On: Automatic Differentiation in Machine Learning: A S...

[adamnemecek]

> I think characterizing duality in this way is kind of superfluous,

It's an analysis done out of necessity. These dualities might not be a 100% in every case, but maybe I care about the ways in which they are similar.

> because the only way all those meanings of duality are the same is in the most abstract sense of the word.

So is a monad. Do you think that in the future, the level of abstraction in mathematics is going to increase or decrease?

[throwawaymath → adamnemecek]

It will increase, which I guess is sort of my point. We already know there's a lot of abstraction. If these things are only alike semantically (two pairs of dual things can be completely unrelated), what does it gain you to point out they've everywhere?

I don't mean to be obtuse, but it strikes me as saying that a city is full of concrete.

[adamnemecek → throwawaymath]

You can think of it as a really nice intermediate language.

It might be hard to build a computer system that lets you reason about both probability and say quantum mechanics.

However it might be easier to build a system that phrases a probabilistic problem in terms of duality and then solves it.

Like why should each of this have it's own foundation when there's one that captures a lot of them?