1. Introduction

The notion of computation plays an important explanatory role in several areas of science. Its application is perhaps most obvious, and least surprising, in computer science. It appears as well, and as a fundamental notion, in several branches of mainstream cognitive science and artificial intelligence research. Talk of computation is also widespread in the many fields of knowledge that employ computational modeling, from astronomy, to meteorology, to molecular biology.

There is an essential difference between the role of the notion of computation in computer and cognitive science and its usage in other sciences. In the latter, computation most often works merely as a tool to model systems that in themselves are not computational. The computer and cognitive sciences, however, focus on systems that not only are supposed to allow computational modeling but are essentially computational. Electronic computers, and arguably cognitive systems, really compute. In order to capture the nature of these systems, an account of what it is for a physical system to perform computations (vs. to be merely computationally describable) is called for: an account of physical, or concrete, computation (Piccinini Reference Piccinini2015).Footnote ¹

In this article, I defend the cogency of a recent theory of concrete computation: the mechanistic view (Milkowski Reference Milkowski2013; Fresco Reference Fresco2014; Piccinini Reference Piccinini2015; Coelho Mollo Reference Coelho Mollo2018). The mechanistic account of concrete computation is particularly promising for providing a robust, objective notion of concrete computation. However, it is a highly articulated theory, with several movable parts making different contributions to its structure. It is thereby important to ensure that all those parts are sufficiently solid, firmly attached, and well oiled, if the theoretical machinery is to work properly. I here tackle one apparently weak spot in the mechanistic view of concrete computation: its joint commitment to the medium-independent nature of computational vehicles and to the existence of teleological functions to compute. This joint commitment leads to a puzzle. The best theories of teleological function available have recourse to the specific (past or present) causal powers of vehicles in bestowing teleofunctions to them and the systems they help compose. But medium independence abstracts away from precisely such specific causal powers. How then can there be teleological functions to manipulate medium-independent vehicles, that is, to compute?

I will argue that the mechanistic view has the tools to answer this challenge satisfactorily, remaining our best picture of the nature of computation in physical systems. In section 2, I briefly present the mechanistic view of concrete computation, focusing especially on the notions of medium independence and multiple realizability. In section 3 I elaborate on the puzzle hinted at above, which it is my task in this article to solve. In section 4 I examine some strategies to answer the challenge, which although unsuccessful reveal interesting features of the conceptual architecture of the mechanistic view of computation. In particular, I show that the view cannot do without appeal to both medium-independent individuation and teleology. Finally, in section 5 I show that the mechanistic view is able to solve the puzzle once considerations about the causally relevant factors that bestow teleological functions on designed and biological computational systems are brought to the fore.

2. Mechanistic Computation

3. Teleological Functions and Medium Independence: A Puzzle

According to the mechanistic view of computation, teleological functions play an essential role in helping to individuate computational systems.Footnote ⁹ In this section, I examine a difficulty that arises for the view in this connection. For it would seem, according to our best theories, that the factors that determine the teleological functions of a system are sensitive to causal powers that hinge on details of its physical constitution—and cannot thereby yield functions individuated in medium-independent terms. It would follow that there can be no teleological functions to compute and, in consequence, that no physical system satisfies the requirements for being a computing system by the computational mechanist’s own lights.Footnote ¹⁰ It would seem, that is, that the mechanistic view of computation cannot appeal to medium independence and teleological functions at the same time. Let us cash out this dilemma more fully, taking first a quick look at philosophical treatment of teleological functions.

Accounting for the notion of teleological function in scientifically acceptable, naturalistic terms has proved to be a rather challenging endeavor. Indeed, the notion is related to concepts such as purpose and end that imply ideas of design and agency that are not straightforwardly accounted for in nonintentional (and nontheological) terms. Compelling and fully naturalistic theories of teleological function have nonetheless been developed, and even though skepticism about them occasionally comes to surface, the consensus for some time has been that teleological functions are bona fide scientific properties, especially central to the life sciences (Godfrey-Smith Reference Godfrey-Smith1993).

