and in a few minutes he'll describe his research on the workings of the visual system. At that time you'll also learn, as those of us on the platform learned last night, that Dr. Hubel is a man of great wit and charm who is given to the pursuit of an amazing variety of intellectual activities. For example, he's a man who's sampled widely amongst academic subjects, including Latin, mathematics, physics, and medicine before finally settling on a career in brain research. He's a man who claimed an early interest in electronics, but soon abandoned it because nothing he built ever worked. He's a man who studied math and physics in college because he found it more interesting to do problems than to learn facts. He's a man who claims that he would much rather do science than read about it. He's a man whose career in neuroscience began when he was drafted into the United States Army and assigned to the Walter Reed Army Institute of Research. And he's a man who describes himself as having spent a disproportionate amount of time studying music, who also enjoys such diverse activities as learning languages, woodworking, computers, photography, and chatting with other ham radio operators. He's also a man who spent the last 40 years studying the mysteries of the visual cortex and who gives us the distinct impression that he thoroughly enjoyed every minute of it. Ladies and gentlemen, would you please welcome Dr. David Hubel, who will speak to us today on the topic of eye, brain, and perception. Well, let me begin by saying how much I'm honored to have been invited here in the first place and to be singled out for this singular honor and being given a degree from this great institute. I feel a bit embarrassed about the degree because all of my colleagues are just as deserving as I am and I suppose the criterion that the powers here get upon for singling me out is my great age, which is probably more than anyone else. And by the way, thank you very much for the very flattering introduction, Timothy Ronson. It's not every day that one gets to talk to a group of 3,000 people. I feel a bit like the baseball players in Fenway Park in Longston. There it's 30,000, but a factor of 10 isn't all that much. I found myself wondering yesterday and today whether the nervousness one feels before giving a talk is linearly related to the number of people in the audience. If that were so, one would certainly feel very justified in being very nervous indeed on an occasion like this. But I don't really think it is. I think it saturates. If you plot nervousness on the y-axis against numbers of people in the audience, my guess is that it peaks and levels off around 30 people or something like that. In fact, 30, which is a kind of an ideal number because it's too many to allow many interruptions from the audience to break one's flow. But it's a few enough so that you can catch people's eye and sort of decide whether there are looks of mystification so that you have to go slower. There's a bit of interaction, which is very nice. With 3,000 people, there isn't all that much interaction. And you don't have that sort of feedback. So there isn't as much reason, I suppose, to be nervous. But one has to say, though, that if the number is 3,000 and you decide 30 is the optimal number, a bit of calculating will tell you that I would have to repeat this lecture 10 times a day for a month. And I think I'd get rather fed up. So maybe 3,000 is reasonable. Well, having got these preliminaries over with the law and the late comers to be seated and so forth, we can get on with the matters at hand. And I'd like to start by saying a few words about why one studies the brain. Of course, there are many levels and many ways that one could approach a question like that. But I think the central thing for me is that if I were forced at gunpoint to say what are the most interesting things in science, I would say the universe and the human brain. The universe sort of speaks for itself. It's hard to beat the universe for interest and scope. It would embrace at least all of astronomy and all of physics and probably chemistry. And I'm leaving life aside for the moment. I take the brain as the other thing of grandiose proportions because after all, it's the most complicated thing we know about in the universe. There may be other distant stars on distant galaxies where there is life and organizational units comparable to brains that are just as complicated, maybe orders of magnitude more complicated. We simply don't know. But as far as our own knowledge goes, there really isn't anything to come close to the human brain. So it is a wonderful thing to study. And I think clearly one of our major motivations for studying the brain, all of us here talking to you this week and probably everyone in neurobiology, that the major motivation has to be curiosity, wondering how this thing works. And then of course there are all kinds of practical side products. If you understand the brain, you understand learning. If you understand learning, you know much more about how to educate people than you would if you didn't. If you can go on and on rattling off things, and not least is the possibility of fixing the brain when it goes wrong. That is the medical aspect of neurobiology. And of course you can't weigh these things. You can't say whether it's more curiosity or more an ambition to help people or whatever. Whatever is the back of one's motivation. There's some of this in all of us, I suppose. But I think if force at a given point to say what I find almost impaling driving force, I would say that it's curiosity to know how this thing works. The curiosity takes two forms. There are two aspects of it that I find most challenging. One is the understanding of the structure itself. That is, if you walk along the beach and there's suddenly confronted with a pretty impressive, you don't know what it's for. You don't have the slightest study of what it's all about. That's the kind of feeling, but much more. So that you have when you're confronted with the structure of the brain. And obviously something terribly complicated, terribly orderly. That's one major source of interest and I would call it, let's say, atomical for one or the other word. The other kind of interest is psychological. The brain obviously does many things. That's why I know that it's complicated. It has to be because it's what we think with, what we perceive with, what we learn with, and so on. So nothing that does all that can do anything but very complicated and very fascinating. And one wants to know how the parts of it work in order to do this for us. There are two ways of course of going about this. You can study the cells that go to make up the brain and that is the nerve cells and the glial cells at a cell by cell level. And this has been an enormously successful pursuit in the last 20 or 30 years. And we by and large broadly speaking have an understanding of how simple nerve cells work. There are details obviously to clean up. But our command of this is very strong and that's an index of how successful neurobiology has been, neurobiology on a single cell and the cell to cell level, the junctions between the nerves. These things we understand. But of course that, although it's essential to understand the built-in blocks of the nervous system, it does not finish the job by any means. We're in the position of somebody who understands resistors and condensers and transistors very well, but who does not know how they are assembled together to make the television set, the computer, the radio or whatever. And the aspect of the whole thing that fascinates me the most is the second, it's what you might call loosely systems. There's several names for this. Integrated neurophysiology would be one. But I'm interested in how the arts is assembled together to give us what we have. I choose, along with many other people in this bracket, I choose the visual system to study because the problems are easy to formulate relevant to other systems, such as the sense of smell, for example. And the techniques are relatively straightforward. It turns out to be much easier to generate patterns on the screen that the animal is facing than it is to generate sounds that may be of interest to the animal. It's easier to imagine what might work to make cells fire. So the vision turns out to be a very good system to study and it is certainly decidedly the most popular part of this is probably simply bandwagon effect, but not entirely. The problem of vision could be rather simply stated, the initial event is clearly that light falls on the retina and in so doing it's falling on 125 million rods and cones in each retina. These are cells that are specialized to take light and turn it into electrical signals. That information is handed on to other cells in the retina and then to still other cells in the retina. There are at least three stages that we can talk about in the retina itself. Finally, the output of the retina goes to the brain and it's up to the rest of the retina, that is the cells that are in addition to the rods and cones. It's up to those cells plus the brain to make sense of the information that falls on the retina, that is to extract from the light and patterns on