Instructor:	Hello, welcome. Should be on, says it's on. Okay. We shouldn't have cut it off so quick, you guys are having a great time and now I'm going to ... But I'm just going to share a little bit of the work I do with you today. Some of you guys may have seen my students trudging with equipment across campus running bizarre experiments with parts and strings. So, you'll see a little bit of what we're doing here. 
	The overall picture I'm going to start from is really only half the story. I'm going to talk about the eye a little bit, and the brain a little bit, just to get you guys organized. That when you see, when you look and you see there's actually a lot going on. It involves more than simply raising your eyelids. 
	You're familiar with the idea that you have a pupil, that's the thing that's dark and there's a cornea up front that helps to focus the light and there a lens that does the fine focusing. Then there's the surface back here with is capable of forming an image, essentially. It's all photoreceptive. 
	Then there's a little tiny spot, right here, called the fovea. Which is where your highest density of visual resolution is packed in there. That's what I use if I want to see somebody or read something, I aim my eye at that place. This is actually a really interesting adaptation because the fovea is ... It's not found in all animals. 
	For humans, we have not only foveation but also very mobile eyes. Like, birds move their head around, not their eyes around because apprehension. We use our eyes to guide our hands. There's a lot about the visual system, I'm not going to talk about the hand system today. But there's a lot about vision that actually has to do with controlling action and the very structure of the eye, the way it's built, is designed to pull in information to make certain parts of space, very available to you in order to control fine actions. 
	Then things go back into the brain. Well, how does this all happen in the brain? This is the front of your brain, naturally this cable from the eye comes through the back of here and connects up at the back. This is where you first visual area is back here, the little bump, the back of your head that you can feel. 
	Then the information goes off in al different directions. It's going to go off and do some face processing, object recognition, space representation for motor control. You have all these different functions that this system has to do. I'm only going to talk about a little of that. But I thought I'd start you off with a couple fun illusions to wake you up a little bit. 
	Let's see if I can get this to work. Where my mouse? Have to find the mouse. Anybody see the mouse? There it is. Okay. This first one requires fixating, so ... What I want you to do is fix your gaze, right there, and keep it there. I'll try to blow this up, can I blow this full screen somewhere? 
Audience:	[inaudible 00:03:14].
Instructor:	I don't know. Can people see this okay? I think it's all right. The blue stuff is supposed to be a little dark. The point here, is if you look at that middle thing, the three green dots that are on the outside should sometimes seem to disappear. If you're successful at keeping your gaze fixed, sometimes all of them will be gone, sometimes some of them will be gone. 
	Those three dots are permanently stable on the screen there. Which your visual system isn't sure whether they're part of the world or not, because there's a lot of motion going on and they're not moving. Sometimes that's something in your eye. That's just one of ... I mean, when you see stuff ... Yeah. You getting it? 
Audience:	[inaudible 00:03:59]. 
Instructor:	Disturbing. Well. 
Audience:	One of them is riding, and one of those is a [inaudible 00:04:01]. 
Instructor:	Cars don't stay still. This is based on this unusual thing where you're fixating your gaze at one place, and you're trying to attend elsewhere. I wanted you to practice doing that behavior because I'm going to come back to using that behavior. Now, let me stop this thing. I can just close that right down, and back over here. Okay. 
	All right. Here's another point about the eye. I talked about it has an image surface at the back that sort of forms an image. That image surface is just a two dimensional plane. It's sort of wrapped around a sphere. But what you see isn't the surface of that, you're not looking at that. You're looking at the world. 
	For example, this is a very famous illusion. Roger Shepard made this, won a presidential award for his work in science perception. These two quadrilaterals that are the table surfaces, are the same shape and size on the screen here. If you believe that, I'm very impressed with you. They really are, but of course what your visual system isn't trying to do. It's not trying to say, what size are those things projected onto my retina? It's trying to ask, what are those things in the world? 
	This, of course, corresponds to a table that you're seeing foreshortened in this direction. This corresponds to a table that you'd see foreshortened in this direction. This must be long table, and this must be a wider table. What you're seeing, what you have is the contents of your experience is a highly processed, interpreted world. Not sort of what's just there. 
	What I'm going to talk about, what I have one more thing to show you. I got to tell you the little personal bit, I didn't want to study perception when I first started out. I didn't think it was that interesting because you just open your eyes and you see, how hard could that be? I want to study cognition, how does that stuff work?
	But when I was in grad school, I accidentally discovered something that kind of blew my mind. Well, it wasn't an accident we discovered it. It took a couple of years to fully discover it. But the net discovery was this, I'm going to walk you through this. This was about 20 years ago, over 20 years ago now. 
