What the heck is a Chu space? And whatever it is, does it really belong with all the rich mathematical structures we know and love? Say you have some stuff. What can you do with it? Maybe it’s made of little pieces, and you can do a different thing with each little piece. But maybe the pieces are structured in a certain way, and you aren’t allowed to do anything that would break this Read more…
What even is logic anyway? Logic is about what patterns of thought are valid. There are different kinds of logic for thinking about different kinds of things. Classical logic is for thinking about truth. Intuitionistic logic is for thinking about proofs. And linear logic is for thinking about resources! What does that actually mean? Well, resources are basically ordinary sorts of things that are usable, and typically are limited. So we’ll understand linear logic Read more…
I found a proof of Sperner’s lemma that I am quite satisfied with a few months ago. I’ll repeat the proof here, but more importantly I’d like to share my thought process that lead to the proof. What is Sperner’s lemma? Look at the triangle below. It’s divided into smaller triangles, and each vertex is colored either red, green, or blue. The edges of the large triangle are each missing each of the three Read more…