retina information that is biologically useful. This is the central problem, this is what we address. I want to concentrate mostly today on what goes on in the cortex, that is the fourth or fifth stage in this handing on of information, but before I even start that I have to make a few remarks for the sake of the people who aren't specialists in biology in the audience about how single nerve cells work. To do that, I need the first slide and if I can get the controls here right, yeah, great, so far so good, I passed that test. Here is the slide that shows three nerve cells and I'm going to point with this laser and so these are three nerve cells. Nerve cells are like any other cell have basically the shape of a jelly bean but that is a cell body containing a nucleus of other structures that are of great interest to the cellular biologist and nevertheless they're very different in shape from any other cell in an organism and the difference is that the cell wall is pulled out into a cylindrical thing called a nerve fiber or an axon and roughly cylindrical it keeps the same diameter for millimeters or inches or yards and a number of other processes that tend to be about the order of a few millimeters in length that are tapered and are called dendrites. It's the job of the dendrites and the cell wall of the cell body to take in information from other nerve cells. It's the job of the axon or nerve fiber to transmit that information along its length in the form of what are called impulses. There's a charge across the membrane that's positive out and negative inside of about a tenth of a volt which for an object this size is a huge potential. That tenth of a volt exists when the cell sits there normally resting. When an impulse occurs it reverses suddenly and for a period of about a thousandth of a second the outside becomes negative and the inside positive and that reversal of potential is very brief and it passes along the length of the fiber in a way that doesn't occur simultaneously over the whole cell so that the impulse is conducted down the axon at rates in the order of the yards per second. When the impulse gets, and of course the impulse passes down as a wave and in its wake there's a recovery process that takes about a thousandth of a second to get over with then the nerve is ready to have a new impulse. When the impulse gets to the end the axon usually breaks up into hundreds or thousands of branches which end on tens, hundreds or thousands of other cells. When the impulse gets down to the next cell it squirts out a chemical called a neurotransmitter and that has the effect on the next cell of making impulses either more or less likely. And depending on the chemistry of the synapse and the, I've lost my, oh here we are. For some reason it no longer shines. What is, do you see the laser? I've lost it too early. Well, depending on the chemistry of the transmitters and the nature of the synapse itself, the synapse is the name given to the junction between two nerves, you have the cell that's being affected in the direction of making it either more or less likely to fire. So if you have a lot of excitatory influences coming into a cell it fires at a more rapid rate. And the rate of impulse is the important thing in any cell. I think it's still, it's going on but for some reason it isn't going through the easier ways to get to the screen. All right, this is the basis then of neurobiology. A cell sits there firing at its own private rate and is driven to fire faster or slower depending on the prevailing inputs coming into it from other nerve cells. Now that is a semester's worth of neurobiology compressed into three or four minutes. And so if you don't, thank you, if you don't follow every word, the reason is that there's a lot of information there and it's been compressed. All right, now if we go on and look how cells tend to be arranged in nervous systems and taking the visual system as an example, here is a bit of nervous system in the retina, here on the left and in the brain over here on the right. Here are the rods and the cones and they are made to emit neurotransmitters to the next stage depending on whether light falls on them or not. And the next stage sends its messages to the third stage. The axons of the third stage assemble into a cable of nerve fibers which is the optic nerve. Each of our optic nerves contains a million fibers. So you have 125 million of these things, you only have a million of these cells for reasons best known to the maker, I guess. Now the information then goes to the brain and this represents the very early parts of the handling of that information by the brain. We have, the technique we use to study a structure like this is to put a microelectrode which is a very fine wire into the brain or into the retina until it comes close enough to a single cell to record the currents that are related to the impulses. So when you get the electrode in the right place you see deflections on the oscilloscope that represent the impulses, each lasting about a thousandth of a second and occurring in rates of a few per second up to maybe 500 per second. So you can take the output of the microelectrode and display it on an oscilloscope but a much more compelling way is to listen to it over a loud speaker and you hear every time the cell fires an impulse you hear a click and so you can judge whether you are being efficient at activating a cell or influencing its firing simply by listening to the clicks. In a typical experiment of the sort that we do we have the animal anesthetized on a table facing a screen like this screen a few yards away and onto that screen by holding a slide projector we can project patterns or spots of light and we search on the screen then to try to find a region over which we can influence any particular cell that we happen to be listening to. It turns out that things are arranged in a very orderly way and a typical cell in the visual part of the brain is very likely to be influenced over a very small region. So for somebody at the back of this room for example a region about like that might be a region over which we could influence the firing of the cell. So in order to take care of the entire 180 degrees of one's visual field and do all of the variety of cells that we see call for an absolutely incredible number of cells but an incredible number of cells is exactly what we have in the brain so there's no problem there. Now if you wanted to be orderly about this you would start at the eye and record for the cells here and see how best to influence them and then go into the brain and compare a typical brain cell with a typical cell in the eye and you would expect to find a brain cell to be more complicated otherwise why have all this complexity of wiring that you do have and that's in fact exactly what you find. It's been known now for many years that a typical cell in the optic nerve representing the output of the retina that is the activity of these third order cells which are called retinal gangrene cells. A typical cell at this level responds best when you shine a small spot in just the right part of the animal's visual field. In this case I'm just the right part of the screen that the animal is facing. You get by far the best and most powerful response from filling up with light a very small circle. If you make the spot smaller than optimal you get a weaker response, a weaker burst of discharges from the cell and it turns out if you make it larger than optimum you also get a weaker response. Something that came as an enormous surprise to Stephen Cooper when he discovered this in around 1950. I'm not going to say much more about the behavior of optic nerve fibers. The main point here is that the optimum stimulus for an optic nerve fiber is a small spot of light shining in just the right part of the animal's environment. I might say that the experiments that I'm going to describe are obviously done on animals and we use animals whose vision we think most closely resembles human vision because that happens to be our major interest. The animals that we've used have been cats and recently monkeys, two species of monkeys, squirrel monkeys and macaque monkeys. I want to just say a word about the use of animals in research. I want first of all to emphasize this research cannot be done, even research on a cellular level or on a systems level in neurobiology. Like most other biological research, it cannot be done without using animals and it's easy to forget that when people urge one to work in tissue culture for example but the tissues that you work on and tissue cultures come from animals so you don't escape having to use animals. The use of animals for human purposes is nothing new. It's as old as civilization and our civilization really has depended on that. When we gather and hunt, we hunt animals, we don't hunt carrots for example. So it's something that is absolutely necessary and basic to our civilization. And when we do this kind of work, we take great care and in fact the law tells us that we have to take great care in case we didn't feel that way, feel like it. We take great care to avoid the animal having any suffering. The work I do is all on anesthetized animals. Many people work on