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Between pebbles and organisms:
Weaving autonomy into the Markov blanket
Thomas van Es1* & Michael D. Kirchhoff2
See published version in Synthese here:
https://link.springer.com/article/10.1007/s11229-021-03084-w
Affiliations:
1Centre for Philosophical Psychology, Department of Philosophy, Universiteit Antwerpen
2School of Liberal Arts, Faculty of Arts, Social Sciences and the Humanities, University of
Wollongong, Wollongong, Australia.
* Corresponding author
Acknowledgements: Kirchhoff’s work was supported by an Australian Research Council
Discovery Project “Mind in Skilled Performance” (DP170102987). Van Es’s work was
supported by the Research Foundation Flanders (Grant No. 1124818N). We would like to
thank Mel Andrews, Mads Julian Dengsø and two anonymous reviewers for comments on a
previous draft of this paper.
Abstract: The free energy principle (FEP) is sometimes put forward as accounting for
biological self-organization and cognition. It states that for a system to maintain
non-equilibrium steady-state with its environment it can be described as minimising its free
energy. It is said to be entirely scale-free, applying to anything from particles to organisms,
and interactive machines, spanning from the abiotic to the biotic. Because the FEP is so
general in its application, one might wonder whether this framework can capture anything
specific
to biology. We take steps to correct for this here. We first explicate the worry, taking
pebbles as examples of an abiotic system, and then discuss to what extent the FEP can
distinguish its dynamics from an organism’s. We articulate the notion of ‘autonomy as
precarious operational closure’ from the enactive literature, and investigate how it can be
unpacked within the FEP. This enables the FEP to delineate between the abiotic and the
biotic; avoiding the pebble worry that keeps it out of touch with the living systems we
encounter in the world.
Keywords: Free energy principle; Markov blanket; autonomy; operational closure; biology;
cognition; the pebble challenge; unification
1
1 Introduction
The free energy principle (FEP) is a principle first
approach to what it takes for a system to
exist. Rather than empirical investigation, the FEP starts from a mathematical principle
that a
system is thought to conform to if it exists. Indeed, FEP researchers seek to provide a general
theory unifying biology and cognitive science formulated almost entirely from mathematical
principles in physics and information theory (see e.g., Friston 2010 2013; Hohwy 2020;
Kirchhoff et al. 2018; Linson et al. 2018; Ramstead, Kirchhoff, Friston 2019). The ambition
is to secure a definition of existence by appealing to constructs in physics and information
theory, and then employing those constructs to derive a principle of self-organization and
cognition (Friston 2019; Hesp et al. 2019). In a nutshell, the FEP states that a system that
maintains non-equilibrium steady-state (NESS) with its environment can necessarily be cast
as minimising free energy. This particular observation can consequently be exploited to
1
show a wide variety of interesting relations to hold between a NESS system and its
environment.
Yet the FEP’s mathematical toolkit is not only applicable to living systems. It is said to be
entirely scale-free
in its applicability. That is, it is intended to apply to any system able to
maintain its organisation despite tendencies towards disorder: from chemotaxis in cells
(Friston 2013; Auletta 2013), neuronal signalling in brains (Friston et al. 2017; Parr & Friston
2019), tropism in plants (Calvo & Friston 2017), synchronised singing in birds (Frith &
Friston 2015) to decision-making and planning in mammals (Daunizeau et al. 2010; Friston
2013; Williams 2018). It has also been applied to model adaptive fitness over evolutionary
timescales by casting evolution in terms of Bayesian model optimisation and selection
(Campbell 2016; Hesp et al. 2019). However, this widespread applicability of the FEP can be
taken as a fault, rather than an advantage.
Indeed, there is a general concern about the FEP’s ability to speak to the essential
organizational dynamics of biology, because it can seem utterly disconnected from biology.
More specifically, the FEP is sometimes considered incapable of uniquely addressing the
organisational dynamics of living systems (van Es 2020; Colombo and Wright 2018).
Because the FEP implies an entirely scale-free dynamics in which any
self-organising NESS
system can be cast in terms of self-evidencing, some worry that this particular view cannot
1 The term ‘non-equilibrium steady-state’ refers to self-sustaining
processes in a system requiring input and
output to avoid relaxing into thermodynamic equilibrium
(= systemic decay/death). It is important to mention
here that the notion ‘steady-state’ in non-equilibrium systems is an approximation to some specified duration of
time - e.g., circadian rhythms over a 24 hour clock cycle or the homeostatic processes involved in maintaining
on average and over time a specific body temperature. So strictly speaking, biological systems are not in steady
states; rather, to say that a system is in a steady-state, X
, at a particular time, is effectively to say that the
probability density over the system’s states during some period of time was X
.
2
capture the specific details of biological organisation that is of interest to the biological
sciences. If true, this undercuts the grand unifying ambitions of many FEP researchers.
We address this worry here. We start by rehearsing the basic tenets of the FEP, with
particular focus on the Markov blanket formalism and how it relates to Bayesian inference
(sect. 2). We proceed to explicate the aforementioned worry by considering the application of
the FEP formalism to a pebble and discuss how the FEP seems to fall short in delivering the
tools to distinguish pebbles from organisms (sect. 3). Prima facie,
its scale-free applicability
makes it seem like it is unable to carve any interesting joints between the abiotic and the
biotic, which would hinder the prospect of a FEP biology. Kirchhoff et al. (2018) make an
initial attempt to address this problem, suggesting that autonomy
is what distinguishes living
from non-living systems. The overarching claim there is that autonomy is the capacity of a
system to modulate its exchange with its environment. Here we supplement this initial
treatment. We first look at ‘autonomy’ from an enactive viewpoint (sect. 4). We then sketch
the contours of how the notion of ‘autonomy’ from the enactive literature could be emulated
with the tools available to the FEP formalisms. This allows us to understand what constitutes
an autonomous system rather than merely using the notion of autonomy as a mark by which
to delineate life from no-life (sect. 5).
