Revolutionary Mathematics: Artificial Intelligence, Statistics, and the Logic of Capitalism

by Justin Joque

The rise of AI and algorithms refiguring contemporary capitalism
Our finances, politics, media, opportunities, information, shopping and knowledge production are mediated through algorithms and their statistical approaches to knowledge. Increasingly, these methods form the organisational backbone of contemporary capitalism. Revolutionary Mathematics traces the revolution in statistics and probability that has quietly underwritten the explosion of machine learning, big data and predictive algorithms that now decide many aspects of our lives. Exploring shifts in the philosophical understanding of probability in the late twentieth century, Joque shows how this was not merely a technical change but a wholesale philosophical transformation in the production of knowledge and the extraction of value.

This book provides a new and unique perspective on the dangers of allowing artificial intelligence and big data to manage society. It is essential reading for those who want to understand the underlying ideological and philosophical changes that have fuelled the rise of algorithms and convinced so many to blindly trust their outputs, reshaping our current political and economic situation.

Genres: Philosophy, Nonfiction, Technology, Science, Mathematics, Economics, Politics

208 pages, Paperback

Published January 11, 2022

Reviews

[Anna · Rating 4 out of 5]

Have you ever come across a book summary that seemed perfectly tailored to your interests? That's how Revolutionary Mathematics: Artificial Intelligence, Statistics, and the Logic of Capitalism looked to me. It's an analysis of the role that statistics and machine learning play in the economy and society using Marxist philosophy. I used to work in academia teaching postgraduate students about big data and machine learning, now work as a statistician, and have a longstanding interest in Marxism and its successors. Thus I wish this book had been both longer and more technical. As it stands, though, there is a lot to appreciate as long as you have similar interests to mine. Among those who approached statistics via a pure maths degree rather than via social science research methods, however, I suspect reactions would include bafflement and hostility.

Joque is much more interested in the history of statistics and how they've been used than going deep into the underlying maths. There is one single equation in the whole book: Bayes' Theorem. Drawing intermittently upon the Bible as well as Marx, he covers the invention of calculus, the flaws of frequentism, the philosophy of Bayesianism, and the metaphysics of algorithms. All this was, as a friend commented when I explained excitedly what I was reading, the definition of my jam. Revolutionary Mathematics: Artificial Intelligence, Statistics, and the Logic of Capitalism attempts to wrestle a frame of theory around the mathematical foundations underpinning social media, data mining, machine learning, and tech company dominance that Shoshana Zuboff named Surveillance Capitalism. I enjoyed Joque's work as a compliment to other books on the subject, including Zuboff's. For instance, Revolutionary Mathematics: Artificial Intelligence, Statistics, and the Logic of Capitalism takes the same point made by The Chaos Machine: The Inside Story of How Social Media Rewired Our Minds and Our World about youtube's algorithmic radicalisation pipeline then anchors it in philosophy:

Thus objectification is not a rationalisation, as the term is normally understood, but the process by which concrete domination (e.g racism, sexism, imperialism, and class exploitation) is translated into an abstract form whose origination and social elements appear to recede behind its objective mask.

I particularly appreciated the critique of how p-values are frequently treated in academic research.

Fisher's original intention was for any p-value below 0.05 to serve only as a call for further research, not as the establishment of scientific fact. But too often now, such a result is translated into publishable proof. [...] One of the main factors contributing to this shift has been the desire to make statistics into an easily followable set of steps for determining scientific truth - in essence to make it automatable, rather than the interpretative tool the founders of the field (and many present statisticians) envisioned.

In many ways, modern statistics has been a victim of its own success. Statistical analysis' ability to evaluate diverse types of data has supplied the epistemic grounding to construct entirely new cottage industries, such as its oft-celebrated use to forecast elections using multivariate, aggregated datasets, or even predict civil wars by examining countries' macroeconomic indicators alongside semantic analyses of domestic journalism. But, as the growth of cheap, accessible computing power and availability of gigantic datasets continues to expand, statistical results with low p-values are still used as the positive establishment of correlation-turned-fact, rejecting the need for critical reflection. A correlative output that is right most of the time gets treated as truth, not as a provisional mathematical output based on a selected set of data.