a way of behaving animals but that sort of work is also done in a way in which the animal does not suffer. There is a certain amount of propaganda on the part of animal rights people that would make you think that these animals suffer terribly. It's absolutely contrary to the fact. There are of course in any field criminals so that there are people who perhaps do delight in making animals suffer. If it's one in a thousand, that's important and one should frown on that and take all possible steps to prevent that sort of thing from happening but you don't do as many people would have us do, abandon the research entirely because of one or two criminals in the entire spectrum of neurobiologists. Any more than you do away with the stock market just because there are a few leveraged people who do leverage buyouts and become billionaires and are criminals in a few of them anyhow, criminals in every sense of the word. You send them to the jail when you find this out. Well, this is my plea is to take with a grain of salt what you hear from the people who would have you think that we would be better off if we abandoned all use of animals and research. It's certainly not true. And while I'm at it, I may say that even though I am quite clear in my own mind that I do the kind of work I do because scientific curiosity largely, I'm also interested in helping be one as it happens Torsten Wiesel and I were lucky and we did find out something about the visual system that made it possible to prevent one of the commonest kinds of blindness. So we didn't necessarily set out to do that and it probably had we set out to do that we wouldn't have succeeded in doing it because we probably wouldn't have laid the underpinnings and got a good knowledge of the basic things in our subject. But it has been successful, enormously successful medically and I don't think the same thing could have been accomplished without using animals. So that's my political part of my talk. Now to get back to this system here, the optic nerve fibers are telling something are most sensitive to roughly speaking circular spots of light in just the right part of the animal's visual field. When you come up to the cortex, the primary visual cortex which is at the one, two, three, four, the fifth, sixth and seventh stages, roughly speaking, you find several profound changes occur. One is that it's at this level of visual cortex that you have the first convergence of input from the two eyes on single cells. So a typical cell in the visual cortex can be influenced by both eyes, not just one. So this must in some way form the basis of our binocular vision and in particular our stereoscopic depth perception and this is something under intense study in a number of labs, including ours. And perhaps a more interesting change is an absolutely incredible change that you have in the kinds of stimuli that these cells respond to. You find that at the cortical level, by and large, cells don't respond any longer optimally to small spots of light in the right part of the visual field. Instead, in general, they respond to short lines in the visual field, a line like a light line on a dark background or a dark line on a light background or an edge boundary like the boundary between this region and this region. These are the kinds of things that turn these cells on. For any given cell, a line is highly likely to be the best kind of stimulus, but for any given cell, you have to shine the line in the correct orientation for that cell. So you have cells that are specialized for horizontal, for vertical, and for all the intermediate obliques. This came as a great surprise to us when we discovered this thing around 1958. It was something that nobody had predicted at all, but it was very gratifying to see this sudden increase in complexity because as I've said, it kind of justifies all of the complexity of the circuits, the complexity that you know is there from looking at the brain under a microscope. What I want to do now is to give you some examples so that you can, as it were, eavesdropped to coin a term that my introducer used a few minutes ago, to eavesdrop on one of these cells to put yourselves in the place of somebody doing this kind of experiment. So you can imagine yourself or us sitting there with a slide projector waving it around on the screen, trying to find the region that is most attuned to the cell that we're studying. What you will hear are the impulses from single cells in the cortical part of the brain, the part of the cortex that is responsible for the initial events that occur in vision. So you are listening, every time you hear a click, the cell that the microelectrone is close to in the cortex is firing an impulse, and you want to maximize the rate of firing of clicks by shining the lights. And I can tell you that when this was first done, it was a real problem to find the best stimulus because one had no idea where on the screen to shine the light, and nothing to indicate from anything that anybody knew that lines would be constituted better stimulus than anything else. Now the first example, these cells that respond best to lines come in three or four varieties, each one more complicated than the next. And I want, I'll show you without commenting on the reason why we think it's simpler and not more complicated, I'll show you an example of a simple cell that responds best to a particular orientation of line. And then I may say a few words about that, and then we'll go on to study what we call complex cells, and finally we'll see one example of what's even more complicated than the complex cell, a cell that's nowadays called an end stop cell. So if we could have the first example, you will be looking at this screen, but we simply televised the screen during an experiment. We need the light, but that's one kind of cell, that's studies that we do. This is one makes that we don't have much knowledge for other sensory systems of this kind. So this region of Cortex is the region that's by far the best understood of any part. It took 30 years or something like that to work out to its present stage, and one is just getting started on most of the other regions. Now, I want to say a few words before I quit. Fascinating aspect of this, and that is the groupings of these cells, the fact that the cells aren't arranged at random throughout, you don't find two neighboring, next door neighboring cells, one interested in one orientation and the other a very different orientation. They're grouped in a very systematic way. And before I get into that, I have to show you sketchily how the Cortex is organized. So we have to get down to brass tacks now and look at a bit of anatomy. So the next slide here is what Eric Kendo would call a cartoon of the Cortex. That is, the system we're working with, you have the eyes, the optic nerves, and then from each eye, they terminate in a structure that I'm not gonna say anything about today called the lateral geniculate body. And the information from it is relayed up to the primary visual Cortex, which is the first receiving area for visual signals. And so this is the area that we're going to be looking at in some more detail now.  I'm just gonna take a minute and describe this because I want to say something about the perceptual consequences of all of this, of all of these orientation selective cells. You see that these cells don't respond to diffuse light and the perceptual counterpart of that phenomenon is the fact that if you take a square like this, we make this square by putting a filter in the slide projector that cuts out 90% of the light. So here we're getting 10% of the slide projector's light. Here, 0% because we put masking tape here. Now we ask, all this stuff on the side is condensation having to do with technical things behind the screen. So ignore that. We ask, what happens if you take the masking tape away but leave the filter in place? So the light, if you have a measuring device, the light coming to you from here is not going to be changed on the next slide. We keep it the same. But look what we see. What was white now is black and still having yellow, okay, right. This is very tricky. Here, the reason for this impressive phenomenon at Harvard, they hiss when you show them those because they don't really believe that the filter is the same. The light coming to you from the center region is the same in this case and in this. And I must say, for the purposes of teaching, I wouldn't put it past myself to cheat and make them different if you can't do that. So you just have to take my word for it. This is an honest demonstration. But you remember that the cells themselves, if the receptive field of the territory that feeds into the cell is entirely within the square area, then changing the light from the square area doesn't change the firing of the cell. The cells are blind to diffuse light. So a typical cell whose territory of interest is within this square isn't going to know whether the square is there or not. The only cells that are going to be stimulated by something like this are the cells whose receptive fields are cut by the edges of the square.  