Sentience and the Origins of Consciousness: From Cartesian Duality to Markovian Monism
Again, this is not mysterious it is just a mathematical statement of the way things are. What is interesting here is that internal states have a dual aspect information geometry that seems to be related to the dual aspect monism—usually advanced to counter Cartesian (matter and mind) duality. On a simple interpretation, one might associate the information length of internal states with the material behaviour of particles or creatures, while the mindful aspects are naturally associated with the probabilistic beliefs that underwrite the extrinsic information geometry of internal states. However, the existence of a dual aspect information geometry does not, in and of itself, give a system mental states and consciousness, but only computational properties (including probabilistic beliefs). Furthermore, the extrinsic information geometry is ultimately reducible to the intrinsic information geometry (and the other way around), in the sense that there is a necessary link between them cf. [65], pp. 11–13. Still, physical, and computational properties are not identical.16
An interesting special case arises if we assume that the conditional beliefs are Gaussian in form (denoted by N in equation (9) below). In this instance, the Fisher information metric becomes the curvature or ‘deepness’ of free energy minima, which is the same as the precision (i.e., inverse covariance) of the beliefs per se.
In other words, distances in belief space depend upon conditional precision or the confidence ascribed to beliefs about external states of affairs ‘out there’. We will return to this interesting case in the conclusion. At the moment, notice that we have a formal way of talking about the ‘force of evidence’ in moving beliefs and how the degree of movement depends upon conditional precision, confidence, or certainty [67,68,69].
To make all this concrete, it is perfectly permissible to express the gradient flows in terms of forces supplied by the extrinsic, belief-based information geometry. This just requires a specification of the units of the random fluctuations in terms of Boltzmann’s constant. This means that we can rewrite (7) in terms of a thermodynamic potential U(π) and associated forces fm(π), where, at nonequilibrium steady-state (see pp. 65–67 in [1]):
The last equality is known as the Einstein–Smoluchowski relation, where μm is a mobility coefficient. This means, we have factorised the amplitude of random fluctuations Γαα=μmkBT into mobility and temperature [12]. Nothing has changed here. All we have done is assign units of measurement to the amplitude of random fluctuations, so that we can interpret the ensuing flow as responding to a force, which can be interpreted as a gradient established by a thermodynamic potential. This thermodynamic potential is just (scaled) surprisal or our free energy functional of beliefs.
These equalities cast the appearance of Cartesian duality in pleasingly transparent terms. The forces that engender our physical dynamics can either be expressed as thermodynamic forces or as self-evidencing; in virtue of the extrinsic information geometry supplied by variational free energy. Mathematically, this duality arises from the fact that the surprisal and variational free energy are conjugate: one rests upon the probability of particular states, while the other is a functional of blanket states and beliefs that are parameterised by internal states. They are conjugate in that they refer to probability densities over conditionally independent (i.e., orthogonal) states; namely, internal and external states.
The point here is that there is no difficulty in moving between descriptions afforded by statistical thermodynamics and self-evidencing (i.e., minimising variational free energy). On this reading, variational free energy is a feature of an extrinsic information geometry induced by beliefs encoded by internal states that have an intrinsic information geometry. This free energy has gradients that exert forces on internal states so that they come to parameterise new beliefs. These new beliefs depend upon blanket (e.g., sensory) states; thereby furnishing a mathematical image of perception. Furthermore, the same Bayesian mechanics applies to active states that change external states—and thereby mediate action upon the world. So, is there anything more to the story?
Active inference will become a key aspect of the arguments below, when thinking about different kinds of generative models; specifically, generative models of the consequences of action. On the above arguments, anything (that exists in virtue of possessing a Markov blanket) can be cast as performing some elemental form of inference—and possessing an implicit generative model. However, not all generative models are equal; in the sense that no two things are the same. Later, we will look at special kinds of generative models that underwrite active inference.
