For the official version of record, see here:
Hansen, M. B. N. (2024). The Contingency of Process, or Why There Is No Computation-in-itself. Media Theory, 8(2), 13–36. https://doi.org/10.70064/mt.v8i2.1116
The Contingency of Process, or Why There Is No Computation-in-itself
MARK B. N. HANSEN
Duke University, USA
Abstract
This text responds to Alan Díaz Alva’s careful and compelling account of the tensions between and ultimate compatibility of Beatrice Fazi’s work on the formal incomputability of computation and my account of computational media in Feed-Forward. I recount Díaz Alva’s reconstruction of the “claim for inversion” I introduce in my book and suggest that the priority it grants the “superject” over the concrescing subject means that all process is both self- and other-determined. Linking this double determination to Whitehead’s insistence on the basal “dipolarity” of process according to which all prehension involves both physical and conceptual feelings, I question what Díaz Alva felicitously dubs Fazi’s “minimal definition of computation as self-determination.” Linking it to Fazi’s effort to isolate the conceptual-formal dimension of computation from its physical-sensible dimension, I try to show that this limitation of computation to self-determination provides the ground for Fazi’s effort to conceptualize computability and the incomputable on the basis of an internal contingency that is purely formal. I suggest that this effort is in fact what Whitehead would call an “abstraction,” which is to say, an empirical experience of “preanalytical,” in-itself unknowable process. Treating it as abstraction allows us to discern the operation of a more basal contingency – an intrinsic contingency – that lies at the core of all process and that is the source for the formalist abstraction (and all other possible abstractions). Returning to Díaz Alva’s generous proposal regarding our respective projects, I conclude that our accounts can indeed be made compatible although on slightly different terms than the ones Díaz Alva outlines. To that end, I introduce an account of the incomputable rooted in the excess of the sensible over computational measurement (Giuseppe Longo) and offer a concrete proposal for how to incorporate the formal dimension (pure potentiality) of computation into the concreteness of process.
Keywords
process, dipolarity, self- and other-determination, computation, intrinsic contingency, abstraction, Alfred North Whitehead, Giuseppe Longo, propositions
Introduction
I want to begin by thanking Alan Díaz Alva for his careful and thought-provoking account of the consequential differences and possible complementarity between Feed-Forward and the work of Beatrice Fazi. Díaz Alva’s synthesizing instincts have helped me better understand Fazi’s project – and also my own. I would like also to thank Simon Dawes for the invitation to respond to Díaz Alva and Beatrice Fazi for her insightful and challenging effort to think computation separately from human rationality. Taking this invitation as an opportunity to reflect on the scope and nature of my commitment to the sensible, I shall examine the role that computation plays in the process of “worldly sensibility.” Specifically, I shall explore Fazi’s claims for the autonomy of computation and the contingency she associates with the uncomputable in relation to the sensible. To this end, I shall proceed by unpacking what I take to be a tension – for me, a productive tension – between Fazi’s definition of computation as Whiteheadian “actual occasion” and her claim that computation involves a contingency that is purely “formal.”
This exploration will take us straight to the heart of Díaz Alva’s concluding argument that our respective projects – mine anchored in “real potentiality”; hers in “pure potentiality” – are complementary efforts to apprehend the “internal contingency” of computation. While I appreciate Díaz Alva’s synthesizing gesture and agree wholeheartedly that computation must be addressed in its (formal) specificity, Whitehead’s insistence on the “dipolarity” of all actual occasions seems to me to preclude the possibility of a purely “formal,” purely “conceptual” act of prehension. Thought from the perspective of the dipolarity of process, the internal contingency Fazi rightly accords computation appears rather to be itself part of a more basal contingency: the contingency intrinsic to process itself. For this same reason, Díaz Alva’s generous attempt to differentiate our respective accounts in terms of a complementarity between “computation” and “computational media” seems to me to contravene the fact that the contingency of computation arises not because of its deployment as media, but rather from out of the indetermination that is the real condition – the real potentiality – for its actualization in the first place.
In the end, I am in solidarity both with Fazi’s effort to think computation as a form of reason distinct from the human and with Díaz Alva’s effort to emphasize the “internal contingency” of computation as process. For me, however, these efforts are best understood as contributions to a more fundamental – and in Whitehead’s sense more concrete – understanding of contingency as “internal” to process itself.
The contingency of process, other-determination, and the claim for inversion
Let me begin by presenting my definition of contingency: contingency is a product of the margin of indetermination that informs process. This margin of indetermination is always relative to a particular “atomic moment” of process, and it arises from the concrete quotient of “real potentiality” that informs it. Real potentiality is the lingering potentiality of the past – what could have become but didn’t – that, in Whitehead’s understanding, belongs to the actual as an unactualized excess available to and for future process.
Understood in this way, contingency correlates with the “superjectal” side of my project, as this is envisioned by Díaz Alva in his insightful account of the double agenda of Feed-Forward. Díaz Alva’s separation of its “superjectal” side from its “pharmacological” side is extremely helpful for two reasons. First, it makes clear that my argument does not just seek to develop a posthuman phenomenology that expands the frame of experience by including what in the book I call “machinic reference.”[1] And to the extent that such an expanded phenomenology depends on broaching the limits of human sensibility in determining what is and can be experienced, it is itself made possible by what Díaz Alva rightly refers to as an ontological dimension of process or what I call “worldly sensibility.” Thus, second, Díaz Alva’s separation very usefully highlights the way that process creates sensibility on the basis of (past) sensibility independently and well beyond the scope of human experience.[2] Díaz Alva furthermore takes note of my claim about the indirectness of media’s genesis of worldly sensibility in relation to human experience: the fact that media, as I put it, impact worldly sensibility prior to and as the very basis for their impact on human experience.