It has nothing to do with the light coming from the center. So it's no wonder that if we keep the light constant, that the cells simply don't respond to that. And so we get the reverse impression of white versus black because what is happening at the edge is reverse. I'm going in one hand from black to light, the other hand from light to black. And the cells that you just see would respond by being inhibited or being excited when you make that change. So they're responding in opposite ways to a stimulus like this. And that's the basis, presumably, of our impression of black versus white. So black and white don't have anything primarily to do with the amount of light coming to you from an object. That's the moral. And that's something that's been known by experimental psychologists for a hundred years. But now we think we are much closer to the physiological basis of this interesting perceptual fact. Well, now let's go on to the brain. Here is the brain of a macaque munking seen from behind. And if I can find the laser again, we have, the brain didn't come like this. In fact, we cut this chunk out of the brain in order to demonstrate something about the anatomy. The part of the animal's brain where you see the arrow, that is the visual part of the brain. That's the back end of the monkey's brain as it is in humans.  So the smooth part of the brain, and I can't really point to it, if one loses it, but the laser's okay. It's just too weak. The upper most part of this cross-section of cortex shows you an example of what cortex looks like. The cortex, cerebral cortex is basically a plate of cells that's been folded up. And the plate is two millimeters from surface to the depth of the cortex. So the very topmost fold there has a thickness of two millimeters. And if we take that and magnify it up, you see something like this where again from top to bottom of cortex is two millimeters. From here to here is about two millimeters. Underneath any square millimeter of cortex, a square millimeter of cortex, you have about 100,000 cells. So each of the dots on this slide, which I can resolve, you probably can't from the back of the room, there are many peppered dots here. Each of those is a nerve cell. Now, we have known for some years that if you look at the parts of the cortex that are fed by the left eye and compare it with the parts of the cortex that are fed by the right eye, it forms a very systematic pattern. So if you inject one eye with a dot of an appropriate type that's carried up by the nerve fibers through the lateral geniculate nucleus up to the cortex, you can stain on the cortex the regions that initially received the input from the two eyes before the eyes mix, before their effects mix. And here is an example of a pattern that you see. This was done by Simon LeVe and an analyst in our lab some years ago. This is the back of the brain. Here was where we had cut out the chunk on a equivalent region.  So we've artificially colored black the regions that get their input from the left eye and white regions from the right eye. So this highly patterned way in which the two eyes join up and share their influences in the cortex is something that has received a lot of study and we still don't understand why these exist. But we know that there is this system of what are called ocular dominance columns in all the world monkeys and in humans. The width of one of these stripes is about half a millimeter. So two stripes corresponding to left eye and right eye take up about one millimeter. So there is a highly organized system and a distribution of left and right eye influences in the cortex. The more important perhaps and perhaps more interesting set of subdivisions has to do with orientation. And in here, this illustrates you may not be able to see this too well from even from the front row. But yeah, here we're drawing a graph. We make a penetration through the cortex which you see in this yellow patch up here. We make a penetration starting at the top and going down through the cortex obliquely. And when we do that, we find that as we go from cell to cell and in a penetration of microelectro that goes about a millimeter, you can record from maybe 50 or 100 cells. As you go from one cell to the next, you map out what each cell is interested in. And you find that each one is specific for orientation. The orientation changes from cell to cell as you go along. So as you progress through the cortex, the optimum orientation shifts progressively by 10 degree steps or something like that so that after a millimeter, so you've gone on all around the clock and are back where you started from. And occasionally you have reversals for reasons that took us years to understand. You come to the point and suddenly as you go further through the cortex, the direction of rotation changes and things go the other way. And that occurs every few millimeters, maybe every five or six millimeters. You know such a reversal. The point here is that the cortex is subdivided into domains. If you make a penetration vertical through the cortex, all of the cells that you see respond best to the same orientation. You can't predict what that orientation will be, but if you pull out the electron and go in somewhere else, you find they all again respond to the same orientation but a different orientation from what you saw before. Going through slant-wise, you get this highly systematized progression of orientation shifts. Now, if you then consider that this same region of cortex is also divided into one millimeter width, half millimeter width left eye and right eye regions, you have existing in the same cortex two systems of subdivisions. And here is a sort of model which we call our ice cube model number two. If this is a chunk of cortex, say a couple of millimeters by a couple of millimeters and two millimeters thick. We think of the cortex that is being divided into slab-like regions. In this direction, these are the ocular dominance columns. And at some other angle, not necessarily right angles to this, to another set of finer subdivisions by orientation. So as you progress through in any old direction, you have a sequence of shifts of orientation. And then after you go through a certain number of orientations, you shift to the other eye, continue shifting orientations. The point here is that the cortex is almost like a crystal. It's so highly systematized and complicated. And this applies to the primary visual cortex. We have said so far. We have good reason to think. In fact, we know that other regions of the cortex are subdivided in analogous ways but the principles are not necessarily the same. In fact, in general, the principles are quite different. Different variables change as you move across the cortex. Also, I've drawn these orientation columns as though they were perfectly flat slabs as though carved out with a knife. But in fact, they're very much more complicated than that. They sort of swirl around. And I'll show you an example of that in just a second. These regions here, which are like pegs that have been punched into the cortex, extend pretty much through the thickness of the cortex. And they are regions in which the cells don't care about orientation at all. Instead, they care about color. And they are, we call these regions blobs mostly because it's, for some reason, noise people because they think blob is a slang term. It turns out not to be. It's in the Oxford English Dictionary. So it's an okay term, but it doesn't annoy people and that's why we use it. But the blobs seem to be part of a system that is dedicated to color. It may be dedicated to other things, but it's at least 50% of the cells in any one blob respond best to color and don't respond well at all to white when you stimulate the screen with white light. So you have packed into this cortex an assembly of variables which is highly orderly and certainly complex with linings. Just to give you an idea of what this pattern of the orientation columns looks like, far from being slabs, they're swirls. And here's an example taken with a technique invented a few years ago by Gary Lays Dell, who was, I think, in Pittsburgh at the time and then moved to Calgary and now is at Harvard. And each of these tiny lines that you could probably, I hope, make out from the back row, but I doubt it somehow. Each of these lines represents the orientation of the cells underneath this voidal cortex. And as you move along the cortex, the direction of the lines change, that changes, every orientation has been assigned a color. So this oblique forward in this direction has been colored in blue. All the cells that prefer that orientation are blue, whereas yellow has been chosen to color this slide and this orientation. Of course, none of this has anything to do with color. It's just to portray the kind of complexity. The point here is that these things are not parallel straight lines. They're very complicated, swirling sorts of formations. And what the basis of that, what the reason is, why it developed that way, we really don't know. Well, this is one region of cortex, but of course this isn't the only area of cortex devoted to vision. The cells in this part of the cortex send their axons to the next door neighboring region. This is called area, visual area one. The axons from visual area one go to several other visual areas, which