Bruineberg and colleagues point out an important, yet hitherto overlooked flaw in the free energy principle (FEP) literature: The term “Markov blanket” has unnoticeably evolved into a more ontologically involved concept of “Friston blanket.” However, the gravity of this problem has been underplayed by some of the proponents of the FEP (e.g., Wiese & Friston, Reference Wiese and Friston2021, p. 4) who ignore the trouble that the reification of formal concepts leads to. We want to highlight one particular issue for the proponents of the FEP, especially of an associated metaphysical programme of “Markovian monism” (Friston, Wiese, & Hobson, Reference Friston, Wiese and Hobson2020; Wiese & Friston, Reference Wiese and Friston2021), concerned with the procedures for identification of Friston blankets in the world.
The problem stems from an important tension: Most other fields of computational modelling use Markov blankets as approximations or optimization tools (e.g., in machine learning for the purpose of dimensionality reduction and variable selection, see Aliferis, Tsamardinos, and Statnikov, Reference Aliferis, Tsamardinos and Statnikov2003; Peña, Nilsson, Björkegren, and Tegnér, Reference Peña, Nilsson, Björkegren and Tegnér2007; Tsamardinos, Aliferis, and Statnikov, Reference Tsamardinos, Aliferis and Statnikov2003; or for causal search, see Bai et al., Reference Bai, Glymour, Padman, Ramsey, Spirtes and Wimberly2004; Pellet & Elisseeff, Reference Pellet and Elisseeff2008). However, the FEP requires an (in principle) exact identification of a unique Markov blanket for each system of interest, what Friston, Heins, Ueltzhöffer, Da Costa, and Parr (Reference Friston, Heins, Ueltzhöffer, Da Costa and Parr2021a) call a “particular partition.” This is necessary because, as Friston argues (Reference Friston2019; Friston et al., Reference Friston, Wiese and Hobson2020), the existence of a Markov (Friston) blanket in a (non-equilibrium) steady-state system is sufficient to prove that the (autonomous, i.e., internal and active) states of the system will “look as if they are trying to minimise (…) the surprisal of states that constitute the thing, particle, or creature. (…) This means that anything that exists must, in some sense, be self-evidencing” (Friston et al., Reference Friston, Wiese and Hobson2020, p. 6). Hence, for Friston, the existence of a particular partition secures that the system will conform to the FEP and allows for deducing it from first principles.
For this reason, in the recent FEP literature, there has been a quickly growing number of attempts to provide solutions to the problem of identifying Markov blankets (e.g., Da Costa, Friston, Heins, and Pavliotis, Reference Da Costa, Friston, Heins and Pavliotis2021; Friston et al., Reference Friston, Heins, Ueltzhöffer, Da Costa and Parr2021a, Reference Friston, Fagerholm, Zarghami, Parr, Hipólito, Magrou and Razi2021b). All those attempts focus on providing sufficiently strong approximations, as developing an exact analytical solution to this problem would require solving difficult open problems in partial differential equations. Additionally, researchers in this research community overlook an even more important issue, namely that both strong approximations of Markov blankets, and hypothetical methods for exact solutions to this problem require a full formal description of the system of interest (i.e., the equation describing its dynamics) at the outset. This defeats the practical purpose of finding Markov blankets.
Hence, the paradoxical tension between Markov and Friston blankets we want to highlight is that the pursuit of the metaphysical programme associated with the identification of Friston blankets under the FEP entails intractable mathematical problems that depend on our prior knowledge of the system's dynamics. But if we had a formal description of the system's behaviour, what new knowledge would Friston blankets provide? They certainly would not allow us to find the boundaries of entities of interest in the wild, since those must be assumed for the purpose of description of the system (even if it takes the general form of a Langevin equation, it still requires the assumption that the system is sufficiently stationary). And, if we assumed the whole causal structure of the system beforehand, there would be no need to refer to Pearl or Friston blankets to show that the system will behave in accordance with the FEP, as this would entirely follow from the description of the dynamics. As a consequence, neither this result nor blankets themselves would follow from first principles, but rather from a fallible heuristic analysis of the system of interest.
On the other hand, if we eschew precision and accept approximate optimization methods for finding Pearl blankets such as those widespread in machine learning and causal search (e.g., Pellet & Elisseeff, Reference Pellet and Elisseeff2008), we can use them as tools of discovery to identify the boundaries of entities (e.g., nodes in neural networks for the purpose of systems neuroscience). Furthermore, showing that a system delineated in this way conforms to the FEP might provide much more insight into the nature of the process, as it would require less knowledge at the outset. However, approximate methods do not allow for the use of the concept of Friston blanket and effectively preclude the viability of the metaphysical programme of the FEP as a naturalist ontology for life sciences.
Perhaps it is too quick to throw the blankets entirely at this point. Nonetheless, we believe that the use of the Markov blanket construct should enable us to solve pressing issues in computational modelling in the sciences of brain and behaviour. While Markovian monism metaphysics is not such a pressing issue, studying the causal and functional dynamics of cognitive systems is. In this context, we need various fallible heuristics for delineating Pearl blankets; that is, many stupid (Smaldino, Reference Smaldino, Vallacher, Read and Nowak2017), approximate, and tractable models, and we need more of them to be able to make use of the error diversity inherent in any heuristic enterprise (Wimsatt, Reference Wimsatt2007). While stronger analytical methods for finding Markov (and Friston) blankets are not necessarily dead ends, the FEP theorists' focus on those difficult methods makes them overlook a lot of lower hanging fruits.
