570468_m_-8623461379238275200_m_1887035240223484366_m_-8356970801222972789_m_-7551019197939790892_m_-82804672655500"><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><u></u><u></u></p>
<p> 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:1pt none windowtext;padding:0cm">
The genomic </span><b>BCDL </b><span style="color:black;border:1pt none windowtext;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>
<u></u><u></u></p>
<p><span style="color:black;border:1pt none windowtext;padding:0cm"> There are no doubt
</span><span style="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="color:black;border:1pt none windowtext;padding:0cm">BCDL</span></b><span style="color:black;background:white">
</span><u></u><u></u></p>
<p><span style="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><u></u><u></u></p>
<p class="MsoNormal"><span style="font-family:Arial,sans-serif"> </span><u></u><u></u></p>
<p><b>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
</b><u></u><u></u></p>
<p><b>#1</b> I fully concur with the latter part of <a href="https://urldefense.com/v3/__https:/doi.org/10.1016/j.pbiomolbio.2018.10.002__;!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqM9CMK80$" target="_blank">
Miller/Torday (2018)</a> statement : <u></u><u></u></p>
<p style="margin:0cm;background:white"><span style="color:rgb(46,46,46)">“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" target="_blank"><span style="color:rgb(46,46,46)">homeostasis</span></a></span><span style="color:rgb(46,46,46)"> 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><u></u><u></u></p>
<p> 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.
<u></u><u></u></p>
<p> 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.
<u></u><u></u></p>
<p> <u></u><u></u></p>
<p><b>#2.</b> 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.
<u></u><u></u></p>
<p> <u></u><u></u></p>
<p><b># 3</b> 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. <a href="https://urldefense.com/v3/__https:/www.mdpi.com/1099-4300/23/4/405__;!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSq8Rs91D0$" target="_blank">
Figure 1 in Markose (2021)</a> 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 style="font-family:Symbol">s</span>(g,g) operator ) known to be controlled by interferon gamma as in
<a href="https://urldefense.com/v3/__https:/www.nature.com/articles/nature18626__;!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqF1KRYvk$" target="_blank">
Jonathan Kipnis Group 2016</a> experiment on rats, could lead to loss of immune capabilities as well as their sociability. Note, the Markose
<b>RFT</b> machinery for the self-other nexus is a different explanation to the evo-devo one given by Kipnis
<a href="https://urldefense.com/v3/__https://linkprotect.cudasvc.com/url?a=http*3a*2f*2fet.al&c=E,1,oLd773HrF_aCgtWnjI-egqgTBJBabXHBEhV_ASbCNjvrs4fCH3rQ9HZWFf4XPIsUL1rA6xRIDZ7O_CJrgQlkYYqyuPsjYY-mHKhFJwzmD9dv7a0,&typo=1__;JSUl!!D9dNQwwGXtA!XF-jXURnDCu4ySaj7hcIkH2-vybbuRWRO4lFebwlJtWqb_yaJyG3xcmfo0bBA9bpK7tF6Rg2cBF4_HycxJRtt7-wMMmv$" target="_blank">
et.al</a>. <u></u><u></u></p>
<p> <u></u><u></u></p>
<p><b>#4</b> 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. <u></u><u></u></p>
<p> <u></u><u></u></p>
<p class="MsoNormal"><b><span style="font-family:"Times New Roman",serif">References
</span></b><u></u><u></u></p>
<p class="MsoNormal"><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>
<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$" target="_blank">
https://www.essex.ac.uk/blog/posts/2021/10/26/how-we-became-smart</a> </span></b><u></u><u></u></p>
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#</span></b><span style="font-family:"Times New Roman",serif">Markose, S.M, 2022,
<span style="color:rgb(80,80,80)">Complexification of eukaryote phenotype: Adaptive immuno-cognitive systems as unique Gödelian blockchain distributed ledger,
</span><span style="color:rgb(50,50,50)">Biosystems, ISSN: 0303-2647, Vol: 220, </span>
</span><a href="https://urldefense.com/v3/__https:/doi.org/10.1016/j.biosystems.2022.104718__;!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqPn2Rp5k$" title="Persistent link using digital object identifier" target="_blank"><span style="font-family:"Times New Roman",serif;color:rgb(12,125,187)">https://doi.org/10.1016/j.biosystems.2022.104718</span></a><span style="font-family:"Times New Roman",serif;color:rgb(12,125,187)">
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#</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$" target="_blank"><span style="font-family:"Times New Roman",serif;color:rgb(112,184,93);border:1pt none windowtext;padding:0cm;background:white">“Genomic
Intelligence as Über Bio-Cybersecurity: The Gödel Sentence in Immuno-Cognitive Systems”</span></a><span style="font-family:"Times New Roman",serif;color:black;background:white">, </span><em><span style="font-family:Calibri,sans-serif;color:black;border:1pt none windowtext;padding:0cm;background:white">Entropy. </span></em><span style="font-family:"Times New Roman",serif;color:black;background:white">23(4),
405; ttps://<a href="https://urldefense.com/v3/__https://linkprotect.cudasvc.com/url?a=http*3a*2f*2fdoi.org*2f10.3390*2fe23040405&c=E,1,MYX9fzR-YZjn1Wl8_9SrWA1FvLGGNOQ3sacYwrqQHVf2V5YbetS_ZLgFWWwUBWe6apNDJXOrMFJ_BBhGgziGh3oqjelhyoVjt787woDDO_LZ4qckWicA0JJXh9M,&typo=1__;JSUlJSU!!D9dNQwwGXtA!XF-jXURnDCu4ySaj7hcIkH2-vybbuRWRO4lFebwlJtWqb_yaJyG3xcmfo0bBA9bpK7tF6Rg2cBF4_HycxJRtt_Nx6ZmH$" target="_blank">doi.org/10.3390/e23040405</a>
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<p class="MsoNormal"><span style="font-family:"Times New Roman",serif;color:black;border:1pt none windowtext;padding:0cm;background:white"><br>
Markose, S.M, 2017, Complex type 4 structure changing dynamics of digital agents: Nash equilibria or a game with arms race in innovations. </span><i><span style="font-family:"Times New Roman",serif;color:black;border:1pt none windowtext;padding:0cm">Journal
of Dynamics & Games</span></i><span style="font-family:"Times New Roman",serif;color:black;border:1pt none windowtext;padding:0cm;background:white">, 2017, 4 (3) : 255-284. doi: </span><a href="https://urldefense.com/v3/__http:/dx.doi.org/10.3934/jdg.2017015__;!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqC_UOvRc$" target="_blank"><span style="font-family:"Times New Roman",serif;color:rgb(112,184,93);border:1pt none windowtext;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="MsoNormal"><span style="font-size:10pt;font-family:Arial,sans-serif">-------------------</span><u></u><u></u></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial,sans-serif">Professor Sheri Markose</span><u></u><u></u></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial,sans-serif">Economics Department</span><u></u><u></u></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial,sans-serif">University of Essex</span><u></u><u></u></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial,sans-serif">UK
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