{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T14:15:15Z","timestamp":1767968115116,"version":"3.49.0"},"reference-count":126,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2021,3,29]],"date-time":"2021-03-29T00:00:00Z","timestamp":1616976000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>This paper gives formal foundations and evidence from gene science in the post Barbara McClintock era that the G\u00f6del Sentence, far from being an esoteric construction in mathematical logic, is ubiquitous in genomic intelligence that evolved with multi-cellular life. Conditions uniquely found in the Adaptive Immune System (AIS) and Mirror Neuron System (MNS), termed the genomic immuno-cognitive system, coincide with three building blocks in computation theory of G\u00f6del, Turing and Post (G-T-P). (i) Biotic elements have unique digital identifiers with gene codes executing 3D self-assembly for morphology and regulation of the organism using the recursive operation of Self-Ref (Self-Reference) with the other being a self-referential projection of self. (ii) A parallel offline simulation meta\/mirror environment in 1\u20131 relation to online machine executions of self-codes gives G-T-P Self-Rep (Self-Representation). (iii) This permits a digital biotic entity to self-report that it is under attack by a biotic malware or non-self antigen in the format of the G\u00f6del sentence, resulting in the \u201csmarts\u201d for contextual novelty production. The proposed unitary G-T-P recursive machinery in AIS and in MNS for social cognition yields a new explanation that the Interferon Gamma factor, known for friend-foe identification in AIS, is also integral to social behaviors. New G-T-P bio-informatics of AIS and novel anti-body production is given with interesting testable implications for COVID-19 pathology.<\/jats:p>","DOI":"10.3390\/e23040405","type":"journal-article","created":{"date-parts":[[2021,3,29]],"date-time":"2021-03-29T16:01:57Z","timestamp":1617033717000},"page":"405","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Genomic Intelligence as \u00dcber Bio-Cybersecurity: The G\u00f6del Sentence in Immuno-Cognitive Systems"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6181-0654","authenticated-orcid":false,"given":"Sheri M.","family":"Markose","sequence":"first","affiliation":[{"name":"Department of Economics, University of Essex, Essex C04 3SQ, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,3,29]]},"reference":[{"key":"ref_1","first-page":"444","article-title":"The digital code of DNA","volume":"421","author":"Hood","year":"2003","journal-title":"Nat. Cell Biol."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1016\/S0378-4371(97)00529-3","article-title":"Bacterial wisdom, G\u00f6del\u2019s theorem and creative genomic webs","volume":"248","year":"1998","journal-title":"Phys. A Stat. Mech. Appl."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1038\/482461a","article-title":"Turing centenary: Life\u2019s code script","volume":"482","author":"Brenner","year":"2012","journal-title":"Nature"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1119","DOI":"10.3762\/bjoc.13.111","article-title":"From chemical metabolism to life: The origin of the genetic coding process","volume":"13","author":"Danchin","year":"2017","journal-title":"Beilstein J. Org. Chem."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1111\/j.1574-6976.2008.00137.x","article-title":"Bacteria as computers making computers","volume":"33","author":"Danchin","year":"2008","journal-title":"FEMS Microbiol. Rev."},{"key":"ref_6","first-page":"424","article-title":"Life, logic and information","volume":"454","author":"Nurse","year":"2008","journal-title":"Nat. Cell Biol."},{"key":"ref_7","unstructured":"In dealing with the biotic implications of digital information storage of the genome, Ref [6] refers to the need to develop a framework that can catalogue and identify the cellular biochemistry which implements specific computational functions. The aim is to identify what Nurse [6] calls segments of \u201clogic modules\u201d that conduct operations within cells and provide a mapping between the cellular chemistry toolkit with the logic tool-kit."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"557","DOI":"10.1016\/S0092-8674(02)00619-0","article-title":"Ribosome structure and the mechanism of translation","volume":"108","author":"Ramakrishnan","year":"2002","journal-title":"Cell"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"497","DOI":"10.1098\/rsfs.2011.0118","article-title":"A mechanical Turing machine: Blueprint for a biomolecular computer","volume":"2","author":"Shapiro","year":"2012","journal-title":"Interface Focus"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"6050","DOI":"10.1039\/C5SC02317C","article-title":"Molecular computing: Paths to chemical Turing machines","volume":"6","author":"Varghese","year":"2015","journal-title":"Chem. Sci."