August 2025's Entries (BT) Diversity from (LC) Diversity Jack Morava Random Past Entries TeXnical Issues Sage advice on viewing this blog and posting comments thereon. Categories, Logic and Physics in ...

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 ...

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? Did you know that the French government offered him a job in military intelligence? The ...

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 ...

From August 2013 to January 2017 I ran a blog called Visual Insight, which was a place to share striking images that help explain topics in mathematics. Here’s the video of a talk I gave last week ...

Last time, I talked about the magnitude of a set-valued functor. Today, I’ll introduce the comagnitude of a set-valued functor. I don’t know how much there is to the comagnitude idea. Let’s see! I’ll ...

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 ...

Previously: Part 1. Next: Part 3 We’ve just finished the second week of my undergraduate Axiomatic Set Theory course, in which we’re doing Lawvere’s Elementary Theory of the Category of Sets but ...

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 ...

In this blog post we discuss the main (‘algebraic’) ideas of term rewriting and how they can be applied to term graph and arbitrary graph (i.e. string diagrams) rewriting. Our group was interested in ...

I wrote a little book about entropy; here’s the current draft: What is Entropy? If you see typos and other mistakes, or have trouble understanding things, please let me know! An alternative title ...