	We can talk about these as two visual textures, this is going to be your fixation work for this demo. You don't have to do anything with it yet, I just want you to observe that this texture and this texture are the same, essentially. They're slightly different in which where the dots are, but they're the same in their density. All I'm going to do now is I'm going to adapt you to textures. I'm going to have you stare at that fixation mark, I'm going to show you a sequence of textures. This is going to take about 20-25 seconds. So be patient. 
	You're going to look right at that fixation mark. Just keep looking at it. Just keep looking. Okay, in a minute I'm going to show you something different. The next one I'm going to show you is two textures that are identical. If you're staring at the fixation mark, they shouldn't look identical at all. The top one should look a lot denser. It fades pretty quickly, I can do you a quick top up. 
	I'll just show you the last adapting one again. Just stare at the center that, and then here's the final pair. This is exactly the same texture, these three dots are here. It's the same texture wrapped around, it's exactly the same texture but it doesn't look the same because your system is adapted. This is an important issue I'm going to come back to, maybe, at the end if there's time. But adaptation is fundamental. 
	The visual system has to sort of figure out what's out there, but it it's using sort of this neural hardware that has to adjust. And because you're moving around all the time, it should expect statistically that basically it's going to get the same kind of stuff everywhere. But if it finds that there's an imbalance, it adjusts itself and fixes itself up. And this is really important. Otherwise, our messy brains could never give us this stable perceptual experience we have. That's adaptation. As I said, that's going to be a player when we get to the end of this story. 
	Okay, now we're getting to the real story. I'm going to tell you about space perception. It turns out that when people evaluate the spaces around them. Particularly, I'm going to be focused on outdoor spaces, they make a lot of systematic errors about how that space is laid out. One of the most salient that's been observed is that hills look really steep. 
	If you ask students how steep the hill is, it comes up from sharpens up to parish. The estimate they give. I don't know, what do you guys think? Most people say 25-30 degrees. We've measured it, it's 5.5 degrees, steepest point. Yep. 5.5. Again, not believable, not plausible. You've seen it, you've walked it. It's not plausible that it's 5.5 degrees, it just happens to be the fact that it's 5.5 degrees. 
	Steepest hill in San Francisco. Well, not the steepest necessarily, but there's a very famous road that's actually ... I'm blocking the name of it right now. 
Audience:	Lombard Street. 
Instructor:	Lombard Street, thank you. Lombard Street, actually, they built the road to wind back and forth across the hill, the hill is so steep. How steep do you think that hill is? Well, it's pretty steep. It's 15 degrees. All right? It looks like a wall. 
	In fact, I had a journal editor who said, "I looked this up on the internet and it's not it's 31 degrees. You're wrong." I said, "No, no. The internet is wrong. Is happens." But it turns out the tangent of 15 degrees is .31, so, if you express it in grade, it's a 31% grade. 100% grade, means 45. 
	So, what happens on the internet is people say 31. Oh, that must be degrees. That's what he'd seen. But it's 15 degrees, that's the kind of error we're talking about. It's a very big, dramatic, error. There are effects, a part of this viewing distance. So, when people stand closer to a hill, versus further away ... I mean, they over estimate when they're close, but they over estimate even more when they're further away. 
	I wanted to try to give you a sense of how we measure this kind of stuff, because we're kind of proud of some of these measurement techniques, I hope we won't be too boring. But, we have a virtual reality system where people where a headset and they're immersed in a world. They can look around it, it's in stereo. We can stimulate surfaces, that are ... That, to them, are just like real surfaces out there. And, what we can do is we can manipulate the slant of the hill and the viewing distance, which is harder when you're like on campus. It's really hard to get a bunch of hills that you can look at from all different viewing distances, and have them all match. This is the control we have. 
	But, we have two different tasks that we can have people do. One of them is to just make a judgment. We have them look at this ball, that's sitting on the surface. And say, what's the slant of the hill at that point? Give it to us in degrees. You might worry, that, well when people say things in degrees they don't know how to use degrees or whatever. 
	So, we have another task that we do. Where we have three balls on the surface of that hill. We say, just tell us whether the distance between this ball and this ball, is longer or shorter than the distance between those two balls. This isn't very good here, because you don't have it in stereo. But with a good stereo view, of course, these two balls along the hill are going to be closer on your retina, then they are in reality. But you'll form an impression of what that is. The geometry of what that point is, where they seem to be the righteous [inaudible 00:11:51] part to match this. We can use to deduce the angle that you're seeing. 