Two main approaches to teleofunction have been particularly influential in the debate: dispositional theories, and selected-effects theories. Roughly, according to dispositional theories the teleological functions of a type of system (or parts thereof) are determined by factors having to do with the occurrent causal dispositions of a (type of) system or its parts. Dispositional theories are thereby ahistorical. Dispositions are understood as counterfactually robust regularities: were certain conditions to hold, a system or part would manifest a certain behavior. Hearts have the disposition to pump blood, for when they are introduced in a complex system with specific characteristics, they display blood-pumping behavior. The most promising dispositional theories of teleological functions are goal based. They have it that the teleofunctions of a system are determined by its dispositions to contribute to certain goals of organisms (Boorse Reference Boorse1976; Maley and Piccinini Reference Maley, Piccinini and Kaplan2017). The relevant goals are fixed by independent considerations, with the more plausible candidates including survival, reproduction, and inclusive fitness. In this picture, hearts have the function to pump blood because by pumping blood they contribute to the survival and inclusive fitness of organisms having them.

Selected-effects theories, in contrast, focus on the causal contributions that past instances of a type of system or its parts made that explain the existence and historical persistence of instances of that type of system or part (Millikan Reference Millikan1984; Neander Reference Neander1991). Selected-effects theories are historical: they make reference to the past history of systems and their parts in order to fix their teleofunctions. The function of a heart is to pump blood, for it is because past instances of hearts in the phylogeny pumped blood that organisms having them survived and reproduced, leading to the existence of organisms with hearts today. Some views have it that natural selection is the only kind of selection that bestows functions on physical (biological) systems (Neander Reference Neander1991; Godfrey-Smith Reference Godfrey-Smith1994). Others tend to be more liberal and allow other kinds of selection processes to play a role in bestowing teleological functions (Garson Reference Garson2011).

The dispute between dispositional and selected-effects theories has been taken to be, at least in part, a matter of different explanatory focus. While dispositional theories are concerned with answering questions about how a type of system works, selected-effects theories focus on explaining why a certain type of system persists over time. Depending on which of these two questions one is interested in answering, one or the other type of theory may be more adequate (Godfrey-Smith Reference Godfrey-Smith1993). This conciliatory outlook on the debate is not widely shared, with proponents of both approaches insisting that there are more substantial dimensions to the dispute—especially regarding descriptive and explanatory adequacy and normativity (Millikan Reference Millikan1984; Neander Reference Neander1991; Garson Reference Garson2011; Piccinini Reference Piccinini2015). For my purposes, there is no need to get into this debate.

This brief presentation of the two main approaches to explaining teleological functions suffices to bring to the fore more clearly the difficulty that the mechanistic account of computation has to confront.

The mechanistic view of concrete computation seems hence to be in dire straits: it claims that computational systems are those mechanisms with the teleological function to perform computations. But the performance of computations, which essentially involves medium-independent individuation, seems to be a bad candidate for being a teleological function of any system—for teleological functions seem to hinge on medium-dependent properties of systems and their components. It looks like the computational mechanist has to give up either the appeal to teleology or the appeal to medium independence. In the next section I assess whether the mechanistic view can survive abandoning either of these two components of the theory (the answer will be no). In the following section I show that hope is not lost: there is a solution to the puzzle after all—there can be teleological functions individuated in medium-independent terms.

4. Some (Unpromising) Responses

There seem to be two immediate ways out for the computational mechanist: (i) eliminate or change the role that medium independence plays in the individuation of concrete computation, so as to make it compatible with appeal to teleology, or (ii) eliminate or change the role that teleological functions play in the individuation of concrete computation, so as to make it compatible with medium independence. Let us examine each in turn.

It may be claimed that the appeal to medium-independent individuation does not eliminate or screen off those causal contributions of vehicles that depend on their physical constitutions. Computational mechanists can insist that computational vehicles are manipulated in light of a subset of their physical, medium-dependent properties—those to which the general rule of manipulation is sensitive. This is the line that seems to be taken by Piccinini, as his definition presented in section 2.2 above suggests. Teleological functions could thereby be bestowed on computational systems in light of the causal contributions that this subset of physical properties makes to organismic goals or to their persistence through selection processes. In other words, although computational systems and vehicles are individuated in medium-independent terms, the factors that bestow the teleological function to compute on them are determined partly by the constitutive properties of the realizing physical media.

I believe that this line of reply will not do. It throws the mechanistic view into a dilemma. It has either to embrace pancomputationalism (or something close to it) or give up multiple realizability.

