by godelski | 2025-05-02 22:51:52+00:00
> do you think math could have ever come into being if it weren't to fill the human need of describing and categorizing the world?

I'm a bit confused. What exactly is the counterfactual[0] here? If it is hyper-specific to categorizing and describing then I think yes, those creatures could still invent math.

But my confusion is because I'm having a difficult time thinking where such things aren't also necessary consequences of just being a living being in general. I cannot think of a single creature that does not also have some world model, even if that model is very poor. My cat understands physics and math, even though her understandings are quite naive (also Wittgenstein[1] is quite wrong. I can understand my cat, even if not completely and even though she has a much harder time understanding me). More naive than say the Greeks, but they were also significantly more naive than your average math undergrad and I wouldn't say the Greeks "didn't do math".

It necessitates a threshold value and I'm not sure that this is useful framing. At least until we have a mutual understanding of what threshold we're concerned with. Frankly, we often place these contrived thresholds/barriers in continuous processes. They can be helpful but they also lead to a lot of confusion.

> What would have been the very beginning of math

This too is hard to describe. Mull over the Poincare quote a bit. There's many thresholds we could pick from.

I could say when the some of the Greeks got tired of arguing with people who were just pulling shit out of their asses, but that'd ignore many times other civilizations independently did the same.

I could say when the first conscious creature arose (I don't know when this was). It needed to understand itself (an object) and its relationship to others. Other creatures, other things, other... objects.

I could also say the first living creature. As I said above, even a bad world model has some understanding that there are objects and relationships between them.

I could also say it always was. But then we get into a "tree falls in a forest and no one is around to hear it" type of thing (also with the prior one). Acoustic vibrations is a fine definition, but so is "what one hears".

I'd more put the line closer to "Greeks" (and probably conscious). The reason for this is formalization, and I think this is a sufficient point where there's near universal agreement. In quotes because I'll accept any point in time that can qualify with the intended distinction, which is really hard to pin-point. I'm certainly not a historian nor remotely qualified to point to a reasonable time lol. But this also seems to be a point in history often referenced as being near "the birth" and frankly I'm more interested in other questions/topics than really getting to the bottom of this one. It also seems unprovable, and I'm okay with that. I'm not so certain it matters when that happened.

To clarify, I do not think life itself necessitates this type of formalization though. I'm unsure what conditions are necessary for this to happen (as an ML researcher I am concerned with this question though), but it does seem the be a natural consequence of a sufficient level of intelligence.

I'll put it this way, if we meet an alien creature I would be astonished if they did not have math. I have no reason to believe that their math would look remotely similar to ours, and I do think there would be difficulties in communicating, but if we both understand Poincare's meaning then it'll surely make that process easier.

Sorry, I know that was long and probably confusing. I just don't have a great answer. Certainly I don't know the answer either. So all I can give are some of my thoughts.

[0] https://www.inference.vc/causal-inference-3-counterfactuals/

[1] https://existentialcomics.com/comic/245