Adam Safron, Michael Levin, Adeel Razi, Zahra Sheikhbahaee, Magnus Bein, and I, have been thinking deeply about some issues at the intersection of symmetry, morphogenesis, self-organisation, and inference. We are so interested in these problems that we want to organise a special issue at the Royal Society Interface devoted to answering them.1 There’s an interesting set of questions at the core of the issue, mainly organised around how symmetry and symmetry breaking, as are foundational to the rest of physics, appear as motifs in biophysics and condensed matter theory. Let me say a little about why these are interesting questions for me, personally.

It seems like it should be possible to connect the language of FEP with some of the objects that we understand well in mathematical physics, given the way FEP extends older variational and dynamical ideas in statistical physics. More generally, it should really be possible to investigate the mathematical principles underlying inference, which we use on an ad hoc basis all the time in deep learning models to say things about all sorts of dynamical systems. The challenges facing, for instance, deep learning foundations, are much like the challenges facing both axiomatic quantum field theory and complex systems theory—we have a lot of ways of looking at the outputs of these systems, or some weaker formulation of them, but we don’t understand how either might supervene on the actual system. One could say we’re stuck doing a kind of theoretical experimentation, attempting to infer how such systems must be by probing them and considering what output behaviours suggest what underlying principles. For deep learning, determining the principles dictating exactly when it works and why it works so well, and what that means for dynamical systems theory, is still a work in progress. To this end, the free energy principle is of particular interest to understanding the inference present in the dynamics of complex systems, like soft matter- and software- based computing systems. A re-axiomatisation of the free energy principle is exactly what I, a complex systems theorist after excessive mathematical rigour, find interesting, and potentially useful to the larger community. Indeed, the unification of mathematical physics with biophysics and computer science aligns with my general philosophy quite strongly, as I think it’s the best way to understand such systems.

When it comes to foundations and axioms, in mathematical physics, the most common organising phenomenon in the universe is the presence of symmetry. Gauge field theories, or theories of particles and fields whose dynamics are invariant under a particular kind of transformation, are the most succesful theories in modern day physics. Gauge symmetry builds the entire standard model of particle physics, as well as accounting for every force we feel. Gauge symmetries extend in both the higher-energy direction to describe strings, as well as the lower-energy direction to describe condensed matter theories. Supersymmetric gauge theories are even better models, having many of the mathematical properties we expect of the universe. The closest fundamental physics has ever had to a concrete theory of everything comes in the form of the holographic AdS/CFT correspondence—also called gauge-string duality. Likewise, symmetry breaking is responsible for the richness of the dynamics of our universe, from the matter-antimatter imbalance that gives everything form, to the Higgs mechanism that gives those forms substance, to the features of complexity like phase transitions and non-equilibria that give substances dynamics, and dynamical systems, life. Everywhere we have sought answers or explanations in modern physics, we have uncovered symmetries. It is for this reason that I really believe this issue asks an interesting set of questions, framed masterfully by my co-editors. In particular, it was the lead editor, Adam Safron, who generated the list of questions and potential insights listed in the issue.

So, look out for more information on where and when this issue is ready to go—we’re aiming for a submission deadline of July, and hopefully the issue will appear not too long after that—and be sure to send something in if you’re working on something interesting.

  1. We previously thought that the MDPI journal Symmetry would be the best place for this, but it no longer seems so (in fact this post has been changed as of February 2022 to reflect this change in the announcement; more on the story will surely be in a future post, which I look greatly forward to writing). ↩