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1101\/sqb.2009.74.027","article-title":"Evolving views of DNA replication (in)fidelity","volume":"74","author":"Kunkel","year":"2009","journal-title":"Cold Spring Harb. Symp. Quant. Biol."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1146\/annurev-genet-112414-054722","article-title":"Eukaryotic Mismatch Repair in Relation to DNA Replication","volume":"49","author":"Kunkel","year":"2015","journal-title":"Ann. Rev. Genetic."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1016\/j.plrev.2013.07.001","article-title":"How life changes itself: The Read\u2013Write (RW) genome","volume":"10","author":"Shapiro","year":"2013","journal-title":"Phys. Life Rev."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"792","DOI":"10.1126\/science.15739260","article-title":"The significance of responses of the genome to challenge","volume":"226","author":"McClintock","year":"1984","journal-title":"Science"},{"key":"ref_15","unstructured":"In this paper, the terms computation and recursive function will be used interchangeably as in the respective titles of the two well-known textbooks [16,17], which cover identical content of operations on encoded information based on a finite alphabet. Computation or recursive functions include all elementary arithmetic, logical operations and also functions obtained from substitution, iteration and recursion. In the latter, functions call on themselves and use inputs that are outputs from previous computations."},{"key":"ref_16","unstructured":"Rogers, H. (1967). Theory of Recursive Functions and Effective Computability, McGraw-Hill."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Cutland, N.J. (1980). Computability: An Introduction to Recursive Function Theory, Cambridge University Press.","DOI":"10.1017\/CBO9781139171496"},{"key":"ref_18","unstructured":"McClintock [14] described the genome \u201cas a highly sensitive organ of the cell, monitoring genomic activities and correcting common errors, sensing the unusual and unexpected events, and responding to them, often by restructuring the genome\u201d."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1146\/annurev.genet.40.110405.090448","article-title":"DNA Transposons and the Evolution of Eukaryotic Genomes","volume":"41","author":"Feschotte","year":"2007","journal-title":"Annu. Rev. Genet."},{"key":"ref_20","unstructured":"Dyson, F. (1985). Origins of Life, Cambridge University Press."},{"key":"ref_21","unstructured":"Dyson, G. (2019, February 05). Review on \u201cIs Life Analog or Digital\u201d, Edge. Available online: https:\/\/www.edge.org\/conversation\/freeman_dyson-is-life-analog-or-digital."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1016\/j.virusres.2006.01.010","article-title":"The origin of viruses and their possible roles in major evolutionary transitions","volume":"117","author":"Forterre","year":"2006","journal-title":"Virus Res."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"870","DOI":"10.1126\/science.312.5775.870","article-title":"Did DNA Come From Viruses?","volume":"312","author":"Zimmer","year":"2006","journal-title":"Science"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"758","DOI":"10.1126\/science.338.6108.758","article-title":"Transposable elements, epigenetics and genome evolution","volume":"338","author":"Fedoroff","year":"2012","journal-title":"Science"},{"key":"ref_25","unstructured":"\u201cIt is becoming increasingly difficult to escape the conclusion that eukaryotic genome evolution is driven from within (italics added) by the stronger winds (with perhaps occasional gale force gusts) of transposon activity. The ability to evoke rapid genome restructuring is at the heart of eukaryotic evolvability\u2014the capacity of organisms with larger and larger genomes to maintain evolutionary flexibility\u201d Fedoroff [24]."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Shapiro, J.A. (2017). Living Organisms Author Their Read-Write Genomes in Evolution. Biology, 6.","DOI":"10.3390\/biology6040042"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1787","DOI":"10.1126\/science.1155472","article-title":"The Eukaryotic Genome as an RNA Machine","volume":"319","author":"Amaral","year":"2008","journal-title":"Science"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1016\/j.tins.2008.02.003","article-title":"RNA editing, DNA recoding and the evolution of human cognition","volume":"31","author":"Mattick","year":"2008","journal-title":"Trends Neurosci."