are called visual area two, visual area three, and another area called MT, each of which sends their fibers back to this region of cortex. So every region of cortex that has been studied seems to send out connections to some other parts of cortex and receive connections back from those cortical areas. What the back connections are for, we don't have any idea. And I'm not exaggerating when I say we don't have any idea what I mean is we don't have the slightest idea of what they're for. Here is just a diagram. There are a number of diagrams published, of which this is perhaps the most simple. And that's why I like it. But the occipital loam alone, which is a region in you the size of the fist, there are something like 18 to 24 of these separate areas of which visual area one, but one I've been describing all along here is just one. It happens to be the biggest, but it sends its output to several other visual areas, each of which has been designated by one of these adages. So this represents all of the visual areas and we don't really know too much about what goes on in any but a few of these. We have a fair idea of what's going on in V2. We have a very good idea of what's going on in MT. This seems to be a region specialized for loom. Beginning about 15 years ago and in the laboratories of such people as Samir, Zaki, and David Van Essen, the mapping of these different areas was done and it was discovered that different areas tend to be specialized according to sub-functions of vision. So we have very good reason to think that visual area two is a strike-like region where any given strike is interested either in color in stereoscopic depth or in form. This is putting it in a very rough way but that's roughly what we think is happening. This area, MT, is full of cells that are responsive to moving stimuli. It's certainly involved in movement. Some people think that visual area four has to do with color and so on. The idea then that sub-functions of vision have their own territories that are concerned with those different sub-functions is something relatively new. That is in my life, it's only been apparent for the last maybe 10, 15 years but it has caused somewhat of a revolution in the field. And one has to ask how all of this is assembled together if indeed it is assembled together. What region of cortex gets its input from all of these different areas so that you see a scene at one and the same time containing color, depth and form and movement. We don't know the answer to that. I don't think there's any compelling logical reason why there needs to be such a region and the further one goes the more one suspects that there in fact is but we really don't know. Maybe in terminating this discourse I should make a few comments on a sort of slightly philosophical question and that is the question of the mind. Where does it come into all this? And my answer to that question is that we're talking about something that exists only in a certain sense of the word, exists. The mind is all that the brain does and I don't think there's anything more to it than that. We tend to want to reify things that is we want to think of the mind as a thing and many neurobiologists do and have the history of this field. But most neurobiologists nowadays I think don't think that the mind is a thing and that these cells somehow feed into the mind as though that were a box of some kind. I don't think most people think that at all.  And that is it's a useful word when you wanna have expressions like I'm of two minds or I have half a mind to do this or that sort of thing. It's a kind of an everyday word of great use but scientifically it's a very treacherous word because it misleads us I think. The astronomers got over this problem around the time of Galileo. Probably Galileo was the single most important step when he looked at the heavens and as Bertolt Brecht said he looked through the telescope and found it but there weren't any. Dr. Kandelman, you have a response? May I begin, in David Hubel's talk he essentially described to you sort of what I think one would call the early stage of his career. In the last five to eight years he's gone to extra striket cortex and looked at the parallel processing of information important for perception. And I wonder whether he could briefly number one elaborate on how information is processed in the extra striket cortex. How we see objects, how we see movement, how we see color. And perhaps extend his discussion on the binding problem to say it a little bit more about what his own thoughts of how a uniform image is created in our brains. That's a tall order, Eric.  Well this is, yes, this is all postgraduate stuff now from now on. I hinted that these various areas beyond the primary visual cortex are to some extent anyhow specialized for different subdivisions of vision such as form, movement, depth, color. And it's, in a way, I guess it shouldn't be surprising that that should be so because if you ask anyone, I often say when I'm talking about this that if you ask a taxi driver in Boston what the subdivisions of vision were, if you could make him understand your question, which is not a certainty, he would probably come up with the same list as any of us that the way we subdivide vision intuitively is into those categories, form, color, depth, and movement. And what is very satisfying in a way is to see that the brain, its organization to a large extent reflects that. The divisions may not be completely punched out and sharp for some of these modalities, but certainly for some it seems to be, and I pointed out an area called MT, which is decidedly involved more than anything else in the sensation of movement. And in a way, none of this is entirely new. One has known for many years, although it's been largely ignored by many people, that there are areas in the brain that are specialized, which when damaged, leave you with defects that are highly selective. So you can have a stroke in a certain area that makes you color blind. And here Tony DeMascio and Oliver Sacks are experts in these areas, among many others. And Tony here has shown us patients when we went to Iowa City for no other reason than to see them, patients who have had their brain damaged and are left unable to recognize faces, for example. So there are regions that are not only specialized for form, but for particular kinds of form. The specialization isn't exactly faces, but it's more or less that. And Tony will probably tell you more about that. We have found physiologically, then, that the counterpart of this is that there are areas where we go and we can record 30 cells one after the other, all of which are influenced predominantly by how far away a stimulus is from the animal. And that is, they're sensitive to particular depths. And we think that they're subserving depth perception. Other areas containing cells, one after the next, highly grouped, each involved in color. So a cell, you know a cell is involved with color when it responds by being stimulated to red light. It's spontaneous activity inhibited by green light and it does nothing in response to white light. It's got to be a cell concerned with color and no question about it. And it's the details, of course, of all any of these things are fascinating and have to be worked out, but the subdivisions are interesting. And as I mentioned, how this is all got together if indeed it is got together so that you look out and see a visual scene is certainly not known for sure, but it's a very interesting area to talk about. And I think several other speakers here will discuss this in time. I don't know whether that answers what you. Yes, would you just say a word about the binding problem? The binding problem, how you think it matters? That's really what I mean. What I understand by the binding problem is how you, what you make out of an object that's moving and happens to be red, for example. Are there two areas separate in the brain, one responding to the movement, the other to the redness? And if so, do they feed in at higher level still to common cell that responds to both of those things? And that's what I'm questioning. We certainly, one hasn't seen such cells, not in that context anyhow. There's certainly cells that respond to depth on the other hand are all orientation selected. So it probably varies from one set of modalities to the next. Churchly? When you were showing us the video, and we could see that the cell would respond maximally, it would really give a sharp burst at bars of light at particular orientations. We could also hear when the bar of light was at other orientations or not there at all, some firing in the background. Now, what it looks like then is that it's not that there's a very narrow band that will turn the cell on, but that the cell is sort of broadly tuned. And also that it's doing something, even when the stimulus isn't there. So how does that make you think about what the cell is representing or what the cell's role is in sort of constructing a visual experience? Yes, our impression is that the cells really are very specialized, and a typical cell will respond very well over a range of maybe 20 degrees to either side, but there'll be a peak that you can specify to the nearest few degrees. And whether that cell can be thought of as mediating one particular orientation or mediating a range of orientations less effectively as you get away from the optimum is really what you're asking. I think we really don't know the answer. I know what my prejudices are, and that is, and I think that they're driven by the sharpness of tuning of these cells, the impression that you get that they really are as specialized as they are, makes us think that it's the optimum orientation that that cell is really concerned with. And when it starts to drop off, other cells are peaking up, and they probably drown out the, in some sense, the activity. I think this is more or less supported by work by people like Bill Newsom who record in Waking Behaving Animals, and have shown that if you find a cell that responds best to a certain direction of movement, if you electrically stimulate that group of cells, you can show that the animal is, in some sense, seeing that movement.  