Counting with Cilia: The Role of Morphological Computation in Basal Cognition Research

“Morphological computation” is an increasingly important concept in robotics, artificial intelligence, and philosophy of the mind. It is used to understand how the body contributes to cognition and control of behavior. Its understanding in terms of “offloading” computation from the brain to the body has been criticized as misleading, and it has been suggested that the use of the concept conflates three classes of distinct processes. In fact, these criticisms implicitly hang on accepting a semantic definition of what constitutes computation. Here, I argue that an alternative, mechanistic view on computation offers a significantly different understanding of what morphological computation is. These theoretical considerations are then used to analyze the existing research program in developmental biology, which understands morphogenesis, the process of development of shape in biological systems, as a computational process. This important line of research shows that cognition and intelligence can be found across all scales of life, as the proponents of the basal cognition research program propose. Hence, clarifying the connection between morphological computation and morphogenesis allows for strengthening the role of the former concept in this emerging research field.

Keywords: morphological computation, basal cognition, morphogenesis, minimal cognition, cybernetics, mechanistic philosophy

The term “morphological computation” can be most generally defined as “computation obtained through interactions of the physical form” (the following exposition of the history of the term follows the one proposed by Paul [1]). Developing from the study of embodiment as a key property of intelligence (e.g., [2]), it has first been understood in a broader way as the interaction of physical form and the complexity of the control of a system [3]. Eventually, itv emerged in the full-fledged form of “morphological computation” in the work of Paul [1] and quickly took off among engineers and artificial intelligence researchers (see, e.g., [4] and the special issue of Artificial Life 19(1)) interested in “unconventional” computing platforms and intersecting with the study of soft robotics. The importance of this concept stems from the fact that it offers an important connection between the popular computationalist view on the nature of the mind and intelligence and the emerging and quickly gaining popularity (at the beginning of 21st century, currently well-established) anti-computationalist perspective focusing on the embodiment of cognitive systems (e.g., [5]). Morphological computation indicates that, in fact, accepting the importance of physical bodies does not preclude the possibility of conceiving the systems under study in computational terms.

However, together with the increasing popularity of the term “morphological computation”, there has been a growing number of instances where it has been applied only loosely. Those conceptual ambiguities prompted a response from Müller and Hoffmann [6], who have scrutinized the existing uses of the term and offered a critical perspective, significantly limiting the scope and applicability of the concept of morphological computation. Despite the importance and the great value of Müller and Hoffmann’s paper, the authors accept a restrictive perspective, which significantly reduces the role of this concept in the debate on embodied cognition.

In the current paper, I wish to suggest that, similar to how counting on fingers has become a paradigmatic example of embodied cognition in complex (‘higher’) mental phenomena, (see [7]), “counting with cilia”—morphological computation processes performed by single cells, such as those involved in morphogenesis—can be considered a crucial example in the debate considering the possibility of so-called computational enactivism [8] (see also [9]). However, this is only possible if we have a more permissive view on morphological computation than Müller and Hoffmann—a view that naturally arises from the mechanistic approach to computation.

As a sidenote, it must be clarified that “counting with cilia” is meant here primarily as a metaphor, as cilia’s involvement in morphogenesis is not fully known, and this phrase does not aim to suggest otherwise. For example, morphogenetic movements use primarily contraction and cell-to-cell adhesion [10], although an increasing body of research investigates the role of cilia for organ development due to their role in human disease (see, e.g., [11]).

The goal of the paper is to provide three contributions to the debate on the concept of morphological computation begun by the influential paper of Müller and Hoffmann [6]. First, I want to highlight that the definition of computation these authors use in their analysis is, in fact, a semantic definition, even though they do not acknowledge this fact. Indeed, if their arguments are viewed from the widely accepted perspective of the mechanistic view of computation, the distinctions and criteria they introduce become untenable and refer to properties that are irrelevant for “computation”. Second, in light of this analysis, I want to provide an alternative set of criteria, building also on the insights of the cybernetic movement. Finally, the paper introduces a novel example of a system that can be considered to be performing morphological computation: the developmental and regenerative morphogenesis in living organisms. I analyze this process with the criteria proposed by Müller and Hoffmann [6] and the ones introduced here, and point out how my perspective offers important advantages for this research. These goals are realized in Section 3, Section 4 and Section 5, respectively. Section 2 introduces the argument made by Müller and Hoffmann [6]. In Section 6, I make a case for linking the analysis of morphogenesis with morphological computation to the debates in the basal cognition research community and suggest what role morphological computation can play for computational enactivism. In Section 7, I conclude by reiterating the key points of the paper.