What all of this points to is a certain priority of the “superjectal” side of my argument over the “phenomenological-pharmacological” side. Díaz Alva captures this priority in his excellent presentation of what I call the “claim for inversion.” According to this claim, the concrescence of actual entities – that part of Whitehead’s metaphysics that is taken by Whitehead himself and by the vast majority of his commentators as the core of process – is in fact a supporting element of another aspect of process, “transition,” that focuses on the power actual entities possess once they are completed, become objectified (i.e., turned into data), and get added to the settled world. In their “new” form, actual entities are “superjects,” and it is as superjects that actual entities harbor the real potentiality that informed their genesis (as concrescences-become-superjects). Recalling that indeterminacy belongs to process because it is “internal” to real potentiality (again, its source is what could have become but didn’t), this means that indeterminacy enters process via superjects even if it gets determined – that is, integrated into new actuality – by concresence. Actualities are not simply “self-determined” but are also “other-determined,” and indeed, they are other-determined before and as a real condition of their becoming self-determined.[3]
If my argument for inversion properly describes the hierarchy between superject and subject-concrescence, then Whitehead himself errs in ascribing the determination of the indeterminate exclusively to the concrescing subject. Although the subject will at some point complete its concrescence, which is to say, the act of prehending the entirety of the settled world, it is originarily the product of a concrete confluence of exteriorities or superjects composing together. Concrescences are, as I put it in Feed-Forward, “sparked into becoming” by the superjectal force of the settled world (Hansen, 2015: 172).[4] That is why I can claim, in lines cited by Díaz Alva, that concrescences are “instruments for the production of worldly superjects, which are the true source of experiential creativity” (2015: 28), or alternately, that “concrescence is not the privileged operation of Whitehead’s philosophy but merely a vehicle for the propagation of worldly sensibility” (2015: 173).
Concrescence, in short, is the product of other-determination, not its source. The concrescing subject does not preexist the process from which it emerges, and it is quite literally the result of the relations among its composing exteriorities which enter into contrast with one another and generate subjective intensity. In this sense, the subject simply is a specific pattern of intensity that is generated by the contrasts among the entities composing it.[5] Furthermore, the contingency at issue in concrescence is the result of the superjects that compose it, and more precisely, of the concrete share of real potentiality relevant to a given atomic moment of process. This means, as I shall argue below, that contingency cannot be purely formal or logical. It also means that there is no contingency-in-itself. And it means, ultimately, that the source of contingency is the concrete process through which the world incessantly updates itself from atomic moment to atomic moment.
All actuality is sensible
The primacy of other-determination also means that there can be no “pure potentiality” in the sense Whitehead presents it in Process and Reality. On Whitehead’s canonical account, it is the “ingression” into concrescence of “eternal objects” harboring pure potentiality (non-temporal entities like qualities, relations, etc.) that decides on the indeterminate, that determines the “how” of process. And it is the concrescing subject (and more precisely, the subjective aim it is given by God) that carries out this determination – which is therefore a self-determination – by “deciding” how to actualize the pure potentiality informing it.
All of this must be revised following the inversion that installs other-determination as the primary, superjectal source of process. Simply put, there can be no pure potentiality in the Whiteheadian sense since potentiality always demarcates a concrete margin of indetermination that characterizes the superjectal world at some given atomic moment of process. Whatever pure potentiality may be, it is always enfolded within real potentiality qua the concrete potentiality for future process at any given moment and from any given perspective.[6]
With this observation, we touch upon a crucial point that will be important when we turn to Fazi’s conception of computation: all prehension, all feeling, is a composition of physical and conceptual elements. “In each concrescence,” writes Whitehead, “there is a twofold aspect of the creative urge. In one aspect there is the origination of simple feelings; and in the other aspect there is the origination of conceptual feelings. These contrasted aspects will be called the physical and the mental poles of an actual entity. No actual entity is devoid of either pole…” (1978: 239). Whitehead refers to this basic entailment of process as its “dipolarity.” This dipolarity follows from Whitehead’s ontological principle, which stipulates that actual entities are the only reasons (“no actual entity, then no reason” (1978: 19)). This fundamental requirement effectively anchors conceptuality in physicality, since the eternal object that is the source for conceptual feelings is always relative to a concrete physical feeling. “From each physical feeling,” stipulates Whitehead’s Category of Conceptual Valuation, “there is the derivation of a purely conceptual feeling whose datum is the eternal object exemplified in the definiteness of the actual entity … physically felt.” This means that, in the final instance, all actuality is sensible: “This category maintains the old principle that mentality originates from sensitive experience. It lays down the principle that all sensitive experience originates mental operations” (1978: 248, emphases added).
If the primacy that Whitehead here grants the sensible does not in itself simply invalidate the very notion that so-called eternal objects harbor pure potentiality, it does suggest that eternal objects can only enter process and make a difference through their concrete ingression into the concrescence of dipolar actualities. On this score, pure potentiality differs from the concept of the universal that it stands in for on Whitehead’s account. Unlike universals, pure potentiality is always constrained by, and thus relative to, a concrete situation: it is always the pure potentiality of a certain state of the settled world, part of the latter’s real potentiality to produce further actuality.
This conclusion follows from Whitehead’s alignment of process with empiricism: “You cannot know what is red by merely thinking of redness. You can only find red things by adventuring amid physical experiences in this actual world. This doctrine is the ultimate ground of empiricism; namely, that eternal objects tell no tales as to their ingressions” (1978: 256). Díaz Alva grasps this point perfectly when he writes that eternal objects “cannot be conceived, known or represented by themselves independently of the actual occasions that they inform” (Díaz Alva, 2024: 24).[7]
The act is always concrete
Fazi would seem to agree. Indeed, she explicitly characterizes computation as a dipolar process: “computational actual entities,” she writes, “determine themselves via the physical manipulation of data (in other words, by physically prehending other computational actualities), but also because they address logically – and not affectively or strictly empirically – their own logical indeterminacy” (Fazi, 2021: 297, cited in Díaz Alva: 24). For Fazi, however, computational actual entities can be differentiated from other actual entities because of the particular type of experience they create:
if we take actuality to be dipolar because brought to realisation via physical and conceptual determinations, then we must also develop an understanding of experience that equally involves processes of actualisation ingressed by physical and conceptual indeterminacy. … computation possesses its own mode of experiencing by basing such experiencing on the abstractive and quantitative nature of the computational method, without the need to resort to a source of indeterminacy that would be external to the computational processing (Fazi in Beer, 2021: 298, emphasis added).