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Chang, W.-L., and Vasilakos, A. (2014). Molecular Computing: Towards a Novel Computing Architecture for Complex Problem Solving, Springer.","DOI":"10.1007\/978-3-319-05122-2"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"198","DOI":"10.1109\/TNB.2014.2349111","article-title":"Security and Privacy in Molecular Communication and Networking: Opportunities and Challenges","volume":"13","author":"Loscri","year":"2014","journal-title":"IEEE Trans. NanoBioscience"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"635","DOI":"10.1016\/j.nbt.2014.12.009","article-title":"Designer cell signal processing circuits for biotechnology","volume":"32","author":"Bradley","year":"2015","journal-title":"New Biotechnol."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1016\/j.ydbio.2007.08.009","article-title":"The regulatory genome and the computer","volume":"310","author":"Istrail","year":"2007","journal-title":"Dev. Biol."},{"key":"ref_33","unstructured":"This includes Neil Dalchau, Sara-Jane Dunn and others at Biological Computation research group at Microsoft Research Cambridge."},{"key":"ref_34","unstructured":"\u201cBiological research is in crisis, we are drowning in a sea of data and thirsting for some theoretical framework with which to understand it\u201d, Brenner [3]."},{"key":"ref_35","unstructured":"G\u00f6del, K. (1931). On Formally Undecidable Propositions of Principia Mathematica and Related Systems, Croom Helm. (Translation in English in G\u00f6del\u2019s Theorem in Focus; Shanker, S.G., Ed., 1988)."},{"key":"ref_36","first-page":"230","article-title":"On computable numbers, with an application to the Entscheidungsproblem","volume":"42","author":"Turing","year":"1963","journal-title":"Proc. Lond. Math. Soc."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"284","DOI":"10.1090\/S0002-9904-1944-08111-1","article-title":"Recursively Enumerable Sets of Positive Integers and Their Decision Problems","volume":"50","author":"Post","year":"1944","journal-title":"Bull. Am. Math. Soc."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Smullyan, R. (1961). Theory of Formal Systems, Princeton University Press.","DOI":"10.1515\/9781400882007"},{"key":"ref_39","unstructured":"Markose, S.M. (2019). The Digital Origins of Intelligence: How We Became Smart and Protean. Keynote Talk at 2019 Bio-Inspired ICT (BICT) Conference, Carnegie Mellon University. Available online: http:\/\/bionetics2019.eai-conferences.org\/keynotes\/."},{"key":"ref_40","unstructured":"Hofstader, D. (1999). G\u00f6del, Escher, Bach: An Eternal Golden Braid, Basic Books Inc."},{"key":"ref_41","unstructured":"The monikers Self-Ref and Self-Rep have been taken from [40]. The acronym Diag (.) for the Self-Ref recursive function, as will be seen, denotes 2-place diagonal matrix entries."},{"key":"ref_42","unstructured":"Marion, J.-Y. (2019, December 09). Viruses in Turing\u2019s Garden. Available online: https:\/\/hal.inria.fr\/hal-00762918\/."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"3319","DOI":"10.1098\/rsta.2011.0332","article-title":"From Turing machines to computer viruses","volume":"370","author":"Marion","year":"2012","journal-title":"Philos. Trans. R. Soc. A Math. Phys. Eng. Sci."},{"key":"ref_44","unstructured":"Elliot, E., and Douglas Kiel, L. (2020). Novelty production and evolvability in digital genomic agents: Logical foundations and policy design implications of complex adaptive systems. Complex Systems in the Social and Behavioral Sciences: Theory, Method and Application, Michigan University Press."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"255","DOI":"10.3934\/jdg.2017015","article-title":"Complex Type 4 Structure Changing Dynamics of Digital Agents: Nash Equilibria of a Game with Arms Race in Innovations","volume":"4","author":"Markose","year":"2017","journal-title":"J Dynam. Game."},{"key":"ref_46","unstructured":"Gregoire, N., and Vasileios, B. (2014). Logic Dynamics for Deductive Inference Its Stability and Neural Basis. Chaos, Information Processing and Paradoxical Games: The Legacy of John S Nicolis, World Scientific Publishing. Chapter 17."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"2608","DOI":"10.1152\/jn.1995.73.6.2608","article-title":"Motor Facilitation during Action Observation: A Magnetic Stimulation study","volume":"73","author":"Fadiga","year":"1995","journal-title":"J. Neurophysiol."