Life beyond the free energy principle: how to survive without invariance

28 February 2024

Since emerging onto the stage as ‘a theory of cortical responses’ in 2005[1], Karl Friston’s free energy principle has undergone numerous costume changes. In its most modest dress, it appears as nothing more than a tautological truism[2]: in its most eye-catching ensemble it is “an existential dyad from which everything of interest about life and the universe can be derived, from biotic self-organisation… to the detailed microcircuitry of our brains.”[3]

Undergirding these various outfits is a simple idea – that existence can be defined in terms of the stability of statistical properties. In earlier, ‘enactive’ presentations of the FEP, this ongoing stability was framed as a proto-intentional process, corresponding to a living system’s homeostatic drive towards its own continued survival.[4] [5] By casting the preservation of this statistical stability in such intentional terms, Friston and collaborators thus proposed that to exist is to succeed in following the rules of (approximate) Bayesian inference,in order to reduce the divergence between expected and experienced states.

All sorts of non-living things also maintain stable statistical properties, however, threatening to turn the FEP into a kind of pan-inferentialism in which even rocks or pendulums are viewed as actively modelling their most likely states. Accordingly, in more recent years, this inferential interpretation has been re-framed in eliminativist terms. Rather than being a principle that “distinguishes biological systems”[6] and underpins “the directedness of the organism towards a meaningful world of significance and valence”,[7] the FEP is now presented as revealing there to be no difference in kind between the survival of an organism and the stability of a pendulum. As such, Friston and co-authors now declare that, “we can construct no useful demarcation between bona fide cognition and dynamics appearing merely ‘as if’ they are cognitive, but which actually reduce to ‘mere’ physics.”[8]

I agree that no demarcation can be constructed with the tools of the free energy framework. It’s fortunate then, that free energy minimization is not exhaustive of everything that the world has to offer. As I argue in my forthcoming book, it is precisely those living systems that are typically presented as paradigmatic free energy minimizers which best expose the limits of this statistical framework.

Statistical essences

The FEP begins with the presumption of a standard essentialist ontology in which any particular system must have some invariant features that identify it as the system that it is and that it must continue to possess so long as it continues to exist.[9] Said features must fulfil a dual role of individuating this system from what it is not and unifying it over time and throughout changes to its accidental properties.

Next, this is given a probabilistic spin, as Maxwell Ramstead describes in a previous post to produce the claim that “Observable things do on average what it is characteristic or typical for them to do.” [my emphasis] This takes us from a categorical set to a ranking of various states or behaviours as more or less ‘likely’ for a particular system. What remains invariant are statistical properties rather than a specific state.  Such systems may occasionally exhibit more uncharacteristic states or behaviours – as long as this occurs only rarely, with a frequency proportional to their likelihood. This means that whenever a system finds itself in an unlikely state it must quickly leave it to return to a more likely one.

In the FEP, unlikeliness is typically expressed in the (unhelpfully psychologistic) terms inherited from information theory as ‘surprisal’ leading to, as Friston puts it, “one simple imperative; avoid surprises and you will last longer”.[10] Because variational free energy minimisation with a simplified model is one way to approximate ‘true’ surprisal, so a system’s minimisation of the latter is then used to support the description of it as performing variational inference. Still, as Mann et al. point out the fact that a system is avoiding unlikely events does not entail that it is using any particular model or any particular approximation technique to do so.[11]

If we dress down the imperative of ‘free energy’ or ‘surprisal’ minimization then, we find that, as a general principle, it is simply the claim that a system must rarely occupy unlikely states or engage in unlikely behaviours. As Colin Klein has objected, this looks more like the statement of a tautology than the discovery of a principle.[12] Still, as with the assertion that “a structure must rest on its foundations”, the fact that a claim is tautologous does not mean that its predicates apply universally. Plenty of things are unfounded and a system can only avoid unlikely states if it actually has them in the first place.