Above, we introduced variational free energy as an expression of particular surprisal. This variational form is a functional of sensory states and a conditional density or belief distribution encoded by internal states. However, the variational free energy also depends upon the surprisal of joint particular and external states, I(η,π)≡−lnp(η,π), see (5). On a statistical view, the corresponding nonequilibrium steady-state density p(η,π) is known as a generative model. In other words, it constitutes a probabilistic specification of how external and particular states manifest. It is this generative model that licenses an interpretation of particular surprisal in terms of Bayesian mechanics and self-evidencing [37]. So, what does this mean for our formulation of beliefs and intention?
Note that we can always describe the dynamics of internal states in terms of a gradient flow on variational free energy. This means that the dynamical architecture of any particle or creature can also be expressed as a functional of some generative model that, in some sense, must be isomorphic with the nonequilibrium steady-state density. This has some interesting implications: from the point of view of self-organisation, it tells us immediately that if we interpret the action of a particle or creature in terms of self-evidencing, it says that the implicit generative model—which supplies the forces that change internal and active (i.e., autonomous) states—must be a sufficiently good model of systemic states. This is exactly the good regulator theory that emerged in the formulations of self-organisation at the inception of cybernetics [45,70].17
We will first preview, heuristically, the final argument in this essay. Because active states depend upon internal states (and the beliefs that they parameterise)—but active states do not depend upon external states—it will look as if particles or creatures are acting on the basis of their beliefs about external states. Furthermore, if a particle or creature acts in a dextrous, precise and adaptive way to fluctuations in its blanket states, it will look as if it is acting to minimise its particular surprisal (or variational free energy). In other words, it will look as if it is trying to minimise the surprisal, expected following an action. This means, it would look as if it is behaving to minimise expected surprisal or self-information, which is uncertainty or its particular entropy.
Anthropomorphically, a creature will therefore (appear to) have beliefs about the consequences of its action, which means it must have beliefs about the future. So how far into the future? One can formalise a response to this question by turning to the path integral formulation of random dynamical systems [12,13,77,78]. In this formulation, we are not concerned with the probability density over states but rather over trajectories or sequences of states. Specifically, we are interested in the probability of trajectories of autonomous states, often referred to as ‘policies’ in the optimal control literature [32]. So, what can one say about the probability of different courses of action in the future?
We can now turn to the information length associated with the evolution of systemic states to answer this question (for a more detailed treatment, see pp. 86–88 in [1]). Recall from above, that the information length reflects the accumulated changes in probability densities as time progresses. If a system attains nonequilibrium steady state after a period of time, then the information length asymptotes to the distance between the initial (particular) state and the final (steady) state. This means that we can characterise a certain kind of particle (or creature) that returns to steady state in terms of the (critical) time τ it takes for the information length to stop increasing:
The probability density qτ(ητ,πτ) is the predictive density over hidden and sensory states, conditioned upon the initial state of the particle and subsequent trajectory of autonomous states. In brief, particles with a short critical time18 will, effectively, converge to nonequilibrium steady-state quickly and show a simple self-organisation (e.g., the Aplysia gill and siphon withdrawal reflex) mathematically, these sorts of particles quickly ‘forget’ their initial conditions. Conversely, particles with a long critical time will exhibit itinerant density dynamics (e.g., you and me). Particles like you and me ‘remember’ our initial conditions and look as if we are pursuing long-term plans.
Convergence to nonequilibrium steady state in the future allows us to relate the surprisal of a trajectory of autonomous states (i.e., a policy) to the variational free energy expected under the predictive density above:
The expected free energy in (12) has been formulated to emphasise the formal correspondence with variational free energy in (5): where the complexity and accuracy terms become risk (i.e., expected complexity) and ambiguity (i.e., expected inaccuracy). This path integral formulation says that if the probability density over systemic states has converged to nonequilibrium steady state after some critical time, then there can be no further increase in information length. At this point, the probability of an autonomous path into the future becomes the variational free energy the agent expects to encounter.