The distinction that is operative here – external versus internal – requires that there be something in virtue of which indeterminacy is either one or the other. That is why Fazi must privilege the self-determination of process over its other-determination. And indeed, she makes precisely this commitment at the moment that she equates experience with self-determination: “all actuality experiences because experience … is equivalent to the process of self-determination of actuality…. I follow Whitehead’s characterisation of experience as self-actualisation to argue that computation’s own experience can be understood to correspond to computation’s own process of self-determination” (Fazi, 2018: 13–14). In his gloss on Fazi’s account, Díaz Alva calls this the “minimal definition of experience as the self-determination of actuality” (Díaz Alva, 2023: 18, n. 14).
But what is it that allows Fazi to isolate one polarity of computation from the other, in apparent disregard for the constitutive dipolarity of all process?What is it that lets her postulate the specificity of the computational act, as she does in the passages just cited, on the basis of “the abstractive and quantitative nature of the computational method”? The answer should now be evident: Fazi’s view of process as self-determination allows her to isolate the conceptual component of process. Only by thus privileging self-determination can she characterize computation as a distinct type of process that is formal, and that, because it is formal, operates on the basis of a contingency which is internal to it and not the result of mere empirical accident – or, as I am proposing, of self- and other-determination according to the generic understanding of contingency as intrinsic to process.
Consider the definition Fazi offers in Contingent Computation:
Contingency is the ontological status of algorithmic operations of ordering and systematising the real through logico-quantitative means. The latter are algorithmic operations that are preset, but which are always ultimately contingent because of their internal indeterminacy. This contingency means that formalisation-as-discretisation never exhausts indeterminacy. Computation is made of quantities, yet these are quantities that cannot be fully counted; an ever-increasing number of axioms can be added to the system, and an ever-increasing number of steps can be added to the calculation (Fazi, 2018: 129, cited in Díaz Alva, 2023: 22).
According to Fazi, what distinguishes this internal contingency proper to computation from external contingency introduced by empirical factors is precisely the formal indeterminacy of computation qua self-determination:
The contingency of computational systems should not be understood in terms of a capacity for accident, wherein the terms of the algorithmic process can deviate from the preset rule. The preset rule does not in fact have to be other than itself in order to be contingent: it does not have to deviate from formal logic or axiomatic deduction in order to embrace indeterminacy, because it is contingent already, at its logical, formal, and axiomatic level, thanks to the infinity that is inscribed in its being preprogrammed (Fazi, 2018: 130, cited in Díaz Alva, 2023 : 22, emphasis added).
Here we encounter what seems to be the endpoint of Fazi’s account. Computation, she tells us, is already contingent because of its formal, axiomatic structure. But wouldn’t this mean that it is contingent before it actually happens, or at least, independently of its actually happening?
Contingency is not a timeless condition that can be inscribed into a formal axiomatic. On this score, we need to distinguish contingency from formal indeterminacy (and from indeterminacy writ large). Contingency is the product of the determination of indeterminacy: it is what results when the excess of the indeterminate is, as it were, forced to condense into a single determination. This means that contingency cannot be decoupled from the operation of process whose product it is: there is no contingency-in-itself, no contingency that is not the contingency of a concrete situation. It also means that contingency cannot be purely formal or logical: even in a case when it arises on the basis of the formal indeterminacy of the axiomatics of computation, contingency is absolutely bound to the event in which it happens.
Contingency, then, is a result of the mechanics of process itself, the fact that process operates, from atomic moment to atomic moment, by deciding on the real potentiality of the just past settled world. Rooted in the dipolarity of process, this generic definition of contingency – as intrinsic to process – not only encompasses both self-determination and other-determination; it also grants the latter its primacy. That is precisely why Whitehead positions the universe itself as the final arbiter of process’s advance: “The doctrine of the philosophy of organism is that … beyond the determination of [the] components [of a concrescence] there always remains the final reaction of the self-creative unity of the universe” (Whitehead, 1978: 42). This unity is not a totality, however; indeed, it is, as Simondon puts it, both less than and more than a whole, at one and the same time both a delimitation of purely open possibility and a decision on an excess of real potentiality, on a concrete margin of indetermination (Simondon, 2020).
Computation is sensible “in-itself”
Computation is contingent, then, not only because of its underlying formalism, but rather for the broader reason that it occurs – like all process – through concrete acts (of self- and other-determination) that decide on an indeterminacy (real potentiality) which is not simply formal and which “evolves” incrementally with each new processual actualization. With respect to computation, this means, as computer scientist A. A. Cavia forcefully puts it, that indeterminacy cannot be anchored in the formal incomputability “internal” to computation but must be indexed on the processual nature of decision, which is to say, on the concrete process of computing itself insofar as it is dipolar and both self- and other-determined:
The intuitionistic view of logic can thus be seen as an insistence on an inferential dynamics over a static axiomatics, presenting a temporal view of truth at odds with the timeless formalist conception of mathematics. This commitment to temporality manifests what Fazi calls “computation’s very own indeterminacy” …. While Fazi locates this indeterminacy in the inscription of the incomputable, this relation is fully elaborated only via intuitionist semantics, destabilizing the appeal to an incomplete axiomatics internal to computation itself and locating it instead in the temporal nature of decision procedures. Such a view serves to reorient Fazi’s account of contingency in formal systems by providing an adequate rendering of the relation between computation and time in line with contemporary physics…(Cavia, 2022b: 134, emphasis added).[8]
Indeterminacy arises from the concrete operation of computation – of computational actual entities – that involves an always singular confrontation of a countable infinity and a finite decision procedure. More simply put, indeterminacy arises from the encounter of formal infinity and physical finitude. If computation is a distinct type of process, that is precisely because it is characterized by dipolarity of this particular type.