In an exceedingly trivial sense, every system will be in its most likely state at each particular point in time, in as much as a known quantity has a probability of one. For talk of minimizable unlikeliness however we need degrees of unlikeliness that can be minimized. To obtain this, we can instead look at a system’s behaviour over some duration and assess whether there is a fixed amount of stochastic variation and/or deterministically recurring dynamics, such that the system will repeatedly revisit states with a fixed frequency.[13] This can be expressed in the form of a stochastic differential equation, the Langevin equation, which Ramstead et al. (2020) propose is so general that it “underwrites nearly all of physics.[14]” We can then describe these fixed frequencies or fluctuations in terms of probabilities that remain invariant throughout the system’s changes in state. So long as the fluctuations are evenly distributed around a subset of states (or a trajectory), or so long as some states are returned to more frequently than others, then these serve as the system’s ‘likely’ or ‘characteristic’ states, towards which it regularly returns.

Finally, if the system over which this probability distribution is defined consists of multiple variables we can divide these up based upon the statistical (in)dependencies between them and call one set a ‘thing’ or ‘agent’ and the other its ‘environment’.  Because each variable has an invariant probability distribution over its possible states we can then measure the divergence between these distributions and treat this as quantifying the former’s accuracy in ‘modelling’ the latter.

There are numerous issues with reifying this ‘Markov blanket’ division as a metaphysical demarcation between a thing and its environment.[15] There are even more issues with an unmotivated move from a symmetrical and commonplace property of covariation to talk of one variable as ‘modelling’ the other.[16] The most important point here, however, is that the decomposability of our variables into covarying subsets is already assumed in the set-up of the invariant joint probability distribution across all these variables. The Markov blanket decomposition describes this separability but it neither explains it nor provides a basis for deriving it.[17] [18]

Like everything else in the free energy framework then, the demarcation of some system into a thing and its environment is downstream of the identification of a probability distribution that ranges over the states of both. The status of the FEP’s subsequent constructions, the question of whether they pick out a principled boundary in the world or merely describe an arbitrary decomposition, depends upon the metaphysical status of the initial probabilistic model. Without this model, there are no probabilities, no surprisals, no statistical independencies, no Markov blankets, and no free energy minimization – sophisticated, expected, generalised, or otherwise.

One weird trick to stay alive

Thus far, I’ve described the FEP as a theory of ‘things’ in general. Yet much of the interest it’s aroused can be traced to its more specific presentation as a theory of biological things in particular by serving as a conceptual analysis of the meaning of ‘survival’. [19] [20] [21] [22] This proposal recalls the mid-20th-century cybernetic view of organisms as feedback control machines – a view exemplified by W.R. Ashby’s claim that there is an “exact equivalence” between the concepts of survival and stability.[23] Still, there is nothing especially vital about this kind of stability amid perturbation. Precisely what made such an analysis so appealing to Ashby and his fellow cyberneticists was its mundanity. It is, as he notes, “usually trivial and uninteresting; it is the pendulum hanging vertically… the cube resting flat on one face.”[24]

Accordingly, Friston and co-authors have now pivoted away from the presentation of the FEP as something that “distinguishes biological from other self-organizing systems”[25] to instead treat it as a more general theory of any ‘thing’. [26] [27] With this increase in scope comes a corresponding decrease in ambition. If pendulums and oil drops are just as much ‘free energy minimizers’ as you and me then simply satisfying the constraints of the free energy formulation cannot account for the emergence of ‘intentionality’ and ‘aboutness’ in organisms alone. [28][29][30] We might be able to describe differences between living and non-living within the class of systems described by the FEP, for instance in terms of dynamical complexity, but the decision of where to draw a line on this continuous scale would be a matter of explanatory interest, not objective physical properties. 

Interpretations of the FEP have largely settled around this recognition that it is inadequate to justify intentional attributions.[31]  One response to this would be to concede that what looked like a “normative account of self-organisation and sentient behaviour”[32]  turned out to be just an over-interpreted modelling framework that may, or may not, be useful in particular cases.[33] Many advocates of the FEP, however, continue to maintain that it is not just a way of modelling things, but an ontological principle that underlies all of physics and determines how every thing must be. Accordingly, if the FEP describes no fundamental  distinction in kind between agents that work towards their own survival and things that merely persist over time,  then no such distinction exists.[34]