The equality in (11) is a little abstract but has some clear homologues in stochastic thermodynamics (in the form of integral fluctuation theorems) [12,79]. Here, it tells us something rather interesting. It means that creatures that have an adaptive response to changes in their external milieu will look as if they are selecting their long-term actions on the basis of an expected free energy. Crucially, this free energy is based upon a generative model that must extend at least to a (critical) time in the future when nonequilibrium steady state is restored. Conversely, if certain kinds of creatures select their actions on the basis of minimising expected free energy, they will respond adaptively to changes in external states.
This formulation offers a description of different kinds of particles or creatures quantified by their critical time or temporal depth in (11). For example, if a certain kind of particle (e.g., a trial or protozoan) has a short temporal horizon or information length, it will respond quickly and reflexively to any perturbations—for as long as it exists. Conversely, creatures like us (e.g., politicians and pontiffs) may be characterised by deep generative models that see far into the future; enabling a move from homoeostasis to allostasis and, effectively, the capacity to select courses of action that consider long term consequences [80,81,82]. Given that the imperative for this action selection is to minimise expected free energy (i.e., expected surprisal or uncertainty), we now have a plausible description of intentional behaviour that will, to all intents and purposes, look like uncertainty resolving, information seeking, epistemic foraging [26,81,83,84,85,86,87,88,89,90]. Alternatively, on a more (millennial) Gibsonian view, action selection responds to long-term epistemic affordances [91,92,93].
This temporal depth may distinguish between different kinds of sentient particles. Again, all of this follows in a relatively straightforward way from information theory and statistical physics. Furthermore, the equations above can be used to simulate perception and intentional behaviour. To illustrate the difference between short term (shallow) inference based upon Equation (5) and long-term (deep) active inference based upon Equation (12), we provide two examples in Figure 4 and Figure 5. The first uses simulated handwriting that is elicited purely on the basis of reflexive responses prescribed by a dynamic generative model (i.e., a pattern generator), while the second calls on the notion of epistemic affordance by simulating saccadic searches and active vision. In the present thesis, simulations of the second sort of active inference may offer a better account of intentional behaviour; namely, beliefs about the consequences of action and subsequent action selection.
Above, we have shown that a duality—between two ways in which states of a system can be conceived of—already arises at a very fundamental level; namely, for all systems that possess a Markov blanket. Their internal states can both be associated with an intrinsic and with an extrinsic information geometry. What metaphysical implication does this have? Does it follow that all systems with a Markov blanket have a mind (because they have probabilistic beliefs about external states)? Are such systems conscious? The formalism itself does not answer these questions: different metaphysical interpretations of the existence of a dual information geometry are possible. In fact, one might ask whether it has any metaphysical significance whatsoever. For the existence of an extrinsic information geometry only means that one can map internal states to conditional probability distributions (over external states, given blanket states). It does not mean that the resulting descriptions refer to entities that actually exist (just as we can ascribe to a lectern the propositional belief that the best way to persist is to do nothing—which does not mean that the lectern actually has a propositional belief; see [99]).
Hence, any metaphysical conclusions must be drawn with care. In what follows, we will first argue that the formalism speaks in favour of monistic views—if we assume that the existence of an extrinsic information geometry has any relevance for understanding the mind and consciousness in the first place. After that, we will discuss different interpretations of the dual perspective afforded by the two information geometries: panprotopsychism, neutral monism, dual-aspect theories, and physicalism. We will argue that physicalism provides the most plausible interpretation. However, we acknowledge that competing interpretations cannot conclusively be ruled out. Hence, we dub the resulting view ‘Markovian monism’. Markovian monism consists of two claims: (1) Fundamentally, there is only one type of thing and only one type of irreducible property (this is why it is a Markovian monism). (2) All systems possessing a Markov blanket have properties that are relevant for understanding the mind and consciousness: if such systems have mental properties, then they have them partly by virtue of possessing a Markov blanket (this is why it is a Markovian monism).
