The thing about donuts and coffee cups is algebraic topology, which I think is a misleading example for most purposes.
Yeah, the donut and the coffee cup only exist once geometry get’s involved. If you’re only looking at topology they are the same object, {R mod 1}x{R mod 1}. I guess that’s kinda the point but it still makes it confusing, like the point of topology is to determine how donuts are like coffee cups when really it’s more like the point of topology is focused on structures abstracted to a degree that causes donuts and coffee cups to become the same object.
Unrelated to that, I’ve been starting to read a text on algebraic topology in the hopes of gaining more insight into manifolds for insight into ML latents / activation spaces / semantic spaces. Do you have any advice in pursuing that direction?
Yeah, the donut and the coffee cup only exist once geometry get’s involved. If you’re only looking at topology they are the same object, {R mod 1}x{R mod 1}. I guess that’s kinda the point but it still makes it confusing, like the point of topology is to determine how donuts are like coffee cups when really it’s more like the point of topology is focused on structures abstracted to a degree that causes donuts and coffee cups to become the same object.
Unrelated to that, I’ve been starting to read a text on algebraic topology in the hopes of gaining more insight into manifolds for insight into ML latents / activation spaces / semantic spaces. Do you have any advice in pursuing that direction?