},{"key":"ref_48","first-page":"557","article-title":"Action recognition in the premotor cortex","volume":"66","author":"Gallese","year":"2009","journal-title":"Brain"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1016\/0926-6410(95)00038-0","article-title":"Premotor cortex and the recognition of motor actions","volume":"3","author":"Rizzolatti","year":"1996","journal-title":"Cogn. Brain Res."},{"key":"ref_50","unstructured":"Ramachandran, V.S. (2021, March 29). Mirror Neurons and imitation learning as the driving force behind the great leap forward in human evolution. EDGE Con-versation. Available online: https:\/\/www.edge.org\/conversation\/mirror-neurons-and-imitation-learning-as-the-driving-force-behind-the-great-leap-forward-in-human-evolution."},{"key":"ref_51","unstructured":"Ramachandran [50] describes this as follows: \u201cIt\u2019s as if anytime you want to make a judgement about someone else\u2019s movements you have to run a VR (virtual reality) simulation of the corresponding movements in your own brain and without mirror neurons you cannot do this\u201d."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"1277","DOI":"10.1016\/S0893-6080(98)00047-1","article-title":"Modelling parietal-premotor interactions in primate control of grasping","volume":"11","author":"Fagg","year":"1998","journal-title":"Neural Netw."},{"key":"ref_53","unstructured":"Marion [43] makes a distinction between a benign viral software which simply prints\/copies itself with the host code embedded in it without changing it. The malign viral software, in contrast, as will be shown, changes the host code to produce the opposite of what the original code produced."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"134","DOI":"10.1016\/j.plrev.2018.12.003","article-title":"Self-referential basis of undecidable dynamics: From the Liar paradox and the halting problem to the edge of chaos","volume":"31","author":"Prokopenko","year":"2019","journal-title":"Phys. Life Rev."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"1795","DOI":"10.1016\/j.neuroimage.2011.08.010","article-title":"Electrophysiological signatures of intentional social coordination in the 10\u201312Hz range","volume":"59","author":"Naeem","year":"2012","journal-title":"NeuroImage"},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"8190","DOI":"10.1073\/pnas.0611453104","article-title":"The phi Complex as the Neuromarker of Human Social Coordination","volume":"104","author":"Tognoli","year":"2007","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_57","unstructured":"Janeway, C.A., Travers, P., Walport, M., and Shlomchik, M.J. (2005). Immunobiology, Garland Science. [6th ed.]."},{"key":"ref_58","unstructured":"Analog defence strategies rely chiefly on protective barriers, toxic molecules, raising temperature, and phagocytic cells that ingest and destroy invading microorganisms (microbes) and larger parasites (such as worms)."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"571","DOI":"10.1146\/annurev.immunol.23.021704.115601","article-title":"A central role for central tolerance","volume":"24","author":"Kyewski","year":"2006","journal-title":"Annu. Rev. Immunol."},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1186\/s13059-016-1079-9","article-title":"Extensive RNA editing and splicing increase immune self-representation diversity in medullary thymic epithelial cells","volume":"17","author":"Guyon","year":"2016","journal-title":"Genome Biol."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"e181","DOI":"10.1371\/journal.pbio.0030181","article-title":"RAG1 core and V(D)J recombination signal sequences were derived from Transib transposons","volume":"3","author":"Kapitonov","year":"2005","journal-title":"PLoS Biol."},{"key":"ref_62","doi-asserted-by":"crossref","unstructured":"Greenen, V. (2021). The thymus and the science of self. Semin. Immunopathol., 1\u201310.","DOI":"10.1007\/s00281-020-00831-y"},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"425","DOI":"10.1038\/nature18626","article-title":"Unexpected role of interferon-\u03b3 in regulating neuronal connectivity and social behaviour","volume":"535","author":"Filiano","year":"2016","journal-title":"Nature"},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"490","DOI":"10.1016\/0167-5699(92)90024-2","article-title":"The cognitive paradigm and the immunological homunculus","volume":"13","author":"Cohen","year":"1992","journal-title":"Immunol. Today"},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"582","DOI":"10.3389\/fnins.2017.00582","article-title":"Autoimmunity as a Driving Force of Cognitive Evolution","volume":"11","author":"Nataf","year":"2017","journal-title":"Front. Neurosci."