A more tractable approach is to learn to use dynamics for perception rather than ("just") statistics. The dynamical physics of a ball rolling is much simpler (lower dimensional, more tractable) than a statistical view of millions of differently illuminated pixels hitting a camera.
(A colleague of mine has a blog post on this issue of "statistics and dynamics" at http://blog.piekniewski.info/2016/11/01/statistics-and-dynam...)
Just plug a webcam into an adequate system and allow it to learn dynamics by trying to predict what it will see next.
Chomsky is almost right for the wrong problem: there won't ever be enough human-labeled data for good generalization. ;)
In x,y space you have that same 50:50 ratio at y=0. But, for every y > 0 the ratio decreases as a higher percentage of S1 is used up just reaching that y height than S2, until all of it is used up and the top segments are 100% s2.
In x,y,z space you get that same picture at z=0. But at any z > 0 more of that S1 is used to than the S2 segment so the ratio must be lower than in x,y or x space.
Moving to 4D and up the same simple idea just continues.