	Right? So, the geometry of that is that, where it's tilted, the closer they can be together and still seem to be the right distance apart. And there's systematic errors that people make in both of these, but they allow us to map out this perceptual relationship between actual slant viewing distance and perceived slant. When we do that, what we find is that ... I'm showing these as sort of ... These are just aligned. 
	At each viewing distance, at a near viewing distance, at a farther viewing distance, what happens is at each viewing distance the slant gets pulled up a little bit more. But at each viewing distance, there's also this relationship between represented slant, and perceived slant. Which is that this slope is like 1.5. This would be accuracy here. But what they're giving us in estimates that increase rapidly. So, they get some idea that what people are doing is they're over representing the environment. 
	They're sort of saying the environment, it's pretty flat. We're not thinking that, they're thinking, oh the environment is really steep! But somewhere back in evolution, somebody said, "This environment is pretty flat. Gravity is really strong. We should do something with this."
	What you're doing is expanding this outward in some sense. The perceptual space that you're working in then, is sort of more exaggerated. I'll come back to that in more detail in a minute, but you can kind of get the idea that this could actually be useful if the brain can make distinctions and more easily can see things different. Then it can use those differences. If it can see those differences, it can use them. 
	I have a slide just to show you that even if we blindfold people and put them on hills, which we like to do, hills seem really steep underfoot. We had people stand on a ramp, our steepest one was 14 degrees. And people estimates of it were actually pretty similar to what it would look like to them. They haven't gained this from visual experience though, because congenitally blind people have exactly the same experience, it's just a part of our representation of space. Now, based on what we've done, we wanted about ... Downhill slant, you might wonder, if you're looking down a hill, should it come up? What should happen? 
	Of course, you guys probably know, we look down ... They look steep too. What we discovered was that as you stand back from the hill. If you stand back so that your gaze is looking on, this was really my post doctor is not able to be here today because he's home with his wife, they just had a baby. If you look down, right along the slope almost, that's when your perceptual experience is the most exaggerated. You feel like you're looking way down, and the whole thing seems really steep. 
	Whereas if you're standing right at the edge of the slope and looking down on it, it doesn't seem so bad. We used the VR to measure this, but this got us to wonder about ... Well, slant is misperceived. But are people really misperceiving which way they're looking? Could it really be? It just didn't seem likely. Like, I'm looking at you. I know, how could I be wrong about that? Yet, what angle am I looking at you with? How much is my gaze declined from straight ahead? 
	We set up a bunch of different experiments, I won't bore you with all the details. But the idea was to sort of see if we could get a sense of do people really misperceive where they're looking, and they do. And in six experiments, we got this 1.5 gain, where I'm not going to go through all these things. It's not appropriate for this forum, but the idea is that we could measure this 16 ways to Sunday and still find this different ... The same outcome, all these different methods. So, what you end up thinking is that sort of [inaudible 00:15:49] self portrait. It's as if we magnified everything. 
	When we look up, we think we're looking up further than we are. That's exactly what a magnified glass would do. If you're looking at a piece of text through a magnified glass, you're making everything [inaudible 00:16:01] bigger. That's what seems to happen in our experience. 
	Now, what's cool about this if you're a nerd like me, is that there's a long history in which we've learned that people misperceive distance. One of the neatest simplest cues to distance, is angle of declination of gaze. If I know how tall I am, roughly, I don't have to know this consciously, I just have to have somewhere in my brain it's represented. I can know that the angle of my gaze on a flat surface, tells me how far away things are. It's a very nice, elegant measure because it doesn't depend on a lot of computation. I only have to measure one variable, it's already inside my head. Not a lot to it. 
	But if I misperceive that variable, as this guy does. Then I'm going to think I'm looking at a closer spot on the ground, then I'll underestimate the distance. Other theories of under estimation of distance are that people are bad at estimating distance. That's the general theory. 
	There's a lot of data about this, we can take our model, just sort of say, if people were thinking they were looking this way when they're actually looking that way. What would they do? Here's some data from a couple different labs, and here's what our model predicts. It's pretty good. So, instead of saying, "People are bad at judging distance." We can say, "No, people have an angular bias. They've expanded the universe in some sense, in this weird way, that changes how distance is seem to them."
	You can do this task. I mean, these are verbal judgements. So, you might say, "Well, it's still kind of verbally." A lot of scientist don't like verbal judgements, very subjective. But you can have people do a different kind of task. Where what they're trying to do is we've done this out in the fields before there was all the construction. But, you have some big pole like a baseball lights, for the baseball fields. Have a big pole, and have somebody position themselves so that they feel like their distance to the pole is the same as the height of the pole. All right? 
