So let me end by summing up the main points of this topic. The first one, and this is just a more general way of saying what I've been talking about these last couple of minutes. The real-world sources of images can't be known directly. The problem is that even though we don't have access to those physical measurements, biology just can't do that for you. We have to behave in the real world as if we knew those parameters and the properties of objects. Otherwise, how could we get along, there has to be some work around to this statement of the inverse problem. 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.