Müller and Hoffmann [6] begin their argument with an overview of the approaches to physical implementation of computation. While this is an important part of the debate on the nature of computation, the question of implementation of computations in physical systems is partially orthogonal to the distinctions relating to the nature of computation in general. More precisely, the semantic view, at least in some versions (e.g., [12]) allows for both semantic and non-semantic perspectives on implementation, although the alternative mechanistic view, with its prohibition on involving semantics in computational descriptions, requires a non-semantic approach to implementation. Importantly, the non-semantic approach to implementation refers only to the criteria of applicability of a computational description to a physical system; it does not preclude the possibility that the physical system in question processes semantic information.

The semantic view of computation has a long history, building on early work by Hilary Putnam (e.g., [13]) and has been initially advanced by Jerry Fodor [14]. Although there are different varieties of the semantic account, they all accept Putnam’s premise of “no computation without representation” [15]. The semantic view requires that for a physical system to be counted as a computer, it must meet two criteria: (1) there must be a mapping defined from the physical representational states of the system to states defined by a computational description (e.g., states of a Turing machine), and (2) the state transitions between physical states must be causal and equivalent to transitions between computational states [15]. The details of these criteria, e.g., the individuation of representations and the sources of their semantic content, differ between varieties of this approach. For example, in a very recent iteration of the semantic view, Shagrir (pp. 179–181 of [12]) proposes to define the content in terms of “aboutness” and takes a pluralistic stance towards its origins.

Müller and Hoffmann [6] begin their analysis by accepting a particular view of computational implementation put forward by Horsman et al. [16]. This definition sets criteria that a physical process must meet to be counted as implementing “real, full-blown” computation:

An abstract initial state mp is encoded into the physical system using IT(mp), giving rise to p; the physical system is left to evolve, reaching p′, which is finally decoded using RT(p′), giving rise to mp′, which we are assuming corresponds to mp′—the desired outcome of the abstract evolution. In this case, the physical system has acted as a computer [6], p. 9.

T refers to a theory of the physical computational device, which encapsulates the correspondences between the abstract computation and the physical computer and a description of the evolution of the physical states. Further, Müller and Hoffmann follow Horsman et al. in specifying that the representation relation they posit is one that a user introduces: “the occurrence of representation is a vital part of physical computing, and computational entities (human or otherwise) are the ones performing it” [16], p. 15. I wish to argue this clearly places their definition of physical computation within the scope of the semantic view of computation, although this is not explicitly acknowledged. This is because this definition claims that physical systems perform computation only if there is an objectively identifiable representation relation between physical and abstract states that is “performed” or introduced by a particular privileged “computational entity”: the user. Horsman et al. clarify with an example of hieroglyphic inscriptions: in their view, between the loss of the language and the deciphering of the Rosetta Stone, such inscriptions were just potential communications, and only once they were decoded did they became communications in actuality. Similarly, a physical system is only potentially a computer until a particular user imposes a representation relation on it, individuating the computations performed and making it an actual computer. The representation relation in their view has, in fact, a semantic nature: it is an abstract description of a physical object [16], p. 4. As such, it goes beyond the accepted non-semantic views of representation, which usually begin simply with syntactic information. Hence, in this view, computational individuation hinges upon the existence of a semantic relation between physical and abstract entities.