Computation is thus sensible “in-itself” in a more fundamental sense than, I think, Fazi recognizes. We can put this quite simply: computation is sensible because it is processual. But let us unpack what exactly that means, what computation is qua process. We have already noted the priority that process philosophy places on the act. Process involves the “becoming of continuity” not the “continuity of becoming”: this means that process occurs through an incessant, incremental sequence of atomic events – the becoming of actual entities and their addition to the world – until, as Whitehead puts it, the “crack of doom” (1978: 228). These events, following Whitehead’s ontological principle, are the only real things and are, in a sense, ontologically self-justifying. From a process perspective, then, computation is a sequence of atomic computations (“computational actual entities”) that compose together as a “society” by taking part in larger, macroscopic computational operations in time. Each of these atomic computations is itself an act – a process – in which superjects combine together to inform the becoming of new atomic actuality. As act, each computation certainly involves an encounter with the “countable infinite” that inheres in the axiomatic formalism underlying computation. But – and this is, I think, Cavia’s point – because of the temporal (or processual) “nature of decision procedures” – this countable infinite always takes a concrete form which is in part determined by the particular “time-criticality” of its finitude and concrete situation.
Moreover – and this is absolutely crucial – the computational act is not just the encounter with the countable infinite in isolation. It also enfolds other elements of other-determination, including myriad concrete factors ranging from data input to hardware and the electricity that runs it. All of this composes together in each atomic moment, and this atomic composition is “prior” to – and is precisely what constitutes – larger macroscopic operations of computation which form computational “societies” in the empirical world. We can thus say that computation is intrinsically sensible (just as it is intrinsically conceptual or “formal”) because it is the result of computational acts that prehend the settled, superjectal empirical world both physically and conceptually, in a “dipolar” real togetherness that, as I shall demonstrate shortly, is “preanalytical,” i.e., “prior” to any separation (and indeed to the possibility of separation).
Understanding each computational act as a “computational actual entity” as just outlined does not and cannot amount, however, to understanding computation exclusively as “self-determination,” following Fazi’s minimal definition. We have already made this argument in a philosophical register, in relation to the processual requirement that process involve both self- and other-determination. Now, however, we can fully grasp why it is the case: namely, that from a process standpoint, computation does not exist as something separate and independent from the myriad concrete processual acts that form its content or materiality. From the standpoint of process, there simply is no “transcendental computer,” no computation-in-itself, but only indelibly concrete, dipolar, atomic computations that are only subsequently assembled together in societies, i.e., macroscopic computational operations.
To the extent that Fazi’s position is rooted in her conception of computation as “self-determination,” where self-determination means exclusively “formal” determination, Fazi’s project thus rests on an abstraction. Indeed, it rests on a particularly telling abstraction, given the process philosophical grounding of her project: the “meta-processual” abstraction of eternal objects from their requisite anchoring via ingression into concrete, dipolar actual entities. This abstraction effectively takes eternal objects to be separate from the acts in which they participate. By understanding the incomputable internal to computation as the inscription in it of logical infinity, Fazi transforms it into something that can only be prehended through a purely conceptual prehension. The formal structure of computation, Fazi observes, “has its own way of being evental, and therefore of ‘experiencing’ insofar as it determines itself vis-à-vis indeterminacy. Via the notions of incompleteness and incomputability,” she concludes, “we discover that the inherent indetermination of computation pertains to its intelligible dimension, and that this indetermination is encountered by way of abstraction: this is a formal indeterminacy, not an empirical one” (Fazi, 2016).
In his recent work on “radical media archaeology,” Wolfgang Ernst insists that computation is a physical operation at its core and thus that, given sufficient time, it could be “encountered” in its concreteness (Ernst, 2022). Ernst’s position provides a helpful context for unpacking Fazi’s claim that the “inherent indetermination of computation” is “encountered by way of abstraction.” As I understand it, the différend between their respective positions coincides with the différend at the core of process thought: between process as the genesis of the concrete and the experience of process through abstraction.[9]
Real togetherness, empiricism, and abstraction
To appreciate the significance of this différend, we will need to take a further look at the mechanics of Whitehead’s process philosophy. The fundament of process, as Fazi correctly grasps, is the concrescence of actuality. I am in agreement on this point, with the important proviso (as discussed above) that concrescence, rather than being the exclusive center of process (i.e., the autonomous operation of self-determination), is in the service of the superjectal operation of “transition” through which worldly sensibility is incessantly re-created out of the real potentiality of the settled world at any given atomic moment. As I understand it, the centrality of concrescence means that process occurs through “complex unity” or “real togetherness.” Prehension (or feeling) is thus an “originary synthesis”: a synthesis of superjects bearing potentiality in a becoming-together that precedes any separation.
Whitehead calls this the “cell theory of actuality” in order to stress that actualities are “cell-complexes” which are not “analyzable into components with equivalent completeness of actuality” (Whitehead, 1978: 219). Philosopher Richard Rorty has felicitously referred to the originary synthesis of actuality as preanalytical unity (Rorty, 1979), meaning both that it will have already happened before any possible analysis (division into parts) and that it is prior to any act of knowledge, to any possible abstraction. Process is the originary, preanalytical synthesis that produces – that simply is – experience from atomic moment to atomic moment, and yet is not graspable as such or in its entirety. There is an ineradicable rift between process qua fundamental experience and any subsequent experience of process. And because of this rift, which can never be fully bridged, any attempt to grasp or to know process must necessarily happen through abstraction. Along with all other enduring entities (“societies” in Whitehead’s generic, technical term), we are thus “condemned” to live in abstraction: we only experience process indirectly, through the abstractions we are able to construct from it.