},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"766","DOI":"10.1126\/science.aag2638","article-title":"Multifaceted interactions between adaptive immunity and the central nervous system","volume":"353","author":"Kipnis","year":"2016","journal-title":"Science"},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"663","DOI":"10.1038\/nri3280","article-title":"Pro-cognitive properties of T cells","volume":"12","author":"Kipnis","year":"2012","journal-title":"Nat. Rev. Immunol."},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1016\/j.yhbeh.2016.09.008","article-title":"Why are behavioural and immune traits linked?","volume":"88","author":"Lopes","year":"2017","journal-title":"Horm. Behav."},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"440","DOI":"10.1016\/j.neuroimage.2005.12.002","article-title":"Self-referential processing in our brain\u2014A meta-analysis of imaging studies on the self","volume":"31","author":"Northoff","year":"2006","journal-title":"NeuroImage"},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.pbiomolbio.2017.11.005","article-title":"Biological information systems: Evolution as cognition-based information management","volume":"134","author":"Miller","year":"2018","journal-title":"Prog. Biophys. Mol. Biol."},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"540676","DOI":"10.3389\/fpsyt.2020.540676","article-title":"Self and the Brain. The Immune Metaphor","volume":"11","author":"Faure","year":"2020","journal-title":"Front Psychiatry."},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"916","DOI":"10.3389\/fnins.2019.00916","article-title":"Role of the Immune System in the Development of the Central Nervous System","volume":"13","author":"Morimoto","year":"2019","journal-title":"Front. Neurosci."},{"key":"ref_73","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1016\/j.neuron.2009.09.044","article-title":"MHC Class I: An unexpected role in neuronal plasticity","volume":"64","author":"Shatz","year":"2009","journal-title":"Neuron"},{"key":"ref_74","doi-asserted-by":"crossref","first-page":"26199","DOI":"10.1038\/srep26199","article-title":"Major Histocompatibility Complex class I proteins are critical for maintaining neuronal structural complexity in the aging brain","volume":"6","author":"Lazarczyk","year":"2016","journal-title":"Sci. Rep."},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"505","DOI":"10.1101\/lm.031351.113","article-title":"MHC class I immune proteins are critical for hippocampus-dependent memory and gate NMDAR-dependent hippocampal long-term depression","volume":"20","author":"Nelson","year":"2013","journal-title":"Learn. Mem."},{"key":"ref_76","doi-asserted-by":"crossref","unstructured":"Carignano, A., and Dachau, N. (2018). A theory for how the antigen presentation profile influences the timing of T-cell detection. biRxiv.","DOI":"10.1101\/480301"},{"key":"ref_77","unstructured":"I am grateful to an anonymous referee for pointing this out. Papers (see [78,79]) that use the G\u00f6del formalism, which predates recursive function theory, generates the G\u00f6del [35] sentence that typically takes the form: PA \u0370A \u2194 \u00acProv(A). Here, A effectively says of itself that it is not provable (\u00acProv(A)), with this undecidable proposition being a theorem (\u0370) in the formal system of Peano Arithmetic (PA)."},{"key":"ref_78","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1016\/S0004-3702(98)00052-6","article-title":"Why G\u00f6del\u2019s theorem cannot refute computationalism","volume":"104","author":"Laforte","year":"1998","journal-title":"Artif. Intell."},{"key":"ref_79","unstructured":"Raatikainen, P. (2015). G\u00f6del\u2019s Incompleteness Theorems. Stanf. Encycl. Philos."},{"key":"ref_80","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/icb.1972.1","article-title":"A reassessment of the forbidden clone hypothesis of autoimmune disease","volume":"50","author":"Burnet","year":"1972","journal-title":"Aust. J. Exp. Biol. Med Sci."},{"key":"ref_81","doi-asserted-by":"crossref","first-page":"1032","DOI":"10.1038\/ni723","article-title":"Promiscuous gene expression in medullary thymic epithelial cells mirrors the peripheral self","volume":"2","author":"Derbinski","year":"2001","journal-title":"Nat. Immunol."},{"key":"ref_82","doi-asserted-by":"crossref","first-page":"1234","DOI":"10.1016\/j.devcel.2012.03.012","article-title":"Transcription Factor Binding to a DNA Zip Code Controls Interchromosomal Clustering at the Nuclear Periphery","volume":"22","author":"Brickner","year":"2012","journal-title":"Dev. Cell"},{"key":"ref_83","first-page":"517","article-title":"Protocadherins mediate dendritic self-avoidance in the mammalian nervous system","volume":"488","author":"Lefebvre","year":"2012","journal-title":"Nat. Cell Biol."