[Fis] New Discussion on Complex Self-Other Interactions and Gödelization of Biology

Markose, Sheri scher at essex.ac.uk
Tue Oct 25 20:42:51 CEST 2022

Dear Colleagues -  I look forward to your valuable comments.

Gödelian Self-Referential Genomic Information Processing: Complex Self-Other Interactions and Novelty Production

Overview for Foundations of Information Science Discussion -

Sheri Markose         25-10-2022

  1.  Background

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.

                  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.  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.

                     Genomic intelligence is a concept introduced in Markose (2021)<https://urldefense.com/v3/__https://doi.org/10.3390/e23040405__;!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqV3O-kDY$  > 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, Markose (2022)<https://urldefense.com/v3/__https://doi.org/10.1016/j.biosystems.2022.104718__;!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqPn2Rp5k$  >.  To explain the latter in contrast to the relative stasis of prokaryotes, which has remain unchanged since inception, Barbieri (2012<https://urldefense.com/v3/__https://www.sciencedirect.com/science/article/pii/S0303264722001022*bib10__;Iw!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqdTKw3lg$  >; 2018)<https://urldefense.com/v3/__https://www.sciencedirect.com/science/article/pii/S0303264722001022*bib13__;Iw!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSq0lIhVMs$  >,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 autopoiesis<https://urldefense.com/v3/__https://www.sciencedirect.com/topics/mathematics/autopoiesis__;!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqDFaksjk$  >. Igamberdiev (2021)<https://urldefense.com/v3/__https://www.sciencedirect.com/science/article/pii/S0303264722001022*bib59__;Iw!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqIQhnjCw$  > gives general principles, but no concrete evidence, for why "living systems during evolution continuously realize the proof of Gödel's theorems (1931)."

                   Significantly, while debunking the idea that the primary source of evolutionary changes arise from random transcription/replication errors, the epochal discovery by Nobel Laureate Barbara McClintock (1984)<https://urldefense.com/v3/__https://www.sciencedirect.com/science/article/pii/S0303264722001022*bib88__;Iw!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqajIC2C4$  > 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.

  1.  Unpacking the Evidence for Gödelization of Biology

                        While operations on encoded information fall under the purview of Computation Theory and Recursion Function Theory (RFT), till recently there was no evidence for how this and Gödel's theorems apply to biology.  Markose (2022<https://urldefense.com/v3/__https://www.sciencedirect.com/science/article/pii/S0303264722001022*bib61__;Iw!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSq6qlj9z0$  >) unpacks the recent breakthroughs here.

                     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.

                     Two other distinctive Gödelian features found in genomic intelligence, using epithets from Hofstadter (1999) are self-reference (Self-Ref) or the online machine execution involving the Diagonal operator and offline virtual self-representation (Self-Rep) of the former.  The breakthrough on the significance of these staples of RFT found in textbooks such as Rogers (1967) and Cutland (1980), starts with the insight from Gershenfeld (2012<https://urldefense.com/v3/__https://www.sciencedirect.com/science/article/pii/S0303264722001022*bib48__;Iw!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqGSrl56A$  >, 2017<https://urldefense.com/v3/__https://www.sciencedirect.com/science/article/pii/S0303264722001022*bib49__;Iw!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqpGCiPPQ$  > Chapter 3 p. 109) as to what the self-referential/Diagonal operator means for biology, where a program g builds machine * to run g (typically denoted as *g(g)). Gershenfeld (2012<https://urldefense.com/v3/__https://www.sciencedirect.com/science/article/pii/S0303264722001022*bib48__;Iw!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqGSrl56A$  >) 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.