On one hand, the computational mechanist may hold that the teleological functions of computational systems are to transform certain physical quantities in a rule-like way. On this picture, it would be transformation of physical quantities in rule-like fashion that contributes to organismic goals or to persistence in the phylogeny, thus determining the computational teleofunctions of the system. The key problem with this move is that this way of individuating computational teleofunctions is too liberal. This sort of teleofunction can be found in a host of systems, many of which are intuitively noncomputational. Cell membranes, thermometers, and simple thermostats have the teleological functions they do because of their transforming certain physical quantities into others in a regular, rule-like manner (e.g., internal ion concentrations into other internal ion concentrations, average kinetic energy into the height of a mercury column or into bending a metal strip). Their teleofunctions would hence count as computational. As they are also plausible examples of teleofunctional mechanisms, they would fulfill the characterization of physical computational systems given in section 2.2. But ascribing computational nature to such systems seems implausible. Taking such liberally individuated teleological functions to be computational teleofunctions leads to a considerable extension of the domain of computational systems, well beyond intuitive boundaries, bordering on pancomputationalism.

On the other hand, if it be insisted—to avoid an overextension of the domain of computational systems—that teleological functions be more narrowly determined, for instance, in terms of the particular kinds of physical quantities that each computational system manipulates, then the characteristic multiple realizability of computations would be lost and, with it, a useful notion of computational equivalence. For then the teleological functions of computational systems would be to manipulate vehicles with a particular type of physical constitution (e.g., voltage ranges in silicon circuits). Electronic computational systems, hydraulic computational systems, and neural-biological computational systems would not be able to perform the same computations, given that each of these kinds of systems would have the teleofunction to manipulate different kinds of physical quantities, and their computations would thus be individuated differently.

Pancomputationalism as well as the abandonment of the multiple realizability of computation and of (broad) computational equivalence have been taken by some not to be knockdown arguments against theories of computation.Footnote ¹¹ But they are big bullets to bite, as they deprive the notion of concrete computation of most of its explanatory power. In sum, taking line of reply (i) does not help the case of the computational mechanist. It leads to a dilemma, with each horn abutting on unfortunate consequences. Let us briefly see whether strategy (ii) has something to recommend it.

The appeal to teleological functions plays a multipronged role in the mechanistic view of computation. Changing or eliminating appeal to the notion puts in jeopardy several positive aspects of the theory. I will mention three.

First, the appeal to teleological functions, taken as objective, observer-independent features of the world, helps ensure the objectivity of concrete computation. As we have seen, mechanisms are partly individuated by a phenomenon or capacity of interest. Some of these phenomena or capacities may be essentially dependent on the explanatory aims and practices of theorists, thus having a marked subjective component to them. Moreover, any physical system can be mechanistically analyzed in light of several different capacities. An electronic computer may be mechanistically analyzed in terms of its capacity to generate heat. The claim that computational systems have the teleological function to compute provides justification both to the view that concrete computations are objective, given that some physical systems have the objective teleofunction to perform them,Footnote ¹² and to the view that their capacity to perform computations is privileged over other capacities they may have but that are not among their teleological functions (e.g., the capacity to generate heat). Reducing or eliminating the appeal to teleofunctions undermines the realist approach to concrete computation that mechanistic views want to maintain.

Second, and relatedly, teleofunctions help define the domain of computational systems in a way that is not too liberal, that is, that does not include more systems than intuitively plausible, avoiding pancomputationalism. By individuating computation partly by means of teleological functions, the mechanistic view considerably narrows down the domain of physical systems that can count as computational. They must be teleomechanisms (ruling out mechanisms, such as weather systems, that do not have teleofunctions), and they must have the teleofunction to compute (circumscribing a rather narrow domain of physical systems that can be candidates for computational nature). Letting go of teleological functions thus risks undermining the ability of the mechanistic view to distinguish computational from noncomputational physical systems appropriately.

Finally, teleofunctions introduce a dimension of normativity that is important in making sense of the possibility of miscomputation, that is, of the fact that there is something it is for computational systems to succeed or fail to perform computations appropriately (see Fresco and Primiero Reference Fresco and Primiero2013; Dewhurst Reference Dewhurst2014; Piccinini Reference Piccinini2015, 148–50). Appeal to teleofunctions provides a straightforward way of accounting for this fact: computational systems miscompute when they produce outputs that are at odds with the computational function it is their teleological function to compute.