},{"key":"ref_84","doi-asserted-by":"crossref","first-page":"779","DOI":"10.1016\/S0092-8674(00)80789-8","article-title":"A striking organization of a large family of human neural cadherin-like cell adhesion genes","volume":"97","author":"Wu","year":"1999","journal-title":"Cell"},{"key":"ref_85","unstructured":"Rose, G. (2012). How to Make Anything: The Digital Fabrication Revolution. Fourth Industrial Revolution, the Davos Reader, Available online: https:\/\/www.foreignaffairs.com\/system\/files\/c0040.pdf."},{"key":"ref_86","unstructured":"Hardy, N., and Westoff, E. (2004). Folding and Self-assembly of Biological Macromolecules. World Sci."},{"key":"ref_87","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1038\/nrg2703","article-title":"Origin and evolution of the adaptive immune system: Genetic events and selective pressures","volume":"11","author":"Flajnik","year":"2009","journal-title":"Nat. Rev. Genet."},{"key":"ref_88","doi-asserted-by":"crossref","first-page":"505","DOI":"10.1111\/brv.12355","article-title":"An evolutionary perspective on the systems of adaptive immunity","volume":"93","author":"Bonhoeffer","year":"2018","journal-title":"Biol. Rev."},{"key":"ref_89","doi-asserted-by":"crossref","first-page":"512","DOI":"10.1016\/j.tics.2011.09.003","article-title":"What is so special about embodied simulation?","volume":"15","author":"Gallese","year":"2011","journal-title":"Trends Cogn. Sci."},{"key":"ref_90","doi-asserted-by":"crossref","first-page":"534","DOI":"10.1073\/pnas.0811843106","article-title":"The specificity of T cell regulation that enables self-nonself discrimination in the periphery","volume":"106","author":"Wu","year":"2008","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_91","doi-asserted-by":"crossref","first-page":"eabd4585","DOI":"10.1126\/science.abd4585","article-title":"Auto-antibodies against type I IFNs in patients with life-threatening COVID-19","volume":"370","author":"Brouwer","year":"2020","journal-title":"Science"},{"key":"ref_92","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1016\/j.cell.2020.08.025","article-title":"Loss of Bcl-6-expressing T follicular helper cells and germinal centers in COVID-19","volume":"183","author":"Kaneko","year":"2020","journal-title":"Cell"},{"key":"ref_93","doi-asserted-by":"crossref","first-page":"eabd4570","DOI":"10.1126\/science.abd4570","article-title":"Inborn errors of type I IFN immunity in patients with life-threatening COVID-19","volume":"370","author":"Zhang","year":"2020","journal-title":"Science"},{"key":"ref_94","unstructured":"The first limitative result on functions computable by T.Ms is that at most there can only be a countable number of these with the cardinality of \u2135 being denoted by \u21350, while from Cantor we know that the set of all number theoretic functions have cardinality of 2\u21350. Hence, not all number theoretic functions are computable (see [17])."},{"key":"ref_95","unstructured":"Ref [10] states \u201cThe resemblance of the Turing machine to naturally occurring molecular machineries that are capable of processing information, such as the ribosome and processive DNA (and RNA) polymerase enzymes, is striking and has recently motivated researchers to start programs on the development of biomolecular computers\u201d."},{"key":"ref_96","unstructured":"Since at least the 1990s, there has been an intense study of the biochemistry of life processes that are deemed to be driven by a self-assembly of biotic macromolecules with mechanistic features [86,97]. The shift in focus from the autonomous nature of this self-assembly to a program for self-assembly in the key transcription and translation processes [85], such that a gene code is viewed as a program that can both build the machine that can be instructed by the same program to read and run\/execute it is also present in [5]."},{"key":"ref_97","doi-asserted-by":"crossref","unstructured":"Steven, A., Baumeister, W., Johnson, L.N., and Perham, R.N. (2016). Molecular Biology of Assemblies and Machines, Garland Science.","DOI":"10.1201\/9780429258763"},{"key":"ref_98","first-page":"1","article-title":"When long non-coding becomes protein coding","volume":"40","author":"Hartford","year":"2000","journal-title":"Mol. Cell Biol."},{"key":"ref_99","unstructured":"Note, analog measurements of state variables, such as chemical concentration, temperature, etc., have to be converted into digital code in order for this to be processed by a digital agent."},{"key":"ref_100","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1016\/j.plrev.2014.04.005","article-title":"Toward a computational framework for cognitive biology: Unifying approaches from cognitive neuroscience and compara-tive Cognition","volume":"11","author":"Fitch","year":"2014","journal-title":"Phys. Life Rev."