Meet the New Math, Same as the Old Math: A Review of Justin Joque’s "Revolutionary Mathematics"

Revolutionary Mathematics convincingly demonstrates that our primary task in a critique of algorithmic logic should not be de-reification, which would presuppose a degree of control over technology that we do not possess. But it doesn’t always follow its own advice.

Meet the New Math, Same as the Old Math: A Review of Justin Joque’s "Revolutionary Mathematics"

Review of Justin Joque, Revolutionary Mathematics: Artificial Intelligence, Statistics, and the Logic of Capitalism (Verso, 2022).

In his Confessions, Augustine of Hippo laments the disconnect between what one wants and what one actually does. Like a late sleeper, he mumbles “the drawling and drowsy words: ‘Presently, lo, presently’; ‘Leave me a little while.’ But ‘presently, presently,’ had no present; and my ‘leave me a little while’ went on for a long while.” Why must it happen, Augustine asks in dismay, that we want to wake up, to engage with reality, yet we nevertheless do nothing? What impels us to contravene our own desires? “[T]he mind is drawn and held, even against its will … ‘O wretched man that I am! Who shall deliver me from the body of this death’?”

Mindlessly scrolling through social media while hating every minute of it, Augustine’s dreamy lament is quite relatable. We all know that TikTok and YouTube don’t care what we enjoy; their algorithms are designed merely to keep us watching and feed us more of the same gruel. Put another way, social media confronts us with the disconnect between our life as objects (homogenized data points, predictable with statistical analysis) and as subjects. On the one hand, these algorithms are fed with user interactions and they produce a nominally “individualized” experience. Yet on the other hand, in order for these algorithms to function, they must reduce their user base to a homogenized and objectified data set. In so doing, they entangle us in algorithmic logic: as subjects we choose to look, and as objects we cannot look away.

Herbert Marcuse described this dynamic in his 1941 essay, “Some Social Implications of Modern Technology,” where he argues that the modern subject is compelled to surrender his or her spontaneity to the technological processes which mediate their life. “Everything cooperates to turn human instincts, desires and thoughts into channels that feed the apparatus,” Marcuse writes. “The relationships among men are increasingly mediated by the machine process.” When we are absorbed in our technology, whether it be in work or free time, it is actually the machines that are using us; just as Marx describes commodities as the agents of market interaction, dragging their owners along with them, modern technology acts on its human users instead of vice versa. In so doing, technology draws us inexorably into its own logic:

The machine that is adored is no longer dead matter but becomes something like a human being. And it gives back to man what it possesses: the life of the social apparatus to which it belongs. Human behavior is outfitted with the rationality of the machine process, and this rationality has a definite social content.

Justin Joque, in Revolutionary Mathematics: Artificial Intelligence, Statistics and the Logic of Capitalism, provides an insightful roadmap of the alien logic of algorithmic technology. The pivot of Revolutionary Mathematics is Marx’s theory of objectification, the “process by which socially negotiated relationships between people are made to appear as relations between objects, and hence as objective.” Joque portrays this process as a form of “objective forgetting” in which machines or technology subsume human agency. “At its heart, objectification is a theory of how objects think, remember and work for us. For Marx, objectification is not, as in contemporary idiom, the process of treating a person like an object; rather, he defines the term as using objects to manage human affairs.” Joque provides a helpful illustration of this process in action:

One experiences this process of objectification acutely when airline representatives look at their computer screen after a canceled flight and sympathetically say, ‘Sorry, but there is nothing I can do; the computer won’t let me change anything.’ One can decry the situation all one wants, but it is clear the system has been built such that even the most persuasive of critiques will not book a different flight. Tellingly, airline representatives are no longer called gate agents; they have surrendered their agency to the computer system.

As frustrating as such experiences are, Jouqe points out that objectification is not necessarily exploitative. Indeed, objectification can be liberatory if it frees us from tedium and drudgery. As he describes, “Objectification is a form of forgetting, but one that is directly productive. It allows objects to relieve us of the necessity of remembering, an unburdening of our minds that is sometimes beneficial.” Nevertheless, Revolutionary Mathematics bears in mind that technology, and the objectification it carries out, is never “neutral”, since it develops in response to specific social and economic incentives. “The force of [algorithmic objectification] inheres not in [its] correspondence with some external reality, but in [its] ability to directly produce a new, distinct social reality. For example, what matters most about credit reports is not their ability to accurately describe an individual’s creditworthiness, but their ability to produce a world that corresponds to their priorities by limiting access to capital.” Because algorithmic technology plays a direct role in reproducing our social and economic reality, Joque argues, it is imperative to understand how and why mathematical algorithms perform their objectivizing functions. In short, the process of objectification serves a twofold function: “first, it allows an object to remember for us; and second, in doing so, the object also believes for us.”