2 Markov blankets, free energy and Bayesian inference
The FEP speaks to what characteristics a system must exhibit for it to exist (Friston 2013). Its
basic premise is that any random dynamical system “that possesses a Markov blanket will
appear to actively maintain its structural and dynamical integrity” (Friston 2013, p. 2).
A Markov blanket is a statistical separation of states that is applicable to any thing that exists
(Hipólito 2020). It is a set of blanket states that separates a system’s internal states from
external states (Pearl, 1988; Beal 2003). The blanket states shield (in a statistical sense)
internal from external states, and vice versa. They can be partitioned into sensory states and
active states. Sensory states capture the influence of external states on internal states. Active
states capture the influence of internal states on external states. Intuitively, any thing can be
separated statistically from that which it is not (Palacios et al. 2020).
3
Figure 1
is a schematic representation of a Markov blanketed system. The gray
circle delineates the Markov blanketed system that separates internal states
(int) from external states (ext). The blanket states, sensory states (sen) and
active states (act) are displayed as surrounding the internal states. The arrows
depict modes of influence. External states influence only one another or
sensory states, while influenced only by active states or one another. Internal
states are influenced only by sensory states, influencing only active states. In
terms of modes of influence, internal states are separated from external states.
(figure taken from Bruineberg, et al. 2018).
In this statistical formulation, the separation between internal and external states implies that
these states are conditionally independent
, given
the states that comprise the Markov blanket.
If we want to figure out the external
states and we know
the values of the blanket
states,
knowing
the values of the internal
states will not offer additional predictive value
, and
vice-versa. This is so by definition, because the blanket states already capture any possible
influence the internal states could have on the external states. A brief example may clarify
this. Say you observe that it is cold. This could be either due to an open window or to an air
conditioning system that is set too strong. If you would observe that, say, the air conditioning
is set excessively high, the observation that it is cold now does not offer further information
with regards to whether or not the window is open. That is, in this case, the observed cold and
the open window are conditionally independent, given that the air conditioning is on blast
(Kirchhoff and Kiverstein 2019; Beal 2003). In terms of the Markov blanket formalism, the
observed cold could be cast as the internal states, the state of the window could be formalized
as the external states with the states of the air conditioning serving as the blanket states. This
example is important because it indicates the widespread applicability of the formalism.
Indeed, it is not necessarily obvious to associate the boundaries induced by the Markov
blanket with physical boundaries, though it does seem to lend itself well to this particular
application. We should nonetheless remain wary about overstating the implications of this
4
statistical
partitioning of states when considering its application onto other systems (van Es
2019, 2020).
Now that it is clear what a Markov blanket is, we can delve into its relation with free energy
minimisation and Bayesian inference. This is a technical story. According to the Second Law
of thermodynamics, the entropy
of any closed system increases indefinitely over time. Any
system that exists, or any Markov blanketed system that retains its structural integrity over
time, seems to temporarily slow down the increase of entropy for as long as it remains intact
(Friston 2012, 2013, 2019; Schrödinger, 1944). Of course, any such ‘resistance’ is only
temporary, as entropy increases upon disintegration, which, in the case of biotic systems,
means death.
For any such system, you can establish a multi-dimensional state space with as many
dimensions as there are variables represented in the state space. Each point in the state space
corresponds to a unique intersection of values for each variable. In this state space, you can
mark a bound of states within which a system can remain intact, outside of which it cannot
(Friston, 2012, 2013). For as long as the system remains intact, the system will continuously
‘revisit’ the states within this bound. This is so by definition, as we define the bound by the
range of values within the system remains intact. With regards to organisms, the viable bound
differs per species: humans remain intact under quite different circumstances than fish do, for
example. Insofar as this bound counts as a description of the states in which the system can
be found when alive, it is also considered to be a mathematical description of a phenotype
(Friston 2013; Kirchhoff et al 2018). On average and over time, any living system is thus
2
likely to be found within the bound of viable states and unlikely to be found outside of it.
That is, we may expect
a system to be within a bound of states that it typically remains within
on average
(Friston, Wiese, Hobson 2020). This implies a probability distribution that can be
laid over the state space so that each state is assigned a probability value (Ramstead et al.
2019; Corcoran et al. 2020; Friston 2013). At any given time the system is encountered, it is
highly likely to occupy a state within the viable bound, and highly unlikely to occupy a state
outside of this. This means that states within the bound are considered high-probability states,
whereas states outside of it are considered low-probability states.
Furthemore, if a system’s internal
states remain within a particular range, this must mean that
the influences
on those states are similarly bounded. An example should clarify this. Consider
an egg and spoon race. An egg-and-spoon runner will need to ensure that the influence on the
egg of their running the race remains within certain bounds, lest the egg move out of the
spoon and break. Let us apply the Markov blanket partitioning method. We shall take the
internal states here to be the egg’s, and the influences it receives via the spoon shall be the
sensory states, the runner is here the environment impacting on the spoon and comprises the
2 See Colombo and Wright (2018) for criticism on the viability of this application onto an organismic system.
5
external states. This means that an egg-and-spoon runner can be cast as keeping a tight bound
on the sensory states
of the Markov blanketed egg for as long as it remains in the spoon.
As it is for the egg-and-spoon runner, so it is for any
system that remains intact over time.
Relative to the viable bound of the internal states of the system, then, we can also establish a
state space for the sensory states
within which the system can remain intact, outside of which
it cannot. Here too, we can determine a probability distribution where states within the bound
are ascribed high probability, those outside of it are ascribed low probability. This is a
probability distribution over external states
, as it relates to the influences on the internal
states by the external states
. In other words, it defines the possible external states that there
could be relative to the internal states, given that the internal states remain within the viable
bound. Of interest here is that the internal states themselves provide all we need (the
‘sufficient statistics’) to compute the probability distribution over the external states. As such,
by knowing the viable bound of the internal states, we can compute the viable bound of the
system’s sensory states.