},{"key":"ref_101","unstructured":"Markose [44], contrasts Fitch [100] Bayesian model of cognition and intelligence with the G-T-P one. The main drawback of the Bayesian model, as with extant decision models, is that they are incapable of a constructive procedure for novelty production. Bayesian inference is statistical and is a far cry from inference by embodied offline simulation in the G-T-P cognitive system."},{"key":"ref_102","unstructured":"John, C., Wooley, J.C., Herbert, S., and Lin, H.S. (2005). Catalyzing Inquiry at the Interface of Computing and Biology, The National Academies Press."},{"key":"ref_103","unstructured":"In standard game theory, the strategies are constrained to lie in a fixed set, such as G or A, and the system is closed and complete with no possibility for exiting from a fixed repertoire and produce novelty (see [44,45]). Some of the G-T-P formalism used here for novelty production in digital systems was first mentioned in Markose [104] and given a detailed derivation in the context of generating novelty production as a Nash equilibrium of a game in [45]."},{"key":"ref_104","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1016\/j.physa.2004.06.085","article-title":"Novelty in complex adaptive systems (CAS) dynamics: A computational theory of actor innovation","volume":"344","author":"Markose","year":"2004","journal-title":"Phys. A Stat. Mech. its Appl."},{"key":"ref_105","unstructured":"Note that a machine listable set or recursively enumerable set Wx"},{"key":"ref_106","unstructured":"Note when focusing exclusively on non-self antigens, a subscript p is used in fp\u00ac!."},{"key":"ref_107","unstructured":"It is well known that, by what is called the SMN Theorem or the Parameterization Theorem [16,17]), new g.ns for recursive operations on extant g.ns can be mechanically generated."},{"key":"ref_108","unstructured":"However, it is well known that only V(D)J motifs that the mTEC selection process can deal with as those self-represented in the Thymic MHC viz. g\u00a0\u03f5 G*, G* \u2282 G as given in Equation (7). Hence, at the negative selection process TCRs, especially, for example, when there is deficiency of the autoimmune regulator AIRE, restricted gene codes do not get \u201cSelf-Repped\u201d in the m-TECs for the training of the T-cell receptors [60]. So, TCRs with motifs \u03c3(f\u25e6g, g) for g \u2209 G* in (7) can cause auto-immune disease."},{"key":"ref_109","unstructured":"Michael Lotz, in his Bio-Inspired ICT (BICT) 2019 Keynote, apocryphally called \u201cKnow yourself, know the enemy\u201d, stated that, while almost 99.9% of genes are the same for humans, only 6% of T-cell repertoires of different humans are the same. Hence, while the V(D)J realizations of some can combat new pathogens because they succeeded in cloning the code for this in the T-cells, others may not due to the random generation of codes in T-cell receptors and hence, without the anticipatory capacity to identify the novel non-self antigen when it strikes a tissue online, they succumb to them."},{"key":"ref_110","unstructured":"Rogers Fixed point Theorem [16] (Section 11.2) states that any total computable function, fp\u00ac!, for the case in question, has as its fixed point an index given by an integer v such that \u03d5fp\u00ac!(v)(s) \u2245 \u03d5v(s), viz. either both sides are defined and are equal or else both sides are undefined. This index for the fixed point for a total computable function f can be obtained constructively. The first part of the proof is already satisfied with the index function \u03c3(.) in the Self-Rep Theorem in (5) for the program for the partial computable function Diag(gn) = \u03d5gn(gn). The next step is to assign the index gn\u00ac to fp\u00ac!Diag(gn) which leads to the function \u03d5\u03d5gn\u00ac(gn) with a TCR motif of \u03c3(gn\u00ac, gn) as in Equations (10) and (11). The final step is to substitute gn\u00ac into fp\u00ac! Diag(gn) to get fp\u00ac! Diag(gn\u00ac), which is the function \u03d5gn\u00ac(gn\u00ac). Then, assign v as the index for \u03d5gn\u00ac\u00a0(gn\u00ac) = Diag(gn\u00ac) = \u03c3(gn\u00ac, gn), which yields \u03d5fp\u00ac!(v)(s)\n        \u2245 \u03d5v(s)."},{"key":"ref_111","unstructured":"On updating Equation (11) with the Liar\/Malware strategy gn\u00ac in the place holder for the other, and assuming v = \u03d5gn\u00ac(gn\u00ac) = Diag(gn\u00ac) = \u03c3(gn\u00ac, gn) is a halting computation then we have a contradiction: \u03d5\u03d5gn\u00ac(gn\u00ac)(s) = \u03d5\u03c3(gn\u00ac,gn\u00ac)(s) = \u03d5fp\u00ac!Diag(gn\u00ac)(s) = \u00ac\u03d5\u03d5gn\u00ac(gn\u00ac)(s). The last two terms follow from Equation (11) when gn\u00ac is substituted for gn in \u03d5fp\u00ac!Diag(gn\u00ac)(s)= \u00ac\u00a0\u03d5\u03d5gn\u00ac(gn\u00ac)(s)."