Vital characteristics

In so far as the applicability of the FEP is supposed to be secured simply by the requirement that every thing must have some invariant defining characteristics its scope can seem hard to deny. As Friston asks, if something does not have characteristic features then how could we observe or identify it?[35] Accordingly, even the critical literature on the FEP has often accepted that this basic requirement and its formulation in terms of stochastic differential equations and probability distributions is sufficiently broad, focussing instead on criticising the subsequent steps of the free energy framework.[36]

When it comes to living systems, however, characteristic features prove surprisingly difficult to pin down. In Friston (2013) they were directly identified with the microphysical states of a system’s constituent molecules, which he concedes does not easily accommodate systems like a flame in which the constituent particles can, “over time wander away or, indeed, be exchanged or renewed.” [37] [38] Strangely, he then contrasts this dissipative property of the flame with a cell membrane – for all that the stability of said membrane is equally illusory. The slime mould Dictyostelium, for instance, cycles its entire membrane within just 4–10 minutes and in all cells, this sort of ongoing material turnover is crucial for regeneration, growth, sensing, and signalling. [39]

Still, the preservation of identity throughout material change is not unique to living systems. The traditional solution to this problem is to propose that the essence of an individual is identified not with a particular clump of material stuff but with some invariant formal properties. Instead of being defined over particular particles, our invariant probability distribution is now defined over the parameters of equations capturing some higher-order features, for instance, concentrations or proportions, that remain stable throughout this material flux [40] [41]

If a concentration changes, we introduce a new parameter describing a stable rate of change. If this changes, we introduce a second derivative describing its stable acceleration – and so on. By means of such higher-order equations and parameters, a mathematical model transforms change into invariance.[42] Accordingly, the free energy literature has not only deployed this hierarchical strategy to incorporate material flux but also as a way to describe transformations in dynamics, as exhibited in cases like learning and development [43] that have been argued to violate its requirement of stability.[44]

Such a multiscale strategy renders the FEP much more flexible than if its requirement of statistical stability were taken to hold directly for every possible microphysical variable of a system for as long as it exists. Not flexible enough, however, to track the behaviour of a living system. For such a strategy to work it must be the case that, at some level, we eventually reach an equation with parameters that are stable enough to be described by the invariant probability distribution of the FEP. In biology, as numerous philosophers and theoretical biologists have argued, there is no such level. [45] [46] [47] [48]

We do not need to look at the creative behaviour of complex cognizers like ourselves to see why. The breakdown of this invariantist approach to existence can already be seen in single-celled organisms like bacteria, which freely incorporate novel capacities via horizontal gene transfer or even via the entire endosymbiosis of other organisms – as in the potential origins of mitochondria and chloroplasts. Crucially, unlike mutations introduced during replication, these lateral mechanisms can transform the possibility space of a simple organism within its lifetime.

Take, for instance, the lac operon of the E. coli. This short section of its DNA allows a bacterium to switch between metabolizing lactose and glucose, dependent upon environmental resources. It is the paradigm example of single-celled behavioural flexibility. Such bistability poses no threat to a sophisticated essentialist ontology, however, and can easily be described by a set of invariant differential equations[49]. What does disrupt the invariantist paradigm is the possibility that at some point in the course of its lifetime an individual E. coli bacterium may have acquired this capacity through the insertion of a lacA gene via plasmid exchange or insertion by a roving retrovirus[50]. Prior to this event, lactose-metabolism was not a latent possibility in that E. coli’s structure. Any set of equations that ranked lactose metabolism as ‘probable’ would have been inaccurate. Any model that did accurately describe the prior characteristics of this individual bacterium, however, could not have predicted the collision that led to its acquisition of lacA, let alone the proliferation of lactating mammals that would transform the E. coli possibility space as a result.

To make existence contingent upon continued compliance with a model is to deny the productive opportunities of such structural reconfigurations. While some model revisions do amount to the cessation of life, others correspond to a creative new way of pursuing ongoing existence. A principle that requires only the preservation of characteristics cannot tell us the difference between the two, any more than it can differentiate between the stable pendulum and the unstable cell. 

Self-individuation

So, contra Ashby and Friston, the difference between living and non-living systems is not just a difference in degrees of behavioural complexity or an increase in the levels of higher-order equations required to reduce this to the preservation of some invariant features. The difference is that for living systems, there are no such invariant and individuating features. This raises the question of how we do manage to identify individual organisms throughout whatever mid-life crises they may undergo.