Further, in Bayesian probabilistic theory, surprise
is a quantity defined as the improbability
of a particular state (Shannon, 1948). If the surprise of sensory states (or ‘sensory surprise’,
not to be confused with agent-level surprise with regards to an unexpected sensation) is high,
the sensory states currently occupy a low probability area in the state space. As
low-probability states are those that endanger the system’s structural integrity, surprise is
kept low, or minimized, as long as the system remains intact. However, sensory surprise is a
probabilistic measure of sensory states. The entire state space of sensory states includes all
possible modes of influence the external states could possibly exert on the internal states.
This is, in principle, an infinite set. Computing sensory surprise directly is thus intractable
(Friston 2009).
This is where (variational) free energy
comes in. Free energy, in the statistical usage of the
term, is a functional of the internal and sensory states a system is in. In this case, free energy
3
is thus, more specifically, the function of a function of the sensory states that is parameterized
by the internal states. Because of this, the value of free energy limits the possible values of
the internal and sensory states. To see why, consider a solution to a simple summation
problem in arithmetics, say it’s 15, and the terms of the equation are non-negative. This
means that none of the terms of the problem can exceed the value of 15. Minimizing the
value of free energy, then, minimizes an upper bound on the probability of sensory states.
This ensures that sensory states remain in high-probability areas in the state space, which in
turn implies that sensory surprise is minimized. Minimizing free energy can thus be seen as
approximately minimizing the otherwise intractable value of sensory surprise (Friston and
Stephan 2007). Moreover, as free energy is a function of only the internal and sensory states,
it is in principle computable (Kiebel, Daunizeau and Friston 2008; Friston and Ao 2012).
3 A functional is a function of a function.
6
In Bayesian probability theory, negative surprise
is equivalent to Bayesian model evidence.
Minimizing
surprise thus maximizes
Bayesian model evidence. The process by which
Bayesian model evidence can be maximized is called Bayesian inference
, sometimes referred
to as self-evidencing (Friston, Killner, Harrison 2006; Hohwy 2016). Bayesian inference then
refers to the particular way a probability distribution needs to be updated in light of new
evidence (Beal 2003). Bayesian inference describes the permissible ‘moves’ one can make in
the formal system of Bayesian probability theory. We can now see that for any system to
remain intact over time, its entropy needs to be minimized on average over time, which
means expected free energy needs to be minimized, which in turn implies the minimization of
sensory surprise, which is done by way of a formal operation called Bayesian inference.
The above story is employed in the FEP as a mathematical description of the homeostatic
processes of biotic systems (Friston 2013). This works, very roughly, as follows. In the
Markov blanket formalism, the Markov blanket is thought to carve out ontological joints: the
internal states map onto the organism itself, and the external states map onto the environment
(Kirchhoff and Kiverstein 2019). The partitioning blanket states map onto the organism’s
modes of interaction so that sensory states are associated with sensory receptor activity, and
active states are associated with the system’s influence on its environment, such as action. It
remains a current debate to what extent this application of the Markov blanket should be
taken literally or instrumentally (van Es 2020; Bruineberg et al. 2020; Hohwy 2016). In this
paper, we will remain neutral in this debate, and instead explore only what can be done
within the formalism, regardless of how it may or may not be implemented in any real
system.
In a realist interpretation, to ‘engage’ in Bayesian inference is considered a fundamental
aspect of life, as without it, the organism would go outside of its viable bounds. This is called
active inference
, and is thought to account for both action and perception by the same guiding
principle (Friston 2013). The probability distributions are embodied and/or encoded by the
organism (and/or the brain). They are to be manipulated, updated and leveraged by the
organism. Through active inference, the organism updates the probability distributions in the
face of newfound evidence, and uses this to infer action policies for its interaction with the
world. Long term activities are thought to require counterfactual inference, which is
associated with the minimization of expected free energy
or free energy on average over time
(Corcoran et al. 2020). Rather than updating the probability distribution to remain within its
viable bounds, this should be seen as the inference of a possible trajectory through the state
space conditioned on bodily movement. This allows the organism to adapt to environmental
fluctuations. After all, the distribution of states within which an organism can remain alive
cannot be simply ‘updated’ when confronted with an environment likely to push the system
7
outside of viable bounds. Active inference thus plays a central role in the realist FEP story of
biological systems.
4
3 Pebble meets Markov blanket
One person’s meat is another person’s poison: the scale-free applicability of the FEP’s
Markov blanket formalism may be taken as a vice, rather than a virtue. In this section we take
up a specific challenge to the FEP that flows from what seems like an overly generous
application of the FEP formalism to a wide variety of phenomena: the pebble challenge. It
challenges the FEP’s ambitions to describe the organizational dynamics of life precisely
because its mathematical formalisms apply equally well to pebbles, and other abiotic systems
as they do to biotic ones. One might therefore worry that the FEP fails to say anything
specific about biology, unless characteristics we take to be specific to biology are not so
specific at all. We describe this challenge in more detail now.
Friston & Stephan (2007) anticipates this kind of challenge to the FEP. They ask, “What is
the difference between a plant [a biotic system] and a stone [an abiotic system]?” (2007, p.
422) They say that the plant “is an open non-equilibrium system, exchanging matter and
energy with the environment, whereas the stone is an open system that is largely at
equilibrium” (2007, p. 422). There is something to this initial observation. Plants are open
systems, i.e., energy and mass can flow between the system and its surroundings. The same,
of course, can be said of stones as environmental forces impinge on their surface area, and
their own existence influences their environment by, say, releasing heat during the day, or
altering pathways for organisms (Olivotos & Economou-Eliopoulos 2016). At first glance, it
thus seems that the FEP applies in the same way to stones, plants and humans.
The FEP (as we saw above) starts from the simple observation “that for something to exist
it
must possess (internal or intrinsic) states that can be separated statistically
from (external or
extrinsic) states that do not constitute the thing” (Friston 2019, p. 4, emphases added). This
Markov blanket formulation would apply to a pebble as follows. The Markov blanket defines
the conditional independencies between two sets of states: the system and the environment.
Pebbles are composed of minerals with different properties, lattice structure, hardness and
cleavage. We can associate these variables as the internal states comprising the system. On
shingle beaches, the second set of states (the environment) would be other pebbles, and so on.