},{"key":"ref_112","unstructured":"It is beyond the scope of this paper to give the detailed recursive function based bioinformatics behind the somatic hyper mutations [113] on B-cells that follow from this point in the host adaptive immune system. The same is the case on how retrotransposon activity can change the germline."},{"key":"ref_113","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1146\/annurev.biochem.76.061705.090740","article-title":"Molecular mechanisms of antibody somatic hypermutation","volume":"76","author":"Noia","year":"2007","journal-title":"Annu. Rev. Biochem."},{"key":"ref_114","unstructured":"There is evidence that it is Type 1 Interferon gamma factor that is needed for this (see [91,93])."},{"key":"ref_115","doi-asserted-by":"crossref","first-page":"643","DOI":"10.1126\/science.abc5902","article-title":"Potent neutralizing antibodies from COVID-19 patients define multiple targets of vulnerability","volume":"369","author":"Bastard","year":"2020","journal-title":"Science"},{"key":"ref_116","doi-asserted-by":"crossref","unstructured":"Egel, R., Lankenau, D.-H., and Mulkidjanian, A.Y. (2011). Two RNA Worlds: Toward the Origin of Replication, Genes, Recombination, and Repair. Origins of Life: The Primal Self-Organization, Springer International Publishing. [1st ed.].","DOI":"10.1007\/978-3-642-21625-1_11"},{"key":"ref_117","doi-asserted-by":"crossref","first-page":"20120869","DOI":"10.1098\/rsif.2012.0869","article-title":"The algorithmic origins of life","volume":"10","author":"Walker","year":"2013","journal-title":"J. R. Soc. Interface"},{"key":"ref_118","unstructured":"See [78] for an analysis that that the G\u00f6del sentence does not imply the anti-computationalism sometimes ascribed to it. My position is that few have recognized that the mirror systems of the AIS and the MNS and the prodigious capacity for novelty production is the consequence of a code based genomic intelligence that has G-T-P recursive machinery at its core."},{"key":"ref_119","unstructured":"Dawkins, R. (1989). The Extended Phenotype Oxford, Oxford University Press."},{"key":"ref_120","unstructured":"Byrne, R., and Whiten, A. (1988). Machiavellian Intelligence: Social Expertise and the Evolution of Intellect in Monkeys, Apes, and Humans, Oxford University Press."},{"key":"ref_121","doi-asserted-by":"crossref","first-page":"F159","DOI":"10.1111\/j.1468-0297.2005.01000.x","article-title":"Computability and Evolutionary Complexity: Markets as Complex Adaptive Systems (CAS)","volume":"115","author":"Markose","year":"2005","journal-title":"Econ. J."},{"key":"ref_122","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1017\/S0266267100002893","article-title":"Modelling Rational Players: Part I","volume":"3","author":"Binmore","year":"1987","journal-title":"Econ. Philos."},{"key":"ref_123","unstructured":"Ref [124] succinctly state this: \u201cin a Nash equilibrium nobody is surprised about what others actually do, or what others believe, because strategies and beliefs are synchronized, presumably due to introspection, communication or learning\u201d."},{"key":"ref_124","doi-asserted-by":"crossref","first-page":"424","DOI":"10.1016\/j.geb.2005.03.007","article-title":"Self-referential thinking and equilibrium as states of mind in games: FMRI evidence","volume":"52","author":"Bhatt","year":"2005","journal-title":"Games Econ. Behav."},{"key":"ref_125","doi-asserted-by":"crossref","first-page":"1600","DOI":"10.1016\/j.febslet.2011.05.001","article-title":"The central role of RNA in human development and cognition","volume":"585","author":"Mattick","year":"2011","journal-title":"FEBS Lett."},{"key":"ref_126","doi-asserted-by":"crossref","first-page":"20180429","DOI":"10.1098\/rsif.2018.0429","article-title":"Origin of biomolecular games: Deception and molecular evolution","volume":"15","author":"Massey","year":"2018","journal-title":"J. R. Soc. Interface"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/23\/4\/405\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T13:53:20Z","timestamp":1760363600000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/23\/4\/405"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,3,29]]},"references-count":126,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2021,4]]}},"alternative-id":["e23040405"],"URL":"https:\/\/doi.org\/10.3390\/e23040405","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,3,29]]}}}