The target article highlights work by, for example, Kirchhoff and Kiverstein (Reference Kirchhoff and Kiverstein2021) and Ramstead, Kirchhoff, Constant, and Friston (Reference Ramstead, Kirchhoff, Constant and Friston2021), where attempts have been made to invoke the mathematical formalism of Markov blankets to justify claims about the bounds of the mind. The strategy highlighted in the target article is, however, not a new one. Rather, it echoes earlier approaches by advocates of dynamical systems theory to similarly use mathematical models of a system's behaviour to justify claims about the bounds of the mind. By placing the target article in the context of this earlier work it might be possible to bring into sharper relief the issues raised in the target article and, more positively, sketch a way forward for Markov blanket theorists.
One well-known model from the dynamical approach to cognition is the Haken–Kelso–Bunz model (Haken, Kelso, & Bunz, Reference Haken, Kelso and Bunz1985), which arose out of empirical work on the dynamics of inter-limb coordination. For example, Kelso (Reference Kelso1984) observed that when people rotated their wrists in an anti-phase pattern while gradually increasing the cycling speed a critical point was reached after which there was a rapid breakdown in the anti-phase pattern with coordination rapidly being reestablished in an in-phase pattern. The model was able to formalise this phenomena using the tools of dynamical modelling resulting in a model containing two parameters: one for cycling speed and one for the relative phase between the two limbs. The power of this model is its generality. Not only can it capture the dynamics of inter-limb coordination but it can also be applied to phenomena like socially coordinated motor behaviour. For example, Schmidt, Carello, and Turvey (Reference Schmidt, Carello and Turvey1990) found that two people seated next to each other, and engaging in anti-phase leg swings, exhibit the same dynamics as inter-limb coordination.
The Haken–Kelso–Bunz model is an example of a nonlinear dynamical system. As Chemero (Reference Chemero2011) argues, only linear systems are decomposable while nonlinear systems are non-decomposable. The upshot of this non-decomposability is that the dynamics of nonlinear systems must be modelled in terms of global collective variables, and that it is not possible to model the system dynamics in terms of separate component parts. That is, the mathematical formalism enforces viewing the two people engaged in inter-personal coordination as a single unified system. The boundaries of this system are not located within a single person but encompass both people. Drawing the boundaries of the system at the edge of a person's skull amounts to splitting the system, a move prohibited by the formalism. The move here is echoed by Kirchhoff and Kiverstein (Reference Kirchhoff and Kiverstein2021) and Ramstead et al. (Reference Ramstead, Kirchhoff, Constant and Friston2021) outlined by the target article. The mathematical formalism of nonlinearly coupled dynamical systems is replaced with the Markov blanket formalism, but the consequence is the same. The formalism used to model the system defines the bounds of the system.
This move is not unproblematic. The explanatory status of dynamical models has been questioned by those advocating for mechanistic explanation (e.g., Colling & Williamson, Reference Colling and Williamson2014; Kaplan & Bechtel, Reference Kaplan and Bechtel2011; Kaplan & Craver, Reference Kaplan and Craver2011). Although it's not possible to replay these arguments here, I will pick out one point that turns on this explanatory worry. The coupling-induced synchronisation observed in intra- and inter-personal limb movements is also found in other physical systems including ostensibly non-cognitive systems like pendulum clocks. Although the model accurately predicts the dynamics of these systems, the model itself, by avoiding reference to the physical facts of the system, does not allow one to predict which systems might exhibit the relevant dynamics. However, if one does examine the physical facts of the system then it is evident why some systems exhibit the relevant dynamics and others do not. In the example of coupled pendulum clocks an explanation that makes reference to the physical facts of the system, their parts, and their interactions – that is, a mechanistic explanation – provides reasons why certain arrangements of pendulum clocks exhibit the relevant dynamics while other arrangements do not. For example, a sketch of a mechanistic explanation might reference vibrations produced by the clocks and the role the wall plays in transmitting vibrations between clocks. This in turn provides an explanation for why clocks placed side-by-side on the same wall exhibit the relevant dynamics while clocks placed on opposite walls do not. Mechanistic explanations might similarly be furnished for why particular limb movements or interpersonal actions exhibit the relevant dynamics. The fact that the system exhibits these dynamics is only part of the story. What is missing is an explanation of why the system should exhibit these dynamics in the first place. The upshot of this is that what licenses application of the model (and what licenses demarcating the boundaries of the system) are some set of facts about the mechanism.