In rivers, the water could be cast as the external states. As seen in Section 2, it is possible to
cast a spatial boundary for anything that exists in terms of a Markov blanket (Friston 2013).
The pebble has a clear boundary separating internal states and external states. The sensory
4 The extent to which this story should be taken in a realist sense so that each biotic system literally performs
advanced statistical operations, or in an instrumentalist sense so that each biotic system’s interactional dynamics
merely correspond to (or ‘instantiate’) the dynamics described in Bayesian inference is still debated (van Es
2020; see Ramstead, Kirchhoff, Friston 2019; Corcoran et al. 2020). A discussion of this debate is outside the
scope of this paper, and it is unnecessary for our current purposes.
8
states of a pebble can be associated with the effects of external causes of its boundary -
stressors such as pressure, temperature and so on. Its active states would correspond to how
the pebble effects external states - e.g., via release of heat back into the environment. The
Markov partitioning rule governing the relation between states dictates that external states act
on sensory states, which influence, but are not themselves influenced by internal states.
Internal states couple back to external states, via active states, which are not influenced by
external states (Palacios et al. 2020). Given that the Markov blanket formulation for a pebble
is possible, it follows that internal pebble states are conditionally independent of external
states in virtue of the Markov blanket states.
5
What does this mean for our FEP analysis of the pebble, given what we have seen in Section
2? Under the FEP, the mere presence of a Markov blanket implies that internal states can be
understood as if they minimise the free energy over the states that make up their Markov
blanket. Technically, since minimising free energy is the same as performing approximate
Bayesian inference, it follows that one can associate the internal pebble states (and its blanket
states) with Bayesian inference. As such, it seems that if (1) anything that exists over time
can be described in terms of a Markov blanket which implies that expected free energy is
minimized by way of Bayesian inference, and (2) pebbles exist, then (3) pebbles can be
described as having a Markov blanket, whose dynamics will appear as though they minimize
free energy by way of Bayesian inference. The formalisms of the FEP that we employed here
therefore seem too general to distinguish between pebbles and organisms. Below we will
discuss what is needed for a formalism to properly address autonomy in Section 4. In Section
5 we will see how FEP’s toolkit can be leveraged to make a headway in providing a
principled distinction between pebbles and organisms.
4 Autonomy meets pebble
The pebble challenge need not be a knockdown argument against the ambitions of the FEP to
address biology and cognitive science. Here we consider a possible reply to it. Our agenda
will be to introduce the notion of autonomy
from enactive philosophy of cognitive science.
6
5 We could, for example, determine the surface molecules of the pebble to be sensory states, adjacent molecules
to be active states, and the remainder of the pebble’s molecules to be internal states, with the environment cast
as external states. The molecules we cast as active states are then shielded from influence of the external states,
while still able to influence the external states, though vicariously through sensory states. Of course, a pebble is
merely an example and this could apply to many abiotic systems. Thanks to an anonymous reviewer for pointing
this out.
6 Autonomy is a central theoretical construct of the enactive approach to life and mind (Varela, 1979; Varela et
al., 1991; Thompson 2007; Di Paolo & Thompson 2014; Di Paolo et al. 2017). Enactivism is a theoretical
framework with roots in theoretical biology, dynamic systems theory, and phenomenology. In enactivism, the
notion of autonomy as operational closure has received special attention in attempting to unearth the
self-organisational dynamics essential to life. Yet the literature so far has fallen short of construing operational
closure in terms of the FEP’s conceptual toolkit. Here we will make a first attempt at conceiving of an
operationally closed system as being composed of a network of Markov blanketed systems that stand in a
mutually enabling relation to one another.
9
Kirchhoff et al. (2018) appeal to this notion in order to distinguish between mere active
inference
and adaptive active inference
. The former can be shown to apply to abiotic systems
such as pebbles (from above) and the generalised synchrony induced in coupled pendulum
dynamics. Adaptive active inference is introduced to make sense of the idea that living
organisms are able to actively change or modulate their sensorimotor coupling to their
environment - which is needed to actively monitor and predict changes to perturbations that
challenge homeostatic variables, which may, sometimes, go out of bounds. However, the
modulation of sensorimotor coupling is merely a (contingent) feature of an autonomous
system. Operational closure and precariousness jointly define autonomy. We build on
Kirchhoff et al’s (2018; see also Kirchhoff & Froese 2017) argument by showing how
autonomy is underwritten by the concepts of operational closure and precariousness (cf. Di
Paolo & Thompson 2014).
4.1 Operational closure and precariousness
Operational closure is central to the conceptualisation of autonomy (Di Paolo & Thompson
2014). It is characterized as a form of organization
in the sense that it specifies the particular
way any system’s component parts are organized in relation to one another. By specifying the
organized ‘unity’ (the system) via this formalism, we also implicitly define its environment.
Furthermore, by defining the system and its environment, we also specify the boundary
through which the system interacts with its environment (Beer 2004, 2014; Maturana and
Varela, 1980).
A system is operationally closed if the processes that make up the system constitute what is
known as a self-enabling network. This means that each of the network’s processes enables
and is enabled by at least one other process in the network. It is empirically possible to
determine whether any particular system is operationally closed by mapping out the causal
processes relevant for the system and how they relate to one another. In particular, one must
look for enabling
relations. Any one process is said to enable another process if its
continuation is partly or wholly constitutive of the enabled process. To explain how this
works, it may help to look at the diagram of an operationally closed system (Figure 2 below).
In this toy system, we distinguish five component processes: A, B, C, D, and E represented as
nodes in the figure. The arrows between them represent enabling relations, so that A can be
seen to enable process B. Following the arrows, we can identify a closed loop in the enabling
relations pertaining to processes A, B, and C. This means that the continuation of A enables
the continuation of B, which enables the continuation of C, which comes full circle and
enables the continuation of process A: the ABC network is thus self-enabling
. But what about
processes D and E? E can be seen to enable process A, yet remains outside of the network as
it is not enabled by a process in the network. D, on the other hand, is
enabled by a process in
the network, but doesn’t loop back and enable a process in the network itself. This is why
ABC can be identified as a self-enabling network, while D and E fall outside the boat.
