Self-referential basis of undecidable dynamics: From the Liar paradox and the halting problem to the edge of chaos

Physical limits of natural computation as the biological constraints of morphogenesis, evolution, and consciousness: On the 100th anniversary of Efim Liberman (1925-2011)

Efim Liberman (1925-2011) introduced in 1972 the idea of natural computation realized internally by living systems. He considered the physical principles employed by living systems as essential constraints that limit the computational process occurring in the course of adaptation, morphogenesis, and neural activity. The most general limits determined by the physical fundamental constants are universal for all nature. However, the more specific constraints are intrinsic to each biological system and can be overcome in the course of the evolutionary process. We discuss the roles of biological macromolecules, particularly the cytoskeleton, in shaping the actualization patterns formed in the internal measurement process occurring in living systems. Cytoskeletal rearrangements determine cellular, morphogenetic, and perceptive transformations in living systems and participate in the combinatorial genetic events that lead to evolutionary transformations. The operation of neurons is based on the transmission of signals via the cytoskeleton, where the digital output is generated that can be decoded through a reflexive action of the perceiving agent. It is concluded that the principles of natural computation formulated by Liberman represent the most fundamental feature of living beings and form the basis for the general theory of biological systems, with essential consequences for understanding metabolic closure, morphogenesis, evolution, and consciousness.

Information structure of heterogeneous criticality in a fish school

Integrated information theory (IIT) assesses the degree of consciousness in living organisms from an information-theoretic perspective. This theory can be generalised to other systems, including those exhibiting criticality. In this study, we applied IIT to the collective behaviour of Plecoglossus altivelis and observed that the group integrity (Φ) was maximised at the critical state. Multiple levels of criticality were identified within the group, existing as distinct subgroups. Moreover, these fragmented critical subgroups coexisted alongside the overall criticality of the group. The distribution of high-criticality subgroups was heterogeneous across both time and space. Notably, core fish in the high-criticality subgroups were less affected by internal and external stimuli compared to those in low-criticality subgroups. These findings are consistent with previous interpretations of critical phenomena and offer a new perspective on the dynamics of an empirical critical state.

Climate warming enhances microbial network complexity by increasing bacterial diversity and fungal interaction strength in litter decomposition

Microbial communities are important drivers of plant litter decomposition; however, the mechanisms of microbial co-occurrence networks and their network interaction dynamics in response to climate warming in wetlands remain unclear. Here, we conducted a 1.5-year warming experiment on the bacterial and fungal communities involved in litter decomposition in a typical wetland. The results showed that warming accelerated the decomposition of litter and had a greater effect on the diversity of bacteria than on that of fungi. Dominant bacterial communities, such as Bacteroidia, Alphaproteobacteria, and Actinobacteria, and dominant fungal communities, such as Leotiomycetes and Sordariomycetes, showed significant positive correlations with lignin and cellulose. Co-occurrence networks revealed that the average path length and betweenness centrality under warming conditions increased in the bacterial community but decreased in the fungal community. Both bacterial and fungal networks in the 2.0 °C warming treatment had the highest ratio of positive links (58.53 % and 98.14 %), indicating that moderate warming can promote the positive correlations and symbiotic relationships observed in the microbial community. This also suggests that small-world characteristics and weak-link advantages accelerate diffusion, and scale-free features facilitate propagation in microbial communities in response to climate warming. Logistic growth and Lotka-Volterra competition models revealed that climate warming enhances microbial network complexity mainly by increasing bacterial diversity and fungal interaction strength in litter decomposition. However, the symbiotic relationship decreased slightly under 4.0 °C warming, indicating that climate warming is a random attack rather than a targeted attack, and the microbial network has strong resistance to random attack, as shown by the highly robust dynamic performance of the microbial network in litter decomposition. Overall, the microbial community in litter decomposition responded to climate warming and shifted its network interactions, leading to further changes in emergent network topology and dynamics, thus accelerating litter decomposition in wetlands.

Complexification of eukaryote phenotype: Adaptive immuno-cognitive systems as unique Gödelian block chain distributed ledger

The digitization of inheritable information in the genome has been called the 'algorithmic take-over of biology'. The McClintock discovery that viral software based transposable elements that conduct cut-paste (transposon) and copy-paste (retrotransposon) operations are needed for genomic evolvability underscores the truism that only software can change software and also that viral hacking by internal and external bio-malware is the Achilles heel of genomic digital systems. There was a paradigm shift in genomic information processing with the Adaptive Immune System (AIS) 500 mya followed by the Mirror Neuron System (MNS), latterly mostly in primate brains, which reaches its apogee in human social cognition. The AIS and MNS involve distinctive Gödelian features of self-reference (Self-Ref) and offline virtual self-representation (Self-Rep) for complex self-other interaction with prodigious open-ended capacity for anticipative malware detection and novelty production within a unique blockchain distributed ledger (BCDL). The role of self-referential information processing, often considered to be central to the sentient self with origins in the immune system 'Thymic self', is shown to be part of the Gödel logic behind a generator-selector framework at a molecular level, which exerts stringent selection criteria to maintain genomic BCDL. The latter manifests 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. This is demonstrated with regard to somatic hypermutation with novel anti-body production in the face of external non-self antigen attacks.