The move by Kirchhoff and Kiverstein (Reference Kirchhoff and Kiverstein2021) and Ramstead et al. (Reference Ramstead, Kirchhoff, Constant and Friston2021) to demarcate the boundaries of the mind gives rise to a similar worry. Is there some set of explanatory facts that licences placing the Markov blanket at the brain, the skin, or at any other “boundary”? On this, the answer is not clear. For example, Kirchhoff and Kiverstein (Reference Kirchhoff and Kiverstein2021) reject the idea of explanation dependent boundaries while Ramstead et al. (Reference Ramstead, Kirchhoff, Constant and Friston2021) appear to at least partially endorse the idea. Kirchhoff, Parr, Palacios, Friston, and Kiverstein (Reference Kirchhoff, Parr, Palacios, Friston and Kiverstein2018) go further and explicitly reference a mechanism sketch in deciding on the location of the Markov blanket (using the example of coupled pendulums). But as the example from dynamical systems theory shows, the formalism itself does not license predictions about which systems are amenable to the formalism and which are. Rather, these predictions are made independently of the formalism on, for example, mechanistic grounds. The Markov blanket theorist is presented with the same challenge. That is, to provide an explanation or prediction of which systems are amenable to the formalism – or because the formalism is applicable to every “thing” (Friston, Reference Friston2019), which systems are amenable to specific applications of the formalism independent of the particular application of the formalism itself.
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The target article highlights work by, for example, Kirchhoff and Kiverstein (Reference Kirchhoff and Kiverstein2021) and Ramstead, Kirchhoff, Constant, and Friston (Reference Ramstead, Kirchhoff, Constant and Friston2021), where attempts have been made to invoke the mathematical formalism of Markov blankets to justify claims about the bounds of the mind. The strategy highlighted in the target article is, however, not a new one. Rather, it echoes earlier approaches by advocates of dynamical systems theory to similarly use mathematical models of a system's behaviour to justify claims about the bounds of the mind. By placing the target article in the context of this earlier work it might be possible to bring into sharper relief the issues raised in the target article and, more positively, sketch a way forward for Markov blanket theorists.
One well-known model from the dynamical approach to cognition is the Haken–Kelso–Bunz model (Haken, Kelso, & Bunz, Reference Haken, Kelso and Bunz1985), which arose out of empirical work on the dynamics of inter-limb coordination. For example, Kelso (Reference Kelso1984) observed that when people rotated their wrists in an anti-phase pattern while gradually increasing the cycling speed a critical point was reached after which there was a rapid breakdown in the anti-phase pattern with coordination rapidly being reestablished in an in-phase pattern. The model was able to formalise this phenomena using the tools of dynamical modelling resulting in a model containing two parameters: one for cycling speed and one for the relative phase between the two limbs. The power of this model is its generality. Not only can it capture the dynamics of inter-limb coordination but it can also be applied to phenomena like socially coordinated motor behaviour. For example, Schmidt, Carello, and Turvey (Reference Schmidt, Carello and Turvey1990) found that two people seated next to each other, and engaging in anti-phase leg swings, exhibit the same dynamics as inter-limb coordination.