So what you make out of a cell that, as I mentioned, responds to modalities is not only concerned with orientation, but with the distance away. I'm not sure. You either say it has two functions or something. It's one thing, of course, to describe what these cells are doing, and that's our business. It's the implications of what they're doing, what that contributes to the animals, to the animals' sight, is a more difficult question, and it's one that's starting to be addressed in Waking Behaving Animals, and one just has to see what they find. Dr. DeMarsie, on the other hand. Just a comment on following on Eric Kendall's previous words. I think that David Duble was very modest, as usual, and he didn't tell you that since the early 1980s to now, along with his collaborator, Marge Livingstone, he has actually detailed, with great precision, the whole flow of this other aspect of visual processing, which relates to color, and in fact we now have a very nice map all the way from the blobs, with which he wants to annoy the competition, into the stripes of V2, and one of the very beautiful aspects of that work is that it dovetails nicely with the kind of observations that we and others have made in the human brain that is lesioned by, for instance, a stroke. And just as there is this precision at the scale of neurons in areas like V1 or V2, there is also a precision at the level of the large-scale systems of the human brain. For instance, when you look at the visual cortex of a human and we look at the calcuring region, which is the region where V1, this primary visual cortex, is located in the human, we realize that there is an upper part to it and a lower part. Well, it turns out that the region in the human brain that is interested in color, using the same words that David used, is in fact always located below the level of the calcuring fissure. So this is not some willy-nilly arrangement in which color could be processed either by the superior visual cortices or the inferior. No, it's always the lower cortices below the level of the calcuring fissure and always in the same location that when there is damage, will lead to the loss of color perception. So there is a very nice arrangement too. And the other things that we know that as we move forward into the brain, for instance, in more anterior aspects of the occipital or the temporal lobe, you just don't see color defects. So there is something which we would call a regionalization of the interest in color. And the nice thing is that you can look at it at the level of individual cells and you can also look at it at the level of the large-scale systems. The other brief comment was on the binding problem which is very much in our minds. What is it that allows us to look at a scene and pick up on movement and shape and color and depth and have it all blended in a coherent structure rather than having it all disassembled by bits and pieces? And one is very nice to hear David say that he really doesn't think that there is one area where that binding is gonna take place. Everything that we see at the level of cortical architecture or at the level of lesions in the human brain suggests that there is no single area. In fact, my suggestion is that using those marvelous feedback projections you will have in the sheer complexity of the connections in those early cortices, everything from V1, 2, 3, 4 and 5, probably even V6 if that exists. We have this massive interaction among regions and it is in that large system that the coherence is being created and the coherence comes out of time rather than space itself. So maybe there is no picture that you now have in your brains of us sitting at this table but in fact many, many pictures that are cohering in time rather than in one place in space. Dr. Sacks. Listening to your beautiful presentation as a physician, I immediately start thinking of clinical situations and the role of experience and deprivation. Recently I visited an island of the colorblind, Pingalap, where about a quarter of the population have a hereditary colorblindness in acromatopsia due to the absence of cones. In some ways these acromatopes are regarded as disabled and second class citizens but they are also understood to have certain strengths as well and in particular it's thought that their motion perception and their perception of form and texture is heightened and this is valued by the color normals. And I would wonder very much about the power of adaptation in a lifelong situation like this and whether this has been studied. I think it would be very fascinating to study it. This is one of my thoughts. The other had a relation to a patient I saw who had had very poor vision in infancy and became totally blind at about the age of two but then through surgery was given some vision at the age of 50. I got a strange ambiguous phone call saying it's a miracle he sees. On the other hand he doesn't know what he's seeing. And it seemed that this man as soon as the bandages were taken off instantly recognized color and movement and orientation but had the greatest difficulty recognizing form even the simplest forms and that there was no transfer from the tactile to the visual so that a touch triangle did not allow him to recognize a visual triangle. He was also deeply puzzled later by the changing appearances of objects when they were seen at different distances and from different angles. And so I wonder if you could tell us something about the role of experience and the powers of adaptation in the development of the early visual system. I don't know whether I can give a satisfactory answer to all the aspects of the question. In fact, I know very well that I can't. It's one of the more fascinating questions is to such things as whether in a blind person the areas of cortex that I was talking about are kind of left high and dry just doing nothing or whether anything else, any other sensations take over those areas. It doesn't look like they do. And certainly what you describe somebody not seeing at all for the first 50 years, did you say? You take away the blindfold and he suddenly is able to recognize orientation and things like that. That must be the cortex working, I assume. The one thing we can say, I think for sure, is that in a higher primate, an animal like a macaque monkey and it's very likely true of us, the wiring that is responsible for the things that I described, the circuits that are necessary to bring about orientation selectivity of cells, which I showed in the demonstration. You can show all of that in a macaque monkey that's just been born. So those circuits are there at birth. Don't depend on detailed visual experience for getting the way they are. That isn't to say that they're wired in totally by genetic means, there are other possibilities. We know that the eyes are supplying impulses to the brain even before birth, long before birth. And some of that can be decidedly patterned as people like Carla Schatz has shown in the last few years. So however those circuits get there, it's not the detailed, it's not something that is learned by going to lectures at 10 o'clock or in the morning or something like that. They're there ready to run as soon as the time the animal is born. Of course, that is not to say that other parts that's true of all parts of vision after all, were not known, born, able to recognize the alphabet. And certainly learning does play a role subsequently in some aspects of vision. But it doesn't seem to be necessary for the aspects that I've described. And I think one looks on those as building blocks and there's no reason why they should be learned in order to get the way they are any more than the optic nerve fibers have to get wired the way they are by some learning processes. And the fact is that they seem not to be. But that doesn't mean that postnatal experience isn't important. We know, I've known for 30 years now that if you take a newborn animal and close the eyelids of one eye for a period of even a few days, certainly a period of a week or two is enough to do this. And then record from the cortex. You find the cells in the cortex simply can't be influenced any longer by the eye that you closed over for all intents and purposes. Even though if you record from the eye