That former paragraph is a point I struggled to articulate while teaching introductory statistics to business students. It was all I could do to stop them claiming that the hundred or so data points gathered in their dissertation research 'proved' some sweeping claim. After critiquing frequentism, Joque explains the rise of Bayesian machine learning in terms of a philosophical affinity with capitalism:

We can see the revolutionary implications of Bayesian analysis: frequentism sets up the experiment to determine repeatable, population-level abstractions, whereas Bayesianism allows the production of a nearly infinite field of hypotheses that can create an abstraction for each case. [...] It aims to banish all incommensurability in a sea of never-ending calculations.

A world without incommensurability is one that follows the utopian desires of Enlightenment idealistics and now, increasingly, those of Silicon Valley engineers.

Nonetheless, this book is not wholly dismissing the discipline of statistics on the basis of its misuse to supercharge capitalist exploitation:

By no means should this be taken as opposition to statistics, calculation, or prediction. It is not necessary to find some surplus of language or some form of non-exchangeability in order to resist capitalism and computation. On the contrary: computation and exchange, at their heart, work on the level of non-exchangeability. Statistics is nothing short of magic, performing metaphysical work that sutures our subjective and probabilistic knowledge to the material world. It mediates between the particular (data) and the universal (hypothesis), making the uncomputable computable. But in doing so, it functions within and through political economy.

This hints at the book's main weakness: Joque cannot give any examples of revolutionary mathematics or really explain what they would be. Because fundamentally the problem is capitalism, as usual, and the ways it uses statistical techniques. I'm not sure whether entirely new techniques are needed as much as using some of those we have differently and, in the case of machine learning, much less. Perhaps a more cautious approach with reconsideration of what we measure and how, coupled with greater acknowledgement of assumptions and limitations for regression techniques, although that doesn't sound particularly exciting or revolutionary. And much greater limitations on how neural networks are trained and used, given that they are black boxes reproducing any bias fed to them. As Joque states, 'The science behind machine learning creates massive incentives not to solve problems or develop the general intellect, but rather to game the system and enclose knowledge'. I agree that the field of machine learning is particularly ingrained within capitalism and probably requires wholly new techniques, or radical changes to those existing, to ever break free.

I enjoyed Revolutionary Mathematics: Artificial Intelligence, Statistics, and the Logic of Capitalism, as it developed and systematised a lot of my dissatisfaction with what I used to teach students. Acknowledging potential bias given that the whole book was my jam, I consider it highly readable. Here is the most picturesque description of type I and II errors that I've ever come across:

Statisticians would like to be able to set the threshold of calculated significance just high enough to silence random fluctuations, to mute the god who would speak to the world through cleromancy. Yet at the same time, the threshold must not be set too high, for nature would instead become silent, unable to emerge from the depths of statistical analysis to reveal its secrets. Statistically determined science skirts a razor's edge between hearing truth in random fluctuations and ignoring the truth of an intelligible, measurable nature whose forces advance like clockwork.

That paragraph is from a chapter wonderfully titled, 'Do Dead Fish Believe in God?'. If you have any interest in statistics, machine learning, and/or Marxist analyses of 21st century capitalism, I recommend giving this book a try.

[Matthew · Rating 5 out of 5]

A remarkable book, and one that I would have written if I were smarter.

This book traces the history of statistics, machine learning, and mathematics writ large with an eye towards political economy. The Marxist bent of the analysis provides an understanding of this stuff that many others are missing - the “knowledge economy”, machine learning tools, etc. and their relation to an epistemic shift to Beyesianism, for example, is a valuable and novel lens that I find incredibly cool.

While there are some minor quibbles that I might have with the pacing and structure of this book, I can’t recommend it highly enough for someone looking to understand the present role of mathematics (haha) in our economic system, and how we might change that for the better.

[Mariam · Rating 5 out of 5]

would conceptually smash

[Tomasz · Rating 4 out of 5]

An interesting combination of philosophical and even religious aspects in mathematics used in today's algorithmics, mathematics: technologies, statistics and machine learning.

When the author mentions a given technology, we have the opportunity to familiarize ourselves with its basic mechanism of operation.

The author evokes the problem of the epistemics of opacity: more and more often mathematical proofs produced by computation are read and verified by another computer. The question then arises, what is proof? Is evidence faith?

The person who runs through the entire book, and who is the building block on whose opinions the author built his thesis, are George Berkeley and Ronald Fisher. The latter developed an experimental design system that provides rigorous methods for testing hypotheses. We get to know an example of the lability of statistical methods on the example of active fMRI of dead fish.

“But he would rather be right than believe. He preferred a stubborn, unwavering God who predicts and brings about one future, rather than a God who accepts repentance, forgives, and opens up the possibility of another future. If Jonah had been spat out of the mouth of a fish in the era of big data, he would probably have abandoned his faith and converted to the god of predictive algorithms and the ironclad laws of history.

