What distinguishes a smartphone, a laptop, and a human brain from a bucket of water, a rock, and a solar system? One plausible answer is that the former are all instances of physical computing systems, while the latter are not. The trouble is that this answer, while undoubtedly intuitive, is more difficult to justify than one might initially expect. This is the problem of computational implementation, and it is the task of explaining under what conditions a physical system can be said to implement a computation. Some have suggested the problem requires an appeal to causal structure (Chrisley 1995; Chalmers 2011), others reference to semantic properties (Sprevak 2010; Shagrir 2022), while others still recourse to talk of mechanisms, Piccinini among them (Miłkowski 2014; Piccinini 2015; Dewhurst 2018; Kersten 2024).

In The Physical Signature of Computation, Anderson and Piccinini put forward a bold new proposal: a physical system is a physical computing system if it bears the physical signature of computation. Anderson and Piccinini dub this the ‘robust mapping account’, and with it they aim to clarify not only the relation between ordinary physical systems and physical computing systems, but also to resolve important outstanding challenges facing computational description in the physical world. Weaving together insights from computer science, physical information theory, and the metaphysics of mind, The Physical Signature of Computation offers a comprehensive and detailed account of the nature of physical computation, written in the characteristically pellucid style one has come to expect from Anderson and Piccinini’s work.

The book is organized into ten chapters, divided (roughly) into three parts. The first two chapters, which mostly involve stage-setting, find Anderson and Piccinini laying out key notions (abstract and concrete computation), distinguishing different positions (mapping, semantic, and mechanistic accounts), drawing important distinctions (computation versus simulation), and explicating desiderata for an account of physical computation (objectivity, explanation, miscomputation, and taxonomy). For those acquainted with the literature on physical computation, or Piccinini’s earlier work, much of this discussion will feel familiar, but for the uninitiated, it aptly serves as a philosophical primer; chapter 2, in particular, provides an admirably clear discussion of the similarities and differences between computational and physical descriptions of physical systems.

Chapters 3 and 4 are where the discussion really gets going. Here Anderson and Piccinini lay out and defend what they take to be the four key criteria for computational implementation. The first, what they call criterion S, states that a physical-to-computational description must map at least some physical elements (states or forces) of a physical system onto elements (input, state, or output) of a computational system. They further add to S that all the lawful physical dynamics of the physical system must generate the computational dynamics of the computational system, dubbed ‘dynamical self-consistency’. The second, labelled criterion P, states that every computational state transition specified within a computational system must correspond to one or more lawful physical state transformations of the corresponding physical system. The third, and arguably most important criterion, states that a physical system’s physical states must bear the same amount of information as the computational states they map to. This notion of ‘physical–computational equivalence’ (or PCE) is crucial to the account. This is because it ensures that inferences about the computational trajectories of a computational system can be made from the occurrence of each and every physical state of the mapping physical system. The fourth, criterion U, states that a physical system must be usable by an agent for a computational purpose. Together, S, P, PCE, and U form the minimal set of criteria that artefacts or natural systems need to satisfy in order to qualify as physical computing systems.

Anderson and Piccinini further suggest that these four criteria can be used to construct an evaluative scheme: a framework for gauging the strength of a given computational implementation. If, for example, a physical-to-computational description can be said to satisfy criteria S and P but not PCE or U, then it is weak; traditional mapping and semantic accounts, for instance, fall into this category. If the description satisfies S, P, and PCE but not U, then it is robust; the mechanistic account lands here. But if it satisfies S, P, PCE, and U, then it is a strong computational description; classic electronic digital computers rise to this level. The strength of each class reflects a distinct, identifiable viewpoint on implementation. Anderson and Piccinini offer a useful flow chart for mapping out assessments according to this scheme (p. 119).

Chapter 5 puts everything together. A physical system is said to be a physical computing system if and only if the physical states of the physical system (or subsystems) map onto the values of the computational variables (state, input, and output) of a computational system (S) in accord with its computational dynamics (P) such that the physical states bear the same amount of information about the computational trajectory of the computational system as the computational variables (PCE). This is the ‘physical signature’ of computation. Physical-to-computational descriptions must be equivalent such that no information is lost when one moves from the physical to computational descriptions of a physical system. Much of chapter 5 is dedicated to fleshing out the sense of informational equivalence required to qualify as a robust physical-to-computational description; it also includes a novel and interesting discussion of how the robust mapping account can be formalized using physical information theory, what the authors refer to as the ‘referential’ approach (pp. 132–42).

Now, if chapters 3 and 4 build the engine, and chapter 5 assembles the chassis, then chapters 6 to 8 provide the test track. For it is here that the robust mapping account is put through its paces against one of the perennial foes of concrete computation: pan-computationalism. Anderson and Piccinini take aim specifically at three different versions of pan-computationalism: an ‘unlimited’ formulation, which states that every physical system can perform every computation; a ‘limited’ formulation, which states that every physical system performs at least one computation; and an ontic formulation, which states that the universe itself is either a digital or quantum computing system. Each formulation gets its own chapter.