To explain this we need to abandon not only the FEP, but the physicist’s entire essentialist ontology of higher-order invariants. Instead, we should draw upon the kind of processual ontology[51] that has a long history in the work of continental and organicist philosophers of biology,[52] which inspired their critiques of the FEP’s cybernetic precursors[53] [54] and influenced a schism between enactive and cybernetic approaches that has often gone unrecognized in the free energy literature.[55] [56]

In place of static invariant features, whether material stuff or formal essence, this alternative view conceives of the identity of a living system as defined by the relations between each successive moment of a process that allow us to “follow it through time.”[57] Dances, stories or movies are familiar examples in which we can identify a continued process without the identification of invariants. Unlike these cases, however, where the validity of a continuation is culturally determined, what counts as the continuation of a living system is not ‘up to us’ but upon the fundamental thermodynamic constraints of metabolism.

The logic of this process is concealed if, as the FEP does, we abstract away from this metabolic activity to treat the stability of a cell and that of a pendulum as being of a kind – guaranteed so long as they succeed in resisting perturbations. To see the difference between these two forms of existence we need to look beneath this generic assumption of stability to see how it is secured from the instability that underlies it. All physical things decay eventually. In the case of the pendulum, we can ignore this decay because it is too slow to matter for the timescales we are interested in. In the case of a living system, as the Dictyostelium illustrates, this decay may be very rapid indeed. Instead, the persistence of the organism depends upon how the energy released by this spontaneous decay is channelled into energy-consuming reactions that re-construct that cell in a manner that allows this cycle of decay and construction to continue.

Thermodynamics sets some invariant constraints upon the continuation of this process but in so far as these constraints are general enough to remain invariant they will not be individuating – for every system will be equally subject to them. Nor do these constraints set any characteristic features that a particular individual must preserve throughout its future existence. All they dictate is what an individual can and cannot do next, given the particular organisation that it happens to have now.  Contra the cybernetic view, it is not the invariance of what is constructed but rather the continuation of constructing that determines whether the organism lives or dies. Within the constraints of this process, anything goes[58].

It is this notion of individuation as a productive continuity without a finished product that invariantist frameworks like the FEP cannot capture, and it is precisely this form of individuation that underpins the proto-intentionality that recent work on the FEP now denies. Isolate a pendulum from any perturbations or energetic flux and it will happily remain in an unsurprising free energy minima without ‘doing’ anything. Isolate an organism and it must continue to counter its own decay, up until the point that the inefficiencies of metabolism overcome it and it dies. As Hans Jonas puts it, “A feedback mechanism may be going, or may be at rest: in either state the machine exists. The organism has to keep going, because to be going is its very existence”. [59]

If we are looking for the proto-intentionality of life then we should seek it in this need of each living individual to keep going, rather than a mere universal necessity of not changing.

The modeller’s quest to pin the organism down and preserve it in aspic destroys the very thing that makes it living. This doesn’t mean that models aren’t useful. There are plenty of features of living systems that will happen to be stable over some period and for certain purposes, it will be useful to model these as invariants. To misinterpret this stability as a necessary principle, however, conceals both its contingent dependence upon underlying instabilities and its propensity to change in ways that said model cannot predict.

This is not a neglect of details, common to all models, but the erasure of difference in kind between objects that can be defined by invariant properties and organisms who will blithely individuate themselves in spite of our attempts to define them. We can construct a mathematical framework which ignores this and, in the context of this framework, the FEP may work as a necessary principle. We should not, however, mistake this framework for reality and we should not treat its erasure of the distinction between intentional processes and mere physical ‘things’ as proof that no such distinction exists.