	You can see this is, in angular terms, this is all about trying to make this distance and this distance the same. And, there's a geometric prediction about where people should position themselves, this guy positioned himself much too far away because subjectively, that's his experience. He's at the right spot. We can made predictions about, again, where exactly people should stand if they're misperceiving. If they have this gain, this magnification by 1.5. 
	This is some data from our lab, but against the model. This would be if they were doing it right, without any error. This is from data from [inaudible 00:18:45] lab in 1988. Turns out, the experiment had been done, he didn't have a model of what was going on. But he'd done the experiment and our data ... He'd gone all the way to really solve things. His data fit our model really perfectly. 
	So, it's really the way that it is. That as people really misperceive this stuff, it really does seem to be the way that they structure they're space. What about ... What does this mean? Well, there's a couple things. If you're a golfer, or skier, or hiker. You do anything that involves having to know distances or slants, you actually tend to learn about some of this stuff. 
	So, some of you who are skiers probably knew about the over estimation of slant, because you've been on ski slopes and you've known about. If you're a golfer, and I put you in an experience to judge distance, or especially if you're a caddy. In the putting it, I don't play golf myself, but they're perfect. They know exactly how far away things are. 
	It turns out, there's another group of folks who are really good at estimating differences on grass. Athletes. Well, why would that be? Well, how far is it to first base? 90 feet. You don't know that, you're not an athlete. That's apparently it. It's worth my athletes, everybody knew the distance of first base. We only had one baseball player in the whole set, but that's just ... how high is the basket above the court? 
Audience:	[inaudible 00:20:07].
Instructor:	10 feet, thank you. The athletes were shocked that there were people on the campus who didn't know these things. Like, what? There's just facts about the world. How long is a soccer kick? Penalty kick. There's lots of these and they know them. If you ask athletes to estimate distances on grass, they give pretty good estimates. And non athletes give very different estimates. This is done in VR, it wasn't fair. 
	We also did it in real world, they did better there too. But the basic story is that for very near distances, athletes are just as bad as you and me. But for farther distances, they're much better. They haven't skilled near space, they just see that the way they see it. But for farther distances, where they've learned things, they get it right. 
Audience:	[inaudible 00:21:02], right? 
Instructor:	Well, that's the thing. This is in VR, in VR everything is distorted. So, ignore that. Pay no attention to the man. 
	In the outdoors for long distances, they were pretty much right on the money. But this distorts everything more than it should. If you have athletes do the high distance matching test, if you had them stand away from the pole to be the same distance as the pole is high, they look just like the non athletes. That knowledge isn't changing their perception of space, they just have a verbal calibration that lets them be more accurate, but it doesn't change how they see things. 
	All right. The last thing, that's really it. You guys have been really troupers to sit here and look at data. What about action? Isn't it a little puzzling? Like, if I'm right and I could be wrong, I think I'm right. We have a lot of data now. But if I'm right, how do we get anywhere in the world? How does this work? 
	Well, think about it. If I want to throw a ball, I can. I've done it before. I know what's going to happen, I've seen it occur. I could be totally wrong about where Ken is. I could be totally wrong about how far this ball is going to travel. As long as I'm wrong in exactly the same way. 
	It's true! Think of your favorite home run slugger, he can be totally wrong about where the ball is, and where the bat is. As long as they're wrong in the same way, every time, he's all set. That's the key to action, is when we act in the world, our actions occur in the world that we're seeing. 
	We don't have to have some magical transform that lets our actions act in the real world while we're seeing a different world. We can act in the world that we see, and as long as that world is distorted in a stable way, as long as it doesn't move around all over the place. We're going to be set. It's a little strange, but it's true. 
	When I throw something, I get feedback about my action from my perception. I don't have some other magic person tell me. Maybe some sports you do learn. In golf, you do have to pay attention about how far did that go in yards or whatever. 
	In most circumstances, when I learn to walk to a chair, I don't have to know how far away that chair is. I have to know how many strides it takes me to get there. This is the kid of task that people can do. You can close your eyes, and pick out a spot. You look at a spot, close your eyes, walk to it. You'll be really accurate. 
	Your action system is calibrated to the world you live in perceptually. That doesn't mean the world you live in perceptually is exactly right, but it means that it's probably the best one. It's this one that's been expanded to make these differences that are most important to us, most available to us. 
	That's my story. Please ask questions. You can ask about anything. 