                      Despite the central role assigned to self-reference for the sentient self in advanced organisms (Gardenfors  2003<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$  >, Northoff et. al, 2006<https://urldefense.com/v3/__https://doi.org/10.1016/j.neuroimage.2005.12.002__;!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqKaUbmro$  > , Newen (2018)<https://urldefense.com/v3/__https://www.sciencedirect.com/science/article/pii/S0303264722001022*bib94__;Iw!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqkgZx_Ng$  > , Miller et.al., 2018<https://urldefense.com/v3/__https://doi.org/10.1016/j.pbiomolbio.2018.10.002__;!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqM9CMK80$  > , etc) only Tsuda (2014)<https://urldefense.com/v3/__https://www.sciencedirect.com/science/article/pii/S0303264722001022*bib114__;Iw!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqPf630Ss$  > and Markose (2017, 2021,2022) have noted how the evolutionary development of Self-Rep mirror structures as in the Gödel Meta-Representation Theorem (Rogers,1967) is necessary for biotic elements to make statements about themselves, first having self-assembled themselves.  This offline embodied Self-Rep, which contrasts with no such structures in prokaryotes, was a paradigm shift 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.

                   The AIS demonstrates virtual offline mirrored self-representation (Self-Rep) in the MHC1 T cell receptors of ~85 % of expressed genes viz. halted 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 Thymic Self  (Ramon and Faure, 2021<https://urldefense.com/v3/__https://www.frontiersin.org/articles/10.3389/fpsyt.2020.540676/full__;!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqRtkoQzk$  >) or 'the science of self' (Greenen, 2021<https://urldefense.com/v3/__https://link.springer.com/article/10.1007/s00281-020-00831-y__;!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSq71KRW4U$  >) are primarily used to identify the hostile other, viz. negation function operators of non-self antigens.  In turn, the Mirror Neuron System (MNS) reuses codes of self-actions from the sensory-motor cortex for social cognition and inference regarding conspecifics via virtual simulations in the MNS (Fadiga et al. (1995)<https://urldefense.com/v3/__https://www.sciencedirect.com/science/article/pii/S0303264722001022*bib35__;Iw!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqek3WNP4$  >; Gallese et al. (1996)<https://urldefense.com/v3/__https://www.sciencedirect.com/science/article/pii/S0303264722001022*bib46__;Iw!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqHLWVVsM$  >; Rizzolatti et al. (1996)<https://urldefense.com/v3/__https://www.sciencedirect.com/science/article/pii/S0303264722001022*bib102__;Iw!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqmxeFzqA$  >).

                 It is conjectured that an identical RFT machinery is involved in the self-other nexus in both the AIS and MNS.  The graphics for Self-Rep Mirror Mapping in the AIS and MNS is given in Figure 1 in Markose (2021)<https://urldefense.com/v3/__https://www.mdpi.com/1099-4300/23/4/405__;!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSq8Rs91D0$  >.

  1.  Detection of Non-Self Antigen in AIS: New Diversity-Selector Model and Gödel Sentence in Genomic Blockchain Distributed Ledger (BCDL)

                     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 fourth 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.

                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 (Smullyan,1961<https://urldefense.com/v3/__https://www.jstor.org/stable/j.ctt1b7x7ww__;!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqtrLoY_E$  >).  The genomic Gödel Sentence in terms of 21 century nomenclature is a hash that helps demonstrate endogenously that the outputs of expressed genes have been maliciously altered. Note, that halting self-assembly gene codes, g * G 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.

                Indeed, how the AIS identifies novel software attacks on own gene codes, g , by malware/parasite negating functions fp¬ ! , which belongs to an uncountable infinite set that cannot be mechanically listed, is stupendous case of uber bio-cybersecurity.

              The AIS implements 'out of the box' astronomic anticipative search for novel non-self antigens necessary for novel anti-body production and cognition in humans manifests unbounded proteanism for novel extended phenotypes, Dawkins (1987), in the form of artifacts outside of ourselves.  This facility found only in the AIS relying on the Recombination Activator genes (RAG 1 and 2) and in the human brain for neural receptor diversity runs into orders of magnitude of 1020 - 1030 that exceed the pre-scripted germline genome size many times over.