10
Figure 2
, a diagram displaying an operationally closed network of enabling
relations. Each node in the figure represents a process in the network, and each
arrow represents an enabling relation. The operationally closed network is
marked by the black nodes; processes outside the operationally closed system
are marked in grey. Each node that is part of the operationally closed network
is marked by having at least one outgoing and one incoming arrow from
another node in the operationally closed network as is described in-text
(inspired by Di Paolo and Thompson 2014).
Precariousness
signifies a natural inclination to decline. In Figure 2 above, for example,
process A is precarious if it would cease were it not enabled by E and C. It may be that not
each enabling process is per se
necessary or sufficient in enabling. If A is precarious, this
does mean however, that jointly, its enablers are both necessary and sufficient for the
continuation of A. As each node in the network is precarious, the network itself is too. This is
crucial for the notion of autonomy in the enactive approach (Di Paolo 2005).
A paradigmatic case that displays operational closure and precariousness is a single cell. A
cell is constituted by a complex network of interrelated causal processes, but, for didactic
purposes, we distinguish three. The first process comprises the metabolic network. The
second process is the membrane-generation of the cell that separates the network from the
environment. The third process consists of the active regulation of matter and energy
exchanges of the cell, via the membrane-induced barrier, with its external environment. By
way of this third process, the system can absorb nutrients from and expel wastes into its
environment to continue its metabolism, looping back into process one.
The metabolic network, process 1, can be divided into subprocesses. A central aspect of
metabolism is the production of enzymes, which exhibits a form of closure in itself. Enzymes
are precarious. As such, when particular enzymes need to be produced, this occurs “in
metabolic pathways helped by other enzymes, which in turn are produced with the
participation of other ones … in a recursive
way” (Mossio and Moreno 2010, p. 278,
emphasis added). That is, the metabolic network in itself can be said to be “enzymatically
closed” (Mossio and Moreno 2010, p. 278). This production network enables process 2: the
11
generation of a membrane that separates the network from its environment. This
semipermeable barrier is necessary for the system to actively regulate its exchanges with the
environment. It both allows the system to take in matter and energy from the environment,
and protect its internal network from external perturbation of the metabolism (Ruiz-Mirazo
and Mavelli 2008; Thompson 2007). The exchange with the environment enabled by the
barrier’s separation is process 3. The limited openness is exploited to allow for the absorption
of nutrients from the environment which can stimulate the maintenance of the membrane
itself, but also “contribute to the production of an ‘energy currency’” (Ruiz-Mirazo and
Mavelli 2008, 376; Skulachev, 1992). Via trans-membrane mechanisms, this ‘currency’ is
cashed out in internal metabolic reactions, transformed to serve as energy resources to
maintain and actively regulate its boundary conditions (Ruiz-Mirazo, Mavelli 2008). This is
to say that process 3 loops back into enabling process 1 and 2. These enabling relations are
visualized in Figure 3 below. Here we can see that operational closure and precariousness
jointly correctly marks a cell as an autonomous system.
Figure 3
illustrates the simplified process network relevant to a single cell.
Process 1, which captures the metabolic network, is represented by the 1 in the
top-left. Process 2, membrane-generation, is represented by 2 in the top-right.
Process 3, the active regulation of matter and energy exchanges with the
environment is represented by 3 in the bottom-right. The environment is
represented by the E in the bottom-left. The arrows between the represented
processes stand for enabling relations as described above. We see that 1, 2 and
3 form a self-enabling network as per the definition above. Each process in the
network enables and is enabled by at least one other process in the network. 1
enables 2 and is enabled by 3. 2 enables 3 and is enabled by 1 as well as 3. 3
enables both 1 and 2, and is enabled by 2 and E. The network here described
thus represents an operationally closed system.
4.2 Autonomy and the pebble
A pebble is not autonomous. Given that autonomy is intended to solve the pebble challenge,
it is important to subject the pebble to the same analysis: is a pebble operationally closed and
precarious? If not, this indicates that autonomy as used here is an adequate concept to
distinguish between abiotic and biotic systems. We distinguish four causal processes that are
12
relevant to the formation and maintenance of the pebble’s structural integrity on a shingle
beach, two of which are directly considered to be determinants of a pebble’s shape and size:
particle abrasion and particle transport. These two processes may be more or less relevant
depending on the particular geological location (Domokos and Gibbons 2012; see also
Landon, 1930; Kuenen, 1964; Carr, 1969; Bluck, 1967). Particle transport refers to the
transport of the pebble by the river. Particle abrasion refers to the collusion with other
pebbles (and other materials) that occurs primarily during particle transport. The remaining
two processes are the fluid flows of the river and the environment that consists of abraders of
a hard enough consistency to allow for particle abrasion.
The four processes in the network are thus: fluid flows (A), environmental abraders (B),
particle abrasion (C) and particle transport (D). Fluid flows enable particle transport, and can
reasonably be considered to enable particle abrasion too. Assuming there are no other moving
objects in the river, the pebble will be unlikely to move from its location and is thus unlikely
to be abraded by other materials, if it is not swept anywhere by the fluid flows.
Environmental abraders only enable particle abrasion. Particle abrasion in itself does not
enable any other process in the network. Particle transport only enables particle abrasion.
This means that fluid flows only enable other processes, but are themselves not enabled by
any other process in the network. The enabling relations are specified in Figure 4 below. This
means that A cannot be part of a self-enabling network. Environmental abraders only enable
particle abrasion, and are not themselves enabled by other processes in the network and thus
B suffers the same fate as A. C, particle abrasion, is enabled by all other processes in the
network, but does not actually enable any other process, and can also not figure in a
self-enabling network. Process D, particle transport, is the only process that is both enabled
by and enables another process in the network, being enabled by fluid flows, enabling particle
abrasion. This enabling chain, however, never loops back into enabling the continuation of
particle transport. As such, Process D too cannot be part of a self-enabling network.