Audience:	[inaudible 00:24:21] psychology. I have like a million questions. I'll try to be brief. So, evolutionary advantage to over estimating to back in the neanderthal days. Right? If you're going to ... If you see a hill and you have to climb it, is it to your advantage to over estimate so that you know you have enough power to make it to the top? Like, if you were being chased or something. 
	I mean, what's the evolutionary advantage from all these perceptions to be enhancing? 
Instructor:	Yeah. So, the way I think about it, is more simple than evolution. Evolutionary stories are complicated. You have to sort of imagine a counter-factual. The fact is, that some of these experiments, we could do them on animals. That is, you could try to see if animals have similar distortions with the matching tasks. I haven't tried to get anybody to do that. 
	But the way that I think about it, is in terms of information processing. I tried to say this earlier, basically, but I could ... I used to want to put it into technical terms, but if you think about having digital TV, well, it's a lot of bandwidth, digital TV has a lot of pixels. It has a lot of flow, that's why if you didn't used to have digital TV, you used to have something else. 
	Our brains don't have digital TV. Our brains have to send information back through and very slow and not very many cables. And they have to code things very efficiently. So, if you go back to on an appreciation of sort of compression algorithms and information processing. Which you find is the best way to code things is to sort of distribute your codes evenly over the likelihood of the occurrence. And if 60 degree hills are never going to occur, don't devote a lot of resources to physical 60 if everything is in the range between 0 and 15, which is pretty much where everything is. Make that bigger. 
	There's never going to be a cost to expanding that. You're going to lose sensitivity other places. There's other examples that I can go on about, it's the same thing. Where we shift our scaling in a perceptual variable to make the part that we care about evident. We actually lose information on other parts. We give up on information, so, we're making choices. But you don't even have to appeal to evolution. It could be happening ... I mean, I think it is. I think it's built in. But we have to run those experiments. 
Audience:	Yeah. The exclamation that you arrive at for [inaudible 00:26:58] distance. But in kind of unexpected invitation. [crosstalk 00:27:02] if you were good at judging slants, you'd still be bad at judging distance because in order to get from slant to distance, you have to calculate the cosine in something. Then you can just say, the [inaudible 00:27:12] trigonometry. 
	But what you're saying is [inaudible 00:27:17] it seems to me, we're bad at judging slants. Good at calculating the cosine and therefore, bad at judging the distance. Is that right? 
Instructor:	No. It has been a puzzle for me as well. That is, your brain could code it wrong, and then just let you see it right. What would be the harm in that? You're saying in a more complicated way, but the fact is, that I haven't thought this through carefully enough to give you a perfect answer, but this is the right kind of answer. I think. 
	When I walk, I experience the cosine. I see how things change. Cosign is about the distance of something relative to the angle. So, if my gaze is down here. I'm going to see how that cosign changes. I actually ... I think the cosign stuff is actually given to me to some extent, by my actions, and by my movements. That's why the system is so readily able to do these transformative geometries that it seems to be doing. 
	There's a lot of folks out there who have argued that the brain uses a non Lucanian representation of space. But it turns out that a lot of them have been modeling it by creating angular expansions, and then doing Lucanian geometry on that. The brain does seem to know a lot about geometry but it's probably from motion, from the fact that it moves around in the world. Which is a very important thing. 
	He was first, sorry. 
Audience:	[inaudible 00:28:39] answer my question, I was going [inaudible 00:28:42] animals. I also worry about animals are closer to the ground, I guess [inaudible 00:28:48]. I have no idea [inaudible 00:28:51]. 
Instructor:	I only have one data point about that question. Because we don't usually collect tight information. There is ... In the gaze stuff, we haven't observed anything. We haven't looked for sex ... We never see sex differences. We throw sex in because if we have an analysis in spacial perception, people want to know that there's not a sex difference. Where there is definitely a sex difference is in peoples judgements or estimates. Verbal estimates of slant of hills. Women tend to give higher estimates than men. And no one has ever explained this. 
	We did, a few years ago, met someone who may have participated the big Alumni survey about the memory for slants of campus paths. And we got a huge sex difference. We included in that survey, for half the people who were in a question about their height, so we could see if there was any correlation between height and slant estimates. There was none. 
	The other factor ... There were like three factors that affected peoples judgements. One was whether we had them do a visual measure, like they could adjust the line on the screen versus a verbal measure. The verbal measures are higher, but the line ones are still very high. 
	Sex made a difference, and knowledge made a difference. If you knew about slants, then you knew to lower your estimate. That was true for women and men. We don't know why women give higher estimates. But it's not because they're shorter. 
Audience:	They wear high heels. 