In sum, reducing or eliminating the role played by teleological functions in the mechanistic account is ill advised. The second line of reply, as the first, creates more problems that it solves. Mechanisms, it appears, cannot have the teleological function to perform concrete computations, since these are individuated in a medium-independent way, while part of the conditions for bestowing teleofunctions, that is, the intrinsic causal powers of components and systems, are not medium independent. If that is so, and either medium independence or appeal to teleofunctions has to be abandoned, computational mechanists end up with a rather unsatisfying set of alternatives in their hands: (i) either embrace pancomputationalism or give up strong multiple realizability or (ii) jeopardize the objectivity of computation and the possibility of miscomputation, all the while risking to fall into pancomputationalism.

The discouraging moral of this section points to an architectural feature of the mechanistic view of computation—an argumentative structure that cannot be meddled too much with, on pain of losing the advantages that the account is supposed to have. Move a part of the account a bit, and the whole edifice crumbles. This is so because the theory spins a close-knit web between teleological functions, computational rules, medium independence, and the relevant causal contributions of physical media. The subset of physical properties that makes the causal contributions of relevance to the computational behavior of a system is determined by the general manipulation rule (i.e., the computational rule). It is the general rule, with its sensitivity to the dimensions of variation of some physical variables, but not others, that determines what parts of the causal structure of the system are important for its computational nature. But such a general rule calls for an objective factor to ground it. For there are an indefinite number of ways of mapping causal goings-on in physical systems onto computational rules (Putnam Reference Putnam1988; Chalmers Reference Chalmers1996). Just looking at the causal operations of the system cannot reveal the computational rule, unless one knows what to look for, that is, if one knows what causal goings-on are computationally relevant. Such an objective factor, according to the mechanistic view, is teleology. It is by having the performance of one or more computations as its teleological function that a system can be carved into the physical components and processes that are causally relevant for performing that function. However, it is medium-independent individuation that allows setting computational rules and, thus, computational teleofunctions apart from rule-like behavior and noncomputational teleofunctions—setting computational and noncomputational systems apart.

The failed attempts examined in this section notwithstanding, I believe that there is a way to keep this fragile conceptual web as it is, saving the cogency of the mechanistic view of computation and safeguarding its qualities as a promising theory of the nature of computation in the physical world. Let us turn to that.

5. Teleofunctions to Compute

In this section, I argue that, contrary to the arguments in section 3, systems and vehicles individuated in medium-independent terms can be involved in the bestowing of teleological functions, at least in the special domain of computational systems. While the case of designed computational systems is relatively straightforward, cognitive computational systems place further challenges that, I will argue, can be addressed only by accepting a version of functionalism about cognition. Given the plausibility of functionalism, together with its foundational role in (much of) the cognitive sciences, I take that this is not a high price to pay for saving the cogency of the mechanistic view of computation.

Before moving to the more complicated and controversial case of cognitive computational systems, it is best to start with the easier one: designed computational systems. Although the debate is open on how best to account for the teleofunctions possessed by artifacts, it is plausible that the intentions of designers play some role in their bestowal, at least in the case of (human-)designed artifacts.Footnote ¹³ On a goal-based theory, artifacts can be seen as contributing to the relevant goals of organisms, which may also include subjective goals that go beyond survival, reproduction, and inclusive fitness (Piccinini Reference Piccinini2015, 115–17). On a selected-effects theory, artifactual teleofunctions can in some cases be determined by biological selection processes, given the specific advantages artifacts bestow on their possessors that explain their persistence, while in other cases they can be determined by rational selection processes, in which rational agents select from alternative designs the one that best fits their intentions and material capabilities, or more basically, by simple trial and error.Footnote ¹⁴

In the case of designed computational systems, the intentions of designers are plausibly to build devices that behave in such a way as to respect the desired computational rules. The latter are typically given a medium-independent specification in terms of logic gates, memory storages, and so on, and their mutual interactions, posing constraints only on the degrees of freedom (and the ways they modulate each other) of potential implementing physical systems. Physical media are then arranged so that their components and activities mirror that computational architecture, implementing the computational description in a physical system.