Müller and Hoffmann further require that the theory T be known a priori. This last criterion has been introduced originally by Copeland [17] as one of the criteria for suitable mappings between abstract computations and physical computers: Copeland states that such mappings should not be constructed ex post facto. However, as Miłkowski [18], p. 33 convincingly argues, referring to cases of reverse engineering of clearly computational systems (in which such mapping is only available posterior to empirical research), this restriction is not well-defined.

This semantic view underlies Müller and Hoffmann’s analysis of morphological computation. Scrutinizing cases discussed in the literature in those terms, most importantly: the (active) passive–dynamic walker (e.g., [19]), the eye of a fly (e.g., [20]), and examples of physical reservoir computing, such as mass–spring systems (e.g., [21]), they come to the conclusion that these systems fall into three classes:

A. Morphology facilitating control: In systems such as the passive–dynamic walker, they argue morphology is better seen as simplifying the controller or enabling particular actions that otherwise would be impossible. Their analysis indicates that, in these cases, there is no representational relation between abstract computation and the morphology of the system—no suitable encoding and decoding can be defined—and the theory of the system does not indicate that its evolution tracks the evolution of the abstract computation.

B. Morphology facilitating perception: In systems such as the eye of the fly, morphology can be associated with a proper computational description: we know well what transformation the morphology of the system performs and can describe it as an input–output (computational) mapping—hence, the evolution of physical states tracks that of computation. However, or so Müller and Hoffmann would argue, the morphology is not “deployed here as a computational substrate to calculate an abstract problem” [6], p. 17, an observation that probably comes from the difficulties with identifying a proper “user” of such a system, who could define the representational mapping between abstract and physical states.

C. Morphological computation: Eventually, systems such as physical reservoir computing constitute the class of systems that can accurately be described as morphological computers, according to Müller and Hoffmann [6]. Such systems are employed in human-designed computing frameworks with controlled inputs and outputs and known dynamics of the system. As a result, such systems clearly meet the criteria introduced above.

The difficulties of defining and individuating representations and of naturalizing their content ultimately led many philosophers, especially within the philosophy of cognitive science, to increasingly distance themselves from the semantic view. In the result of the emergence of the new mechanism philosophy [22], the main competing view has crystallized in the form of the mechanistic account of computation (cf. [18,23,24]). The mechanistic view defines physical computation as processing of vehicles according to rules sensitive to some properties of the vehicles. Computational vehicles are symbols over which the computation is performed. These are encoded in a particular physical medium, but most theories of computation take this medium to be relevant only insofar as computational rules are specific to differences between different portions of the vehicle along one dimension of variation (single physical property). For example, in the case of neural computation, neuronal spike trains are the vehicles, but computation is often taken to refer to their medium-independent properties, such as spike rates. Crucially, processing is performed by a mechanism that is functionally organized to perform this computation. Here, different varieties of the mechanistic account will differ, among others, by the view of function they accept. The concept of function, although no less problematic than that of representation, is, however, more basic; hence, difficulties with establishing its naturalized definition seem to deter philosophers to a lesser degree.

Proponents of the mechanistic view reject the requirement of encoding/decoding or representational relation between an abstract object and a physical one. Instead, computation under this view corresponds to any instance of information processing, where one can distinguish a particular mechanism that performs information processing as its function. The identification of computation with information processing (although at times contended within the mechanistic view, see Piccinini [23]) refers to purely syntactic information without presupposing its representational character. In particular, Miłkowski [18] draws on MacKay [25] and makes use of the concept of “structural–information–content”, which is ontologically “cheap”, as any physical process that has at least one degree of freedom (independently variable property) will carry some structural information (given this very precise sense of information, Piccinini [26], in fact, concedes that computation is always information processing).