Instructor:	Jeez, that's going to be ... People have asked that one before. But, yeah. I don't actually think that's right. I know. I understand why you'd say that. 
Audience:	I'm afraid of heights only when I'm facing the height. There is a metro station in Washington, I think the [inaudible 00:30:46] circle one [crosstalk 00:30:50]. When I get to it, I [inaudible 00:30:51] straight drop, into the center of the Universe. The only way I can get down there is holding the fence sides and closing my eyes. Sometimes I turn around and hold onto the sides. 
Instructor:	Yeah. 
Audience:	Can you talk me out of that by telling me it's not 100% or 12% or something? Or is that just ... Is that something [crosstalk 00:31:10]-
Instructor:	It's so visceral. Yeah. It's like the athletes, they can tell me what the right answer is but it's not going to change how they see it. 
Audience:	It's my fear [inaudible 00:31:18] what you're talking about. 
Instructor:	I don't know. 
Audience:	I can't see [inaudible 00:31:26]. 
Instructor:	I don't study fear. There's a bunch of ... There's a little cottage industry of people who do stuff about how to sphere affect perception of height, perception of slant. They always do a terrible job on their experiments. So, I don't think I know anything from them. Yeah. 
	That's the answer is there's definitely a phenomenon there, but I don't think anybody knows the answer. It's sort of ... Yeah. 
Audience:	I find the link between the action and the intellectual side of perception [inaudible 00:32:07] really interesting. The study you did with the athletes, I wonder ... That makes me think about [inaudible 00:32:17] specialties at work and [inaudible 00:32:19] tell you the difference between [inaudible 00:32:25]. So, the way that those become lenses, seems interesting [inaudible 00:32:35] the perceptuals that a lens [inaudible 00:32:38]. 
	Then, I also wonder if this distinction of [inaudible 00:32:44]. Can you say athletes are good at measuring distance on the ground, but when they do it vertically, that's different. Is that because in their discipline, in their location, and they're expertise, they don't know vertical distances, but they know [inaudible 00:32:58]. All left fielders. 
Instructor:	Well, catching a baseball is a different story. That's all about controlling the velocities on the retina. You don't have to know anything about distance or height, or anything. But when we did the study last year, with athletes, we wanted to get a bunch of field athletes. We wanted to get a bunch of basketball players, wanted to see if the basketball players would be better at height. And the other folks would be better at distances. 
	What we discovered is everybody is an expert at height. In the matching task, we can't tell what ... We can't tell one from the other. We can't tell what's being exaggerated, what's being underestimated. We think it's mostly underestimated distance. 
	If you ask people, [inaudible 00:33:49] students, to estimate the height of that column and you let them stand. They can look to see where their height matches up, and they count up. Everybody is an expert because everybody knows how tall they care. It turned out that peoples estimates of the heights of objects that are not too tall. Like if you ask about the water tower, which we've done, that's too many heights, they screw that one up. But everyone is an expert in height, so we couldn't discriminate between the basketball players and the others, and the non athletes. Everybody was right about estimating the heights of the objects we showed them. Which were like light bulbs in a parking lot. That's an area where everyone has expertise, because we all know how tall a person is. 
	Your question about sort of measurement, like potters clay or something like that. The stuff that I'm looking at, the sort of magnification of space, strikes me as so universal and so odd. It has nothing to do with anybody's expertise as far as we know. Maybe it does. 
	But the kinds of things you're talking about, feels like it sort of imagining transformations. What do I know about this? You have to have some cognitive reference, that's what 20 pounds looks like. That's an ounce. If people learn those correlations, that can then scaffold their perception. They know what to look for. But it's more probably an attentional thing, than an perceptional expansion of almost the literal kind that I'm arguing for here. 
	At the back. 
Audience:	[inaudible 00:35:27] you were saying 1.5 [inaudible 00:35:30] up, down, sideways, [inaudible 00:35:34]. 
Instructor:	Not sideways. 
Audience:	[crosstalk 00:35:35] but you know, [inaudible 00:35:37]. Same number across people, across everything. Now that you know the number, is there anything [crosstalk 00:35:44]-
Instructor:	I can't tell you about that. I'm going to a secret society, Pythagorean's. And ...
Audience:	[crosstalk 00:35:50] biology of the eye. 
Instructor:	No, no. It's a really good question. 
Audience:	[crosstalk 00:35:52].
Instructor:	It's a really good question. Here's the ... I'm joking about the Pythagorean society, but, the sign function. Take a sign function from zero to 90, it basically as it crashes through zero it's going at an angle. Then it compresses up to 90. Throughout this region, it's got a gain of 1.5.