that was closed over, you find that it's perfectly normal. Somehow in the cortex, the relative emphases of the two eyes is upset when you disable one of the eyes by closing the lids. And if you leave the lids closed for long enough, you can show that even though, let's say for three months, you can show that then there again, the eye seems to work perfectly normally if you unclose the lids and test it, for example. But you find the same cortical deficit, cells aren't influenced by the eye that was closed. And that's permanent. By and large, if you leave open the eye and leave it open for a year and then go in and record, you find that there hasn't been much recovery. So it's a long story and I'm just giving you a few of the basic facts. But the whole question of how these things get there is a fascinating one. How things wire themselves up prior to birth, how they can be influenced by disturbances in the environment subsequent to birth has been something that's interested us very much. And we think that it bears not only on the physiology of vision, but it has very broad implications for fields like psychiatry. For example, you have a child that's neglected, left staring at the ceiling for the first year of life. It's no wonder that the personality may be disrupted in a way that can't easily be repaired. You've got to use these circuits at the right time. Otherwise, you may have trouble getting them to develop at any age. Well, this is part of a very huge subject. One aspect that's being studied now in many labs, not ours, is the aspect of the degree to which you can change the wiring of the cortex by experience. And this undoubtedly varies from one area of cortex to another. And the visual cortex doesn't seem to be particularly modifiable, but it's certainly now known that it is, to some extent, modifiable. That's been learned in just recent years. I think, well, so she did just a couple of what we hope are quick responses to questions from the audience. First, does the introduction of the microelectrode in your recording technique modify, or do you have any reason to believe that it modifies the function of cells? Yes, did you, yeah, you all heard the question. Our impression is that the microelectrodes that we use, if we use them carefully and introduce them carefully, make no difference to the cells that we're studying.  But aside from unlucky events like that, there's no reason to think that the microelectrode is changing things at all. It needn't have been that way. Before one did the experiments, one could certainly have worried about the disturbing the system by the introduction of this wire. But the wires are very slender. And so it's not our impression that it really changes anything. Another question is regarding the animals. Are they under a local anesthesia or general? And the point of the question appears to be, do the cats need to actively look at the screen or are you measuring a more passive response? That's, it's a marvelous thing to ask. In the experiments that we do, the animal is under a general anesthetic. And you might ask, does that not disturb the system even more than the microelectrode might? It turns out that general anesthetics may exert their main influence on the brain stem, not on this part of the cortex. Whatever, however that turns out to be, it doesn't look as if the anesthetic has a major qualitative responses that we see. There's no doubt that the deeper the anesthetic, the more sluggish the cells are in their responses. But the specificity tends to be maintained. That is, you can easily determine the orientation selectivity, even though the peak response may not be as perky and vigorous as it would be in a fully awake animal. The animals that we use are definitely surgically anesthetized, so they're not feeling anything. One could, in principle, do the same kinds of experiments under local anesthetics, although it would be a rather grim thing to do to an animal, and we don't do that. You can, however, implant the electrode surgically, let the animal recover. And I started this business in the middle 50s by recording from awake alert kittens. And one of my big troubles was artifact that looked like sine wave generator at about 20 per second or something like that, and it turned out that it was an artifact coming from the animal's purring. So there was no doubt that the animal was reasonably content in my mind if I had to worry about purring. You can do these experiments, in any case, in alert awake animals, and what you find when you do that is not very different from what you find in our experiments and fully anesthetized animals. That the comparison has been made and the differences aren't very large. Maybe it's that people haven't looked at the right things. And for all we know, if with the animal, with its eyes closed, if it imagined a line in a certain orientation, maybe the cells that we're recording from would fire under circumstances like that. We don't, at the moment, have any way of telling, but in principle, you could do this experiment by training the animal in some way as it were, think of one form or another, to see if these back connections from subsequent regions to the region that you're studying, if those connections are doing anything, and it would be fascinating to know. But the short answer is that we do, our animals are fully anesthetized. One more question. Would you hazard a personal opinion of whether the activity of visual areas, one, two, or even further into the occipital cortex are linked to conscious experience, or are these processed still part of early unconscious processing of visual input? And I guess in hazarding your personal opinion, you might ask, how would you assess that, particularly where you're studying animals? Yeah, it's certainly a question that is not without difficulties. The animals that we study are clearly not conscious. So you can have this cells without having consciousness. But what role they play in consciousness is I find a very hard question because I think it's so difficult to know exactly what one means by the word conscious. We have a rough idea, just as we have a rough idea of what we say the word mind. These are legitimate words, but when you subject them to the cruel and unusual punishment of scientific discourse, then you have to really know what you're meaning in a sharply defined way. And that becomes very difficult indeed. And but what we would like to know is what I alluded to before and it's certainly related to the question. And that is if an animal were paying attention to a stimulus or not, would that make a difference, for instance, in the firing of the cell? This is something that many people are very interested in. And in visual area one, the area that we work in, it doesn't seem that it makes a terrific difference unless I've missed some recent papers in which it did. But one doesn't really have the feeling that these areas are necessarily involved in attention in any case. But that's very dangerous to say that. Maybe the question hasn't been posed in the right way. I'm not sure, I quite agree with that, David. First of all, I think Bob Wurtz's experiments were on V1 in which he asked an animal, he mapped the receptor field when the animal attended to the stimulus and when it didn't attend to the stimulus. And there was a brisk response when the animal attended to the stimulus that when it didn't attend. And I think Desimonus confirmed those kinds of results. But I think the more interesting issue is to what degree V1 might participate in conscious awareness of a particular visual object. And I think there's one interesting clinical entity which does bear upon that. It's the patients who have blind sight in which they are clinically defined as being blind. And if you ask them, can you see this picture? They will say, absolutely not. And you say, well, guess, is that a picture or an orange? And more than chance, they will say that that's a picture. It's not an orange. And if you show them an orange, they say, I cannot see that orange and I certainly can't see the orange color. But if you ask them to guess between alternatives, they will more likely than chance, guess it correctly. So here are people who are completely unaware of the fact that they're perceiving anything and yet they have some subliminal unconscious perception, if you will. And I thought that one way of thinking, and a number of, perhaps Dr. Saxon, Tony could comment on this, but a number of those patients do have V1 damage and that the thought is that perhaps information goes from the colliculus or the lateral geniculate directly to V2 and subsequent areas so they can have some minimal perception. But because V1 is not involved, they may not have conscious participation in that perception. I wonder what the other people would sort of comment on that. Maybe Tony has something to add to that because you had these wonderful experiments where galvanic skin resistance responses were produced by visual stimuli that the parent, the patients weren't aware of, so. Yeah, probably an even better example than blind sight is what happens in the what we call covert recognition of faces. So if you have a situation in which you have people who are no longer able to recognize