Why Can the Brain (and Not a Computer) Make Sense of the Liar Paradox?

Ordinary computing machines prohibit self-reference because it leads to logical inconsistencies and undecidability. In contrast, the human mind can understand self-referential statements without necessitating physically impossible brain states. Why can the brain make sense of self-reference? Here, we address this question by defining the Strange Loop Model, which features causal feedback between two brain modules, and circumvents the paradoxes of self-reference and negation by unfolding the inconsistency in time. We also argue that the metastable dynamics of the brain inhibit and terminate unhalting inferences. Finally, we show that the representation of logical inconsistencies in the Strange Loop Model leads to causal incongruence between brain subsystems in Integrated Information Theory.

Complexity Economics in a Time of Crisis: Heterogeneous Agents, Interconnections, and Contagion

In this article, we consider a variety of different mechanisms through which crises such as COVID-19 can propagate from the micro-economic behaviour of individual agents through to an economy’s aggregate dynamics and subsequently spill over into the global economy. Our central theme is one of changes in the behaviour of heterogeneous agents, agents who differ in terms of some measure of size, wealth, connectivity, or behaviour, in different parts of an economy. These are illustrated through a variety of case studies, from individuals and households with budgetary constraints, to financial markets, to companies composed of thousands of small projects, to companies that implement single multi-billion dollar projects. In each case, we emphasise the role of data or theoretical models and place them in the context of measuring their inter-connectivity and emergent dynamics. Some of these are simple models that need to be ‘dressed’ in socio-economic data to be used for policy-making, and we give an example of how to do this with housing markets, while others are more similar to archaeological evidence; they provide hints about the bigger picture but have yet to be unified with other results. The result is only an outline of what is possible but it shows that we are drawing closer to an integrated set of concepts, principles, and models. In the final section, we emphasise the potential as well as the limitations and what the future of these methods hold for economics.

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

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.

Breaking of the Trade-Off Principle between Computational Universality and Efficiency by Asynchronous Updating

Although natural and bioinspired computing has developed significantly, the relationship between the computational universality and efficiency beyond the Turing machine has not been studied in detail. Here, we investigate how asynchronous updating can contribute to the universal and efficient computation in cellular automata (CA). First, we define the computational universality and efficiency in CA and show that there is a trade-off relation between the universality and efficiency in CA implemented in synchronous updating. Second, we introduce asynchronous updating in CA and show that asynchronous updating can break the trade-off found in synchronous updating. Our finding spells out the significance of asynchronous updating or the timing of computation in robust and efficient computation.

Introduction to the special issue on physics of mind

In recent years, both fields of physics and psychology have made important scientific advances. The emergence of new instruments gave rise to a data-driven neuroscience allowing us to learn about the state of the brain supporting known mental functions and conversely. In parallel, the appearance of new mathematics allowed the development of computational models describing fundamental brain functions and implementing them in technological applications. While emphasizing the methodology of physics, the special issue aims to bring together these trends in both the experimental and theoretical sciences in order to explain some of the most basic mental processes such as perception, cognition, emotion, consciousness, and learning. In this editorial, we define unsolved problems for brain and psychological sciences, discuss possible means toward their respective solutions, and outline some collaborative initiatives aiming toward these goals. The following problems are defined in gradual order of difficulty: what are the universal properties of human behavior across conditions and cultures? What have each culture learned over historical times and why should specific elements of knowledge be accumulated over cultural evolution? Can computational psychiatry help predict, understand, and cure mental disorders? What is the function of art and cultural artifacts such as music, fiction, or poetry for the cognitive system? How to explain the relation between first-person subjective experience and third-person objective physiological data? What neural mechanisms operate on which mental content at the highest levels of organization of the hierarchical brain? How do abstract ideas emerge from sensory-motor contingencies and what are the conditions for the birth of a new concept? Could symmetry play a role in psychogenesis and support the emergence of new hierarchical layers in cognition? How can we start addressing the question of meaning scientifically, and what does it entail for the physical sciences?

Strategic Information Processing from Behavioural Data in Iterated Games

Iterated games are an important framework of economic theory and application, at least since the original work of Axelrod’s computational tournaments of the early 80’s. Recent theoretical results have shown that games (the economic context) and game theory (the decision-making process) are both formally equivalent to computational logic gates. Here these results are extended to behavioural data obtained from an experiment in which rhesus monkeys sequentially played thousands of the “matching pennies” game, an empirical example similar to Axelrod’s tournaments in which algorithms played against one another. The results show that the monkeys exhibit a rich variety of behaviours, both between and within subjects when playing opponents of varying complexity. Despite earlier suggestions, there is no clear evidence that the win-stay, lose-switch strategy is used, however there is evidence of non-linear strategy-based interactions between the predictors of future choices. It is also shown that there is consistent evidence across protocols and across individuals that the monkeys extract non-markovian information, i.e., information from more than just the most recent state of the game. This work shows that the use of information theory in game theory can test important hypotheses that would otherwise be more difficult to extract using traditional statistical methods.