	If we're coding these things in terms of a sign function, which means that we're representing the amount of height over the amount of length of the surface that would fit. And it would explain the 1.5. I can't understand how that works exactly for the gaze part, but it doesn't fit a sign function pretty well. But we don't understand why. 
	Here. 
Audience:	[inaudible 00:36:47] has anyone ever found [inaudible 00:36:56] required to walk up, grades of various [inaudible 00:37:02]. 
Instructor:	Yeah. 
Audience:	I wanted to imagine [inaudible 00:37:06] that it takes [inaudible 00:37:14] how many degree [inaudible 00:37:16]. 
Instructor:	If it was doing that, what's the multiplier for? If it's a multiplier, the multiplier drops out of the equation. 
Audience:	[inaudible 00:37:26] effort is not simple linear functions of grade. 
Instructor:	But this is the simple linear function of grade. Yeah, it's a multiplier. The reason that I'm sort of rejection various is because there's a lot of folks out there that have argued that slant perception is based on perceived effort. They've done a lot of terrible experiment, and we've debunked them. We've been very busy debunking them over and over again. I'm not very receptive, as you see, to [inaudible 00:37:57] suggestion. 
	That's why I'm saying, it doesn't even make sense. But numerically, it doesn't make sense. 
Audience:	Trust me, this is how [inaudible 00:38:05] on a case by case basis. I'm just asking you for your assistance to because the multiplier catches the relations of slant and effort, in general. I'm not expecting you [crosstalk 00:38:22]-
Instructor:	So the-
Audience:	[crosstalk 00:38:24] will transform this 1.5 into a higher number. 
Instructor:	So, you're saying the 1.5 is basically the height versus straight distance ratio, for effort. 
Audience:	Biologically wired in based on how many [crosstalk 00:38:38] based on certain various [crosstalk 00:38:44]. 
Instructor:	Yeah. I don't know the data. I see, now, what you're saying. 
Audience:	That's your sign option, right? That's the [inaudible 00:38:49] you have.
Instructor:	That's right. That's what's we'd have to find out. Is if we could show that there was a 1.5 relationship of [inaudible 00:39:01] for slope versus flat. 
Audience:	The amount of height you have to [inaudible 00:39:06] is going to ... For a given horizontal distance is going to go the sign of that angle. You're only doing work. You're not even working to go forward, you're only doing work to go [crosstalk 00:39:19]-
Instructor:	Yeah. But then I don't understand how it gets ... If I'm trying to compare a 2 degree slope, to a 4 degree slope. Representing it as 2 and 4, versus 3 and 6, tells me exactly the same information. It's just a multiplier. I can't compare it to zero, there's no comparison. That's why I'm having trouble with this. 
	It's an interesting suggestion. 
Audience:	Knowing that it takes twice as much effort, does not necessarily most relevant. Most relevant is knowing that it takes 10 [inaudible 00:39:51]. That it's perceiving a constant ratio, loses the information of exactly how much work it's going to take you to get on that scale. That's what matters. 
Instructor:	Well, would you predict that putting a heavy backpack on somebody would make the hill look steeper? 
Audience:	No, because that assumes [inaudible 00:40:04] these changes online [inaudible 00:40:08] experience. As opposed to having [inaudible 00:40:11]. 
Instructor:	Would it differ from person to person? 
Audience:	Why are you asking me? 
Instructor:	I don't know. Because I hate the effort theory, and they've proposed all of these things. And they've all turned out to be wrong. I'm just saying. 
Audience:	[inaudible 00:40:31]. 
Instructor:	The more interesting court cases are just about recognition of faces and things like that. Where you've seen a guy because he sold you a trick at the train station. But then you misidentify him later because he seems familiar in a line up. 
	With this stuff, we know that people are going to misdescribe things. So, depending on whether you're an expert or not, your sense of what the layout of the space would be, or your description of it will be different. But in terms of actually recognizing a person, or something like that. 
	Or what happened, or what view did they have? 
Audience:	[inaudible 00:41:16]. 
Instructor:	But people are terrible at judging spacial relationships. I mean, they're good at in one sense. But they're also bad in another. Of course, in events when you're an eye witness, you're trying to reconstruct it from memory there's all kinds of problems because you really weren't playing close enough attention to all the things. 
	If you walked out of the room and had to name everybody, you just can't do ... You don't store everything about the world. Wish I could answer ...
Audience:	It's there if you want to hire an expert witness, you need an athlete. 
Instructor:	There you go. 
Audience:	For distance. 