The Marxian understanding of objectification, as described in Revolutionary Mathematics, differs in a small but significant way from how the term is often thematized. As Joque observes, “It is common today [to assert that] objectification comes to mean that individuals, rather than relationships, are treated as objects.” Indeed, he clarifies, this is not an incorrect interpretation of Marx, but it doesn’t capture the entire dynamic. Joque helpfully contrasts the Marxian theory of objectification with its reinterpretation by Marx’s contemporary interlocutors:

Contemporary understandings of objectification have strayed slightly, but in a theoretically important way, from this reading of Marx. Georg Lukács is partially responsible for this wandering with his interpretation of objectification—or reification, as the term is often translated with his writing—as the point when “a relation between people has taken on the character of a thing.” Rather than focus on the process by which objects manage our affairs—even if the outcome is that relationships are taken as objects—Lukács is concerned with the outcome of this process and what it occludes. On this level, his conclusions are half right. Objectification is obfuscatory, but what is obfuscated is not fundamentally that people or relations are treated as objects, but rather that objects are made to think in the place of people.

Algorithms obfuscate social relations, Joque argues, but obfuscation is not the algorithm’s primary function. “Objectification is obfuscatory, but what is obfuscated is not fundamentally that people or relations are treated as objects, but rather that objects are made to think in the place of people.” Just as Marx describes the almost magical ability of capitalism to render incommensurate labor or commodities equal and fungible, Joque observes that “in the case of computation, it is a process of comparing, and thus calculating, seemingly incommensurate information about the world. Such mysteries cannot be negated simply because they are seemingly spurious, for as long as those mysteries “work”—economically, materially, theologically—the simple act of showing what they are “really doing” will never be enough to disempower them.” Joque insightfully points out that our primary task in a critique of algorithmic logic is not one of dereification, which presupposes a degree of control over technological processes that we do not possess. Even if everyone were to realize the way internet algorithms perpetuate domination, such understanding would not negate their function of facilitating and perpetuating the existing laws of exchange.

Despite this caveat, Joque proceeds with a deep dive into the mathematics behind algorithmic computing in order to uncover the underlying metaphysics behind what they are “really doing”. This analysis is focused in particular on the historical shift away from frequentist probability and towards Bayesian statistics. Briefly, this shift is one away from empirical description and towards subjective prescription—and is particularly well-suited to the maximization of value in consumer marketing. “For frequentists,” Joque describes, “probability represented something more empirical than ideal: probability was not the ratio of some equally likely event (such as the one-in-two possibility of getting heads [in an idealized coin flip]), but the long-run frequency of a physical system.” In the traditional frequentist framing, “it is nonsensical to make probabilistic statements about single, concrete events. … either it rains tomorrow or it does not—there is nothing properly probabilistic about it.” Instead, what frequentism can describe is the long-run behavior of systems for which rigorous scientific description is possible. For such systems, predictions can be accurately made within concretely-computable margins of error. Frequentist framing is useful for accurate empirical descriptions, but it falters when attempting to predict the future behavior of systems which are not predefined.

Bayesian statisticians, on the other hand, “understand probability as a measure of subjective belief.” That is to say, Bayesian statistics provide a mathematical framework for making predictions about systems for which no comprehensive description is available, while constantly incorporating new information into future guesses. The popularity and near-universal adoption of Bayesian statistics in contemporary algorithmic logic, Joque observes, is explained by its utility in predicting market behavior. “Bayesian statistics provides methods and an ideology,” in Joque’s words, “both of which are well suited to informational capitalism.” With ever-expanding databases of ever-finer consumer data, Bayesian statistics provides an effective method for predicting market behavior accurately without ever attempting to explain how or why this behavior operates the way it does. As Joque describes, “the Bayesian revolution provides a key set of methods for informational capital, allowing the computation of knowledge from data.” But in so doing, and unlike frequentism, Bayesian statistics never makes any claim to truth. Instead, what Bayesianism has to offer is a continually-evolving justification of subjective belief, albeit one which is very effective in making economic decisions.