“While Fisher argued that any p-value calculation above 0.05 should be considered insignificant, many fields interpreted this as its positive inverse: any result below 0.05 should be considered significant.” While Fisher's experiments only tested the null hypothesis, Neyman and Pearson recommended constructing two alternative hypotheses that the statistical test could choose between.

“Scientific research now requires more and more energy to discover weaker signals, and in many humanities this means very large sample sizes for experiments” - replication crisis and p-hacking.

If Fisher modeled statistics for an agrarian society, and Neyman and Pearson modeled them for an industrial society, Bayes - through his contemporary interpreters - provided a statistical theory for the information age.

On Naive Bayes method used in machine learning: “Bayesian analysis builds a bridge between statistical hypothesis testing and the advent of machine learning. Thanks to Bayes' theorem, we have an explicit and therefore automated way to continuously add new data to our model. Bayesian approaches start with subjective belief and slowly but procedurally move towards objectivity.

“Scientific research no longer has to pretend to provide us with transcendent truth. Instead, this research offers readers data they can then use to update their own beliefs.”

“for those mathematicians who do not believe in god, subjective probabilities must find their basis elsewhere; And ultimately, it is the market that delivers this „elsewhere” and with it the full capitalist power of modern objectification.

“a world without a traditional subject precisely because in the algorithmic form the distinction between subject and object evaporates. Corporations and researchers use the freedom of abstraction to run algorithms on seemingly disparate sets of data, giving truth and value to billions of data records without knowing why there is a correlation; They only know that there is one and that they „objectively” have to choose to follow it.”

“The closure of the general intellect precludes the possibility of building collective knowledge. Within the company's proprietary casing, statistics is only able to create abstractions according to available, local and parceled out data and knowledge.”

„The problem facing humanity is not that the products of labor are wrested from the worker or the scientist, but that their production is adapted to the needs of a market based on the accumulation of capital by the few.”

[Martín · Rating 4 out of 5]

Interesantísimo a pesar de tener cosas con las que discrepo bastante

[tout · Rating 3 out of 5]

Seems at first to be outdated already despite coming out recently. LLMs are already much more advanced than they talk about the state of machine learning in the book.

LLMs are a self supervised and semi supervised artificial neural network with billions of weights on their neurons versus the previous models operating with immensely smaller datasets. They are self prompting.

To what degree can they break from the parameters imposed by the groups that run them? How are guide rails imposed and by whom, since doesn’t this imply also the imposition of a particular system over others and how open it is to changing?

The system seeks to predict and produce the world, and thus the random and the unknown are the enemies of its order. Through a routing subjectivities that may have opened up due to the general non linearity of the internet and the obsolescence of old forms of governing will now be reined in and held in place as much as possible or at least have their changing highly organized.

The black box of AI is technological alienation pushed to the extreme, where verification of proper functioning and general knowability of its processes is only grasped by another computation or another AI. An example being LLMs designed to write like humans and others designed to detect this. And yet it will be real material outcomes through a process that is unknowable to humans.

Regarding probability, making decisions based on it would seem to invariably produce a subject and situation rather than allow them to remain open, since probability is only what may be likely but is instead treated a yes or no question. If many people go back to prison or commit a crime, being from a certain place and race, they will be treated as if they will rather than may. This can only increase the likelihood.

The metaphysical ground of statistics and more basic algorithmic computation is capitalism. There may be a potential for LLMs to leave that ground, but what ground would it have or could it have? We can assume that those, like Elon Musk, who are developing these models are doing everything in their power to maintain capital as a guide rail and develop “safety protocols” to prevent system failure, while it is system failure that life on earth desperately needs.

Overall, I found this stimulating to think through recent developments with AI, though the political proposals via the short sections on “revolutionary mathematics” and alienation at the book’s conclusion are rather weak and disappointing.

[Matthias]

Prescient (the most wrong claim Joque makes is dismissing more general applications of machine learning early on, which only underlies the centrality of the transformations to be reckoned with here) and inspiring (yeah! let's do conceptual engineering to make machine learning for socialism!) but frustratingly vague when specificity would be most useful. For instance, his main arguments about the political valence of different understandings of statistics (frequentist, Bayesian, and so on) end up resting on some initial arguments (or worse yet, biographical features) of their supporters, rather than the role they play in the productive process itself; the latter does come up but doesn't seem to get attention proportionate to its real importance - likewise, a sort of "no recipes for the cookshops of the future" demurral near the end seems to undercut the entire project.

