alt Hacker NewsIt would be interesting if this kind of work could ever be extended to show the limitations of mathematical reasoning in animals and humans.
For example, just as a dog will never understand a fourier transform, there are likely ideas that humans cannot understand. If we know what our limits are, I wonder if we could build machines that can reason in ways we aren't capable of?
I think it is a naive assumption that such a limitation even exists ("exists" in a sense that it is actually useful, by being consistent and somewhat simple to describe).
We investigated similar ideas for language (=> Noam Chomsky), where we tried to draw clear, formalized limits for understanding (to show e.g. how human capabilities contrast with animals). The whole approach failed completely and irredeemably (personal opinion), but researching it was far from useless to be fair.