Unfortunately, it is at this point that Revolutionary Mathematics does the precise thing it warns us never to do—it succumbs to the temptation that a deep-enough understanding of the mechanisms behind the technological process can free us of its power. After exposing the metaphysical contradictions behind algorithmic computing, Joque calls for us to develop a “revolutionary mathematics” that will supplant the market-driven mathematics which power our technology. “[W]e must imagine and construct new mysteries and new modalities of exchange that can enable computation and calculation outside and beyond capitalism.” If our current mathematics presents as objective what is actually human and thus absorbs us into its own logic of domination, the hope goes, a “revolutionary” mathematics would do the opposite. “If we are to move beyond the injustices of these systems, both economic and algorithmic, we must ultimately, like the infidel mathematician, propose new mysteries that can build bridges, trouble old mysteries and undo archaic ideologies.”

But the contradictory nature of such an endeavor is already apparent:

[T]o engage in a revolutionary mathematics is to disavow any belief that we can get under our abstractions, to see “what is really there” and regulate away their problems. Instead we must reckon with this world of abstraction and alienation. This requires us to create and build the world from different mysteries and different exchangabilities: ones that deny the power and reality of imperialism, and even the most basic form of capitalist exchange, by which one trades their work for the capacity to continue living.

If we fully understand “what is really there”—and why it is there—it is hard to see how the act of imagining something else being there would alter reality. After rigorously unveiling and demystifying algorithmic logic, the search for “new and empowering mysteries” feels suspiciously like fleeing back into the misty realms of ideology.

In other words, while a central mission of the book is to dispel the objectivizing power of big data algorithms, Revolutionary Mathematics never quite lets go of their fetishistic power. After adopting the theory of objectification—that machines “think for us”—Joque reckons that if we think for them first, then when they’re doing our thinking they’ll think our thoughts the way we want to think them. This is all well and good, but it ignores a crucial step: the machines don’t think for us because they’re trying to be helpful; they think for us because, in so doing, they impose upon us a thought process conducive to the market. Here is where a lesson from Augustine (or Marcuse) might be helpful—despite knowing how objectification works, despite knowing that we are giving part of thought processes over to the machines, we are simply not able to choose how we are subjected to the process of technological objectification. Even if we know that understanding how the machines “really work” is not enough to disempower them, the temptation is overwhelming to think that maybe—if we understand the algorithms behind the algorithms well enough to reinvent them in just the right way—we can disempower them this time.

As a fellow math nerd, I sympathize with this temptation, but alas, we should take Joque’s early warnings to heart in time to resist his later idealism. Our inability to stop scrolling through social media is not caused by social media itself, nor social media algorithms. Likewise, new algorithms—“new mathematical mysteries”—will not make it easier for us to look away. This inability is firmly grounded in our material relationship with society.

As John Terese recently argued, it is precisely this relationship that we do not understand. What we lack, Terese writes, is “a properly materialist theory of ‘social’ media.” It is tempting, for instance, to credit the algorithm economy with the ills that Joque describes—imperialism, domination, the collapse of social life over the past few decades, and the generally ephemeral nature of contemporary society. But “[u]nfortunately social media did not cause ‘the fragmentation of everything’,” Terese writes, “and its existence alone cannot explain why the last decade has been one of unprecedented and supreme stupidity.

Instead, social media is better understood as a consequence of the fragmentation wrought by the crisis of the social.” We have grown accustomed to the flattening of life by social media without ever gaining the tools to understand it. Here Terese reminds us that the understanding of algorithmic metaphysics (and the social media through which it expresses its logic) as powerful and mysterious ignores its historical and materialist underpinning. In other words, “the algorithm” fits neatly within Marx’s theory of fetishization. In the hazy realm of mathematical theory, the products of the human brain appear as autonomous figures endowed with a life of their own, rather than what they really are: expressions of concrete human activity. In other words, social media algorithms fulfill concrete economic functions behind our backs, whether we understand it or not. Like the sleeper Augustine describes, we hate waking up because we don’t want to go to work in the morning, not because of some mysterious power in the nature of sleep. Likewise, new mathematical mysteries will never have the power to demystify the old ones unless the material conditions on which they operate are fundamentally changed.

Taylor Hines teaches at Arizona State University.