> There are two opposite ways to present what is called the "lattice of partitions".
Yes, this really bit me in the butt in [Lecture 10 - Chapter 1: The Logic of Partitions](https://forum.azimuthproject.org/discussion/1963/lecture-10-chapter-1-the-logic-of-partitions/p1). I couldn't make up my mind whether to think of "learning more" as moving from a coarser partition to a finer one - that is, learning more distinctions between things - or as moving from a finer partition to a coarser one - that is, learning more connections between things. I picked the latter, but then I realized this doesn't match a story I'm trying to tell later.
Obviously the best thing to do is explain _both_ viewpoints, and take this as an opportunity to expose the students to the joys of "opposite categories", or at least opposite posets. But I'd been wanting to put that off for a while. Now I've got to fix my exposition a bit.