So we've talked now about line lengths and their perception and angles and their perception and the discrepancy that exists between the physical measurements of lines and angles and the way we see them. What we haven't talked about yet is object size. So certainly object size is related to intervals, line lengths and angles. They're all in some sense about size. But, considering size in its own right has been a long standing domain of psychology and psychophysics and there are a whole bunch of different phenomena that I want to describe to you now. And show how the same explanation that we've been using to get around the inverse problem with respect to line lengths and angles applies to single sizes of objects as well. So, let's first look at the classical size contrast effects as they're called. And I've represented seven of them here, A through G. And all of these have names, I'm not going to belabor you with the names of these, although we will talk in more detail about one of them. Let me explain what's going on here. So in each case what people are asked to do, what you as the observer is asked to do or a psychophysical subject is to compare the perception of the light gray circle In two different context. In this context versus this context. In this context versus this context and so on for the rest of the seven that are illustrated here. And in each of these cases, the two central circles in light gray are physically exactly the same. The phonology that people have been interested over the decades. And again these examples go back to the 19th century, the names that were attached to them are generally names from long ago. In each case the light gray circles are seen as somewhat different, despite their physical identity. Again, this is now sort of a familiar sequence. So look, for example, at this first one, which we're going to talk about in more detail. And compare your perception of the size of this circle to this circle on the right. They look a little bit different. The circle on the left looks a little bit larger than the circle on the right. And in each of these different contexts, the size of the two circles look a little bit different. Sometimes the one on the left looks larger than the one on the right, sometimes the one on the right looks larger than the left. In every case the context that's being provided by the surrounding circles or circle is changing your perception. Of the size relationship between two identical circles, the light gray circles in the center. So, again, one sort of has to ask what's going on, and one issue is, well, these aren't very big effects. Maybe we shouldn't worry about them too much. And as in the case that I've shown you before, luminance and color, line lengths and so on. They can actually be very big discrepancies and often are. So let me show you an example that I [COUGH] invite you to take to look at in more detail and play with yourselves. This is on the purveslab.net website that I've referred to a bunch of times. And it allows you to interactively play with this difference in apparent size of two figures that are identical. And I think here you'll be amazed, when you go to the website and do this, to see how remarkably different the appearance of size of these two gold figures can be as a function of their placement in the context. Whether this figure is seen in the foreground or the same figure in the background. So let me make sure you understand what's going on here. This figure is exactly the same size as this figure even though they look very different in size. And when you move this figure to the background as I'm drawing here, you'll see when you interactively do this. Emphasize changes. And the difference is not trivial. It's about 20%. Depending on the context and the setup that you use, the differences in the apparent size of objects, the discrepancy between the real measured size of this figure. And you can take a run, show yourself right away in this picture that these two figures are the same physical size even though they look different, this one looking much smaller than this one. So I invite you to go and play with that, move the figures back and forth, test how much the discrepancy is for you. It will be on the outer 15 or 20% I think. And convince yourself that these are not trivial effects. These examples that I've shown you here are not trivial effects, they can be very large and as before in the case of luminance and color and line lengths and angles, they demand some kind of explanation. Why are we seeing these different gray circles for example? We're going to go figure that our identical, why are we seeing them as different sizes in different contexts? Sometimes bigger, sometimes smaller. There's a whole raft of phenomenology here that demands some kind of explanation. And each one of these examples is a challenge to anybody who wants to say well, yeah I understand why we see sizes as being different. These are very subtle and can be compelling, but they are subtle in this case. And they need some kind of explanation and the question is what should that be.