Miłkowski [18], pp. 77–78 explicitly touches upon the topic of morphological computation. He argues that given a mechanism that is (evolutionarily) designed to perform the function of processing information and that can be clearly individuated (as is the case in biological systems, with delineated cells, tissues, etc.), the computational function can be ascribed to it. It does not matter whether this function is performed thanks to the morphological features in a physical, analogue way, or thanks to some other (possibly medium-independent) properties of the system. Miłkowski builds on the example of the mechanism of the pressure-difference receiver in crickets cf. [27], a case resembling that of the eye of the fly—so a case of morphological perception in Müller and Hoffmann’s framework. This view can be also expanded to provide a criterion to differentiate morphological computation from other types of computation: in the morphological case, computational vehicles are processed in a medium-dependent way, with computational rules being sensible to their physical properties. In the case of the pressure-difference receiver, the criteria are met, and a computational description in terms of sound filtering can be successfully ascribed to the system. This is, however, more than a minimal restriction that (some flavors of) the mechanistic account requires: in fact, all cases of sensing can be counted as computation, as they all involve information processing (the minimum would be for them to compute an identity function, although in physical systems, it is more complex as the information is most often transduced and digitized, either into bits or into nerve cell firing patterns—so it undergoes a nonlinear transformation).

Just as in the eye of the fly, the pressure-difference receiver in crickets falls neatly under the scope of “intrinsic computation” in Müller and Hoffmann’s framework. In their view, intrinsic (natural) computation is classified as “real” computation only if there is a user, the encoding and decoding processes are designed, and the computational description can be applied a priori (i.e., only the criterion of having a suitable theory describing evolution of states is met). However, under the mechanistic view, these additional criteria are not relevant, and nothing excludes the examples of “intrinsic” computation out of the realm of “real” computation.

Hence, the tripartite classification of Müller and Hoffmann [6] introduced above under the mechanistic view must be simplified. Above, we have seen that simply accepting the mechanistic criteria of computation dissolves the distinction between morphological perception and morphological computation (for clarity, I will refer to this class of processes simply in terms of morphological information processing as, for practical reasons, it may at times be relevant to distinguish between these different classes of computational processes). I turn now to the discussion of the other class of processes: morphological control. In that endeavor, I will refer to the cybernetic tradition to introduce key distinctions.

The cybernetic tradition, in particular the so-called first wave of cybernetics, has influenced both computationalist and anti-computationalist views in the scientific study of mind, philosophy of mind, and—by extension—in philosophy of biology (see for overview [28,29]). Froese [30,31] points out that these two veins of evolution resulted from one crisis in the original cybernetic thought, related to the emergence of W. Ross Ashby’s work, in particular, his Homeostat [32] (although the treatments in [28,29] do not assign as great of an importance to this point). The Homeostat presented a proof-of-concept for the design of an ultra-stable system, which through simple controllers is able to maintain a stable pattern of activity even in the face of major perturbations of the environment (e.g., a reversal of polarity of the phenomenon it is supposed to control) through a change of internal organization or structure. Ashby did not see the tension between the design of the Homeostat, a dynamical system through and through, and the notion of computation, as he himself calls it an “analogue computer” [32], p. 99, which constantly searches the parameter space to maintain its computation of a (more-or-less) constant function in the face of changing inputs. Interestingly enough, in Froese’s analysis, the appreciation of the insights coming from the Homeostat eventually led to the emergence of enactive cognitive science and of second-order cybernetics. The former view adamantly rejects computationalist explanations of cognition, disregarding Homeostat’s computational nature underscored by Ashby.

Importantly, there is largely an agreement among commentators (e.g., [28]) that the original perspective on computation of cyberneticians falls under the umbrella of the mechanistic view. However, the important contribution of cybernetics that I want to build upon here concerns specification of the concept of “control” in terms of feedback loops.

The argument for keeping “morphology facilitating control” as distinct in the mechanistic framework of morphological computation could be made by reference to the seminal concept of “intentional stance” introduced by Dennett [33]: it is simply not necessary to invoke information processing to describe the operation of, e.g., a passive–dynamic walker. The concept of “intentional stance” was proposed by Dennett to account for ascription of mental states to various systems, including ourselves and other human beings. Dennett proposed that whereas some systems can appropriately be described from a physical or “design” perspective or stance, referring to their dynamics or designed functions, respectively, some require a more abstract account. This is the case with humans or other animals, where we decide to ascribe mental states—beliefs, desires, intentions—to be able to explain and predict their behavior. What I mean here, in the context of “morphology facilitating control”, is that whereas we might decide to describe the movement of a passive–dynamic walker by referring to the concept of information (e.g., information about the steepness of the incline being processed to establish appropriate speed of movement), a less abstract description, in fact, works better (e.g., in terms of forces and classical mechanics). However, the argument along these lines that Hoffmann and Müller [34] originally offers is not entirely correct, as they invoke the sufficiency of dynamical systems’ description for these kinds of systems but ignore the fact that those can be also used for computational systems [35]. In fact, they are the primary way to describe the operation of analogue computers (formally speaking, they both involve differential equations to describe the processes; see, e.g., [36]).

