Now, let's talk about geometry. Geometry is another very big deal and vision. We see lines, we see angles, we see shapes, they can be simple, they can be very complicated and you might say well, maybe the strangeness that we've been talking about, the discrepancy between physical and subjective reality. Physical reality and subjective experience. Maybe that doesn't apply to geometry. But here's a simple example, and again, as I said, we'll come back to all of these and deal with them in more detail. But here's a simple example that makes the point. Now this also this discrepancy also applies to our perception of physical reality in relation to geometry, perceived geometry versus physical geometry. So the dimensions, the length and width of this table in green, look very different from the dimensions of this table. You say, well yeah they're obviously different dimensions to these two tables. But again, that's really not the case. If you take these two tables. And you can use a ruler if you've got one, to make these measurements and convince yourself. Or you can look on the website. I'll say a little bit more about the website later on which I'm going to invite you to explore. Yous'l lee that these two sets of dimensions are exactly the same. When you rotate this table 90 degrees, the length and width are the same as the length and width here. So again, in geometry, wow, something weird is going on, and what is that? Let's take a look at angles, another, angles that's, in addition to sort of length and width, angles is a simple aspect of geometry that we all learned about in grade school or junior high school. And here are examples of the four angles that look very different. This angle looks oblique or obtuse. This angle looks acute. This angle looks, more or less like a 90 degree angle. And this angle looks different from all the rest. So here are four examples of angles that look radically different from each other. Well, it turns out that they are all actually 90 degree angles. And you can, again, take a coat hanger, bend it into a 90 degree angle, hold it in different positions. And you'll see that you can It's not something I cooked up for the purposes of the course. You'll see that this is easily demonstrated to yourself or your friends. These are all 90 degree angles, even though they look very different. So, this also applies to motion. And here what you're going to see, you don't see anything right now, but you're going to see a line moving from left to right across the screen. And then we're going to take the same line, move it across the screen and we're just going to look at it, instead of just looking at it in the full screen, we're going to look at it through a peephole, through an aperture. And you'll see that the perception of the speed and the direction. They both change. Speed is more subtle, but it's very obvious that the direction is changing. And let me show you that. So here is the line moving across the screen from left to right. Now we see exactly the same line moving left to right, but we see it moving through a peephole. And you saw the direction of the line change from that direction to this direction. Well, again, that's not a small change. That's a change of 30 degrees or so. And again, you just can't ignore this and say well we understand direction, until we understand this kind of phenomenology. So what's the basic issue that comes out of these kinds of demonstrations. And let me say up front that you might think that these are illusions, that again these are exceptional in some way that these demonstrations. I said I didn't cooked them up for this course but nonetheless, you might think that they are exceptions to a rule. That's not the way we're seeing stuff all the time. But let me tell you that there are no illusions in the sense that we're seeing everything that we look at when we look out at the world in this way. We're seeing lightness and darkness, we're seeing color, we're seeing geometry, we're seeing motion. We're always seeing these qualities of vision. Discrepant from the way they're measured in the physical world. These are not exceptional demonstrations at all. You can show these things, find these things, in reality every moment of every your waking life. So what's the problem that this raises? Well, I think it should be pretty obvious to you that we behave successfully in the physical world. We wouldn't be here to have this conversation if that weren't the case. Vision is a sensor modality that works well for us and has always worked well for our ancestors in whatever form it's taken over the course of evolution. So it works, but we don't see the world according to the way it's really measured. So that when we do anything in the world, when we reach out and grab, as I just did, my cup of coffee, or when we catch a ball, when we do anything in the world, we are behaving successfully. Despite the fact that you're not seeing in perception the corresponding reality that physical instruments simple will they maybe or complex measuring the physical world. So, that's an absolutely fundamental problem and the question that raises Is what is going on? So I made the point that these are in no way exceptional. These are not illusions in the way that it might be presented to you in a psychology course. The implication being that, yeah, we see stuff correctly most all the time, but every once and a while there's a stimulus that we see incorrectly, we call that an illusion. No, no, no, that's not the way it is. We see everything in this mode, all the time. And that, of course, leads to the question that we're going to dwell on a lot in the course, which is why is this? Why is our perception at odds with reality and how does that square with the fact that we succeed?
