sabotista

It depends a lot on your problem, of course.

Game-playing (e.g. AlphaGo) is computationally hard but the rules are immutable, target functions (e.g., heuristics) don’t change much, and you can generate arbitrarily sized clean data sets (play more games). On these problems, ML-scaling approaches work very well. For business problems where the value of data decays rapidly, though, you probably don’t need the power of a deer or complex neural net with millions of parameters, and expensive specialty hardware probably isn’t worth it.

Pythagoras is believed to have come up with the just intonation (exact rational) figures. At the time, irrational numbers were distrusted and despised so, as you noted, the perfect fifth really was exactly 3:2.

But it’s likely that a 12-tone system won out because lg(3/2) is so close to 7/12, even if this was never a conscious decision. 19, 31, and 53 are also credible candidates per continued fraction expansion, but unwieldy for physical instruments (although some computer music does use 53-TET).