I would thus agree with Fazi’s claim that the formal indeterminacy of computation is only “encountered by way of abstraction,” though not quite, I think, for the reason she offers. Far from being the basis for a distinct type of contingency that can only be experienced conceptually, the formal indeterminacy of computation, understood as the formal incompleteness of any system that is countably infinite, is an abstraction from the preanalytical process that constitutes the operation of computation qua act and that, like all acts of process, is dipolar, at once both physical and conceptual. Put more simply: the mathematics of infinity only exists as a static and timeless formal system because of concrete acts that operate on – and are informed by – formal indeterminacy. It is an abstraction from such concrete acts.
In itself, such abstraction is neither good nor bad. Indeed, it can be helpful analytically for understanding the formal dimension of computation, as Fazi’s work illustrates in a particularly powerful way. But when its status as abstraction is disavowed, what results is a “fallacy of misplaced concreteness,” the (mis-)taking of an abstraction for the really real things.
This is precisely the situation of “metacomputationalism” which Fazi finds to be a bad abstraction. Operating as a closed deductive system, metacomputationalism deploys computation as an abstraction in a bid to control the contingency of the world. With its assumption that, as Fazi puts it, “rational calculation can explain and encompass every element of actuality” (Fazi, 2016), metacomputationalism positions computation as an idealized operation that seeks to master external, empirical contingency by submitting it to “computational abstraction.” On this view, Fazi writes, axiomatic systems are made “to serve the agenda of a logos that aims to assign, through chains of sequential operations, an inferential and procedural form to the real [. . .] when seen in this light [computational axiomatics] transfers its deductive and determinist structure from the mathematical and technological to the societal, the economic and the political” (Fazi, 2018: 98–99). Fazi convincingly argues that the contingency at issue in such a transfer is “external” contingency because it situates contingency in the encounter – the entanglement – of computation with reality.
As I see it, however, Fazi’s own position cannot entirely avoid the problem of mistaking computational abstraction for the really real operations of process, albeit for quite different reasons than the metacomputationalist position. Indeed, in the passage cited at the end of the previous section, Fazi stipulates that the “inherent indetermination of computation” can only be “encountered by way of abstraction.” This seems certainly to be the case to the extent that computation is itself founded on an abstraction: the abstraction of the sensory into data, i.e., that which is computable. As an abstraction, computation is a mode of knowing reality and provides an important perspective, but one that is rooted in the empirical world (in the sense that it is an abstraction from preanalytical process). Fazi, however, wants to understand computation not simply as a mode of knowing process (what Whitehead means by abstraction) but as an abstract act in itself, as a determination of process (“self-determination”) that is distinct because it operates exclusively on and with conceptual data. Her aim here is understandable (and is one that I share): she feels that this is the only way to do justice to computation as a form of process, which is to say, to grasp how the formal dimension of computation (i.e., computational contingency) actually matters in its own right and not just as a vehicle to manage and control empirical reality external to it. And it is certainly the case that the form of potentiality involved in computation seems to differ from the contingency of the sensible.
The key question, however, is how does it so differ? As I understand it, Fazi’s position is that computation, precisely because it operates on a formal axiomatic system (the “countable infinite”), involves pure potentiality. For her, accordingly, the myriad possibilities at issue in computation can be likened to eternal objects, since, like colors or other sensory qualia, they “exist” somehow independently of the operations into which they are ingressed and are not exhausted through ingression. As I see it, however, this purely formal dimension of computation is itself and can only be a part of computation as a larger, formal and physical, operation, an operation that combines self- and other-determination. Indeed, this is, as I understand it, precisely the point Cavia is trying to make in calling for an inductive account of computational formalism where the formalism itself – far from being an inert axiomatic of countable infinity – evolves dynamically in conjunction with the concrete situation being computed (self- and other-determined) at any given moment. What this means, I think, is that pure potentiality is always contained within real potentiality, and therefore constrained by the facticity of the past. Although it may designate a form of potentiality that differs from the potentiality sedimented in physical acts, it is not – and simply cannot be – “pure” potentiality if pure means unalloyed with the sensible. Indeed, the margin of indetermination introduced by the potentiality involved in computational formalism is always a factor of a concrete situation, and thus is itself constrained, this is, delimited, by the specific – and finite – potentiality of the past, what could have become in the just past moment of process but didn’t. In terms of contingency, this means that the formal contingency introduced by computational formalism must be a part of the contingency of process itself: it is one factor among others that is at issue in the process of (self- and other-) determination through which process creates new actuality at any given atomic moment.
This conclusion is important in relation to the topic of contingency that is my focus here, and also the focus of Díaz Alva’s article: it is what establishes that contingency is intrinsic to process itself. Contingency results from the determination of an indeterminacy that is at issue, always in a concrete configuration, in every act, every real togetherness, of process. In relation to this intrinsic contingency – what I’m calling the contingency of process – the forms of contingency that Fazi differentiates, formal and empirical, and perhaps even those that Díaz Alva introduces, internal and external, are derivative, empirical abstractions. In sum, computation is intrinsically sensible and it is intrinsically contingent, prior to the distinction between formal and empirical, internal and external. It is a processual operation that, from atomic moment to atomic moment, incessantly enfolds the (constrained) pure potentiality of its formalism into the real potentiality of its processual happening.