The argumentation in these chapters is sustained and meticulous, in several places drawing on the resources developed in the evaluative framework of chapter 4. To provide just one brief example, against a Chalmers-inspired argument for unlimited pan-computationalism using a finite-state automaton (FSA), Anderson and Piccinini argue that at best the construction amounts to offering a weak computational description (it satisfies criteria S and P but violates PCE; pp. 158–60). But given that physical–computational equivalence (PCE) is a necessary requirement on physical computation, such an argument fails to establish anything like a robust physical-to-computational description, and so can be rejected. Chapter 8 also has some really nice discussion of how ontic pan-computationalism problematically erases the distinction between a simulator and its simulated target system.

In chapter 9, which I found the most interesting, Anderson and Piccinini shift gears slightly and connect their account to computational theories of mind. After some preliminary stage setting (a mind is defined as a system exhibiting cognitive capacities and possibly consciousness), they argue that while cognition can be explained by neural computation—which is amenable to the robust mapping account—further supplemented with a notion of teleological function, consciousness is a bridge too far. Consciousness, they suggest, involves more than just computation; it likely requires physical qualities that go beyond computational description.

This discussion I found slightly hasty. For example, after nicely laying out several options on the nature of consciousness, including computational functionalism and non-computational functionalism, Anderson and Piccinini respond to the former view: ‘But eliminativism [illusionism] falls flat. If “conscious phenomenal experience” were purely a matter of structure and causal powers, we should conclude that there would just not be any conscious phenomenal experience. But at least sometimes, we do have phenomenal experiences’ (p. 262). This is a bit too quick. Claiming that ‘phenomenal’ consciousness is not what some take it to be, as the illusionist does, is not the same as denying that consciousness exists full stop.

Chapter 10 rounds off discussion by consolidating the robust mapping account, relating it back to the four initial desiderata (objectivity, explanation, miscomputation, and taxonomy) and the three accounts laid out in chapter 1 (mapping, semantic, and mechanistic), along with briefly sketching a unifying account of biological and artefact computation.

Taking a slight step back, among the book’s many carefully crafted arguments and insights, there are a few loose ends briefly worth noting. One is that some readers may wonder about the relation between this new account and Piccinini’s previous work on mechanistic computation (for example, Piccinini 2015), which holds that computational explanation is a species of mechanistic explanation, and computational mechanisms are a special type of functional mechanism. While there is some brief discussion of mechanistic computation (chap. 10.3.3), and it is suggested the two accounts are indeed compatible, one may still be left wondering whether this new account, if correct, leaves the mechanistic account in a slightly awkward position. Has the mechanistic account now become obsolete? Should those attracted to this view close up shop or is there more work to be done?

A second, somewhat curious omission is the relation between computational description and computational modelling practice in other domains, such as cognitive science and neuroscience. Several authors, for instance, have recently attempted to wed their implementational accounts of computation quite closely to the explanatory practices of these domains; some have even criticized implementational accounts for failing to do so (for example, Shagrir 2022; Chirimuuta 2024). The Physical Signature of Computation, in contrast, is largely occupied with conceptual refinement, formalization, and metaphysical argument, with a heavy emphasis on computer science and engineering. This is certainly valuable and welcomed work, but one may be left wondering how this new account squares with computational explanation and modelling practices elsewhere.

Finally, and I offer this more as a warning than criticism, some readers may find the level of detail in certain places of the discussion slightly overwhelming. While much of the formal heavy lifting is postponed to the two appendices, the book can, particularly in the dense thicket of arguments against pan-computationalism, make for some hefty reading, despite Anderson and Piccinini’s admirable efforts to keep things accessible.

Taken as a whole, The Physical Signature of Computation is a clear triumph. Anderson and Piccinini have put forward a substantive, meticulously crafted work, not only in terms of a novel and sophisticated account of implementation, but also in terms of working out the formal implications. With expert clarity and attention to detail, Anderson and Piccinini have offered an excellent example of how to assemble a clear-headed, rigorous treatment of physical computation. The book will be of interest not only to philosophers with a taste for metaphysical argument and formal detail, but those more generally interested in understanding the foundations of contemporary cognitive and computational science.

Luke Kersten
University of Alberta
kersten@ualberta.ca

References

Dewhurst, J. (2018). ‘Individuation Without Representation’, British Journal for the Philosophy of Science, 69, pp. 103–16.

Chalmers, D. (2011). ‘A Computational Foundation for the Study of Cognition’, Journal of Cognitive Science, 12, pp. 323–57.

Chirimuuta, M. (2024). The Brain Abstracted: Simplification in the History of Neuroscience, MIT Press.

Chrisley, R. (1995). ‘Why Everything Doesn’t Realize Every Computation’, Minds and Machines, 4, pp. 403–30.

Kersten, L. (2024). ‘An Idealised Account of Mechanistic Computation’, Synthese, 203, available at .

Miłkowski, M. (2014). ‘Computational Mechanism and Models of Cognition’, Philosophia Scientiae, 18, pp. 215–28.

Piccinini, G. (2015). Physical Computation: A Mechanistic Account, Oxford University Press.

Shagrir, O. (2022). The Nature of Physical Computation, Oxford University Press.

Sprevak, M. (2010). ‘Computation, Individuation and the Received View on Representation’, Studies in the History of Philosophy of Science A, 41, pp. 260–70.