Today I heard from David Benson that Jack Morava died yesterday. This comes as such a huge shock that I can’t help but hope Benson was somehow misinformed. Morava has been posting comments to the ...

August 2025's Entries Jack Morava Random Past Entries TeXnical Issues Sage advice on viewing this blog and posting comments thereon. Optimal Transport and Enriched Categories IV: Examples of Kan-type ...

Quick question. Classically the harmonic oscillator Hamiltonian is often written 1 2 ( p 2 + q 2), while quantum mechanically it gets some extra ‘ground state energy’ making the Hamiltonian ...

Did you know that Lawvere did classified work on arms control in the 1960s, back when he was writing his thesis? You can read more here: Yes, that’s right. For technical reasons the n-Category Café ...

How do you count rooted planar n -ary trees with some number of leaves? For n = 2 this puzzle leads to the Catalan numbers. These are so fascinating that the combinatorist Richard Stanley wrote a ...

The monoid of n × n matrices has an obvious n -dimensional representation, and you can get all its representations from this one by operations that you can apply to any representation. So its category ...

Any action of a finite group G G on a finite set X X gives a linear representation of G G on the vector space with basis X X. This is called a ‘permutation representation’. And this raises a natural ...

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, ...

Next: Part 2 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, ...