With this conclusion in hand, let us return to Díaz Alva’s generous proposal concerning the complementarity of Fazi’s and my arguments. I am in agreement with Díaz Alva that there is room in a broad conception of process for an account of the specificity of computation as a distinct type of process. However, I remain skeptical that Fazi’s account can be reconciled with mine quite on the terms Díaz Alva proposes. Two reasons in particular come to the fore. First, the role of pure potentiality in computation must be constrained by the larger situation-specific past potentiality into which it has ingressed and in which it is thus contained. And second, all process – computation included – must be understood as a result of self- and other-determination. From my perspective, therefore, Fazi’s claim that computation is the self-determination of actuality on the basis of a potentiality that is purely formal cannot avoid abstracting away the fact that computation also involves the other-determination of actuality, and for that reason is necessarily anchored in the sensible. If there is indeed a form of computational contingency proper to computation, it simply cannot be autonomous, i.e., purely formal. Rather, like all acts of process, it must be conjoined together with the larger hybrid contingency – the reserve of real, i.e., constrained potentiality – that informs process.
If we reconceptualize Fazi’s argument for computational contingency in this way, by integrating it into a broader contingency, then, I think, our respective accounts can indeed be made compatible with one another. So reconceptualized, Fazi’s account provides a crucial perspective on computation: as an abstraction of computational abstraction itself, so to speak, it allows us to grasp, i.e., to know, the consequential specificity of computation as preanalytical process, namely that its operation happens through incremental acts of processing an ever-changing, concretely configured, and (in Cavia’s sense) “intuitionist” “countable infinity.” Understood in this way, Fazi’s isolation of computational contingency serves both as a way to qualify the specificity of computation qua process – computation involves a formal aspect of contingency – and as a mode of abstraction that allows us to know computational process in a way that, unlike the metacomputationalist position, does not commit the fallacy of misplaced concreteness by taking itself for the really real things.
The rift between the physical and the organic
On my reckoning, the incomputable that Fazi identifies with computational contingency cannot be restricted to computation qua self-determination. Instead, it names the excess that is a composite of self-determination and other-determination and that is intrinsic to actualization (i.e., to computation qua actual entity). To the extent it exceeds the parameters of Fazi’s purely formal account, this conception of the incomputable aligns with another, distinct effort to complicate Turing’s mechanical digitization of the continuum, that of polymath mathematician Giuseppe Longo.[10] In his “Letter to Turing” and his recently published book, Le Cauchemar de Promethée, Longo enlists Turing as the theoretical core of his critique of what he calls the “myth of the digital,” which, like the metacomputationalist perspective criticized by Fazi, seeks to close the gap between computational simulation and reality. Yet where Fazi’s own project focuses on supplementing Turing’s account of computation by discovering an incomputability at the heart of the very operation that separates what is computable from what is not, Longo turns instead to Turing’s work on biology where he discovers a distinct – and more fundamental – processual notion of incomputability. To Longo’s eye, Turing’s final paper, “The Chemical Basis of Morphogenesis,” published two years after his 1950 paper on simulation, marks a consequential shift in Turing’s understanding of computation. Specifically, this paper introduces a distinction between model and simulation which is rooted in the very distinction – between preanalytical process and abstraction – that we find at the core of process philosophy. Whereas the concept of model recognizes the rift separating process from any knowledge or abstraction of process, simulation effaces the riftbecause it, in a particularly powerful contemporary fallacy of misplaced concreteness, simply takes itself for reality.
Longo emphasizes how Turing’s turn to biology situates computation in a more encompassing context, one that exceeds the scope of discrete mathematics and the image of computation built on it. Addressing Turing directly, Longo writes: “in contrast to your discrete-state machine, [in your Morphogenesis paper] you grasp the role of the continuum, of the interplay between non-linear dynamics and physical measurement, which is always an interval, always approximate” (Longo, 2018: 80). What Turing grasps in particular is the presence of the continuum as an excess underlying, informing, and serving as a critical check on computation. Specifically, Turing discovers the operation of fluctuations – physical phenomena “below the best measurement possible for a measuring device” – which evade measure and are thus excluded from the computable not as what can’t be computed but rather as an incomputable dimension of computational measurement. Insofar as such fluctuations are amplified over time (i.e., across incremental acts of process), ultimately forming phenomena that are “both observable and unpredictable,” they constitute a source of indeterminacy, randomness, and incomputability within process, one that is properly immanent to the process the measurement of which transpires in every act of discrete computation, and indeed in every act of process. This means that indeterminacy haunts the domain of the mathematical discrete, the countable infinite, from within, in the form of a sensible residue: the operation of measuring the sensible does not occur without remainder, and the remainder, which marks the lingering “presence” of the continuum, remains as trace of this indeterminacy within the operation of discrete computation. Insofar as it participates in and is part of the operation of the computable, the indeterminate remainder of the sensible takes form as a formal-sensible “incomputable” within computation.
On this account, the incomputable is a source for ontological creativity (Díaz Alva’s third type of contingency) that is not simply formal and internal to computation qua self-determination but rather also indelibly sensible because rooted in other-determination and the superjectal creativity informing computation qua actual entity. Unlike the “empirical contingency” Fazi denounces, this incomputability does not arise from an ex post facto encounter of already actualized computation with the sensible, but rather from the sensible excess, the superjectal other-determination, that is part of the becoming of computation at every atomic moment, a sensible excess that computation can therefore be said to harbor within itself, as a kind of “extimate” inside. Ultimately, by showing that computation always arises on the basis of sensibility – of a sensibility that is internal to its becoming – Longo’s account demonstrates conclusively why computation qua actual entity (that is, computation as both Fazi and I define it) is and must be dipolar, indelibly both physico-sensible and mental-formal.
