So this lesson then is going to entail an empirical explanation of the flash-lag effect that we've just been talking about. The first thing that you need to do, just as we have in these other domains that we've discussed in previous modules, you have to get the experience if you want to say that this is empirically explained and make a case for it by the evidence that you can adduce, you need to get the frequency of occurrence of speeds of moving objects in the world as they project onto the retina. So, how do you do that? I mean, that's more complicated than getting the data. Remember, before we used photometers, we use laser rays scanners, there really is no apparatus today that can get you the information you need. So if you want to ask what's the frequency of occurrence of speeds of moving objects projected onto the retina, information we need to make an empirical explanation. You really have to do this in computer simulation and that's what's being shown here. So what this red outline is, is an artificial space. But it's a perfectly good visual space. And if you did have the wherewithal to do this In the real world with moving objects and the frequency occurrence of their projections over the retina, you would do it in this general way that I'm going to describe to you. You might think that you could do this using just a movie film, but remember the object or the exercise is you have to relate 3D to 2D, and a movie film is just in 2D, and you just can't do that. But setting this up, in this way, to simulate what's going on all the time in the real world, you can populate this visual space With objects, and let's consider in the case of speeds that these objects are just points or dots. You populate them with dots that are introduced into this space moving at different speeds and in different directions. And again since you're doing this on a computer you can do this with as much precision as you like, you can populate this with millions of dots moving in different directions at different speeds that simulate what's going on in the real world. And the only assumption that you have to make in this and it's the assumption that's made in what I'm going to tell you next, is that there is equal probability of stuff in the real world moving in different directions at different speeds. And obviously that's really not quite right, I mean objects in the world are subject to gravity. They are probably moving down somewhat more often than they're moving up because of gravity. We live on the surface of the earth, so you know that's a limitation as well. But to a first approximation, this is a perfectly good way of asking the question, what's the frequency of the currents of speeds of moving objects in the world as they project onto the retina? Let's take an individual moving dot like this one. It projects onto the retina here. And again, with millions of moving objects in this visual space, in this real world space that is a visual space, you can ask what the frequency of occurrence of objects is, you get a perfectly reasonable answer. And when you do that, you find that you get a result that is perhaps surprising, although it makes good common sense I think, and it's shown here. So when you plot this as the probability of occurrence, against image speed. So image speed is increasing, and the probability of occurrence, the frequency of occurrence is going up in this direction. You see an unusual distribution of speeds on the retina. That are projected onto the two dimensional image plane of the retina that I've just been talking about. You see a probability of occurrence that's sharply shifted to the left, when you consider it as a function of speed. Well why should that be? Well, let's go back. To answer that question, consider again these dots moving across this perfectly okay but artificial real world space. So I think you can appreciate that the fastest speed you are going to see projected onto the retina is for a dot that's moving in the photo plane or close to the photo plane in the plan that cuts frontally across this space. Any dot that moves either away from the screen, or towards the screen as these dots is going to project more slowly. Why is that? It's because again, assuming they all have the same physical speed, and I think you can appreciate this very easily. When the traverse is in a direction like this, the distance that's traversed by this object having the same speed, is less. Then the distance traversed by the object moving in the frontal plane, or a plane that's close to the frontal plane. Because it's moving at the same speed, let's imagine this one and this one, and we're moving in the same speed, it's going to traverse the same distance and that's going to take more time. Each dot is going to have to be iterated more in this interval than in this interval and that's why you get this shift to the left that people have appreciated for a long time. This is not news to anybody who studies motion in terms of projections onto the retinas. So this shift to the left is readily explained by the fact that objects moving at the same speed in different directions project onto the retina at different speeds. There's a huge bias to the left as a result of that, because objects moving in the frontal plane are the fastest than any other object that's moving in a different plane, either away or towards the image plane, is going to be moving more slowly. Now, let's take this data and present it in a cumulative form, that is we're just taking these probabilities and presenting them in cumulative form so that we can get a rank based on the frequency of occurrence of the flash lag, image speeds at different points on this cumulative curve. This cumulative curve just being all of the experience that we human beings have had over our ancestry [INAUDIBLE] individual lives, of speeds of objects, dots in this case, moving in different directions. So, this is being translated into our experience, so that we can give each one of these speeds. 20 degrees per second. 40 degrees per second. 10 degrees per second. A rank in terms of the frequency of occurrence of that speed in our human experience indicated by this cumulative curve determined by the artificial simulation of the speeds that we experience on our retinas coming from objects in the real world that are going to be a little bit different than this, but generally within this ballpark. So, how can we explain the flash-lag effect on that basis? Well, these red dots are the predicted outcomes. The predicted lags based on the ranks that I just mentioned. So here are the empirical ranks that I just described. And here is the predicted lag, and you can see that the empirical results that we talked about before the lags that people actually see, fall very close to the predicted line that you see based on an assumption that the flash-lag effect is explained by the frequency of occurrence of these speeds that we've actually see in our daily experience or lifetime experience that our ancestors are always seeing. So as in the case of lightness, brightness, geometry, color, in all these other instances we use the same idea to explain the discrepancy between the subjective impression of what we see in any of theses domains and what's going on in the reality of the physical world as it is measured with instruments. And here again, the flash-lag effect can be explained pretty well by the empirical information, the cumulative information that just describes what we human beings have always seen in terms of correlation of speeds on the retina to speeds in the real world. And the frequency of the currents of speeds on the retina. Allow us to generate behaviours that allow us to succeed in the real world. Even though the speeds in the real world we can't know. We don't know. We can't measure them. That's just an impossibility presented, once again, by the inverse problem.