Summing it up, there is no self-enabling network to be found in the processual network
surrounding pebbles. This means that, under the operational closure formalism, pebbles are
not marked as autonomous.
7
7 Our treatment of the pebble case may seem disanalogous with our treatment of the cell case. The discussion of
the cell case treated a few important internal
processes such as metabolism and membrane-generation next to
the external
processes concerned with exchanges with the environment. Our take on the pebble case seems to
lack in internal counterparts to the external processes. This speaks to what the operational closure formalism
indicates, which is that the pebble simply is not an operationally closed system. This means that, in terms of this
formalism, there is no ‘internal’ to speak of that could
operate (semi-)independently of the external processes.
13
Figure 4
represents the process network relevant to a pebble on a shingle
beach. The nodes with letters A, B, C and D in the figure represent the
processes A, B, C, and D mentioned in-text respectively. The arrows represent
enabling relations so that the arrow going down from A to C means that A
enables C. Each node is coloured gray to indicate that the network is not
operationally closed, as no process except for D enables and is enabled by at
least one other process in the network. The network can thus not be said to be
self-enabling.
5 Autonomy meets Markov blanket
Operational closure and precariousness provide the principled distinction between
autonomous and non-autonomous systems. It is this distinction that seems difficult to capture
within the Markov blanket formalism of the FEP: indeed, following Section 3, it seems as
though both organisms and pebbles can be said to minimise free energy and can thus be cast
as engaging in Bayesian inference. In Section 4 we have seen two notions from the enactive
literature that are apt at capturing the difference between biotic and abiotic systems. As such,
there is good reason to attempt to incorporate the enactive notion of autonomy into the FEP
(Kirchhoff et al. 2018; Palacios et al. 2020).
A few FEP conceptions of autonomy exist in the literature, so it is important to discuss these
and why they fall short of capturing operational closure and precariousness. According to one
usage of autonomy, the internal and active states of any Markov blanketed system are
considered autonomous states
, because their values are not directly influenced by the
environment (Friston, Wiese, Hobson, 2020). Yet this does not aid in a distinction between
biotic and abiotic systems, as any Markov blanketed system by definition has internal and
active states. One may also think the presence of active states in a system is crucial, as active
states are what, in the FEP formalism, allow an organism to modulate their exchange with its
environment. Yet, recall from Section 3 that a pebble also has active states. It would be
strange to think that a pebble’s existence has no influence on its environment merely because
it does not act
on its environment. A pebble’s mass will influence the state of the water that
14
may surround it, or the movement of the adjacent pebbles on a shingle beach, and influences
the behaviour trajectories of organisms in its vicinity. These sorts of influences will be
formalised as active states in the Markov blanket formalism. As such, we will be able to
identify external states dependent on the pebble’s active states in the same way we can do so
for organisms.
Yet, one may object, a pebble’s exchange with its environment is much, shall we say,
simpler, than an organism’s. This is roughly what is captured in the distinction between
between active
particles and inert
particles, discussed in Friston’s 2019. The distinction here
8
rests on what is called the ‘information length’ of a system, the technical specifics of which
are outside of the scope of this paper. Broadly, one could say the information length of a
9
system corresponds to the size of the ‘viable bound’ of the system under scrutiny as we have
discussed it in Section 2. This means that a high information length is associated with
systems whose internal states display a large degree of variability, whereas low information
length is associated with systems whose internal states remain largely static, or consistently
revisit a very small set of states. This seems to make headway into distinguishing biotic from
abiotic systems, yet fails to draw a divide in kind,
offering only a gradual distinction in
degrees
, leaving room for a grey area between biotic and abiotic. Take the pebble, for
example. For the sake of argument, let us concede that the pebble’s information length is
sufficiently low to be termed an inert
particle. Yet consider now a shingle beach, consisting
of a large amount of pebbles, that lies at water. We can consider the beach as a whole to have
its own Markov blanket, forming an ensemble
of the individually blanketed pebbles at the
beach. The complexity of the internal states of the shingle beach as a whole as it maintains its
integrity (continues being a shingle beach) in spite of the environmental fluctuations (the
water flowing on and off-shore, weather circumstances, etc.) increases exponentially as we
imagine it to be larger, comprising more distinct and varied pebbles, each of which ‘respond’
differently to the varying temperatures and kinetic forces. This increases the associated
information length of the shingle beach. We could do this for increasingly complex abiotic
systems until, one could imagine, the information length starts to look a lot like that of a
single bacterium. The crucial point here is that relying on a system’s information length may
not necessarily pick out biotic systems exclusively, and remains a difference in degree
, as
opposed to a difference in kind
.
10
A final suggestion that could be thought to pick out organisms over pebbles is that of
non-equilibrium steady-state (NESS). According to the FEP’s more recent formulations ,
11
8 Thanks to an anonymous reviewer for pointing this out.
9 See Friston’s (2019) unpublished manuscript for a description in technical detail.
10 What this means is that the grey area is not inherently
a fault, yet conceding this does not help us in
distinguishing the pebble clearly from the organism.
11 Contrary to, say, Friston (2013), the condition of a system being at NESS with its environment seems to have
replaced the initial clause of being locally ergodic (see Friston 2019; but also Hipólito 2020; Ramstead, Badcock
et al. 2019) . Discussion of this change and its philosophical implications are outside of the scope of this paper,
but see Bruineberg et al. (2020) for preliminary discussions.
15
any Markov blanketed system that is at NESS with its environment can be cast as minimizing
free energy (Ramstead, Badcock et al. 2019). For a system to be in a non-equilibrium
steady-state so defined means that the system is far from equilibrium and, in virtue of
systematic environmental exchange, remains in the same state over time. Yet being in a
steady state implies that the system remains in the same
state over time (Gagniuc 2017). This
means that, for a dynamically changing organism in constant flux, this only holds by
approximation or within certain specific timeframes. An extreme example are butterflies that
just got out of their cocoon, which corresponds to a massive change in the organism’s states,
but humans can just as well hardly be said to occupy the same state over time. A pebble is
12
in no need of environmental exchange to remain a pebble and is thus not at NESS. Yet it is
also known that NESS does not uniquely pick out biotic systems (see for example Bernard
and Doyon, 2015; Pourhasan, 2016). As such, it remains of import to look at the enactive
approach to autonomy and how this could be approached from within the FEP.