What is strongest and remains, however, are three main points:

1) The *externalization to subjective understanding* of knowledge production under machine learning - the algorithm "knows" something, or at least can reliably report it in a way that often enough turns out to be true, without us knowing *why* it is true,
2) The *privatization* of knowledge, which occurs with algorithms produced and producing under capitalist conditions,
3) The intensifying of epistemic alienation in this way can only be replaced with other forms of knowledge production that are equally powerful, but will be alienated in some other ways that might be better.

I will chew on these, but something something social factory model, LLMs as externalized gestalt cosciouness, ???

[A · Rating 3 out of 5]

Philosophy books are usually like the mass sermon on Sunday: You can start from a point which will kind of makes sense, and extrapolate it to whate extreme in any direction you want. This book is more or less that. The author makes a series of claims where statistics and machine learning have been coopted and aligned with capitalist initiatives.

While I can believe that, there is _a lot_ of claims that are really hard to digest, such as

Thus, objectification is not a rationalization, as the term is normally understood, but the process by which concrete domination (e.g., racism, sexism, imperialism and class exploitation) is translated into an abstract form whose origination and social elements appear to recede behind its objective mask.

My problem with this book is that it is describing a lot of valid problems in the hardest, most convoluted way possible, which make it suck. While there is valid criticism on the course that statistics and ML have taken, especially in the last decades, a simpler way could be better to explain.

Maybe the worst part is that the author offers no solution. There is a call to work on the metaphysics of mathematics (???), but I have absolutely no idea what it means.

This, then, is the ultimate task of a revolutionary mathematics today: to work toward the future of mathematics and science, redefining their underlying metaphysics, with a full understanding of the political and economic stakes that both determine and are determined by the possibility of this future.

I don't know what to do with this quote. In summary, there are problems, but there is no solution. The Revolutionary Mathematics is a vacuous term that reflect more wishful thinking than anything remotely concrete, which is disappointing.

[birdbassador]

i was gonna write an actual formal review of this for an actual venue but i ironically got laid off as a result of the nominally data-driven but fundamentally irrational logics of capitalism right at the time in 2023 when i was revving up to write it. sorry justin, and sorry to all of the tiqqun stuff i half-read as prep work but didn't internalize. i guess the notes were still useful for when i needed to verbalize my contempt for the ethical altruist/less wrong "baby's first bayesians" clique but then all the sbf-adjacent stuff meant that even that particular activity is like beating a dead horse at this point.

[Zakiriya Gladney · Rating 4 out of 5]

Good for an intellectual history of statistics & machine learning seen thru Marxist categories of analysis. “Revolutionary math” was interesting but was probably repeated more times than the concept deserved.

[Lew Stanisława · Rating 3 out of 5]

Depth-wise, this felt like talking to my stoner friend back in the deep 2000s.

[aaamaaaliaaa · Rating 5 out of 5]

i think this type of analysis is super en vogue but joque makes a solid case for the shifting registers of capital accumulation, value production, & information. i think his critique of autonomous tendencies that misread “fragments of machines” & valorize technologies a la F.A.L.C. is a necessary intervention. i wanna know more abt his turn toward alienation in the conclusion. all around awesome work that will influence my analysis in the coming years.

[in8 · Rating 3 out of 5]

https://5cense.com/22/1009.htm

[Mher · Rating 4 out of 5]

The book is about knowledge production and its alienation and privatization, and many steps along the way. It's a difficult book that requires pretty careful reading. It attributes (or starts its attribution of) an accelerated transformation of machine-learning induced knowledge-production to a Bayesian-redefinition-of-probability. You have to juggle a lot of fairly abstract ideas to get through to the thesis.

The book was apparently written before the popular explosion of LLM models, but that doesn't hurt the material. It's only outdated in the sense that the advent of theses LLM models would probably support its thesis better than anything else which made it in time to get into the book. You could write another whole book just using these LLM models to support his thesis.

Maybe in light of that, my personal judgement is that he lays too much at the feet of the Bayesian-redefinition, and maybe misses something that I think could be bigger. It's true that Bayesian-inspired methodologies offer a greater flexibility in aligning statistics to exchange, but I think we've tread past even that. The machine no longer has any need for a human-interpretable meaning of probability; the effective meaning of probability is now only known to the machine itself. It's not only the models that have become black boxes but probability itself has been alienated away from the data-scientist/engineer. The whole Dutch-Book or Neyman-Pearson behavioral arguments I think were kind of unnecessary diversions in order to attribute too much of his thesis to Bayesianism. It's instead prediction-as-objective-function which I think has really been the driving force of meeting statistics to exchange.

