In the next lesson, I'm going to discuss the answer to that question in terms of what we've talked about before. An empirical explanation, that again is defined as an explanation of these phenomena based on the frequency of occurrence of your experience with these different stimuli, with these different contexts in which you see the same physical object as being bigger or smaller, sometimes to a pretty significant degree. So let's go back and talk about one of these effects. The first one here, and this is called the Ebbinghaus effect, and let's discuss the genesis of this particular effect. Again, we could talk about any one of these, but this is a simple one that's been much considered and is a good example to discuss. So who is Ebbinghaus? Ebbinghaus, like the generator of all of these effects, was a late 19th century, early 20th century psychologist, basically, and he, a very famous guy. He's best known for his work on memory, but he came up with the so-called Ebbinghaus effect that I just showed you. And the question now is okay, you want to explain this in empirical terms. Everything else didn't really have an explanation for it, and frankly, no one else has over the decades. These are not central issues in neuroscience, well, although perhaps they should be. We want to ge the empirical data that indicates once the frequency of occurrence of this circles that have the same size in different context. So getting the data entails what we did before, applying to a scene such as this one, a template that corresponds to the Ebbinghaus effect. So let's talk about this in a little bit more detail so that you understand it. But the general point is that the strategy we're using here is exactly the same strategy for determining by analyzing laser scan, data of the real free world, and the frequency recurrence of projections from that world onto your retina. What the incidents of different contexts and circles it is in terms of the frequency of it's occurrence in your experience, not just you personally, but as I've said many times before, in the experience of our species over the eons of evolution. So let's look at this template that we're going to use to get the data that we need, using again, the same source of lots and lots of laser scanned 3D scenes and the application of the relevant template many, many times, millions of times, so that seem to get a probability distribution of how often have different context with central circles appear. So this is just an illustration of the template, so the central circle is the same. And now, we're going to test the central circle or the frequency of the occurrence of the central circle in relation to circles that are smaller, a little bit bigger, a little bit bigger, a little bigger, and fairly big. So this was the Ebbinghaus effect. When you saw the same circle, the dotted line circle in the context of smaller circles, it looked larger, somewhat larger, that's the Ebbinghaus effect, that one that you're seeing in the context of larger circles. Go back and look at the Ebbinghaus Effect, and you'll see what I'm talking about here. So getting the data is, in one sense, straightforward. Just using a bunch of different size circles in the context and asking how does the occurrence, or the frequency of occurrence of those different contexts affect the overall frequency of occurrence of the Ebbinghaus effect when the circles are small, a little bit larger, or large. And that's what's being compared. In the Ebbinghaus effect, you're comparing, an example of which, the surrounding circles are small to a context, a different context in which those surrounding circles are larger, and that's what's causing, in some way, we don't know yet, but in some way, the effect that makes the two central circles look somewhat different in size. So we'll go back and look at the Ebbinghaus circles if you need to, at this point, to understand what the effect is. Here's just an example of the application of the template. So here is the template when the circles are large. Here is a template when the circles are small. These are just examples of the natural seams from the digital images of the laser-scanned images that we saw before and talking about line lengths and angles. So it's exactly the same strategy, but now being applied in a different context to try and explain that whole raft of classical size illusions as they're called. And in this case, the Ebbinghaus effect, the Ebbinghaus illusion in particular. So when we apply millions of terms, context of large circles again. So I'll do a center circle that's the same size, and when you apply this template, as I said, millions of times to get a probability distribution of how often we are getting this context in our experience of the circle that's in the center and how often we are being exposed to or getting this context of the circle that's in the center. So when you do that, these are the results that you get. So this is a little bit complicated, let me try to explain it. These different colored lines indicate the diameter of the surrounding circles, little ones versus bigger ones. That's the data that we are trying to get, and they're each color coded, so a small surrounding circle is color coded in black, a somewhat larger one in yellow, a somewhat larger one in green and so on. And you can see again, not surprisingly. I mean, I think you would expect this that the frequency of occurrence of the same circle in different surrounds is different. So take any particular size of a central circle, which is what's illustrated here on the x axis of the graph. So there's a different frequency of occurrence for the central circle of any particular size in the context of circles in the surround that are of different sizes. That's just another way of saying or describing the Ebbinghaus effect, but the point of doing this is that when you apply the templates to real world scenes for frequency of occurrence of the different contexts for the same central circle, the different circle sizes in the surround is very different. And that's what the curves of each of these different-sized surrounding circles is indicating, again, showing on this axis how this varies. So let's go back to these classical effects. The one we've been talking about here is the Ebbinghaus Effect. As I said before, each one of these has a different name, each one of these has a different effect. But suffice it to say that each of the phenomenon, if the circle is bigger or smaller in your perception, depends on the frequency of occurrence of the circle in human experience, your experience and the experience of the species or the eons of evolution. So as we talked about before in the context of explaining empirically the lengths of lines and why we see them so strangely and why we see angles so strangely, acute angles being perceived as generally larger and obtuse angles as smaller, this is exactly the same empirical theory applied to these classical effects. And suffice to say that each one of these can be explained in the same empirical way. This is a complicated explanation that I realized, and I doubt that you will get more than the general idea, but in a course like this, that's all that I really intend. But if you are interested in going back into the details in the resources for the course, you can access the original papers and take a look at them. And I suggest that in any event, you review this whole topic in relation to the general idea that the frequency of occurrence whether it's lines, angles, different size circles that change the appearance of the size of an object, that all of these have the same underlying explanation. They can all be explained in terms of the frequency of occurrence of experience, and I should make the point that the reason for that is that your perception of size, big to small, is a ranking. You have a perceptual ranking of size that doesn't correspond to physical reality, we've shown that again and again. But where a line interval, an angle, an object like these circles ranks within that range of percepts, determines what you see. Why do you see it that way? Again, because of the inverse problem. You don't have the information about the physical size of any of these objects, and that's a problem, and it's the same problem in what we're talking about now as it was for line lengths, for angles, and previously, in the topics in which we talked about, luminance and color. So it's really one size fits all here, and that's important to recognize.