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 ...

I’d like to share here a personal project which might be of interest to the readers of this blog: the Clowder Project. Clowder is a wiki and reference work for category theory built using the same ...

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 ...

• a 2-rig over a field k is a Cauchy complete k -linear symmetric monoidal category is a line object if there’s an object y with x ⊗ y ≅ I. is a bosonic line object if it is a line object and the ...

Last time I began explaining how a chunk of combinatorics is categorified ring theory. Every structure you can put on finite sets is a species, and the category of species is the free symmetric 2-rig ...

These are some lecture notes for a 4 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 am ...

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, ...

September 2024's Entries The Space of Physical Frameworks (Part 5) Let’s think about how classical statistical mechanics reduces to thermodynamics in the limit where Boltzmann’s constant \ (k\) ...

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 ...

Posted by John Baez 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. The ...

I’m a little bemused by the popularity of the Galois theory notes. I’ve made quite a few sets of course notes public before, e.g.: Fourier analysis General topology Linear algebra Category theory But ...