That’s a dramatic thing to say, that science has abandoned cause and effect. Isn’t that exactly what all of science is about?

Of course, but you cannot see this noble aspiration in scientific equations. The language of algebra is symmetric: If X tells us about Y, then Y tells us about X. I’m talking about deterministic relationships. There’s no way to write in mathematics a simple fact — for example, that the upcoming storm causes the barometer to go down, and not the other way around.

Mathematics has not developed the asymmetric language required to capture our understanding that if X causes Y that does not mean that Y causes X. It sounds like a terrible thing to say against science, I know. If I were to say it to my mother, she’d slap me.

But science is more forgiving: Seeing that we lack a calculus for asymmetrical relations, science encourages us to create one. And this is where mathematics comes in. It turned out to be a great thrill for me to see that a simple calculus of causation solves problems that the greatest statisticians of our time deemed to be ill-defined or unsolvable. And all this with the ease and fun of finding a proof in high-school geometry.

You made your name in AI a few decades ago by teaching machines how to reason probabilistically. Explain what was going on in AI at the time.

The problems that emerged in the early 1980s were of a predictive or diagnostic nature. A doctor looks at a bunch of symptoms from a patient and wants to come up with the probability that the patient has malaria or some other disease. We wanted automatic systems, expert systems, to be able to replace the professional — whether a doctor, or an explorer for minerals, or some other kind of paid expert. So at that point I came up with the idea of doing it probabilistically.

Unfortunately, standard probability calculations required exponential space and exponential time. I came up with a scheme called Bayesian networks that required polynomial time and was also quite transparent.

Yet in your new book you describe yourself as an apostate in the AI community today. In what sense?

In the sense that as soon as we developed tools that enabled machines to reason with uncertainty, I left the arena to pursue a more challenging task: reasoning with cause and effect. Many of my AI colleagues are still occupied with uncertainty. There are circles of research that continue to work on diagnosis without worrying about the causal aspects of the problem. All they want is to predict well and to diagnose well.

I can give you an example. All the machine-learning work that we see today is conducted in diagnostic mode — say, labeling objects as “cat” or “tiger.” They don’t care about intervention; they just want to recognize an object and to predict how it’s going to evolve in time.

I felt an apostate when I developed powerful tools for prediction and diagnosis knowing already that this is merely the tip of human intelligence. If we want machines to reason about interventions (“What if we ban cigarettes?”) and introspection (“What if I had finished high school?”), we must invoke causal models. Associations are not enough — and this is a mathematical fact, not opinion.

People are excited about the possibilities for AI. You’re not?

As much as I look into what’s being done with deep learning, I see they’re all stuck there on the level of associations. Curve fitting. That sounds like sacrilege, to say that all the impressive achievements of deep learning amount to just fitting a curve to data. From the point of view of the mathematical hierarchy, no matter how skillfully you manipulate the data and what you read into the data when you manipulate it, it’s still a curve-fitting exercise, albeit complex and nontrivial.