The Haken–Kelso–Bunz model is an example of a nonlinear dynamical system. As Chemero (Reference Chemero2011) argues, only linear systems are decomposable while nonlinear systems are non-decomposable. The upshot of this non-decomposability is that the dynamics of nonlinear systems must be modelled in terms of global collective variables, and that it is not possible to model the system dynamics in terms of separate component parts. That is, the mathematical formalism enforces viewing the two people engaged in inter-personal coordination as a single unified system. The boundaries of this system are not located within a single person but encompass both people. Drawing the boundaries of the system at the edge of a person's skull amounts to splitting the system, a move prohibited by the formalism. The move here is echoed by Kirchhoff and Kiverstein (Reference Kirchhoff and Kiverstein2021) and Ramstead et al. (Reference Ramstead, Kirchhoff, Constant and Friston2021) outlined by the target article. The mathematical formalism of nonlinearly coupled dynamical systems is replaced with the Markov blanket formalism, but the consequence is the same. The formalism used to model the system defines the bounds of the system.
This move is not unproblematic. The explanatory status of dynamical models has been questioned by those advocating for mechanistic explanation (e.g., Colling & Williamson, Reference Colling and Williamson2014; Kaplan & Bechtel, Reference Kaplan and Bechtel2011; Kaplan & Craver, Reference Kaplan and Craver2011). Although it's not possible to replay these arguments here, I will pick out one point that turns on this explanatory worry. The coupling-induced synchronisation observed in intra- and inter-personal limb movements is also found in other physical systems including ostensibly non-cognitive systems like pendulum clocks. Although the model accurately predicts the dynamics of these systems, the model itself, by avoiding reference to the physical facts of the system, does not allow one to predict which systems might exhibit the relevant dynamics. However, if one does examine the physical facts of the system then it is evident why some systems exhibit the relevant dynamics and others do not. In the example of coupled pendulum clocks an explanation that makes reference to the physical facts of the system, their parts, and their interactions – that is, a mechanistic explanation – provides reasons why certain arrangements of pendulum clocks exhibit the relevant dynamics while other arrangements do not. For example, a sketch of a mechanistic explanation might reference vibrations produced by the clocks and the role the wall plays in transmitting vibrations between clocks. This in turn provides an explanation for why clocks placed side-by-side on the same wall exhibit the relevant dynamics while clocks placed on opposite walls do not. Mechanistic explanations might similarly be furnished for why particular limb movements or interpersonal actions exhibit the relevant dynamics. The fact that the system exhibits these dynamics is only part of the story. What is missing is an explanation of why the system should exhibit these dynamics in the first place. The upshot of this is that what licenses application of the model (and what licenses demarcating the boundaries of the system) are some set of facts about the mechanism.
The move by Kirchhoff and Kiverstein (Reference Kirchhoff and Kiverstein2021) and Ramstead et al. (Reference Ramstead, Kirchhoff, Constant and Friston2021) to demarcate the boundaries of the mind gives rise to a similar worry. Is there some set of explanatory facts that licences placing the Markov blanket at the brain, the skin, or at any other “boundary”? On this, the answer is not clear. For example, Kirchhoff and Kiverstein (Reference Kirchhoff and Kiverstein2021) reject the idea of explanation dependent boundaries while Ramstead et al. (Reference Ramstead, Kirchhoff, Constant and Friston2021) appear to at least partially endorse the idea. Kirchhoff, Parr, Palacios, Friston, and Kiverstein (Reference Kirchhoff, Parr, Palacios, Friston and Kiverstein2018) go further and explicitly reference a mechanism sketch in deciding on the location of the Markov blanket (using the example of coupled pendulums). But as the example from dynamical systems theory shows, the formalism itself does not license predictions about which systems are amenable to the formalism and which are. Rather, these predictions are made independently of the formalism on, for example, mechanistic grounds. The Markov blanket theorist is presented with the same challenge. That is, to provide an explanation or prediction of which systems are amenable to the formalism – or because the formalism is applicable to every “thing” (Friston, Reference Friston2019), which systems are amenable to specific applications of the formalism independent of the particular application of the formalism itself.
Conflict of interest
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