Genomic Intelligence as Über Bio-Cybersecurity: The Gödel Sentence in Immuno-Cognitive Systems

Abstract

This paper gives formal foundations and evidence from gene science in the post Barbara McClintock era that the Gödel 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 Gödel, 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 1–1 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 Gödel sentence, resulting in the “smarts” 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.

Toward the Relational Formulation of Biological Thermodynamics

“…As biological systems realize internal computation [91,92], the codes underlying biological organization possess a capacity to grow up through the attainment of indefinite statements within them by meaning, which corresponds to the process of proving the incompleteness the-orem. This idea relates to my earlier paper [42], and it was developed in consequent publications [43,44,111].…”

Innovation and information: Smooth and ongoing change, or turbulence and cognitive over-stress? On the complex deep structure of innovation

“…This is, in fact, undecidability and non-computability of novel constellations, which are not at all in the knowledge and experience fund of the agent yet. It fuses developments in mathematical undecidability theory, paleobiology, genome biology, virology / immunology / epidemiology (in medicine and in computer science) and refers to capacities that early eukaryotes had developed billions of years ago: developing novel paths towards "self-other" comparisons (be it "good" innovations or "bad" infections/ malware/virus invasions, both types completely unknown to the agent) and radical agent proteanism (e.g., Casti, 1994;Markose, 2004Markose, , 2021. And again, this suggests that the issues of information, cognition and innovation are, first, closely interconnected, and, second, all but settled.…”

Autopoiesis and Eigenform

“…We may regard ~B(gg) as located and coded, so that it points to what in the system must be eliminated by the system's "immune system". The idea of Goedelian sentences as fundamental to formal biological immune systems is due to Markose [13].…”

“…We have a fully reflexive domain to work with via the partial recursive functions. Markose [13] has pointed out that this gives powerful access of recursive function theory to biological and, indeed, autopoietic structures. The Kleene fixed point theorem is the right level for the recursions of computer science and also for biology, where the ongoing functions are open-ended and partial recursive.…”