Badiou and Computers

Now that Andrew and I have posted all episodes of the Being & Event podcast, I wanted to return to two details from the series and offer a bit more explanation. The first (here below) will expand on something from Episode 3. The second, in a future post, will address something I said about Badiou, which, it turns out, has been directly contradicted by Badiou himself! In other words, a mea culpa is in order. More on that soon.

To recap, in Episode 3, I made three observations about Badiou to help structure the discussion. The first observation was a point about politics, that Badiou is essentially a modernist, and specifically that he is a political modernist. The second was a point about math: that Badiou gives us not just a description of mathematics but a definition of mathematics. I articulated that definition across different episodes in the podcast series, and also wrote about it here, giving it the name Badiou's Principle. The third point was about technology, a point that may be posed as a question: Is Badiou a digital philosopher? I want to say yes, at least to some degree. And that question deserves a longer post all on its own. Regardless, any discussion of whether or not Badiou is a digital philosopher stumbles over an awkward truth. Badiou hardly ever talks about the digital. Badiou hardly ever ever about computers. This philosopher, known the world over for his overweening interest in mathematics and formalization, has only rarely addressed the most important instance of mathematical formalism in the world today, namely digital computation. Why is this?

I have three possible answers, or maybe three-and-a-half. The first is the simplistic and obvious answer from biography: old dog, new tricks; Badiou didn't grow up with computers. This answer likely has some explanatory power. But I rarely appeal to these kinds of biographical justifications. They just seem so arbitrary, especially when there are so many Olds with a deep and intuitive knowledge of digital machines. So let's ponder the question a bit further.

From biography to disciplinarity... Another essentially accurate albeit simplistic answer comes from Badiou's context and scholarly discipline. Badiou has always worked on "pure" mathematics, whereas computer science is mostly part of "applied" mathematics (despite branches of CS that are eminently theoretical). Badiou's ontological project vs. programming and computer science -- they're just two different domains, one inherently abstract and theoretical, the other tied to real machines, running real procedures, bound by real physical constraints like heat, electricity, and time. As with the first answer, I'll categorize this answer as "mostly true, but fundamentally boring."

(A corollary to the second answer gives us answer no. 2.5: the question of infinity. In short, computers can't do it, but Badiou needs it badly. Digital computers are fundamentally incompatible with philosophical concepts like infinity. Ask computer scientists about infinity and they will laugh at you. It just doesn't enter their domain of practice, because it physically can't. At the same time Badiou has a long and sustained relation to infinity. It traverses much of his work, including long sections in Being and Event, not to mention the entirety of The Immanence of Truths. In other words, infinity might help explain why Badiou doesn't, or can't, talk about digital computers. Because that tech is hopelessly, inescapably finite.)

Okay so we already have 2.5 answers to the question. None of the answers are very good, though. So I'll offer one final answer, which might be more persuasive. Here I want to appeal to the particularities of Badiou's own philosophical position, not just the macro context of where he stands in the field of human knowledge. When considered more extensively, the question of infinity and the pure/applied distinction reveal a deeper truth: computers lie exclusively on one side of the impasse described by Badiou in Mediation 26-27 of Being & Event. This impasse is so important to Being & Event that we might simply give the proper name "being and event" to the impasse itself. Badiou's project requires some ability to straddle the gap between two forms of rationality.

These two forms of rationality have been described in different ways. Hegelians will talk about bad infinity and good infinity. Cantor had his two sizes of infinity as well, which are analogous. Ancient mathematicians spoke of the arithmetical and the geometric. I tend to favor terms like digital and analog. For Badiou it's normal being (also called natural being) versus the abnormal event subtracted from the state of the situation. Whatever the vocabulary, a simple truth remains, that we're dealing with two radically different manifolds of existence, and a gap or impasse between the two. My claim is that computers only have access to one of the two -- the arithmetical manifold -- and thus are trapped on one side, with no access to the other side, much less to the gap between them.

Let's be stubborn and obvious on this point: computers are state machines. Turing said this many years ago; it's no less true today. Computers operate exclusively within what Badiou calls "the state of the situation." They have access to a certain domain, specifically the domain that Badiou has called "bodies and languages." (We might translate Badiou's phrase instead as "data and procedures.") Computers don't and can't straddle the impasse of ontology. And therefore, in a very literal sense, computers don't have access to truth procedures; they can't be subjects in Badiou's sense of the term; and thus they don't have any concourse with truth.

So this explains why computers have no pride of place in Badiou's system. Although it doesn't explain why Badiou avoids computers completely. For instance, Badiou could have easily inserted computers into Part 2 of Being and Event, even if they don't really fit well elsewhere in the treatise.

Regardless, this is my current thinking on a nagging question that has long confused me while reading Badiou. He loves math and logic, but Badiou hardly ever talks about computers. I've tried to give a few reasons why. Initially we can say that computers simply don't conform to some biographical and contextual details that help define him as an intellectual (pure/applied, old dog/new tricks, and so on). But beyond these details, which I consider ultimately superficial, we can also answer the question via recourse to the specific arguments of Being and Event (along with related works), that is, while computers could be inserted relatively early into Badiou's narrative -- around the point when he discusses arithmetic, state, and ordinality -- computers ultimately have little role to play in the culmination and outcome of Badiou's narrative (exception, impasse, event, subject, truth, generic, etc.). And that, at least, is a somewhat compelling explanation for why Badiou, of all people, doesn't talk about computers.


Postscript: a podcast listener, Joe McCarney, reminds me of two texts that might undermine the above claims. The first is Badiou's essay "Infinitesimal Subversion" from volume 9 of the journal Cahiers pour l’Analyse (admirably reprinted -- and also restaged in web form -- by Peter Hallward and Knox Peden, the latter being our guest interviewee in Episode 1). Badiou addresses Alan Turing by name at the start of the essay, a relatively rare reference for Badiou, and he discusses algorithms throughout. The piece is certainly vivid on the question of Hegel, infinity, etc., but alas I never saw much else in that text that helps us with computation. The second text recommended by Joe is Badiou's The Concept of Model, which I'll admit never really resonated with me, despite having tried to work through that book on two different occasions. So I'll trust Joe on this point, and hope to return to that text in the future with the aim of deepening the discussion around the theme of "Badiou and computers."