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 ...

The second fact is perhaps not very well known. It may even be hard to understand what it means. Though the octonions are nonassociative, for any nonzero octonion g g the map ...

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, ...

In this post and the next, I want to try out a new idea and see where it leads. It goes back to where magnitude began, which was the desire to unify elementary counting formulas like the ...

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, ...

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.

A physical framework often depends on some physical constants that we can imagine varying, and in some limit one framework may reduce to another. This suggests that we should study a ‘moduli space’ or ...

I’ve just arXived my notes for Edinburgh’s undergraduate Galois theory course, which I taught from 2021 to 2023. I first shared the notes on my website some time ago. But it took me a while to arXiv ...

When is it appropriate to completely reinvent the wheel? To an outsider, that seems to happen a lot in category theory, and probability theory isn’t spared from this treatment. We’ve had a useful ...

Fibrations are a fundamental concept of category theory and categorical logic that have become increasingly relevant to the world of applied category theory thanks to their prominent use in ...

such that the following 5 5 diagrams commute: (for f: x 0 → x 1 f:x_0\to x_1 and y ∈ 풞 y\in\mathcal{C}, we write f ⊗ y f\otimes y to mean f ⊗ id y: x 0 ⊗ y → x 1 ⊗ y f\otimes\operatorname{id}_y: ...