So this lesson, then concerns how you would gather the information empirically that you need to answer that question of why we're saying in the guidelines in this peculiar way. And how about explains the apparent length that has been documented as the way which we actually see for lengths of lines. So the first issue here is, okay, you want to get the information that relates the objects in the physical world lines in this particular instance, line length in this particular instance. To the frequency recurrence of those projected line wings onto the retina that we human beings have seen forever. And how do you do that, or how could you do that? Well, the answer is to use a machine like this. This is actually a very sophisticated machine. It's called a laser range finder. And let me tell you a little bit about them before I go on to tell you what the information is that it allows us to gather and use to explain the line length phenomenology that we've just been talking about. The laser range finder sends out a laser beam from its rotating heads, so this head is rotating from left to right and back again. And as it's scanning the scene, a laser beam is being sent out from a source in the head to objects in the environment. And that's of course travelling at the speed of light and inside this machine is a quartz clock that measures the difference between the time the laser beam goes out and the time it takes to come back from the reflective surface of an object that it hits and be recorded by the scanner. And it's amazing that that enormously short period of time can be accurately measured. But this is what's done here, it tells you what the distance and direction of every point in theses scenes that I'll talk about a little more in detail in a second. It tells you what that physical reality is, and allows you to relate it to the frequency of occurrence of line lengths that are projected onto the retina. Now, where did this machine come from? Well, it's obviously not made for neuroscience, it's made for architects and construction companies in the course of building whatever it is that the architect wants, if it's a major building, you won't use it for your house but you use it for building a skyscraper and the light. The architect and the construction engineers need to know, well, is this proceeding is the building proceeding according to plan by using the laser scanner to scan the building as it goes up, you can tell within fractions of a centimeter within a few millimeters whether the blueprint is being acurately executed in the construction of the building. We are using it for a completely different purpose. But the idea is the same. Let's talk a little bit more about the scenes that it's scanning and how it really represents information that we can use. So here's a natural scene. It happens to be a scene on the Duke campus that we transported the laser range scanner to, to many sites of naturally constructed scenes of the Duke campus, to ask what's the frequency of occurrence of lines that are existing in space? And what's that frequency of occurrence translate into when you talk about perceptual experience of line lengths. Well, this is just a digital photograph taken with a digital camera of one of those scenes as an example. And here is what the laser range scanner returns to you from the same scene. So this is a color code and it's in meters. And the heat map here is showing you that when the distance is very short when the object is closed to the laser range scanner, it's shown in red, and this is now laser scanned image. And when it is blue, that means that the object are greenish that means the object is further away, when it's sometimes black as this little instances. It mean that the beam never hit any object at all but the distance was infinite and that's just returned as black. So, what this is allowing you to do is as I said to know exactly the distance and direction within a few millimeters of every point it is seen like this. Then use that information to find out what the frequency of occurrence is of our experience with lines of different lengths as they project onto our retinas. Well, how do you do that? Well, here is another scene from the Do campus, just again to show how this is done technically. And here is a blow up of the pixels that would be in any position on the scene and lines at different orientations that are going to be applied to the scene. A vertical line, horizontal line, and oblique line. And by applying lines of different lengths repeatedly to the scene, you are going to find out how often was that the case that align of a certain orientation and length return from the scene a valid line that was actually out there in the scene. That's equivalent to asking what's the frequency of occurrence of projections onto your retina of lines of different lengths and orientations with respect to the real world that the laser scanner is telling you about. So that may be a little bit complicated, but let's look at these lines in the scene. So these white lines are lines, again, like this one would be this line applied to the scene and it returns a valid straight line. So there really is a straight line in visual space on this path corresponding to the line that you applied to the scene. Understand that these are not lines in the sense of edges. These are lines in a sense of geometrical definition of the line a series of points that geometrically form a straight line. So that's a valid return and all of these white points are lines at different orientations and lengths that were applied to the scene that returned. Yes, there is a line in physical space in this particular scene. That is a valid source of a straight line at that orientation. The red lines conversely. And I think you can see this pretty easily and understand intuitively. So again, let's take a straight line, apply it to this region of the scene. And the red line indicates that it didn't make a valid return. There was no straight line at that position in the scene in that orientation. This line fell on a bunch of leaves and tree trunks and so on. That didn't form a straight line and physical space and so returned an invalid response to that application. Again, this red line, also invalid, why, because line at that orientation and length is not a straight line that exists in physical space, it's crossing a series of stones on this wall that invalidate the source as a straight line. Same thing here. So, you, in this way, get a distribution of valid and invalid returns that tells you what the frequency occurrence of lines at different orientations and different lengths is projected onto your retina from many scenes in the real world. And these applications of course have done that many times but literally millions of times so that you get frequency distribution in terms of the real world in relation to the frequency of occurrence a projections on to your retina. So you may have to think about that a little bit but it's not that hard to grasp what the purpose of this exercise is or why it works.
