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Maps and territories, smoke, and mirrors

Published online by Cambridge University Press:  29 September 2022

Karl Friston*
Affiliation:
Wellcome Centre for Human Neuroimaging, Queen Square Institute of Neurology, University College London, London WC1N 3AR, UK k.friston@ucl.ac.uk

Abstract

It is a pleasure to comment on Bruineberg et al. – who raise some interesting questions of a philosophical and technical nature. I will try to answer three questions posed by the authors. Are Pearl and Friston blankets different things? Are Markov blankets used in an ontological sense? Is there a privileged Markov blanket?

Type
Open Peer Commentary
Copyright
Copyright © The Author(s), 2022. Published by Cambridge University Press

Are Pearl and Friston blankets different things? Yes and no. Markov boundaries, blankets, chains, and fields are just ways of carving nature at its joints, in terms of conditional independencies. For example, the “present” constitutes a Markov blanket that separates the “past” from the “future.” Pearl and Friston blankets are just Markov blankets applied in different settings. Pearl blankets (as defined here) are the minimal Markov boundaries in directed acyclic Bayesian networks. Friston blankets (as defined here) are exactly the same thing formulated for dynamic Bayesian networks. This distinction is important because Markov blankets are defined in terms of conditional independencies that require a well-defined probability density. In a dynamic setting, there are two candidates for this probability density: either the (nonequilibrium steady state) solution to density dynamics (e.g., obtained by the Fokker Planck formulation) or the probability density over paths through state space (e.g., obtained via the path integral formulation). It is probably the move to a dynamic setting that has led to puzzlement in the philosophical literature; especially, in understanding the link between sparse coupling in dynamical systems and the ensuing conditional independencies. (This puzzlement generally arises when focusing on linear edge cases; e.g., Biehl, Pollock, & Kanai, Reference Biehl, Pollock and Kanai2020.) However, Pearl and Friston blankets are just Markov blankets in the usual Markovian sense (Pearl, Reference Pearl2009).

Are Markov blankets used in an ontological sense under the free energy principle (FEP)? Yes. In the FEP, they are used in an ontologically robust sense, to model the actual boundaries of living systems (in other words, to model features of the territory) (Friston, Reference Friston2013). One may be a realist or an instrumentalist about this usage (i.e., about the features of the map), but in either case, the aim is to model the actual properties – in this case, the real boundaries – of actual systems.

In relation to the distinction between maps and territories, the FEP says something quite radical, and philosophically significant: it says, heuristically, that to exist at all is to become a map of one’s territory (i.e., to entail a generative model of one’s environment). It might be helpful to think about map-making as the sense-making implicit in any internal states that are equipped with a Markov blanket. Internal states are effectively generating a coarse-grained map of the territory beyond the Markov blanket. On this reading, the distinction between a (living) map and the accompanying territory only exists in virtue of a Markov blanket, which allows the map to mirror the territory, while allowing a separation of the territory from the map.

Is there a particular Markov blanket that is privileged for principled reasons? No. There is no unique Markov blanket or partition that is privileged under the FEP. However, this does not imply that particular partitions of a system are arbitrary. A failure to appreciate this precludes a proper treatment of the nature of things and, in particular, their scale invariance. Given a set of states at a particular scale, there are potentially many different partitions that have nontrivial Markov blankets. In other words, there are many ways of carving nature at its joints – as illustrated with the knee-jerk example in the target article.

The within-scale composition of Markov blankets is especially important in defining the architecture of generative models entailed by internal dynamics. Not only do Markov blankets define the structure of hierarchical generative models but also – within a hierarchical level – the factorisation afforded by Markov blankets can be read as modularity (Colas, Diard, & Bessiere, Reference Colas, Diard and Bessiere2010; Parr, Sajid, & Friston, Reference Parr, Sajid and Friston2020b). Indeed, this aspect of Markov blankets speaks to their foundational role in the FEP; in the sense that variational free energy is a functional of a mean field approximation to posterior beliefs – and a mean field approximation entails a factorisation that just is a specification of Markov blankets (Dauwels, Reference Dauwels2007; Winn & Bishop, Reference Winn and Bishop2005). This factorisation is ontological because it specifies the functional and computational architectures that are realised by (e.g., neuronal) message passing and implicit Bayesian belief updating. This means that the FEP rests on Markov blankets within (the internal states that are enclosed by) Markov blankets (Palacios, Razi, Parr, Kirchhoff, & Friston, Reference Palacios, Razi, Parr, Kirchhoff and Friston2020).

Finally, at the between-scale level, there is no privileged scale. The deeper question here is how one scale maps to the next and what variational principles are conserved over scales – and the implications for the top-down and bottom-up causation between scales (Kirchhoff, Parr, Palacios, Friston, & Kiverstein, Reference Kirchhoff, Parr, Palacios, Friston and Kiverstein2018; Palacios et al., Reference Palacios, Razi, Parr, Kirchhoff and Friston2020; Parr, Da Costa, & Friston, Reference Parr, Da Costa and Friston2020a). Formally, this is probably best dealt with using the apparatus of the renormalisation group. This apparatus has been applied in a realist fashion to the synthetic soup (see Figure 11 in Friston [Reference Friston2019]) and instrumentally in the modelling of neuronal dynamics in the brain (Friston et al., Reference Friston, Fagerholm, Zarghami, Parr, Hipólito, Magrou and Razi2021). In brief, it's Markov blankets all the way down – and all the way up.

Financial support

This work was supported by funding for the Wellcome Centre for Human Neuroimaging (Ref: 205103/Z/16/Z); and a Canada–UK Artificial Intelligence Initiative (Ref: ES/T01279X/1).

Conflict of interest

None.

References

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