Anderson and Piccinini (2024) offer a foundational approach to understanding physical computation. The book’s primary aim is to defend the notion of physical computation against trivialization.
Critics argue that ascribing computation lacks a factual basis, which, if true, would render computational explanations ineffective by stripping them of explanatory power. Piccinini has long criticized such subjectivist approaches as ungrounded, and this work addresses these questions more deeply. Another threat to the cognitive value of computational explanations is “pancomputationalism”—the realist view that computation is ubiquitous. If everything computes any function, as subjectivists and pancomputationalism claim, then computational explanations lose their significance. Even if computation is widespread but not trivial, as suggested by limited pancomputationalism, physical computation loses its uniqueness.
In contrast, the authors advocate for a narrower perspective. Surprisingly, their account moves away from the new mechanistic explanation framework that Piccinini (2015) successfully defended. Instead, they introduce the “robust mapping account.” This approach asserts that robust computational descriptions are essential to capture the “physical signature of computation.” Unlike weak mapping accounts, which only require that physical states correspond to computational states and that state transitions align, the robust mapping account stipulates that physical states must convey the same information about computational evolution as their computational counterparts. This information-theoretic condition extends beyond previous attempts by incorporating trajectory-based criteria.
The robustness requirement renders the new account resilient to common objections regarding the objectivity of computation. One potential counterargument might attempt to gerrymander “computationally irrelevant” states or subsystems. However, such attempts appear unpromising at first glance, as excluding these states could disrupt the informational alignment between physical and computational state transitions. Nonetheless, in cases of apparent computational indeterminacy—where a single physical system seems to implement multiple computations (Fresco, Copeland, & Wolf, 2021)—referencing irrelevant states might help clarify concurrent computations.
Additionally, Anderson and Piccinini mention a strong mapping account, which mandates that the computational system be usable. This aligns with the mechanistic account (Piccinini 2015) but has faced criticism. The usability criterion distinguishes merely complex mechanisms from those that are operationally controlled, such as by a biological agent. For instance, a physical mechanism too large to be managed by any conceivable agent would fail this criterion.
A noteworthy implication of the robust mapping account is its independence from the mechanistic framework. It can complement other accounts, such as Shagrir’s (2022) semantic approach to computational individuation, or integrate into a mechanistic perspective.
However, the necessity of the mechanistic account of computation remains unclear. In fact, it’s perplexing that the mechanistic account isn’t entirely dismissed. Surprisingly, it reappears in Chapter 9, linking computation with the study of the mind. While this is understandable given the ongoing debates over computationalism in cognitive (neuro)science and philosophy of mind, as a philosopher of scientific practice, I believe the understanding of computation varies significantly across scientific disciplines. For example, neural computation is closely tied to cognitive representation, unlike reservoir computing or real-time control theory. While this observation isn’t backed by a systematic study, I suspect that neural computation holds unique explanatory requirements.
A challenge arises when trying to reconcile the mechanistic requirements in Chapter 9 with the book’s earlier sections. Consider medium independence, which holds if the defining effect of a property is itself multiply realizable purely through degrees of freedom and their organization. The robust mapping account doesn’t necessitate medium independence. Although physical-to-computational equivalence is medium-independent, distinguishing between structural terms (like degrees of freedom) and constitutive terms is unclear. Section 2.3.2 elaborates on this by defining structural terms as those referencing physical materials or components and their interactions. However, since materials and components are typically described in structural or relational terms, the distinction remains blurred.
For instance, consider hydrogen molecules interacting with oxygen to form an explosive mixture. The process can be fully explained by analyzing the system’s degrees of freedom. Initially, three molecules (two H₂ and one O₂) have a total of 18 degrees of freedom: 6 per molecule (3 translational, 2 rotational, 1 vibrational). After the reaction, the two H₂O molecules each have 9 degrees of freedom (3 translational, 3 rotational, 3 vibrational). This redistribution maintains the total degrees of freedom and explains the reaction’s dynamics. The explosive nature arises from the rapid energy reallocation from chemical bonds to kinetic energy in the new vibrational and translational modes. This analysis aligns with principles of statistical mechanics and quantum chemistry, demonstrating that degrees-of-freedom-based explanations are both sufficient and necessary for understanding molecular interactions and their macroscopic effects.
Therefore, the medium-independence requirement seems redundant. While medium-independent properties exist at any scale, their supposed special role remains unconvincing, despite Anderson and Piccinini’s observations.
In summary, while I advocate for the inclusion of mechanisms in a physical account of computation (Miłkowski, 2013), the discussion of the physical signature of computation in this book tempers my optimism regarding these prospects.
