In this fourth module, we're going to talk about seeing motion, which is a whole nother category of perceptual quality that we see. We see motion in addition to lightness and brightness, color, geometrical forms, line lengths, angles, and so on that we've discussed before. So this is an important topic, since seeing motion is obviously critical to our behavior and well-being in the world the success of that behavior. And let me begin by some definitions and there are three of them that I want to tell you about that I think are critical for understanding the framework of the discussion. The first of these is the motion in physical space that generates the motion on the retina that we end up seeing once the retinal image is processed by the rest of the visual system. So motion in visual space is defined by translation and/or rotation in the three dimensions of Euclidean space the x, y and z axes that I'm sure you all are familiar with. This generates a physical speed of motion on the retina and that leads to a perceived speed, and the physical speed on the retina and the perceived speed are two different things. Perceived speed as with all the other topics that we've been discussing is subjective, perceived, reported and as we'll see it doesn't correspond with the physical speed either, in 3D space or in the retina. The other aspect in addition to speed that defines motion is its direction, and again there is a direction on the retina, and that is different from, and importantly distinguished from, the perceived direction. So direction and speed are the two qualities that define our subjective sense of motion, and they're related to physical speeds in the 3D space that defines the external world and to the 2D space that defines the retinal image.