Welcome back to this third module in visual perception and the brain. And this module concerns seeing space. That's a broad and complicated topic and I'm going to divide it into two big sections. The first one in topic one is going to be about seeing geometry. And the second one is about seeing distance in depth. And these are related aspects of seeing space but they're different off to consider them as separate topics. So let's begin in topic one, by talking about the way in which we see geometry. The first lesson concerns geometrical illusions. When I put illusions in quotation marks, I think this won't surprise you based on what I've said before. I've put it in quotation marks to emphasize the point that, just like seeing luminance, seeing color, these are not really illusions. This is just the way we see geometrical figures whether they're line lengths, angles, simple shapes, and we'll go through all of these. Let's begin with talking about some of the classical effects, or illusions if you look at them in a psychology textbook, that have been discussed over the last 100 years or so. Each of them has a name and I'm going to tell you a little bit about each one. But these are considered the classical Geometrical illusions, again with a caveat, that I said that these really indicate the way in which we see geometrical figures not exceptions to some rule of seeing them normally most of the time. Each of them has a name, let's first talk about this so called Hering effect. Ewald Hering was the 19th century vision scientist who put opponency on the map in terms of color. This effect is named after him and what he devised, or what he demonstrated, was that when you put two lines, these two red lines, against a background of radiating lines, the two red lines are physically parallel but when you see them against this background Hering showed, they look a little bit bowed out in the middle of the lines and I think you can see that pretty clearly. The second effect is called the Poggendorff illusion. And Poggendorff again, was late 19th century or late 20th century psychologist, in this case, who made himself live on in history by attaching his name to this important effect. So what is it? The Poggendorff effect is that when you look at a line, and this is equilinear line, that is it's the same line going behind the occluding black bar and coming out on the other side from the black bar, the entrance point and the exit point don't look exactly the same. This point looks as if it's coming out a little higher along the length of the occluding bar than the entrance point here so that discrepancy is referred to as the Poggendorff effect. The next one I want to tell you about is, and we're going to come back to this one, this is the simplest one and the easiest one really to discuss in empirical terms, which is in many ways the point of this exercise. This is called the Inverted T effect, or as we'll see later, the Lincoln hat effect and I'll explain that when we come back to look at this one in more detail and it refers to the fact that the red line here and the black line here are again physically identical, and you can take a ruler and determine that for yourself. But when you look at them in this configuration, the vertical line looks longer than the horizontal line. And as I say, we're going to come back to that and talk about that in more detail. This effect is called the Mueller-Lyer illusion and it's perhaps the most famous of these effects. You probably all, or many of you will have heard of this, and it refers to the fact that these two red lines are again identical in length but when they are respectively decorated with what you might call arrow tails in this case and arrow heads in this case, they no longer look exactly the same. This one looks a little bit longer than this one. That's the impressive Mueller-Lyer effect. Again, Mueller-Lyer was a psychologist and his name, in the late 19th century, early 20th century, and his name was attached to this. Same for the Ponzo effect, which is the last of these effects that I want to describe to you. It refers to the fact that these two lines, are again, identical in length but when they are placed in the context of these two black lines that are more or less converging at some distant point in space, you see this line as being substantially longer than this line. That's the Ponzo Effect. As I said, all these effects are classical geometrical illusions that you'll find In any psychology textbook. There are also more realistic effects. This one is called the tabletop illusion, and if you look at the green tabletop and compare it to the red tabletop, again, the dimensions of this one being length and breadth and the dimensions of this one being length and breadth, they look very different. It would be hard to imagine that these two surfaces, the green surface on the left and the red surface on the right are identical, but in fact they are identical. And if you take this table and rotate it 90 degrees, the length and breadth of these two tables are exactly the same. Again, you can take a ruler and verify this for yourself. The context of the scene makes them look very different. Again, making a point that, gee, what we see is very different than physical measurement. Same point I made in discussing luminance, the same point I made in discussing color. We're now just applying the same general idea, or emphasizing the same general idea of this universal discrepancy between measured physical geometries and their perceptual consequences. The same discrepancy applies to angles and this is an engaging illustration that makes this point. This angle looks very different from this angle. They both look different from this angle, and all three look different from this angle. So here are four angles in a scene that look remarkably different from each other, and yet if you take a physical measuring instrument, a protractor in this case, you can easily demonstrate to yourself. And it's shown here in this lower panel that each of these angles is in fact 90 degrees. Now, another point that's well worth making, very important to make, is that as in the cases that we discussed before of lightness as a response to luminance, color as a response to the spectral distribution of energy in the spectrum of light that we see, intuitions are not very useful in trying to explain these phenomena. And let me take the Mueller-Lyer effect to kind of make that point. Again, remember that the Mueller-Lyer effect is that when the line is decorated by arrow tails as in this case, the line looks longer than when the same line, the same physical line is decorated by arrow heads. As in this case, psychologists in the past have thought these actually represent, or could represent, something that you see in an ordinary seam, and that your experience with those seams is maybe what's making you have this illusory perception. Again, just a general effect, but we'll let that go. So the scene that people have had in mind, psychologists have in mind, in trying to explain this one is that the left hand panel here, this one, looks kind of like what you see if you were looking at a receding corner of a room, whereas this one looks like what you would see if you were looking at a corner of a room that's coming at you. And you can imagine, looking around the space in which you're sitting that there are many instances of receding and protruding corners, and that the Mueller-Lyer effect could conceivably be due to that familiarity with the carpentered geometry that we see all the time in the habitats that we operate in these days. Well its pretty easy to show that that's not the case because the Mueller-Lyer effect, seeing this line as longer than this line, occurs whatever you decorate the ends of the lines with. Circles in this case, squares in this case, again this line looks longer than this line, it doesn't make any difference what you put on the end of the line, as long as they are protruding in this case, and overlapping, in the second case, you're going to see the effect. You could put an old shoe on the end of the line, and as long as you arrange it in the way these are arranged, you're going to see that effect. So again, the point is there's no easy intuition that you can bring to say, well, this is obviously because the way in which we've seen things in some familiar setting. It just doesn't work that way as in the previous cases. Now, there's another point that's worth making here and that is that these effects are apparent in real world scenes. I mean, you could imagine and people have imagined, well maybe these are kind of again something that you see only if you see these designs on a piece of paper or on a computer screen. No, no, that's not the case at all. So let's look at the Müller-Lyer affect and the diagram here is intended to make the point. Of course, you're still looking at it on the computer screen, but if you were to take some pieces of wood and actually construct an object like this and put it on the floor or either table top, or whatever, you would still see the mirror eye illusion. So it has nothing to do with any kind of possible peculiarities that could arise from seeing stuff on a two-dimensional piece of paper or computer screen. Similarly, for the Poggendorff illusion, which remember, the Poggendorff effect is taking the same collinear line, in this case a railing that's extending behind an occluder, in this case the pillar. And you see here, this actually happens to be downstairs in the lobby, from where I'm recording this. But, you can again, find these instances, everywhere, if you look for them. So physically, it's obvious that the railing is the same piece of stuff, but in reality, or in the reality of this scene, if I go down to the lobby and look at this, I see exactly the same thing, I see the Poggendorff effect perfectly well. That is the effect that the entrance point of the railing on this side seems to be at a different height than the somewhat higher height of the exit point on this side of the equator. So the point is a simple one, you can see these phenomena every place. You don't have to think that, or worry about the fact that maybe they are special effects that don't exist commonly in the real world.