It builds on things I’ve discussed here, but it goes further. Let me explain a bit. A bit is just a binary alternative: 1 or 0, true or false. That’s how it works in classical logic. We could also ...

Apr 29, 2026 In the last episode of my column in Notices of the American Mathematical Society, we looked at a particle moving in an attractive central force whose strength is proportional to the ...

In the last episode of my column in Notices of the American Mathematical Society, we looked at a particle moving in an attractive central force whose strength is proportional to the inverse cube of ...

How category theory can be used to help coordinate collections of interacting large language models. Agent frameworks are popular. (These are frameworks for coordinating large language model agents, ...

The previous post introduced the plumbing calculus: typed channels, structural morphisms, two forms of composition, and agents as stateful morphisms with a protocol for managing their state. The ...

These are some lecture notes for a 4 1 2 \frac{1}{2}-hour minicourse I’m teaching at the Summer School on Algebra at the Zografou campus of the National Technical University of Athens. To save time, I ...

Despite the “2” in the title, you can follow this post without having read part 1. The whole point is to sneak up on the metricky, analysisy stuff about potential functions from a categorical angle, ...

I’ve been blogging a bit about medieval math, physics and astronomy over on Azimuth. I’ve been writing about medieval attempts to improve Aristotle’s theory that velocity is proportional to force, ...

I haven’t been carefully following quantum field theory these days, but some folks on the Category Theory Community Server asked me what I thought about recent work using the ‘amplitudohedron’ and ...

In Part 1, I explained my hopes that classical statistical mechanics reduces to thermodynamics in the limit where Boltzmann’s constant k k approaches zero. In Part 2, I explained exactly what I mean ...

Sep 30, 2024 Let’s think about how classical statistical mechanics reduces to thermodynamics in the limit where Boltzmann’s constant \(k\) approaches zero, by looking at an example.

I keep wanting to understand Bernoulli numbers more deeply, and people keep telling me stuff that’s fancy when I want to understand things simply. But let me try again.