Bruineberg and colleagues point out an important, yet hitherto overlooked flaw in the free energy principle (FEP) literature: The term “Markov blanket” has unnoticeably evolved into a more ontologically involved concept of “Friston blanket.” However, the gravity of this problem has been underplayed by some of the proponents of the FEP (e.g., Wiese & Friston, Reference Wiese and Friston2021, p. 4) who ignore the trouble that the reification of formal concepts leads to. We want to highlight one particular issue for the proponents of the FEP, especially of an associated metaphysical programme of “Markovian monism” (Friston, Wiese, & Hobson, Reference Friston, Wiese and Hobson2020; Wiese & Friston, Reference Wiese and Friston2021), concerned with the procedures for identification of Friston blankets in the world.
The problem stems from an important tension: Most other fields of computational modelling use Markov blankets as approximations or optimization tools (e.g., in machine learning for the purpose of dimensionality reduction and variable selection, see Aliferis, Tsamardinos, and Statnikov, Reference Aliferis, Tsamardinos and Statnikov2003; Peña, Nilsson, Björkegren, and Tegnér, Reference Peña, Nilsson, Björkegren and Tegnér2007; Tsamardinos, Aliferis, and Statnikov, Reference Tsamardinos, Aliferis and Statnikov2003; or for causal search, see Bai et al., Reference Bai, Glymour, Padman, Ramsey, Spirtes and Wimberly2004; Pellet & Elisseeff, Reference Pellet and Elisseeff2008). However, the FEP requires an (in principle) exact identification of a unique Markov blanket for each system of interest, what Friston, Heins, Ueltzhöffer, Da Costa, and Parr (Reference Friston, Heins, Ueltzhöffer, Da Costa and Parr2021a) call a “particular partition.” This is necessary because, as Friston argues (Reference Friston2019; Friston et al., Reference Friston, Wiese and Hobson2020), the existence of a Markov (Friston) blanket in a (non-equilibrium) steady-state system is sufficient to prove that the (autonomous, i.e., internal and active) states of the system will “look as if they are trying to minimise (…) the surprisal of states that constitute the thing, particle, or creature. (…) This means that anything that exists must, in some sense, be self-evidencing” (Friston et al., Reference Friston, Wiese and Hobson2020, p. 6). Hence, for Friston, the existence of a particular partition secures that the system will conform to the FEP and allows for deducing it from first principles.
For this reason, in the recent FEP literature, there has been a quickly growing number of attempts to provide solutions to the problem of identifying Markov blankets (e.g., Da Costa, Friston, Heins, and Pavliotis, Reference Da Costa, Friston, Heins and Pavliotis2021; Friston et al., Reference Friston, Heins, Ueltzhöffer, Da Costa and Parr2021a, Reference Friston, Fagerholm, Zarghami, Parr, Hipólito, Magrou and Razi2021b). All those attempts focus on providing sufficiently strong approximations, as developing an exact analytical solution to this problem would require solving difficult open problems in partial differential equations. Additionally, researchers in this research community overlook an even more important issue, namely that both strong approximations of Markov blankets, and hypothetical methods for exact solutions to this problem require a full formal description of the system of interest (i.e., the equation describing its dynamics) at the outset. This defeats the practical purpose of finding Markov blankets.
Hence, the paradoxical tension between Markov and Friston blankets we want to highlight is that the pursuit of the metaphysical programme associated with the identification of Friston blankets under the FEP entails intractable mathematical problems that depend on our prior knowledge of the system's dynamics. But if we had a formal description of the system's behaviour, what new knowledge would Friston blankets provide? They certainly would not allow us to find the boundaries of entities of interest in the wild, since those must be assumed for the purpose of description of the system (even if it takes the general form of a Langevin equation, it still requires the assumption that the system is sufficiently stationary). And, if we assumed the whole causal structure of the system beforehand, there would be no need to refer to Pearl or Friston blankets to show that the system will behave in accordance with the FEP, as this would entirely follow from the description of the dynamics. As a consequence, neither this result nor blankets themselves would follow from first principles, but rather from a fallible heuristic analysis of the system of interest.
On the other hand, if we eschew precision and accept approximate optimization methods for finding Pearl blankets such as those widespread in machine learning and causal search (e.g., Pellet & Elisseeff, Reference Pellet and Elisseeff2008), we can use them as tools of discovery to identify the boundaries of entities (e.g., nodes in neural networks for the purpose of systems neuroscience). Furthermore, showing that a system delineated in this way conforms to the FEP might provide much more insight into the nature of the process, as it would require less knowledge at the outset. However, approximate methods do not allow for the use of the concept of Friston blanket and effectively preclude the viability of the metaphysical programme of the FEP as a naturalist ontology for life sciences.
Perhaps it is too quick to throw the blankets entirely at this point. Nonetheless, we believe that the use of the Markov blanket construct should enable us to solve pressing issues in computational modelling in the sciences of brain and behaviour. While Markovian monism metaphysics is not such a pressing issue, studying the causal and functional dynamics of cognitive systems is. In this context, we need various fallible heuristics for delineating Pearl blankets; that is, many stupid (Smaldino, Reference Smaldino, Vallacher, Read and Nowak2017), approximate, and tractable models, and we need more of them to be able to make use of the error diversity inherent in any heuristic enterprise (Wimsatt, Reference Wimsatt2007). While stronger analytical methods for finding Markov (and Friston) blankets are not necessarily dead ends, the FEP theorists' focus on those difficult methods makes them overlook a lot of lower hanging fruits.
Acknowledgements
We want to thank Mel Andrews, Conor Heins, Dalton Sakthivadivel, and the Active Inference Lab for helpful clarifications.
Financial support
This work was supported by the Ministry of Education and Science (Poland) research grant (W. R., DI2018 010448), as part of the “Diamentowy Grant” programme; National Science Centre (Poland) research grant (M. M., P. L., grant number 2014/14/E/HS1/00803) and Leverhulme Doctoral Scholarship (T. K.).
Conflict of interest
None.