Propositions: Vehicles for shaping the contingency of process
If it is understood as a fully generic, wholly unconstrained, static or “eternal” repertoire of possibilities, the term “pure potentiality” is a misnomer. As I argue in Feed-Forward, Whitehead makes a category error when he introduces this notion as an entailment of his conception of eternal objects. [11] Rather than being necessary to explain the contingency of the “how” of process, eternal objects seem to me to be a legacy of Whitehead’s residual Platonism. To the extent that Fazi aligns computational formalism with the pure potentiality of eternal objects, she effectively divorces potentiality from the concrete situation it bears upon and treats it as a static, “eternal” possibility repertoire. In the terms of my above argument, she follows Whitehead in categorically separating pure potentiality from real potentiality when it should rather be understood as a component of real potentiality, and thus as a formal potentiality that is, like all potentiality, constrained by the facticity of (just) past process. This again is due to the fact that computation, like all process, is both self- and other-determined. Accordingly, if computational prehension involves the mechanical, processual discretization of the infinite, as Turing established, it must take the form of a concrete act, meaning that it must arise out of a concrete situation, with a given quotient of real potentiality, part of which takes form as “pure” potentiality, understood as the concrete repertoire of possibilities that could have ingressed in just past actuality but didn’t, and that continue to exert their “superjectal” force on the next processual act, the next computation.
If this means that the formal dimension of computational prehension cannot be identified with “pure” potentiality, how indeed should we account for it? I would suggest that we turn to another Whiteheadian concept: the proposition.[12] Qualified by Whitehead as “lure for feeling,”[13] the proposition is the means by which eternal objects are made to ingress into actuality. In this respect, they are a sort of mediator that transforms the wholly unconstrained potentiality of universals into a concrete repertoire of possibilities relative to a particular situation:
The absolute generality of the notion of any, inherent in an eternal object, is thus eliminated in the fusion [of physical and conceptual feeling in a propositional feeling]. In the proposition, the eternal object, in respect to its possibilities as a determinant of nexūs, is restricted to these logical subjects. … The proposition is the potentiality of the eternal object, as a determinant of definiteness, in some determinate mode of restricted reference to the logical subjects. This eternal object is the ‘predicative pattern’ of the proposition (Whitehead, 1978: 257, emphasis added).
As “lures for feeling,” propositions are proposals emanating from the settled world of superjects – hence proposals bound by the concrete real potentiality of that world. Otherwise put, they are the concrete form through which eternal objects become part of real potentiality. In order for the actuality they propose to become actual, propositions must be taken up in prehending feeling.
However, prior to (and in order to be available for) being taken up (or not taken up) by feeling, propositions suspend the dative bond linking the (just past) conceptual feeling to the (just past) physical feeling, leaving in its wake the conceptual feeling as datum of the propositional feeling, on the one side, and “indication” of possible logical subjects, on the other:
…the datum of the conceptual feeling reappears as the predicate in the proposition which is the datum of the integral, propositional feeling. In this synthesis the eternal object has suffered the elimination of its absolute generality of reference. The datum of the physical feeling has also suffered elimination. For the peculiar objectification of the actual entities, really effected in the physical feeling, is eliminated, except in so far as it is required for the services of the indication. The objectification remains only to indicate that definiteness which the logical subjects must have in order to be hypothetical food for that predicate. This necessary indication of the logical subjects requires the actual world as a systematic environment. […] The proposition is the possibility of that predicate applying in that assigned way to those logical subjects (Whitehead, 1978: 258).
What we find in this difficult passage is an account of the suspension operated by the proposition as lure for feeling. By suspending the physical datum (or “dative bond”), the proposition is able to wield the potentiality of the eternal object as a concrete quotient of potentiality proposing itself to a concrete repertoire of possible logical subjects. The proposition thus provides a mechanism for a de-actualization of just past actuality such that the unactualized potentiality it harbors becomes liberated to inform new actuality in the form of a lure for feeling addressed to (a finite repertoire of) possible logical subjects. When a proposition is taken up in new actuality, the prehending subject actualizes the possibility of one among these logical subjects.
Insofar as it expresses the potentiality of eternal objects in concrete form, as part of a larger real potentiality informing a situation, the proposition introduces a mechanism by which the formalism of computation can inform actuality directly, at the level of preanalytical process. Specifically, by taking the form of variant propositions about how the settled world at a given atomic moment might generate new actuality at the next atomic moment, the possibilities that computational formalism generates are both created out of the formal potential of computation and anchored in concrete process (and thus delimited to some finite set of possibilities). The formal incomputability that Fazi rightly insists is internal to computation thus joins with the larger, generic incomputability that characterizes all abstraction and all “objectification,” and that is exemplified by Longo’s (and Turing’s) account of the sensible excess produced by any act of measurement, computational or otherwise. If there are indeed two forms of contingency in operation here – a contingency stemming from the incomputability internal to computation and another arising from the indeterminacy of process itself – both contribute to the “real potentiality” of a concrete situation. As two facets of the generic operation of process, which is always specific to a concrete situation, they thus belong to and inform a single generic form of contingency – the contingency of process – that is “ontologically productive” precisely because it is intrinsic to the preanalytical real togetherness of process itself.
References
Amoore, L. (2020) Cloud Ethics: Algorithms and the Attributes of Ourselves and Others. Durham: Duke University Press.
Beer, D. (2021) ‘Explorations in the Indeterminacy of Computation: An Interview with M. Beatrice Fazi’, Theory, Culture & Society, 38(7-8): 289-308.
Cavia, A. A. (2022a) Logiciel: Six Seminars on Computational Reason. Berlin: The New Centre for Research & Practice.
Cavia, A. A. (2022b) ‘Compression Artefacts: On the Aesthetics of Compressibility’, in D. Cecchetto(Ed.) My Computer Was a Computer. Catalyst M. Beatrice Fazi. Seattle: Noxious Sector Press, pp. 127-146.
Díaz Alva, A. (2023) ‘Technics and Contingency: Ontological Productivity in Computation’, Media Theory, 7(2): 37-76: https://journalcontent.mediatheoryjournal.org/index.php/mt/article/view/587.
Ernst, W. (2022) ‘Which Kind of Media ‘Philosophy’ for Computation? A Rather Radical Media Archaeological Comment’, In D. Cecchetto(Ed.) My Computer Was a Computer. Catalyst M. Beatrice Fazi. Seattle: Noxious Sector Press, pp. 89-126.
