Let me just introduce, because we're going to come back to this again and again in the next lesson, The Inverse Problem, what do I mean by the inverse problem? Well, let's look at this diagram which is the inverse problem as it applies to luminance, as it applies to our perception of dark and light in relation to the physical reality of more or less intense light coming from patches in a scene. So this is just a diagram of the world we live in, and I think you will recognize the basic elements that it comprises. So first of all, there's always a source of illumination. That source can be in the natural world in which we've evolved, the Sun, the Moon, the stars, or it can be indoor light. But there's always a source of illumination, a source of photons that fall on object surfaces, and those surfaces have physical properties. They have properties that cause them to reflect some of the light, and absorb some of the photons that fall on them and that reflected light is directed to the eyeball which I diagrammed here. And it passes through an atmosphere. Well, the atmosphere is also a contributor to what we end up seeing, to the physical number and quality of photons that reach the eye because the atmosphere is made up of stuff. It's made up of oxygen and nitrogen and other gases. And you'll recognize that there are particles in the atmosphere, water particles, dust particles, all kinds of contaminants. These take away, change the light that's reaching our eyes and this has been know for centuries, so the stimulus that falls on our retina is a compilation of illumination, reflectance, transmittance. Transmittance is the name we give to the alteration of the light by the atmosphere, what comes through, what doesn't comes through the atmosphere. So the stimulus is always a compilation, a conglomeration of those properties. There are many other properties that can affect the light that reaches our eyes, but those are the main ones. So what's the point of showing you this? The point of showing you this is that if you take the illumination, the reflectance, and the transmittance and you think about how they form a retinal stimulus. You'll see that there's no way of getting back to the relative contribution of these physical realities that are making up the stimulus that falls on your retina. You can't reverse engineer. You can't go back from a stimulus by any sort of logical means that you could think of to parse, well how much of the stimulus is due to transmittance? How much to reflectance? How much to illumination? You can't do that because they're all entangled in the stimulus, and there's no way of getting them disentangled by some piece of logical magic. So what's going on? Well, this is the inverse problem as it applies to luminance. The luminance, the intensity of light that falls on our eye is always a combination of illumination, reflectance and transmittance. To behave in a world we need to know how much was altered by transmittance. How much was altered by reflectance? How much was due to illumination? These are the parameters in the physical world that we need to know to behave in it. But they're all entangled here, and they can't be logically disentangled. This is the inverse problem, or more properly said, the inverse optics problem. The inverse problem is just a general statement about this rule that we're talking about specifically in vision. No way of getting back to luminance from the stimulus that's on the retina. So that's the inverse problem as it applies to the light intensities that we see, the lightness or darkness that we see. But the same thing applies to geometry, and in fact, all the other qualities of vision that we've been discussing, and we'll come back and discuss all these in more detail. Let me show you this inverse problem as it applies to geometry. Because I think it's also very easy to see why it is that we have trouble seeing or we would have trouble seeing the physical parameters of the world, the line lengths, the angles, the shapes that are out there. Why we have this discrepant perception of the stuff that's really easily measured in the physical world, that's there in reality. So here again is the stimulus on the retina. And you see that this very same stimulus can be coming from objects in the world that have different sizes, that are at different distances, that have different orientations. And how is the observer going to know whether this stimulus on the retina, this identical stimulus on the retina, is being generated by this, this, this? That is objects that are different in size, in distance, in orientation and 3-D space. How do we know what's out there geometrically? And the answer is that that's really a problem, that's the inverse problem as it applies to geometry. It applies as well to color and motion. Let me just show you quickly how the same inverse problem applies to seeing motion. It also applies to color, we'll talk about that later, but let me show you this before we end this lesson. So, here is the retina shown diagrammatically now, it could be any detecting surface, but let's consider it to be the retina, and here is the stimulus on the retina. And now in motion of course we're not talking about a single stimulus, it's a changing stimulus, it changes over some period of time, that's what motion is all about. And what you're going to see here is that the very same stimulus on the retina moving across the retina can be generated by, again, objects that are different in distance, in size, in speed and direction of motion. And this just raises the same problem in motion that we've raised in these other situations. So here again you can see the object moving across the retina is unchanged, but the objects that are generating it, let me show you this again. The objects that are generating it are very different. They're moving at different speeds, at different directions and yet the stimulus on the retina is the same. So how do we know what the motion, the real motion is that we need, as I say, to grab one of these rods, catch a ball, do anything that we see in response to moving objects? How is it that we can do that?