Why do we rule out dualistic interpretations of the dual information geometry? First, note that dualism is still consistent with the existence of an extrinsic information geometry. However, consider any properties that a system has by virtue of the fact that its internal states encode probability distributions over external states. Since the dynamics that can be described with reference to these properties can equivalently be described without regarding internal states as representations of probability distributions, there is a sense in which both perspectives are reducible to one another. Hence, the dual information geometry itself does not entail property dualism. Therefore, if one believes that there are irreducible mental properties, one has to posit them in addition to, and largely independently of, properties entailed by the existence of an extrinsic information geometry. But this means that mental properties will not be instantiated (partly) by virtue of the existence of a Markov blanket (contradicting claim (2) above). In other words, dualism is more or less orthogonal to the formal treatment.
However, we do believe that the existence of an extrinsic information geometry tells us something interesting about the origin of minds and consciousness. Under the assumption that properties entailed by the existence of a Markov blanket are relevant to understanding mental properties, we therefore have to reject dualism. This still leaves different metaphysical options open.
According to panpsychism, mental properties are fundamental non-physical properties and are instantiated by all micro-level entities. Hence, this amounts to a form of property dualism, which we ruled out above. Note, again, that dualism is compatible with the formal treatment presented here, but it would not be an interpretation in which properties entailed by the existence of a Markov blanket have any explanatory relevance to the existence of minds and consciousness—because panpsychism already presupposes mentality as a fundamental part of reality.
However, there is a variant of panpsychism, viz. panprotopsychism, that could, in principle, be described as a Markovian monism. In short, panprotopsychism is “the view that fundamental entities are proto-conscious, that is, that they have certain special properties that are precursors to consciousness and that can collectively constitute consciousness in larger systems.” [100], p. 259. These special, non-structural properties are protophenomenal properties that are not identical to (micro-)physical properties (otherwise, even physicalism could be considered as a form of panprotopsychism, [100], p. 260). There is nothing it is like to be a system that has just a single protophenomenal property. However, if a system displays a sufficiently large number of protophenomenal properties, or if they are arranged in the right way, then the system will also have phenomenal properties (which are constituted by collections of protophenomenal properties).
From the point of view of Markovian monism, one could identify properties entailed by the existence of a Markov blanket with protophenomenal properties. An example is the property of encoding a conditional probability distribution over external states. However, it is unclear to us to what extent this could be regarded as a non-structural property. Furthermore, a robust version of panprotopsychism would have to presuppose that all systems with a Markov blanket actually represent probability distributions—as opposed to just being systems that can be described as if they represented such distributions. Below, we will suggest that a realist interpretation of descriptions afforded by the extrinsic information geometry should be contingent on further conditions. This is why we would not interpret Markovian monism as a version of panprotopsychism.
Neutral monism is normally read as a family of views; according to which the fundamental layer of reality consists of ontologically neutral entities. Different versions of the theory make different claims about the sense in which basic entities are neutral (see [101], who lists five different options). The most popular options seem to be views according to which the basic entities are (a) intrinsically neither mental nor physical or (b) intrinsically both mental and physical.
A great advantage of neutral monism is that it solves the mind-body problem without postulating two basic types of entity (mental and physical)—the significance of this is that worries about psycho-physical interaction (that plagued Cartesian dualism) disappear. The only causal interaction in question involves neutral entities (however, the problem of mental causation may reappear, in the sense that macro-level mental properties may still be causally irrelevant, see [102], pp. 33–34).
Markovian monism could be specified as a version of neutral monism in which basic entities are intrinsically neither mental nor physical. There are two conjugate ways in which things that exist can be described: either from the perspective of the intrinsic information geometry or from the perspective of the extrinsic information geometry. Under the assumption that neither perspective is privileged, one would have to conclude that reality is, fundamentally, ontologically neutral.
However, this would also presuppose a realist interpretation of descriptions in terms of the extrinsic information geometry (i.e., one would have to assume that all systems with a Markov blanket actually represent probability distributions and perform computations). Furthermore, it would have the consequence that even relatively simply systems, such as single-cell organisms, would have a mind (as suggested by [103]). For these reasons, we would not interpret Markovian monism as a version of neutral monism.