Instructor:	For distance. But not height, everybody is fine. 
Audience:	So, on one hand you said that my perception is wrong in the same way that my action is wrong, I'm fine. But on the other hand, if the athlete perception is less wrong-
Instructor:	They're perception is just as wrong. They're judgment is different. Their judgment is different, their perception hasn't changed at all is what I would argue. That's why, when they do the matching test they look just like other folks. When they do a verbal estimation, they know that's going to 90 feet or that's going to be 100 yards. It's only that they're ability to convert it to a verbal thing. Which, of course, their motor system has no idea what they're talking about. It just knows how to throw the ball to the right distance. It doesn't have any idea. 
Audience:	Okay. So, the athlete is just converted somehow [inaudible 00:42:34] representation [inaudible 00:42:33]. 
Instructor:	Yeah. It just knows. It knows that looks kind of similar ... Like, that's about a soccer goal kick. That's 12 yards. 
Audience:	Now, if there's two people standing and they're judging again and both misestimate up, [inaudible 00:42:47] I can't possible go. Is there a connection between that person's perception and their feeling that they can't go? They're subjected judgment on that. 
Instructor:	That's has to be necessary getting back to this question. I'll tell you a personal story, when I was at boy camp scout many years ago. The camp counselor I was with, was a rock climber. He took the kids to climb a rock and most the kids could scramble up it. But it was vertical, and I wasn't going to even try. You cannot climb a vertical surface, it was probably 30 degrees. 
	Certainly, this is the whole thing. Your experience of it is going to overwhelm your choices. You can try to talk yourself out of it, the snake is fine. It's not going to hurt me. But that's not going to do anything. I do think it affects folks differently, depending on how they perceive it. 
Audience:	You looked at [inaudible 00:43:51] space versus object space? 
Instructor:	We only look at a sort of [inaudible 00:43:56] space for this kind of research. For slant perception, we've studied small surfaces, not really objects but they're small surfaces here. You get the same kind of sign function, representation of slant in your space as you get for large hills. That function doesn't seem to depend on the size of the surface. 
	It's a real, just the way we see slant, is that sign function. 
Audience:	[inaudible 00:44:21]. 
Instructor:	The data we have right now, show that for side walls we get the same kind of distortion. That's different from ... As I was saying, actually, when you ask to be able their gaze direction, we don't get the same distortions left and right. We're not sure if that's because it's easier to sort of tell we're not [inaudible 00:44:46]. Oops. 90 is here, whereas up here ... It's really hard to tell where 90 is up there. 
	But with slant, it's the same for these kinds of surfaces, this way. 
Audience:	I've got two questions. One, is the type. Is there a point [inaudible 00:45:06]? 
Instructor:	I'm sure there is. But I don't know how hard. Like the water tour, it's printed at the base of the water tower how high it is. That was very convenient of them. 
Audience:	[crosstalk 00:45:21] heightens it. 
Instructor:	I can't tell you that. To the base, if I remember, it's 35 meters to the base. To the base of the water tower, to the top of the column before it expands out. That's a height that people can't count off the number of people. 
Audience:	My other question is, you were saying that one person finds out that the [inaudible 00:45:45] estimate is slow. Is there a way to [inaudible 00:45:49] regularly more accurate after that [crosstalk 00:45:52].
Instructor:	Here's what you do. If you see a slope that's 20 degrees, it's probably 5. If you see a slope that's 30 degrees, it's probably 8. 
Audience:	So, just tell myself and then I'll be good. 
Instructor:	Yeah. If you say, "Oh, that's 20 degrees. It's probably five." You won't believe it for a little while, but then you get an [inaudible 00:46:07] measure it. You'll see. 
	There's totally a transform. Might be different for different people, slightly. But it's not that hard. 
Audience:	One last question. Just curious [inaudible 00:46:21] might not have as [inaudible 00:46:24]. 
Instructor:	Yeah. My collaborator in Colorado is supposed to be collecting that data for us. He's been having personal problems. So I don't have the data yet. Why does it work this way? But, yeah, we don't know. We do know that kids estimates of distance, based on their judgements of the sizes of things. If you have something that's far away, and you have to compare it to something here. 
	Little kids don't know how to adjust for distance. The point at which they start to be able to get it just like adults and make that adjustment is the point at which they can say, "When things are further away they look smaller." They behave very much the way our perception is. 
	It looks like kids have the same kind of distance distortions we do. Whether that maps into the height distance matching, I don't know for sure. But I'm guessing it's going to, based on that. Great question. 
	All right. Thank you guys so much. This was fun.