Fazi, M. B. (2016) ‘Incomputable Aesthetics: Open Axioms of Contingency’, Computational Culture, 5: http://computationalculture.net/incomputable-aesthetics-open-axioms-of-contingency/.
Fazi, M. B. (2018) Contingent Computation: Abstraction, Experience, and Indeterminacy in Computational Aesthetics. London: Rowman & Littlefield.
Hansen, M. B. N. (2015) Feed-Forward: On the Future of Twenty-First-Century Media. Chicago: University of Chicago.
Hansen, M. B. N. (2023) ‘Prosthesis for Feeling: Intensifying Potentiality through Media’, in C. Voss, L. Engell and T. Othold (Eds.), Anthropologies of Entanglement: Media and Modes of Existence. London: Bloomsbury.
Jones, J. (1998) Intensity: An Essay in Whiteheadian Ontology. Nashville: Vanderbilt University Press.
Longo, G. (2019) ‘Letter to Turing’, Theory, Culture & Society, 36(6): 73-94.
Longo, G. (2023) Le Cauchemar de Promethée. Les Sciences et Leurs Limites. Paris : Presses Universitaires de France.
Rorty, R. (1979) ‘Matter and Event’, in E. McMullin (Ed.) The Concept of Matter in Modern Philosophy. South Bend: University of Notre Dame Press.
Simondon, G. (2020) Individuation in the Light of the Notions of Form and Information. T. Adkins (Tr.). Minneapolis: University of Minnesota Press.
Whitehead, A. N. (1978) Process and Reality: An Essay on Cosmology. New York: The Free Press.
Notes
[1] I introduce “machine reference” as an extension of “symbolic reference”: it correlates machinic sense perception (in the place of sense perception proper) with bodily perception (perception in the mode of causal efficacy) thus extending the sway of the correlation that underlies perception in its typical, double-referenced mode (Hansen, 2015: 116).
[2] In this way, Díaz Alva underscores the fact that, for Whitehead, experience is never that of a given enduring entity, never exclusive to some particular “society,” but always experience for the entire settled world involved in its happening.
[3] This is precisely what Whitehead means when he contrasts his philosophy of organism with Kant’s transcendental idealism: “Thus for Kant the process whereby there is experience is a process from subjectivity to apparent objectivity. The philosophy of organism inverts this analysis, and explains the process as proceeding from objectivity to subjectivity, namely, from the objectivity, whereby the external world is a datum, to the subjectivity, whereby there is one individual experience” (Whitehead, 1978: 156).
[4] The genesis of a “subjective aim” that guides concrescence to its completion is thus the sui generis work of some concrete configuration of superjects coming together – and entering into intensity-generating contrast with one another – and not, as Whitehead claims, something that God decides.
[5] For an interpretation of Whitehead along these lines, see Jones, 1998.
[6] Here we broach a bigger debate about the status of so-called eternal objects that pits Whitehead against no less a figure than John Dewey for whom eternal objects must themselves emerge from a concrete world. I discuss this debate in Hansen, 2015: 171ff.
[7] If this is the case, there is a contradiction at the heart of Whitehead’s notion of eternal objects to the extent that he defines them in terms of their radical independence from the sensible (temporal) world: as “any entity whose conceptual recognition does not involve a necessary reference to any definite actual entities of the temporal world” (Whitehead, 1979: 44). How can eternal objects be radically independent in this sense while also meeting the requirement, imposed by Whitehead’s ontological principle, that they be ultimately anchored in the physical-sensible?
[8]A similar claim can be found in Cavia’s booklet, Logiciel (2022a: 74-76). Engagement with Cavia is beyond the scope of my purpose here. However, I would substitute the term “process” for his term “time” in this passage since, on Whitehead’s atomic theory of time, time itself is a product of the incessant oscillation of process, the oscillation between self- and other-determination.
[9] I have analyzed this différend via what I call the “speculative ban” that forbids direct identification of the metaphysics of process with the empirical experience that it generates and that Whitehead introduces to explain how experience is what it is (Hansen, 2015: 88-91).
[10] Interestingly, Longo reads the same primary sources as does Fazi – specifically Gödel and Turing – but comes to quite different conclusions.
[11] In Feed-Forward, I argue that we should reject both this notion of “pure potentiality” and that of “eternal objects.”
[12] I have developed a fuller account of the potential of propositions in relation to media in Hansen, 2023. I draw from Louise Amoore’s work in Cloud Ethics and in particular her inspiring ideas for how we might build doubt into algorithms.
[13] “A proposition has neither the particularity of a feeling, nor the reality of a nexus. It is a datum for feeling, awaiting a subject feeling it. Its relevance to the actual world by means of its logical subjects makes it a lure for feeling” (Whitehead, 1978: 259).
Mark B. N. Hansen is the James B. Duke Professor in and Chair of the Program in Literature at Duke University. Hansen holds an appointment in the Department of Art, Art History and Visual Studies, and is Co-Founder of Duke’s Program in Computational Media Arts & Cultures and Co-Founder/Director of the s-1: Speculative Sensation Lab. In work that ranges across a host of disciplines and areas, Hansen mines philosophical resources to explore the technicity of the living and the technical distribution of worldly sensibility in our contemporary technoculture. Hansen is the author of Embodying Technesis: Technology Beyond Writing (2000); New Philosophy for New Media (2004); Bodies in Code (2006); and Feed-Forward: On the Future of Twenty-First-Century Media (2015). He has also published numerous articles and several co-edited volumes on topics ranging from cybernetics to media art. Hansen’s current project, Mediation Beyond Media, adopts a process philosophical perspective (Whitehead, Simondon) to explore the constitutive belatedness of differentiated media forms in relation to the worldly mediation they mediate.
Email: mark.hansen@duke.edu
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