3 ms·
It wasn’t a historical accident that triangles came before coordinates. Coordinates are more abstract than triangles quite generically for humans. (When we teac
by jessriedel 3y ago
It wasn’t a historical accident that triangles came before coordinates. Coordinates are more abstract than triangles quite generically for humans. (When we teach children numbers, we start with the natural numbers and then later introduce negative numbers.)
I claim it’s only because you and I have internalized them so well that they both seem intuitive, which is what allows you to prefer the coordinates approach due to its greater generality to negative angles.
In any case, as another commenter said, I think you basically agree with the author’s main point and are disagreeing with a minor point (which is to some extent a manner of taste).
- jerf 3y agoThis is another way of looking at the concept of Kolmogorov Complexity and relating it to real life... which thing you consider the most "natural" encoding of these concepts, and thus the "shortest", can depend very heavily on your "native mathematical language". One not even reach out to strange hypothetical aliens who think utterly different than us. Multiple people all firmly raised in the modern conventional human mathematical landscape can vary, as is seen right here. Though it does occur to me to wonder what an alien in a very obviously hyperbolic universe would consider the most natural. Or one of the beings that lives in Greg Egan's universe with two time and two space dimensions.