In other words, the computational blueprint is the basis of the intentions of designers of computational systems. Specific types of physical media are selected in light of their capacity to implement the medium-independent characterization that they are supposed to satisfy. Computationally equivalent systems can thereby be built out of different materials and components. The contributions that computational artifacts make to goals or to selection are independent of details about their physical constitution, insofar as computationally equivalent but differently physically constituted systems make the same contributions. There are likely to be differences in speed, size, energy consumption, and so on, between different types of physical implementations. Although these may influence to some extent the specific teleological functions of computational mechanisms (e.g., in limiting which functions they can compute in a certain interval of time or in which circumstances they can be usefully applied), they do not jeopardize their general teleofunction to perform computations. These considerations lend force to the claim that, as far as designed computers are concerned, their teleological functions are primarily characterized in medium-independent terms, for the intentions of designers of computational systems—which help bestow teleofunctions—involve medium-independent blueprints.

The mechanistic view of concrete computation is thus able to avoid the worry presented in section 3, at least for designed computers. The question then becomes whether a similarly fortunate result can be obtained for biological, nondesigned computational systems such as, plausibly, cognitive systems. Things get trickier here, as appeals to intentions of designers are clearly not in the cards, but I believe that there are promising paths for a computational mechanist to tread. I will explore a similar strategy to the one applied to designed computers: showing that medium-independent characterizations of the causal goings-on in biological, cognitive computational systems are explanatorily primary in determining their teleological functions.

In arguing for this, Chalmers’s (Reference Chalmers2011) notion of organizationally invariant properties proves useful. Organizationally invariant properties remain invariant as long as the abstract causal structure of a system—what Chalmers calls its causal topology—remains unchanged. In Chalmers’s words, a property P counts as organizationally invariant “if any change to the system that preserves the causal topology preserves P.” The causal topology of a system, in turn, is defined as “the pattern of interaction among parts of the system, abstracted away from the makeup of individual parts and from the way the causal connections are implemented” (337). The notion of an organizationally invariant property is closely related to medium independence. Insofar as such properties are individuated in a way that fully abstracts away from the physical constitution of their realizers, they are individuated in medium-independent terms.Footnote ¹⁵

The notion of organizationally invariant properties embodies an important assumption of much work in mainstream cognitive science—the endorsement of functionalism. According to functionalism, it is the special abstract causal structure of systems (their causal topology) that makes them into cognitive systems, not the physical constitution of their parts. Any system with the right kind(s) of causal structure will have states and processes that count as cognitive, regardless of the materials their vehicles are made of. What matters, in other words, are the input-output relations between components of the systems, regardless of how they are realized. By the lights of functionalism, what makes a system cognitive is its causal topology, and thereby cognitive states and processes are primarily characterized in terms of organizationally invariant properties. It follows that computational explanation is particularly appropriate to cognitive states and processes, for it captures what is most relevant about them: their role in the abstract, medium-independent causal structure of the cognitive system (Chalmers Reference Chalmers2011, 337).

Functionalism about cognition opens a promising avenue for the computational mechanist, as it suggests that the causally relevant properties when it comes to cognitive systems are organizationally invariant and thereby medium-independently individuated. If that is so, then the appropriate way of individuating the causal properties relevant for bestowal of teleological functions, be it in terms of contributions to organismic goals or to persistence in the phylogeny, is in medium-independent fashion. In other words, if cognition is essentially a matter of having the right kind(s) of causal topology, and a cognitive system is such insofar as it instantiates the right kinds of input-output relations between its components, as functionalism has it, then the properties relevant for bestowing teleofunctions on cognitive systems are primarily organizationally invariant ones.Footnote ¹⁶

Focusing on the medium-dependent causal properties of cognitive systems would miss what is distinctively cognitive about them—their causal topology. This can be clearly illustrated by appealing to counterfactuals. Were cognitive systems composed fully or partly of a different material than neurons and glia, they would function in the same way as actual cognitive systems,Footnote ¹⁷ provided that the causal topology of the former and the latter were the same (and that the different medium is suitably connected to and able to interact appropriately with sensory surfaces and motor effectors, maintaining the appropriate input-output relations between components). Any change in physical constitution, insofar as it preserves the system’s causal topology, preserves its contributions to organismic goals and persistence in the phylogeny.Footnote ¹⁸ In the case of cognitive systems, that is, what is causally relevant to bestowal of teleological functions, both for goal-based and selected-effects accounts, is their abstract, medium-independently individuated causal structure—which is best captured in computational terms (Chalmers Reference Chalmers2011, 342).

