At a recent EAG afterparty, bored @Algon suggested that he explain something to me, and I explain something to him in return. He explained to me this thing. When it was my turn, I thought that maybe I should do the thing that had been on my mind for several months: give a technical explanation of monads starting with the very basics of category theory, and see how long it takes. It turned out that he knew the most basic basics of category theory, so it was a bit more of an easy mode, but it still took something like 50 minutes, out of which maybe half was spent on natural transformations. A few minutes in, @niplav joined us. I enjoyed drawing diagrams and explaining and discussing a technical topic that I love to think about, in the absurd setting of people playing beerpong one meter from the whiteboard, with passers-by asking “Are you guys OK?” or “WTF are you doing?” (“He’s explaining The Meme!”). It was great to witness them having intuition breakthroughs, where you start seeing something that is clear and obvious in hindsight but not in foresight (similar to bistable figures). Throughout, I also noticed some deficiencies in my understanding (e.g., I noticed that I didn’t have a handy collection of examples with which to illustrate some concepts). I felt very satisfied afterwards.
Can confirm that I was bored (no room for a sword-fight!), knew very little category theory, and learned about monads. But at least now I know that while a monad is not like a burrito, a burrito is like a monad.
Rant: Man, I don’t like how unwieldy the categorical definition of a monoid is! So very many functors, transformations, diagrams etc. And they’re not even particularly pleasing diagrams. The type-theoretic definition of a monad, as covered in this lovely n-lab article, felt less awkward to me. But admittedly, learning the categorical definition did help with learning the type-theoretic definition.
At a recent EAG afterparty, bored @Algon suggested that he explain something to me, and I explain something to him in return. He explained to me this thing. When it was my turn, I thought that maybe I should do the thing that had been on my mind for several months: give a technical explanation of monads starting with the very basics of category theory, and see how long it takes. It turned out that he knew the most basic basics of category theory, so it was a bit more of an easy mode, but it still took something like 50 minutes, out of which maybe half was spent on natural transformations. A few minutes in, @niplav joined us. I enjoyed drawing diagrams and explaining and discussing a technical topic that I love to think about, in the absurd setting of people playing beerpong one meter from the whiteboard, with passers-by asking “Are you guys OK?” or “WTF are you doing?” (“He’s explaining The Meme!”). It was great to witness them having intuition breakthroughs, where you start seeing something that is clear and obvious in hindsight but not in foresight (similar to bistable figures). Throughout, I also noticed some deficiencies in my understanding (e.g., I noticed that I didn’t have a handy collection of examples with which to illustrate some concepts). I felt very satisfied afterwards.
https://x.com/norvid_studies/status/1931841744754323941
Can confirm that I was bored (no room for a sword-fight!), knew very little category theory, and learned about monads. But at least now I know that while a monad is not like a burrito, a burrito is like a monad.
Rant: Man, I don’t like how unwieldy the categorical definition of a monoid is! So very many functors, transformations, diagrams etc. And they’re not even particularly pleasing diagrams. The type-theoretic definition of a monad, as covered in this lovely n-lab article, felt less awkward to me. But admittedly, learning the categorical definition did help with learning the type-theoretic definition.
That was very useful for me, thankyou!
Follow-up question: can you give an example of a plausibly-most-fun non-conversation experience you’ve had?
[REDACTED but you can DM if you want to know]