                The Rogers (1967) fixed point indexes for yet to happen fp¬ ! attacks by the non-self antigens are generated in the AIS  in most ingenious fashion: a large number of codes/indexes purported to be of different fp¬ ! on each self-repped  g 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 { fp¬ , gn } denoted by g¬. When the attack by fp¬ !  takes place in real time in the periphery involving the said pair { fp¬ , gn }, 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.

               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 BCDLs first invented circa 2009.  The genomic BCDL 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.

                    There are no doubt 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 BCDL

                    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 RAG genes in the immune system and stringently self-regulated by a BCDL driven by the principle of autonomy of the life of the organism and an agenda to be hack-free.

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

#1 I fully concur with the latter part of Miller/Torday (2018)<https://urldefense.com/v3/__https://doi.org/10.1016/j.pbiomolbio.2018.10.002__;!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqM9CMK80$  > statement :

"As self-referential cognition is demonstrated by all living organisms, life can be equated with the sustenance of cellular homeostasis<https://urldefense.com/v3/__https://www.sciencedirect.com/topics/biochemistry-genetics-and-molecular-biology/homeostasis__;!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSq8F9h1Jc$  > in the continuous defence of 'self'." However, Miller/Torday do not use any of the code based RFT Gödel style Self-Ref mirror structures for genomic information processing.

                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 Self-Rep offline structures of self as in the Rogers (1967) RFT 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.

                It will be interesting to compare the bacteria-phage arms race in prokaryotes with the one in the AIS antibody production outlined above. I have reached out to John Mattick and Silvia Sanchez Ramon on these issues.

#2.  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.

# 3 A common Self-Rep mirror RFT machinery for self-other recognition in the AIS 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 RFT to guide the discussions.  Figure 1 in Markose (2021)<https://urldefense.com/v3/__https://www.mdpi.com/1099-4300/23/4/405__;!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSq8Rs91D0$  > 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 offline Self-Rep *(g,g) operator ) known to be controlled by interferon gamma as in Jonathan Kipnis Group 2016<https://urldefense.com/v3/__https://www.nature.com/articles/nature18626__;!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqF1KRYvk$  > experiment on rats, could lead to loss of immune capabilities as well as their sociability.  Note, the Markose RFT machinery for the self-other nexus is a different explanation to the evo-devo one given by Kipnis et.al.

#4 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 Self-Ref and Self-Rep 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 Self-Ref and Self-Rep, let alone that the Gödel Sentence is like a hash 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.

#Blog on University of Essex Website: How we became smart - a journey of discovery through the world of game theory and genomic intelligence https://urldefense.com/v3/__https://www.essex.ac.uk/blog/posts/2021/10/26/how-we-became-smart__;!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqVgSsoLo$  

#Markose, S.M, 2022, Complexification of eukaryote phenotype: Adaptive immuno-cognitive systems as unique Gödelian blockchain distributed ledger, Biosystems, ISSN: 0303-2647, Vol: 220, https://urldefense.com/v3/__https://doi.org/10.1016/j.biosystems.2022.104718__;!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqPn2Rp5k$  

#Markose, S.M, 2021, "Genomic Intelligence as Über Bio-Cybersecurity: The Gödel Sentence in Immuno-Cognitive Systems"<https://urldefense.com/v3/__https://doi.org/10.3390/e23040405__;!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqV3O-kDY$  >, Entropy. 23(4), 405; ttps://doi.org/10.3390/e23040405

Markose, S.M, 2017, Complex type 4 structure changing dynamics of digital agents: Nash equilibria or a game with arms race in innovations. Journal of Dynamics & Games, 2017, 4 (3) : 255-284. doi: 10.3934/jdg.2017015<https://urldefense.com/v3/__http://dx.doi.org/10.3934/jdg.2017015__;!!D9dNQwwGXtA!RRmmHQCs_Cav9UXiPz27dODNI-Kke3ky-PhpVLOvgOETwB-s3hTK7egkhJHf5AFKr0UuxLxzixSqC_UOvRc$  >

Professor Sheri Markose
Economics Department
University of Essex
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