The apparent solution in geometry is, again, as it was in luminance and
color percepts, to generate our percepts on line lengths,
angles, sizes of simple objects, like the circles we were just
talking about on the basis of accumulated trial and error experience.
This is the work around that we and other visual animals
have apparently evolved to resolve the conundrum of the inverse problem.
And if you say, well, what's the evidence of that's the way it's working,
it's that in each of these cases, the response that we see,
whether the stimulus is lines, angles, or sizes, can be explained on this basis.
We can predict on this basis through the empirical ranking of line lengths,
angles, or sizes what we actually see.
And that's really the bottom line of this, that the evidence in all these
domains based on the same general work around to the ingress problem,
is a pretty compelling set that would be very difficult,
in my opinion, to explain in any other way.
You can take one of these phenomena and make a specific ad-hoc explanation.
But if you take the totality of this, it's very hard to think of any other way
of explaining the way in which we perceive lines, angles, and object sizes.