Making and Breaking Symmetries in Mind and Life

Dear Colleagues,

In this diverse collection of articles, we will explore the roles of symmetry in complex adaptive systems across scales, ranging from the emergent dynamics of biophysical mechanisms to the shaping of underlying adaptations through ontogenic and phylogenetic processes. Across these theoretical and empirical explorations, we hope to demonstrate that the study of symmetries may help illuminate fundamental properties of living and intelligent systems. Towards this end, we will consider a broad range of perspectives on (a)symmetries, exploring the extent to which intersections may be found between seemingly disparate phenomena.

One of the most powerful applications of symmetry-related concepts can be found in what physicists refer to as a “gauge theory.” [1] Whenever we observe a quantity that leaves a system's dynamics invariant with respect to some local frame of reference for that quantity, we can understand that quantity as a kind of abstract symmetry that is preserved by rectifying forces from a system-governing gauge field. [2] That is, deformations of gauge field geometries are understood as ‘fictitious’ forces; these forces restore the local symmetry of quantities that are dynamically invariant, by recording the system's interactions with the field of possible "gauges" for that quantity. Gauge theories provide a general way of modelling physical systems. Notable use-cases range from general relativity's handling of gravity as emerging from deformations of spacetime, to attractive and repulsive forces with respect to electromagnetic fields. These theories are so far-reaching that the word ‘fictitious’ may potentially be left out of descriptions of these emergent forces, as it may be the case that there are no other kinds. [3]

These ideas have also been applied to biological systems with the concept of “morphogenic fields.” [4] Here, we would like to make this connection to gauge theories explicit. The ability of biophysical systems to construct and preserve their phenotypic forms (as symmetries) across time via their action can be understood as governance by a gauge field that generates these attracting states.

This sort of gauge-theoretic perspective on biophysics has also been suggested to govern brains as goal-seeking systems guided by hierarchical information processing and prediction-error minimization, as described by the Free Energy Principle. [2, 5-7] That is, the attracting states of nervous systems are understood as entailing predictions, where the consistent realization of these predictions can be viewed as the preservation of goal-states as preserved quantities/symmetries. Along these lines, mental causation may be understood as a kind of ‘fictitious’ force over neural dynamics and their functional consequences with respect to perception and action. Intriguingly, symmetries may play yet another (qualitatively distinct) essential role in mental causation with respect to the phenomenon of symmetry breaking, where irreversible processes and arrows of time may be required for establishing the conditions for realizing cognitive work cycles. [8,9]

The roles of symmetries as perceptual invariants and inductive biases have also been identified in machine learning. [10] Could these physics-inspired algorithms help illuminate computational principles enabling the remarkable intelligence of biological systems? Could the particular ways in which informational symmetries function in brains help inspire advances in artificial intelligence? To what extent can the study of conservation laws of nature provide more powerful and interpretable approaches to machine learning? [11,12]

We believe these same principles can be understood as applying to morphogenesis as a kind of generalized predictive coding, [13] so providing a way of understanding the kinds of unusual causation observed in living organisms as complex adaptive systems. Perhaps we may even think of pre-theoretic intuitions relating to the nature of living phenomena, where the notion of “elan vital” and “life force” may potentially receive some (limited) support from abstract formalisms. [14,15] Indeed, we believe gauge theoretic forces can be understood as governing not just ontogeny, but also phylogeny as a free energy minimizing process (and where development is itself understood as a peculiar kind of evolution). [16–19]

In addition to describing how symmetry is central to fundamental processes by which complexity arises through evolution and development, this collection will also consider the roles of symmetry with respect to the functional properties of particular mechanisms:

• How is it that symmetry breaking occurs with respect to laterality in biological systems? [20–23]
• What is the functional significance of asymmetries in the organization of nervous systems? [24–34]
• Do some phenotypic asymmetries reflect less powerfully effective morphogenic fields and overall less fit organisms? [35–37]
• What are the roles of symmetry with respect to affective responses, such as those involved in mating behavior? What kinds of symmetry tend to be preferred by organisms, and why? Are such affective responses explainable in terms of innate sensitivities, or are preferences for symmetrical features discovered because of associations with general robustness (and potentially evolutionary fitness)?
• To what extent do symmetry preferences come “for free” via predictive coding, where symmetrical structures may be easier to predict/compress, and where efficient prediction-error minimization/compression constitutes a foundation for valence for living organisms? [38–40] Does greater ease of perceptual integration across hemispheres contribute to aesthetics for bilateral symmetries?
• To what extent do external symmetries help to induce similar forms internally, where maintenance of these internal symmetries may contribute to valenced phenomena due to their consequences for prediction-error minimization (i.e., the annihilation of free energy gradients)? [41,42]
• How do these symmetries play out in the context of the principle of detailed balance—an equilibrium steady state of the sort studied in quantum and statistical mechanics? This assumption is licensed in many situations in which the dynamics describing a system’s Jacobian are symmetrical, so ensuring detailed balance. However, given that this symmetry cannot be assumed in systems in which detailed balance is broken, to what extent does this limit gauge theoretic interpretations of brain processes? [43]
• Along which dimensions are symmetries most important for nervous system functioning (e.g. connectomic resting state networks as reflecting harmonic functions)? [44] Could such organizational principles be evidenced by responses to different forms of music, [45] or fractal-structured visual stimuli, [46] or potentially the phenomenology associated with psychedelic states? [47,48]
• Did such sensitivities create selective pressures that over phylogenic time increased the prevalence of symmetrical phenotypic properties, which further placed selective pressures on the detection of such symmetries as honest indicators of evolutionary fitness? [49]
• To what extent do different morphologies result in different kinds of free energy gradients when perceived/compressed? To what extent were phenotypes selected to display high-dimensional symmetries because of their compression potential? Could such signaling partially explain the large number of genes related to facial structure in humans? [50]
• Could evolutionary arms races with respect to the displaying and perceiving of symmetries have contributed to major transitions in evolution, such as the massive phenotypic complexification associated with the advent of eyes around the time of the Cambrian explosion? [51,52]

These are just some of many questions that may relate to the nature of symmetry in mind and life. Our goal for this collection is to bring together as many perspectives as possible, so that we may come to better perceive the multiple dimensions along which symmetries may be found in nature.

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Dr. Adam Safron
Prof. Dr. Michael Levin
Prof. Dr. Adeel Razi
Dr. Zahra Sheikhbahaee
Dr. Dalton Sakthivadivel
Dr. Magnus Bein
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