But, you're not really rejecting my example, you're proving it. The human ability to generalize the concept of a 2d platformer is limited to a very narrow range of "intuitive" generalizations that have deeply baked assumptions in them like "locality of action". So when we try to replicate the ability to "generalize", at some point we have to recognize that we can't "generalize in general" but rather we have to deeply bake in certain assumptions about what sorts of variations on the learned theme are possible. Mario with some sort of gimmick that still respects locality of action is doable, the fourier transform of Mario isn't.

This is a problem because we are approaching AI from an angle of no a priori assumptions about the variations on the pattern that it should be able to generalize to. We just imagine that there's some magic way to recognize any isomorphic representation and transfer our knowledge to the new variables, when the reality is we can only recognize when the domain being transferred to is only different in a narrow set of ways like being upside down or on a bent surface. The set of possible variations on a 2d platformer we can generalize well enough to just pick up and play is a tiny subset of all the ways you could map the pixels on the screen to something else without technically losing information.

We could probably make an AI that bakes in the sort of assumptions where it can easily generalize what it learns to fourier space representations of the same data, but then it probably wouldn't be good at generalizing the same sorts of things we are good at generalizing.

My point (hypothesis really) is that the ability to "generalize in general" is a fiction. We can't do it either. But the sort of things we can generalize are exactly the sort that tend to occur in nature anyway so we don't notice the blind spot in what we can't do because it never comes up.