In sum, the computational mechanist, if also a functionalist, can reply in the following way to the puzzle I set out above. Theories of teleofunction are concerned with the causally relevant properties that contribute to organismic goals or persistence. As the foregoing line of reasoning suggests, in the case of cognitive systems, courtesy of functionalism, such properties are organizationally invariant ones. Organizationally invariant properties are individuated in a medium-independent way. It follows, as the computational mechanist would want, that cognitive systems possess teleological functions that are characterized in medium-independent terms.

There are thus good reasons to think that teleological functions can be individuated in a medium-independent way in the case of designed and biological computational systems. That means, contra the arguments in section 3, that there can be teleological functions to manipulate medium-independent vehicles according to general rules, that is, there can be teleofunctions to compute. The success of my line of argumentation for what regards cognitive computational systems hinges on the success of functionalism as a framework for understanding cognition. Consequently, the plausibility of the mechanistic view of computation, as I here defend it, goes hand in hand with the plausibility of functionalism. I take this to be a comforting outcome. Despite the recent attacks against multiple realizability, and in consequence against the support for functionalism, the latter remains the most promising overall framework for understanding the nature of cognition currently available.

It does not follow from my arguments that computational and functional explanation are identical. While computational explanation is a type of functional explanation, not every functional explanation is computational. This follows from the fact that functional explanation, in contrast to computational explanation, needs not be, and in most cases is not, medium independent (and in some cases may not even involve multiple realizability). Moreover, as we have seen, most systems that are functionally explainable are not teleological, and some may not even qualify for mechanistic explanation (see sec. 2.1). Most importantly, the foregoing argument applies only to those systems for which organizationally invariant properties play causally relevant roles and are thus explanatorily primary in making sense of their workings. Physical systems of enough complexity can in most cases be functionally analyzed in terms of the abstract causal roles of their components. However, for most systems their functional analysis does not involve organizationally invariant properties, in contrast to computational systems.

To illustrate the difference, take digestion.Footnote ¹⁹ A functional decomposition of the digestive system is no doubt possible. There are subsystems for allowing food to get inside the organism, for breaking food into smaller and more easily processable bits, for transporting food to subsystems dedicated to breaking it further into substances of use to the organism, for absorbing those nutrients, and finally for getting rid of the material that fails to be absorbed. The functional decomposition of the digestive system is quite illuminating: we get a breakdown of the functional components, the work they do, and how that work is subdivided into different stages responsible for different parts of the process of digestion.

The properties of subsystems that are relevant for explaining their causal contributions to digestion are not organizationally invariant properties—they are not individuated in medium-independent terms, although they may be multiply realizable. Every realization of a digestive system must be such as to be able to break down bits of food, thereby placing constraints on the possible realizing physical media—constraints that go well beyond degrees of freedom. Moreover, digestion cannot take place at all without food, which although a variegated category, also places constraints on the physical constitution of its members, whereby the ‘inputs’ to the digestive system must be individuated in medium-dependent terms. Therefore, the causal topology of digestion (its abstract causal structure), although interesting, is not what is primarily explanatory of the capacity of digestive systems to digest. In consequence, the teleological functions of digestive systems are best characterized in terms of properties that are not organizationally invariant. Digestive systems are functional but not computational.

The foregoing considerations lend force to the idea that, when it comes to computational systems, both biological and designed, the factors that ground their having teleological functions are organizationally invariant properties, which are individuated in a medium-independent way. The teleological functions of these systems are thereby to be characterized in medium-independent terms. Contrary to first appearances, in the domain of designed computers and cognitive systems (in the latter case, courtesy of functionalism), there can be teleofunctions to manipulate medium-independent vehicles according to rules. That is, as the mechanistic view of computation has it, there can be teleological functions to compute.

6. Concluding Remarks

In this article, I have argued for two main points. First, I have shown that the joint commitment to medium independence and to teleology plays an essential and ineliminable role in the mechanistic view of concrete computation. Second, I have argued that, contrary to appearances, there can be teleological functions characterized in medium-independent terms. A crucial tenet of the mechanistic view of computation is therefore secured: there can be teleological functions to compute. The account, especially in its more recent versions, proves to be conceptually coherent and stable. Furthermore, in light of its many positive features—which I have not had the chance to explore in detail here—it holds much promise for providing an adequate, naturalistic theory of what it is for physical systems to compute.