So the thing I wanted to emphasize in this lesson is the inverse problem, as it applies to motion. And the things that we've just been talking about, apparent motion and after effects, are really not relevant to the inverse problem, as we've discussed in lightness, brightness, color, and geometry. And that's in a way why I've given them sort of short shrift even though because they're part and parcel of motion phenomenology, I think they deserve mentioning. But there is a critical aspect. A motion that does depend on the inverse problem or that does involve the inverse problem, as we've discussed it in these other domains. And that, again, is the reason that you see these obvious disconnects that I'll show you in a minute between speed in reality on the retina and what we see. And again, a disconnect between the direction that is in the world on the retina and in our subjective sense. There is the same kind of disconnection and these kinds of disconnections depend, as we've discussed before, on the inverse problem. So I want to demonstrate to you what the inverse problem is in motion. And I think the easiest way to think about this is to think of objects being projected onto an image plane. Again, you can take the image plane here as the retina. And take some objects that are in the real world, like these rods, and as depicted here in the diagram, they're at different distances and different orientations. And they have different sizes. So this is the kind of inverse problem that we discussed in talking about geometry, but the problem applies just as much to thinking about motion. So when these objects move, you can appreciate that they're all going to project onto the retina as the same image, even though the sequence of images now that's moving across the retina, that's generated by these different objects in real world terms. They are all moving at different speeds and in different directions, as can be seen here and here, as they traverse the image plane of the retina. But they're all projecting the same image onto the retina as they make this traverse. So how is the observer again to know what the real speed and direction of the moving object is when there is again this one to many inverse problem? The same sequence of images on the retina representing many different possibilities in real world space in terms of the speeds and directions of objects that are out there. So this is the inverse problem in motion. And it's just as daunting to think about the phenomenology of motion and how the inverse problem is resolved in the context of moving objects. As it has been in the domains of lightness, brightness, color, and geometry that we have already discussed.