5.1 On self-individuation
A system is considered operationally closed only if it exhibits a network of self-enabling
processes. That is, each process in the network enables and is enabled by at least one other
process in the network. This means that any operationally closed system is inherently
composed of multiple individually distinguishable component processes. Taken together,
these individually distinguishable component processes form a larger network that
self-individuates
, and generates its own boundary between itself and its environment. The
Markov blanket formalism is well-equipped to capture this hierarchical boundary generation
of processes (Palacios et al. 2020). If we take each component process to have a Markov
blanket, and the larger, operationally closed network to have a Markov blanket too, the
generation of a self-enabling and self-individuating process network can be cast as the
hierarchical self-organization of a Markov blanketed ensemble
of Markov blankets. Palacios
et al. (2020) show how, with a few crucial assumptions, single cells can be shown to
aggregate quite naturally into a larger ensemble. In this particular way, we can consider each
node of the network to be Markov blanketed, and the ensemble-network to be Markov
blanketed in itself, as shown in Figure 5 below. The nodes of the operationally closed
network need not be operationally closed themselves, which means that the nodes themselves
need not invite being divided further into another layered network. We can thus ground
operational closure in terms of Markov blanket ensembles without inviting an infinite regress.
This maps onto a single cell organism too. Consider that each organelle of a single cell can be
distinguished statistically from the rest of the cell, thus establishing a Markov blanket
(Palacios et al. 2020), without in itself being operationally closed and thus not in itself
12 The FEP may be able to accommodate ‘wandering sets’ (see Birkhoff 1927) which could account for changes
to a system’s viable bound over time, though it remains to be seen whether this could accommodate drastic and
sudden changes such as the butterfly’s (Friston 2019).
16
requiring to be composed of a self-enabling process network under the current definition of
operational closure.
Figure 5 describes the operationally closed single cell system with a Markov
blanket around the ensemble of process networks that make up the system. The
process relations described are just as they were in Figure (x: cell). The circle
around the self-enabling network of 1, 2 and 3 represents the Markov blanket
around the ensemble.
Although this captures a key feature of operational closure, self-individuation (or
membrane-generation in terms of a single biotic cell), it falls short of accounting for the
conditional enabling network that differentiates autonomous from non-autonomous systems.
Hierarchical self-organization is only part of the enactive story of autonomy. Indeed, the
pebble challenge could be reformulated as a shingle beach challenge
so that the beach can be
cast as an ensembled Markov blanketed system that engages in Bayesian inference,
composed of individually Markov blanketed pebbles. The distinction between abiotic and
biotic thus remains blurred, even in a hierarchical perspective.
5.2 On operational closure and enabling relations
There are a few differences between just any Markov blanketed system and an operationally
closed Markov blanketed system that we need to capture. Operational closure is a particularly
structured
manner of self-organization (Maturana and Varela, 1980). Increased structure over
time implies that the long term entropy (informally a measure of disorder; Friston 2013) is
low, which means that sensory surprise must be low too. The ensemble’s states are
constituted by the component states, which means that the component states inherit this low
surprise. This is a key aspect of understanding operational closure in the FEP.
We can exploit the lower surprise internal to the network further by, for the sake of
exposition, ignoring the system’s environment. For each particular node, its sensory states are
17
entirely determined by the active states of the other nodes in the network (Palacios et al.
2020). More specifically, if A enables B, that means that the active states of A must have an
important influence on B, which in turn means that the active states of A are significantly
determinant of the sensory states of B. Conversely, if B is enabled only by A, its sensory
states are entirely determined by the active states of A. This means that, within the network,
each node’s sensory states are determined by the active states of its enablers. This implies
that the sensory surprise of any node is at a nearly absolute minimum, given
the active states
of the enabling nodes.
In light of this, an enabling relation is closely related to the notion of coupling
. Any two
nodes can be said to be coupled when they are in a relation of mutual
influence (Friston
2013). In active inference, the generative models associated with two coupled systems will
approach one another over time, giving rise to what is known as generalized synchrony
. As
the coupled two systems continuously interact, they become attuned to one another; they
adapt to one another (Friston 2013). This attunement means that the influence they have on
one another becomes increasingly well accommodated. In mutual attunement, this entails
changes in the extrinsic
probability distribution in the state space, so that the sensory states
associated with the active states of the coupled system are increasingly likely. On the scale of
the network, this means that the nodes as part of the network, i.e.
on a network-level scale,
are in a tight coupling relation. This is to say that each node’s influence will enable, and thus
largely determine, another node’s states that will, by virtue of being part of the network,
couple back the initial node to enable and largely determine its own states either directly or
indirectly. An operationally closed network, then, can be taken as a tightly coupled network
of Markov blanketed nodes.
Note however, that, prima facie
, the notion of coupling is not necessarily applicable to any
two nodes in an enabling relation within the network. We thus cannot simply transcribe the
enabling relations between nodes as coupling relations. A coupling relation is symmetrical
insofar it prescribes mutual influence. This does not mean that the interaction needs to be
identical in both
directions of influence, but it does imply that the interaction is minimally
bidirectional: the active states of one node determine the sensory states of another node and
vice versa
. Taken in this sense of direct influence, an enabling relation is not. An enabling
relation can be asymmetrical, as we see in nodes 1 and 2 in Figure 5 above. This means that
we would miss out on asymmetrical enabling relations if we were to transcribe them as
coupling relations in a model. Moreover, an enabling relation concerns a specific type of
influence that one node has on another. Consider that any random two systems may, for a
certain duration over time, be coupled in a mutually disruptive
fashion. This means that rather
than enabling
one another, they instead inhibit
one another. This distinction too may be lost if
we were to transcribe enabling relations as coupling relations. Crucially, however, we can
say
that the individual nodes are at least indirectly coupled to one another from a network
perspective.