References
Anderson, N. G., & Piccinini, G. (2024). The Physical Signature of Computation: A Robust Mapping Account. Oxford University PressOxford. doi: 10.1093/9780191872075.001.0001
Fresco, N., Copeland, B. J., & Wolf, M. J. (2021). The indeterminacy of computation. Synthese, 199(5), 12753–12775. doi: 10.1007/s11229-021-03352-9
Miłkowski, M. (2013). Explaining the Computational Mind. Cambridge, Mass.: MIT Press.
Piccinini, G. (2015). Physical Computation: A Mechanistic Account. Oxford: Oxford University Press.
Shagrir, O. (2022). The nature of physical computation. New York, NY, United States of America: Oxford University Press.
Thanks to Marcin Milkowski for his commentary. We will respond to his comments on medium independence in a separate post, to be published on the Brains blog after all the commentaries are up. Here, we address his other comments.
First, Milkowski writes that “the discussion of the physical signature of computation in this book tempers my optimism regarding” … “the inclusion of mechanisms in a physical account of computation”. We see no grounds for pessimism: nothing about the robust mapping account we advocate goes against the inclusion of mechanisms in an account of physical computation. In fact, one aspect of the constraints we articulate – the requirement that distinct physical states map onto each individual value of each variable in a computational description – is essentially a mechanistic constraint that is motivated both by mechanistic accounts and by essential considerations in the physics of computation. At any rate, as we say in the book, the requirements articulated by our robust mapping account can be incorporated within mechanistic accounts of computation.
Second, Milkowski writes that “in cases of apparent computational indeterminacy—where a single physical system seems to implement multiple computations—referencing irrelevant states might help clarify concurrent computations.” The robust mapping account explicitly allows that a given physical system may implement concurrent computations and spells out how these computations must be related to one another for all of them to be implemented robustly. The enabling concept is that of computational embedding (Sect. 2.5.2), which recognizes that some degrees of freedom may be computationally irrelevant for one implemented computation and computationally relevant for another. If one computation is embedded within another, and Physical-Computational-Equivalence (PCE) is satisfied for both computations, then both are robustly implemented by the system. One need not resort to claims that physical computation is subjective or indeterminate, which require implementation claims that demonstrably violate PCE (see Sect. 4.3.6 and Sect. 5.2.2), to account for concurrent computations and do so within the robust mapping account.
Third, Milkowski expresses concern about our usability criterion (U), which lies at the heart of strong computational descriptions. He characterizes our usability criterion as distinguishing “merely complex mechanisms from those that are operationally controlled, such as by a biological agent.” He also points to alignment with the usability desideratum of Piccinini’s (2015) mechanistic account, which, he says, has “faced criticism.” While our usability constraint does indeed align with Piccinini’s earlier usability desideratum in some respects, our criterion has roles and aims that are specific to our classification of computational descriptions, within which weak, robust, and strong physical-to-computational mappings are defined. We clarify these aims and roles below, and then address Milkowski’s concern.
Within our classification system, strong computational descriptions are the most restrictive. As defined, strong descriptions include all our defining criteria for robust computational descriptions, already legitimating physical systems that satisfy these criteria — usable or otherwise — as computational implementations according to our account. Strong descriptions go further, also satisfying our usability criterion. The usability criterion requires that “(t)here exists a computationally transparent use plan compatible with the physical description of (physical system) PS which specifies physical intervention protocols and conditions that would enable agents to use PS to compute (computation) C reliably for inputs of their choosing” (p. 113).
Milkowski seems worried that “a physical mechanism too large to be managed by any conceivable agent would fail (the usability) criterion.” We agree. If no conceivable agent can make use of physical system PS to compute C because PS is “too large,” then no conceivable agent could possibly have a use plan that would enable it to use PS to compute C. Usability would indeed be precluded in that case, and PS could not satisfy a strong physical description. But PS could still satisfy a robust computational description, which would legitimate PS as a physical computing system that implements computation C. Nothing in our account precludes there being robust physical implementations of computing systems that are not usable, which should address (what we take to be) Milkowski’s concern.
While this concern is the only specific concern related to usability that Milkowski spells out, we note that his characterization of our usability criterion as distinguishing “merely complex mechanisms from those that are operationally controlled” seems to misunderstand that criterion. Satisfaction of our robustness criteria alone distinguishes “merely complex” physical systems from those that implement computations – those that bear physical signatures of computations. Satisfaction of the usability criterion requires satisfaction of an additional computational transparency condition: if system PS is to satisfy Usability for computation C, then system PS proper must fully implement C. This blocks false attribution of PS as an implementation of C in scenarios where any of the computational work required to implement C is not done by PS proper — if any of this computational work is outsourced to external systems used to encode inputs, read outputs, or control the flow of computation in use of PS to compute C.
— Neal Anderson and Gualtiero Piccinini
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