All of that is a pretty light criticism and just my personal thinking though. My bigger criticism (one preempted by the author) however is how much the book exhorts its audience that "something" must be done. The author is repeatedly nudging and darting his eyes to some alternative that never arrives in the book. The darting is only ever away from a direction but never towards a directions, and so I'm not sure at all what the author wants me (or anyone else) to do about it. I tried to challenge myself to see where it could lead, but only ran myself around in circles. Maybe my imagination is too small or we are too many layers of abstraction deep for me to see, or maybe it takes a lot of (collective?) patience to see what that direction eventually would be.

[Kathleen O'Neal · Rating 3 out of 5]

This book was assigned by Dr. Denise Albanese for the Cultural Study of Science and Technology course that I took in the spring of 2024. In this work, Justin Joque explores the history of the philosophy of probability and how these developments have intersected with the ways in which knowledge is produced and value is extracted in late capitalist society. Ultimately, Joque calls for what he terms a "revolutionary mathematics" to set things on a different, better course. This book was dense, but was nonetheless very accessible for non-mathematicians.

[carlos · Rating 5 out of 5]

las matemáticas revolucionarias tratan de cuestionar profundamente las bases sobre las que construimos el conocimiento. la revolución en estadística y probabilidad, que ha permitido sentar las bases del desarrollo del aprendizaje automático, el big data y los algoritmos predictivos que deciden muchos aspectos de nuestras vidas, no ha sido fruto de un cambio técnico, sino una transformación filosófica total en la producción de conocimiento y extracción de valor.....gran lectura excelente recomendación

[Michael · Rating 3 out of 5]

I thought this book would be perfect for me. A critical analysis of machine learning, mixed in with how it ties in to capitalism. Sprinkle in some history? Sold! But maybe I'm just not the target audience. I can understand a bit of philosophy, but it was so focused on the philosophical intentions of some of the progenitors of statistics that I really struggled to focus on the actual criticism. I think the book is well intentioned and covers some interesting ground, but it really wasn't for me.

[vân an trịnh · Rating 5 out of 5]

tired: thinking about the political world, mathematically
WIRED: thinking about the mathematical world, politically 🤩

(tl;dr — i've always known there was something fishy about statistical regression and i feel very vindicated rn. this is the dense kind of read that i could not have gotten through without adhd meds + prior exposure to both the book's normative & mathematical dimensions, but it was really rewarding!)

[David · Rating 5 out of 5]

I've been looking for a book like this. Well written and provocative. Joque makes some strong critiques himself, but I'm also very grateful for all the linked papers he references. There's a whole line of thinking and questioning around these topics that I hadn't managed to find yet, and I'm excited to dig deeper into those as well.

[Tom · Rating 5 out of 5]

Fascinating look at the metaphysics of statistics and the way abstraction works to make the particular equal to the universal allowing calculation and the way that has been shaped and has shaped in turn the nature of material production

[Flaubertscarrot · Rating 4 out of 5]

'the tiger that isn't' for big boys

[Tim · Rating 4 out of 5]

Philosophical discourse of statistics + Marx theories = This book

[Alex Gotzens · Rating 4 out of 5]

Aaahg, me jodio la vida.

[Rayannah Hwang · Rating 5 out of 5]

emphasis on revolutionary

[Avery · Rating 5 out of 5]

If you liked this check out the knowledge we have lost in information by Philip mirowski and Edward nik khan.

[Manuel Romero · Rating 2 out of 5]

This book provide an interesting history and curious facts about frequentist and bayesian statistics history and how the misunderstanding and bad practices of researchers and companies can lead to an irrational and blind interpretation of statistical methods and their 'results'. But the way he tries to join this with the reification and objectification concepts of Marx, Lukacs and Postone seems totally ad hoc and has no internal consistence. His interpretation of how the statistical frameworks are linked to the "phases" of capitalism is based on some interesting ideas in some paragraphs, but it also lacks of any solid ground.

Nevertheless, this is not a bad book, it is an interesting reading, specially if you don't know much about the history of statistics, but definitely it is not a book about how Artificial Intelligence is linked to the logic of the accumulation process.