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4 comments left on “Life beyond the free energy principle: how to survive without invariance”

  • One brief additional comment: this all has a great deal to do with quantum physics and how it draws significant limitations on the Newtonian mechanistic worldview; my own feeling is that the person whose work has addressed this issue most effectively and with some important implications is Ruth E Kastner with her Relativistic Transactional Interpretation of Quantum Physics (NOT ‘Mechanics’, because the whole point of the quantum rectification of Newtonian ‘Mechanics’ is that the mechanistic formalism is misleading and inadequate). The other area of human thought and endeavour where there is a deep connection is in Philosophy (as well as, to some degree, Theology). This is, of course, a huge topic. But I have found the process metaphysics of Charles Sanders Peirce, and particularly the recognition of the crucial role of ‘Mediation’ or what Peirce called ‘Thirdness’ (in his ‘New List of Categories’), or ‘Evolutionary Love’ in his process metaphysics. The dominant nominalistic worldview in which we find ourselves is what Peirce called ‘Necessitarianism’, which, effectively, is a mechanistic world without ‘Thirdness’ or Mediation and, as well, real communication. And, in addition, I have found the work on phenomenological ethics brought forward by Emmanuel Lévinas to be deeply important and relevant as well, particularly in view of Lévinas’s ideas about Time, and his attempt to work toward a ‘de-formalisation’ of time. This, in fact, as far as I can tell, is huge and relates to the distinction between ‘Synchrony’ and ‘Diachrony’ in the context of intersubjectivity. Which is part of any important work on Lévinas’s philosophical approach to time and temporality.

    • Kathryn Nave says:

      Thanks for the comments Gary. Lots of rich connections to draw upon but you’ve particularly prompted me to take an overdue look into Peirce’s work again, which I haven’t done in a very long time!

      I’ll say that Rosen’s work is also very much in the background of my thoughts on this, though I’m still grappling with the specifics of his arguments about non-computability.

  • I agree with what you are saying here, Kathryn. And have made comments about this on the blog of Matt Segal related to his reference to your work here (‘Agency and Perception in Whitehead and the Free Energy Principle (dialogue with Tim Jackson)’ https://wordpress.com/read/blogs/13668059/posts/11655

    I would suggest a potential ‘corrective’ which is the work of relational biologist, Robert Rosen, on ‘anticipatory systems’ and his final two books on ‘Life Itself’, both published by Columbia University Press. In making a categorical distinction between ‘mechanisms’ and ‘organisms’, Rosen is opening up a ‘new vista’ in my opinion. And it also relates to the work of Tim Eastman that he writes about in his book, ‘Untying the Gordian Knot’ and the issue of ‘context’ and its influence on behaviour. Rosen makes a categorical distinction (using the mathematical theory of categories) between ‘organisms’ which he categorizes as ‘complex’, and ‘mechanisms’ which he categorizes as ‘simple.’ The distinction is based on two fundamental criteria: 1. the question of closure to efficient causation (organisms are; mechanisms are not), and 2. the presence of ‘closed causal loops’ within their relational model (organisms have them; mechanisms do not). What this means is that predicative math works for mechanisms, but not for organisms; mechanisms are ‘computable’ while organisms are not; mechanisms are ‘algorithmic’ while organisms are not; mechanisms comply with the ‘ontology of states’–meaning that they can be partitioned into ‘states’ and ‘laws’ governing them, while organisms do not; mechanisms are strictly deterministic, while organisms are not. The functionality of mechanisms is ‘context-independent’, while the functionality of organisms is sensitive to context. The function of a mechanism can be fully predicted on the basis of its structure; the function of an organism cannot be fully predicted from its structure. A mechanism can be simulated by a Turing machine; an organism cannot be simulated by a Turing machine. And, in his book, ‘Essays on Life Itself’, Rosen makes the point that the Incompleteness Theorems of Kurt Gödel imply that the mechanistic formalism doesn’t work for modeling living organisms, and that any attempt to ‘formalise’ organisms is doomed to failure. I think this may well have something to do with how time works differently for mechanisms as distinct from organisms. Put simply, for mechanisms, time is discontinuous and synchronic–for mechanisms, time operates in a stepwise manner; for organisms, time is continuous and diachronic–for organisms, time flows continually. One interesting corollary to this: the mechanistic worldview is consistent with the way the left hemisphere understands the world, while the organismic worldview is consistent with the way the right hemisphere understands the world as I would see to be consistent with the approach to the division of the functionality of the hemispheres as elaborated by Iain McGilchrist. OK. I will stop there. Obviously, there is a whole lot more to this!