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# On Revolutionary Mathematics

### A review of Justin Joque's recent book about artificial intelligence, statistics and the logic of capitalism

By any measure Justin Joque set himself quite a challenge. In *Revolutionary Mathematics* he attempts to connect the underlying calculative, statistical and codified models of our technologically dense environments with the wider logics, forces and movements of capitalism. The aim is to find those connections so that they might then be severed. The inevitable result is restless struggle between the unshakable materiality of technology and the hopeful, perhaps even idealistic, dreams of what a computationally advanced postcapitalist future might hold.

The reader might be wondering why we should turn to maths at all, and why, for that matter, it can be thought of in revolutionary terms. Developments in data driven machine learning and artificial intelligence have made choices about statistical models a matter of profound social consequence. Those models are making these new worlds. When the data gathered about people become so powerful in shaping lives and opportunities, then maths is no intellectual curiosity, it becomes deeply political. The way those data are used, the analytics, their outputs and outcomes expose individuals to a long history of equation-making. In this context, Joque is arguing, the maths create the conditions; changing the maths can therefore change those conditions.

The inevitable difficulties of Joque's task translates into the book's constantly shifting focal points. It moves in tightly upon statistical modelling, with some particularly useful discussion of Bayesian approaches and their seemingly open-ended insights, before widening onto market forces and broader theories of objectivity and knowledge, before then tightening back into the microscopics of technique. The coverage of the models and methods in particularly is genuinely revealing. Yet as it zooms in and out the book becomes a little dizzying. Books can be productively disorientating of course, unsettling things is part of what Joque is aiming for here, but it nevertheless makes it hard to plant your feet on a solid argument. That telescoping staircase in Hitchcock's *Vertigo* comes to mind.

The issue here is not so much the way the reader has to manage the ins and outs, it’s the connective tissue. The distance between the detail of the maths and broader analysis of the structures and conditions is vast. Here lies a key problem with writing about such technological formations, the minutiae matter to the overall picture but they often reside far from the big issues that they pixelate. By aiming to handle both extremes, Joque is left with these wide-open spaces to link together. The long threads are drawn, but they inevitably stretch to a thin gossamer, occasionally to the point of near invisibility. The book, in this sense, is suggestive rather than conclusive. As it moves to its final pages it can’t quite muster a fully formed set of ideas for how a different type of computational logic might emerge, at least not one that is unhampered by the established code/capitalism nexus.

Joque is clear that one set of ideals should replace the other, but that web of connections only provides enough of a foundation to acknowledge the apparent necessity rather than reinforce its details. The future being proposed, in which a commodity focused computation is overhauled, remains only an impression. The refrain of ‘new mysteries’ and ‘new objectifications’ gives some flavour without providing edges to get hold of.

When Joque argues that to take advantage of the technologies being explored it is ‘only through their communal, socialised usage will we be able to turn data into meaningful and productive knowledge’, it ends up feeling like an insurmountably great distance from our current circumstances. Similarly, the roots seem far too deeply set for us to readily ‘imagine and construct new mysteries and new modalities of exchange that can enable computation and calculation outside and beyond capitalism’. When faced with such arguments it’s easier to start wondering if what Joque is arguing for is impossible. The connections between capitalism and computation just seem to be too entangled to be inseparable. Instead, and this might sound fatalistic, by seeming so distant and dream-like the book reinforces just how powerful and immovable the vast platforms and devices of our technological infrastructures actually are. The moment for separation probably passed some time ago and long before these algorithmic systems, social media and automated systems took hold.

Given their sheer difficulty the answers may understandably remain elusive, yet the ambition of the challenge Joque sets-out in *Revolutionary Mathematics* pitches the reader deep into reflections on what calculation and computation mean for the way the future is to be ordered. If things aren’t too late for the type of change of course that Joque argues for and if we are still able to make a step into a technologically defined postcapitalist future, then we might also need to be careful that we aren’t simply replacing one calculative way of thinking with a different version of the same thing. In their experience and outcome one data-led form of automated analytics is likely to feel very similar to another, however their accompanying statements about values and subjectivity might vary. As Joque himself warns, there is a risk we will ‘only reproduce the logic we hope to escape’. Equally though, we might be concerned that seeking to establish a new logic of computation and calculation, however improbable its realisation might appear at this current moment, may also bring with it some unintended consequences and a not altogether different feeling future.