Even without a concept of “even number”, wouldn’t this neolithic human be able to figure out an algorithm to compute the right answer? They just need to scan the line, flipping a mental switch for each black pebble they encounter, and then add a black pebble if and only if the switch is not in the initial position.
If I understand correctly, in the post you linked Scott is saying that Haitians are functionally innumerate, which should explain the difficulties with numerical sorting.
My point is that the partity function should be learnable even without basic numeracy, although I admit that perhaps I’m overgeneralizing.
Anyway, modern machine learning systems can learn to perform basic arithmentic such as addition and subtraction, and I think even sorting (since they are used for preordering for statstical machine translation), hence the problem doesn’t seem to be a lack of arithmetic knowledge or skill.
Note that both addition and subtraction have constant circuit depth (they are in AC0) while parity has logarithmic circuit depth.
Well, given how hard it is for Haitians to understand numerical sorting...
If I understand correctly, in the post you linked Scott is saying that Haitians are functionally innumerate, which should explain the difficulties with numerical sorting.
My point is that the partity function should be learnable even without basic numeracy, although I admit that perhaps I’m overgeneralizing.
Anyway, modern machine learning systems can learn to perform basic arithmentic such as addition and subtraction, and I think even sorting (since they are used for preordering for statstical machine translation), hence the problem doesn’t seem to be a lack of arithmetic knowledge or skill.
Note that both addition and subtraction have constant circuit depth (they are in AC0) while parity has logarithmic circuit depth.