So, in this lesson I want to come back to the length of lines that was prevalent in the classical effects that I showed you few minutes ago. I want to come back to the length of lines and delve more deeply into how we see them. And how those details of the way in which we see them can be explained by an empirical analysis. By taking into account the frequency of occurrence of lines of different lengths that we've actually seen in the world. And how this frequency of occurrence can explain the way in which we organize our perception of lines. Remember, we have a range of lengths, they can be shorter, they can be longer, that's a perceptual range. How we've organized that range of lengths on the basis of experience can explain the phenomenology in seeing the same physical line in different context as being different lengths. So let's come back and talk about the Inverted T effect or the Lincoln Hat Illusion, same thing. It's referred to as the Lincoln Hat Illusion, for those of you who are not familiar with Lincoln as a US president, he was always seen wearing a stove pipe hat like this and it just makes a nice kind of analogy for this effect which is seeing a vertical line as being longer than a horizontal line. Again, the vertical line here being the height of this hat versus the width of this hat. So, what is it in detail, that people actually see? Do they just see vertical lines as longer than horizontal lines, or is there more to it than that? And as you can imagine, or as you might imagine, people have studied this for a long time. Beginning in the 19th century with a careful presentation to normal observers, the series of lines like this, asking them by making adjustments to report a length of the line seen in relation to the horizontal line. So the horizontal line we take as kind of the reference line, when we ask, okay, when you see a vertical line, adjust that to the length that you perceive of the horizontal line. When you see an oblique line, this one for example, adjust it to the length that corresponds to the length that you're seeing of this one. And you can actually go on the PurposeLab website, purposelab.net website, and play with this yourself and make these kinds of adjustments, and see that they are very real. The result of making that kind of test under careful circumstances is shown here in this panel on the right. So, what this is, is on the axis of the graph. The orientation of the line that's being presented to the observer. So this is 90 degrees, that's a vertical line. This is 180 degrees, that's a horizontal line. And 120, 150, 30, 60, those are all oblique lines. So we're just graphing results of the test that's being made here. And on this axis is the perceived line length. The adjustment that people have to make using the horizontal line as the reference line, 0. And asking, well, how much do they have to increase the length of lines at any and all of these orientations, as one goes around the range of possibilities from a horizontal line to a vertical line? So what's the result? The result is that, of course, one as I said before and is obvious in the Lincoln hat effect, that the vertical line is seen as longer. It's seen as a being about 10% longer than the horizontal line. So if you make tests of normal subjects and do it on yourself, you'll see a vertical line as about 10% longer than the horizontal line. But the effect is a lot more subtle than just that simple description. What you see here is that as the line approaches vertical, you actually have a peak that's higher, closer to 12, 13, 14%. About 20 degrees away from vertical, which is 90 degrees, and you see that on either side as you come up to a vertical or go down from vertical, you see a peak that's maximal at about 20 degrees off vertical. So what's that all about? I mean this is not something that's easy to explain in terms of what you may have seen. This is impossible to explain, frankly, unless you take an empirical approach to this and ask, what is our experience with lines in the real world over the eons of human evolution and or individual lifetimes as well? How could that experience, how can that empirical experience, the frequency of occurrence of projected line lengths onto the retina coming from the physical stuff in the 3D world, how could it explain this sort of McDonald's arches psychophysical effect that, as I say, has been documented repeatedly. So that's a tough question and the next lesson is going to be directed to how exactly can one approach that issue.