18
The network perspective can also capture the sense in which operational closure depends on a
network’s constituents
. Consider, for example, how the free energy of a Markov blanketed
ensemble of Markov blankets depends on the free energy of its constituents (Friston, 2013).
Nonetheless, the shingle beach considerations in Section 5.1 remain valid.
5.3 On precariousness and limits
The Markov blanketed ensemble of Markov blankets has been important in our
characterization of self-individuation and operational closure, so one could think it to cover
precariousness as well. The idea is that an ensemble’s free energy is determined by the free
energy of its constituents, which means that if the constituents’ free energy is minimised, the
free energy of the ensemble is minimised too. It is important to note that this hierarchical
dependence is a crucial feature of precariousness in organisms. That is, organisms and their
component processes are inherently precarious. Yet what is typical of precariousness is not
the hierarchical dependence relation: it is the natural inclination to decline.
More important here is the FEP requirement of a system to be at NESS with its environment.
As we have seen, this implies that the system requires continued environmental exchange to
maintain its state. Barring the limiting remarks
of the applicability of NESS to real, living
organisms noted above at the start of Section 5, the continued environmental exchange
requirement for maintaining its state is exactly what precariousness demands
. Some employ
this feature of the FEP to construe cancer, for example (Manicka and Levin 2019; Kuchlin et
al. 2019).
13
Furthermore, the low sensory surprise of an enabled node, given the active states of enabling
nodes may also be able to capture an organism’s precariousness
. Recall that precariousness
appears on two levels in an autonomous system. Each process in the network is precarious,
and the network as a unity is too. Network-level precariousness is built into the FEP at its
very core. Any system needs to put in work to be able to maintain its boundaries with the
environment and continue existing. This means that without this work, the system will
disintegrate, which is to say the system is naturally inclined to cessation, yet remains intact
due to the ‘efforts’ of the system. In this sense, the organism can be taken as precarious.
However, this line of thinking invites an unintended implication on the node level. Consider
that high-probability sensory states are those for which they are largely determined by their
enablers’ active states. The cessation of a process, further, is associated with leaving expected
bounds. When a process ceases, its active states will thus by definition leave expected
bounds. This implies that the sensory states of an enabled node would be highly surprising
(given its ceasing enabler’s active states) so that it’s likely to enter an unviable state and
cease as well. This seems to entail that if any random enabling node would cease, the sudden
13 Thanks to an anonymous reviewer for pointing this out, which inspired further considerations regarding
operational closure as well.
19
increase in sensory surprise for the enabled nodes would sooner or later cause each other
process in the network to fall like dominoes. After all, their own cessation will cause a spike
in sensory surprise in the nodes they enable, and so on. As the network is composed only of
processes that both enable and are enabled by at least one other node in the network, no
single process will be spared. In certain cases, this is to be expected. Consider our toy
description of a single cell in Section 4.1 above. If we were to cease any of the processes in
that network, the entire network would collapse. Each process is essential for the continuation
of the network. However, this is only a contingent fact of our toy description. As stated
above, it is not necessary for each enabling process to be individually necessary or sufficient
for the continuation of the enabled process. This flexibility is key in our understanding of
operational closure, yet is orthogonal to the domino effect we find on a node-level of
description. This shows that, though this approach is able to capture certain characteristics, it
is not capable of incorporating precariousness on both a network- and a node-level of
description.
Further, if we intend to capture the essential organizational dynamics for biotic systems,
abstracting away the environment misses the point. By defining what something is (the
system, or the unity
), we indirectly define that which it is not (the environment) (Beer 2004;
Friston 2019). This is exacerbated by the fact that for each probability distribution over
internal states, there is an associated probability distribution over external states that specifies
the expected influences of external states (Friston, Wiese, Hobson 2020). Even in the
presence of an external environment, an operationally closed system intrinsically defines its
environment as well as its boundary through which it can interact with the environment (Beer
2004 2014; Friston 2012). In an ecological situation, any one node’s surprise is thus not at
nearly absolute minimum, but can still be said to be particularly
low, given the active states
of its enablers.
In sum, we have presented some ways to consider conceptualizing operational closure and
precariousness in terms of a tightly coupled network of Markov blankets. There is a sense in
which tightly bound network-scale coupling, and particularly low sensory surprise of enabled
nodes given the active states of enabling nodes, can capture operational closure and
precariousness. This can be taken as a proof of concept. Further simulational research may
aid further in the incorporation of autonomy into the FEP by putting the approach here to
work.
Conclusion
Many FEP researchers hold the FEP to support a grand unifying ambition to account for a
wide variety of phenomena, among others the organizational dynamics of living and
cognitive systems. Yet a common criticism is that it is overly general and cannot distinguish
between biotic and abiotic systems, making it seem uninteresting from a biological
20
perspective. We addressed this worry by elaborating on earlier suggestions to incorporate the
enactive notion of autonomy into the FEP framework. In Section 4, we described how
operational closure and precariousness are concepts fit to handle the pebble challenge. In the
subsequent section, we made a first attempt at incorporating the enactive language of
autonomy into free energy language. We discuss different aspects of autonomy in the
enactive approach and how they could potentially be transcribed into the FEP formalism. The
FEP quite naturally accounts for self-individuation, a corollary of operational closure. The
same applies to the bi-directional dependence relation of an operationally closed system and
its component processes and a Markov ensemble and its nodes. Yet the enabling relation
central to operational closure proves more challenging. There are implications with regards to
the statistical relations between nodes for any operationally closed system such as an enabled
node’s low sensory surprise in light of its enablers’ active states that we show the FEP can
account for. Precariousness is also shown to be difficult to incorporate on a node-level
(although the ensemble level is able to capture some basal features of precariousness), and
the complexity of an ecological environment places limits on surprise-minimization
descriptions as leveraged before. The FEP can thus emulate a limited version of autonomy as
it appears in the enactive approach. Simulation modeling can further help incorporate this
notion of autonomy into the FEP formalism.
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