Nonetheless, they are correct in the fact that a physical description (i.e., Dennett’s physical stance) pitched at the level of classical mechanics suffices for systems such as the passive–dynamic walker, and no reference to informational notions is needed for this purpose.

However, even using the term “control” to refer to the passive–dynamic walker is not so obvious: its behavior is, in principle, no different from that of a billiard ball rolling down an incline, and one would not invoke the term to describe the ball (in fact, unless the incline somehow constrains the movement of the ball, one may be more likely to call it uncontrolled). While a feedback loop (see [37], p. 12) is not a necessary condition of control—we would say that a person who simply presses the gas pedal while keeping the steering wheel still controls the vehicle (provided the vehicle operates normally and no spurious relationships are in play), even if s/he does so terribly and dangerously—“feedback” does delineate a particularly interesting subset of control processes. Feedback loops were initially defined by Wiener (see also [38]) by reference to a number of canonical examples, such as a thermostat or a watt governor (for an important case study in philosophical debates on the role of representation for cognition, see, e.g., [39], controlling the operation of a steam engine). Essentially, a feedback loop provides an informational relation between the output and input of a process through which the process can be better adjusted. To return to the car example: as soon as the driver opens his/her eyes, s/he will be able to relate the input (pressing of the gas pedal) and the output (a quickly approaching concrete wall) and act on the input to return the system into viable conditions (stop pressing the gas pedal and bring the car to a stop). Importantly, Conant and Ashby [40] distinguish between “error-controlled” and “cause-controlled” regulation. These can be illustrated with an example from Ramsey [41]: consider two drivers following an S-shaped road in cars that lack windows so that the drivers cannot actually see where they are going.

Car A is equipped with a proximity sensor that informs the driver when s/he is approaching the edge of the road. Car B is provided with an accurate map, which the driver uses along with a simple dead-reckoning strategy to guide his/her way along the road. This is contrasted with a third car, Car C, that lacks any sort of driver and bounces off the railing. All three cars manage to move along the road despite their differing strategies. The first two cases (Cars A and B) correspond to error-controlled and cause-controlled regulation, respectively. What is relevant for current purposes is that in both cases a sort of information processing is required. In the case of Car C, no informational processes are involved; the movement of the car proceeds similar to the movement of “a marble in a pinball machine” [41], p. 194—not so different from a passive–dynamic walker.

This brief discussion shows that the class of cases that could be classified as “morphological control” is heterogeneous, and the examples provided by Müller and Hoffmann [6] fall mostly under the category that one may call “not even control”. Consider again the primary example of a passive–dynamic walker: its walk down an incline is no different (in terms of a control) than a billiard ball rolling down the incline or a marble in a pinball machine bouncing off the edges. If components of control are present in those systems (e.g., in the passive–dynamic walker with actuators), they do not perform the control function in virtue of their morphology but rather in a more classical way.

However, if we look at examples from the class “control with feedback” (comprising both error-controlled and cause-controlled examples), it turns out that there are systems that perform control in virtue of their morphology and qualify as computational according to the mechanistic criteria. The examples of the thermostat and the watt governor can be brought up here: these simple systems compute very basic functions (“less than”), and they do so in virtue of their structural and morphological properties (the shape or size of a metal bar in a classical thermostat, the angle between the arms in the watt governor). Although obviously these systems can also be defined with simpler, physical descriptions, these computational ascriptions seem sufficiently warranted.