faces consciously, so they have a condition called face agnosia. So they look at their own faces in the mirror, they look at the face of a friend or relative and they don't know who they are anymore, although they can look at the face and perceive the face and describe it. Well, it turns out that those individuals can, in fact, when they are placed in a situation in which you record from their skin, you record for skin conductance in a polygraph apparatus, they give responses that are very indicative of correct recognition of those faces that are truly familiar from those that are not. This is an even more powerful example than the blind sight and is very replicable. The situation is there all the time. In both cases, I think that what is happening is not consciousness and recognition in the full sense of the term and of course those terms are treacherous, as David pointed out, but what is happening is that there is, for instance, in the situation of blind sight is really guesswork. Given a constraint relative to a stimulus, the person has enough information to be biased in choosing one versus another in a forced choice paradigm. So the person doesn't really know about that stimulus. The person knows a little bit that is relative to the stimulus and then is placed in the situation of making a choice that is biased. It is quite possible on your other comment about pathways that, for instance, blind sight, at least in the detection of light or in the detection of light in a quadrant that pathways that would bypass V1 would project directly, for instance, especially to parietal cortex and to the visual areas that are on the border of occipital and parietal cortex and would help you make that response. At this point, we're going to close.  We wish you all a good lunch. I'm the next sacrificial lamb. Very good. Exactly what we were hoping for. It was wonderful. It's just right.  I'm going to make a living, Dave.


Now moving on basic transformations. Is it clear what happens when you replace X with X minus H? What happens when you replace X with X plus H? Everything is clear Just to quickly recap in any function if you replace your X with X plus H where H is some positive quantity The graph is going to shift H units to the left right Let me just take this example Let me take this function Y. Okay So let's say Y is equal to I'll take another function Fx is equal to I take a Same function Same type of function X square Minus 5x Let's say plus 4 Yeah, this is my function Okay, all of you can see the function now Now in this function, I am going to replace. I am going to plot another function by replacing my X in the function of H with X plus 2. Do you see the red graph? What has happened? It has got shifted two units to the left correct Yes, in the same way if I replace my X with X minus 2 You would realize that the graph will now shift two units to the right direction correct In a similar way if you replace your Y with If you replace your Y with Y plus K Your graph is going to move up by K units if K is positive Okay, and if you replace your Y with Y minus K the graph is going to go down by K units Yes, I know Let me show you that in the same function. I'm not going to plot Yeah, so Y is equal to X square minus 5x Plus 4.  Y plus 2 means the graph is going to go Down.  Is that fine? So now we are going to continue with The session that we have over here So this concept is Understood by all of you that when do we get a positive answer and if you follow upper minus lower and Integrate from a lower value of X to a higher value of X You will always get a positive answer. Is that clear? Now there are some area that you can actually calculate by considering Horizontal strips in the previous case I talked about vertical strips now There are some area which you can find only by taking Horizontal strips, let's say I want to find the area given by this figure Okay, and let me tell you these are two curves X equal to f of y and X equal to g of y another important thing here is that we need to write the equation of the curves as X equal to f of y and X equal to g of y in this case Unlike the previous case our equation was written as Y equal to f of x and y equal to g of x right so here you have to make X the subject of the formula I'll tell you why it is required So let us say you are integrating the area or you are finding the area Sandwiched between these two function Okay, between y equal to a till y equal to b So what you're going to do next is you are going to take at a distance of y a thin horizontal strip like this So you are going to take this trip. Yes or no? thickness is dy correct Now if I ask you What is the height of the strip? Height of the strip will be dy no doubt about it correct What is the? Width of the strip what is this distance? You would say it is nothing, but the difference of the X coordinates at these two points, so it is nothing but X2 minus X1 correct and If you look deeply what is X2 X2 is nothing but f y So X2 is nothing but f y X1 is nothing but G y yes or no So the difference in this is going to give you the width of the strip and which if you multiply with the height is Going to give you the differential area da right and now I'm going to integrate this from Y equal to a till y equal to b and Remember if you want your answer to be a positive one if you want this answer to come out to be a positive one Ensure that this is positive and This is positive Now can somebody tell me how do you ensure that? Fy minus g y is positive Any guesses, how do you ensure f y minus g y is positive? Fy should always be the curve. We should write on the right or left Right right exactly. It should write on the right and G y should be the curve. We should lie on the left because right minus left means you are Doing a higher value of X minus a lower value of X remember as we go right on the X axis We start getting positive values or increasing values of X and as we go to the left of the X axis We get decreasing value of X So right minus left will always be positive so if you do right minus left and integrate from a Lower value to a higher value You will always get a positive answer you would never need a modern all Is that clear? So guys in order to know whether my curve is on the right or left we again have to be very very good with our Graphs if graphs is not good. This chapter is not meant for you correct So graph and the transformations which I have discussed so far are the biggest prerequisite along with some understanding of functions In order to excel in this chapter Are you getting this point? now The first question that arises in our mind is When we are solving the graph when you're solving the question of area under curves What is the first thing that we should do? So let me point out the first thing first always plot the graph as Accurately as possible Plot the graph as accurately as possible This is the first step that you should do okay second step is Second step is decide whether you have to choose Vertical steps integrate or horizontal steps to integrate or you could use both This is the biggest call which you should take whether I can integrate the area by just using vertical steps Or just using horizontal steps or would I need both? That means How would my integration process be less if I break the area into strips Let me give you a very simple case to understand point number two Let us say I have a circle Okay, let's say the circle is y is equal to f of x equation and I have a parabola the parabola is Let's say y is equal to Y is equal to G of x okay, and I want to find out this area I want to find out this area Okay Now what kind of steps would be suitable to find out this area any guesses? Horizontal horizontal would be the most suitable one why for very simple reason is Your if you make a horizontal strip like this Let me choose some other color if you take a horizontal strip like this You are only going to use the curve on the right Which is going to be your now here the equation is not given to you in the form of x equal to F of y so first you need to convert this as x in x equal to some let's say h of y and This also you have to convert x equal to some k of y So this area could be easily found out if you could know the y coordinate of this point. Let's say a So you can integrate it or you can find the area easily by doing The x on the rightmost function, which is your h of y Minus k of y that is your curve on the left of the function left of the strip That means where does this lie and this lie so this lies on this and this lies on this Correct, so the difference of the x coordinate from 0 to a this would simply give you the answer in straight away one shot However, if somebody wants to solve the same question by taking vertical strips Let me tell you what challenges the person will face Let's say first of all he has to find this point, which is a this point, which is B okay and He would require to choose Two definitions of the strip one like this and Another one like this Correct You would need two definitions of the strips one is this fellow and another is this fellow Yes, I know So can you tell me what expression should he write? Assuming that the circle is y is equal to f of x and the parabola is y is equal to g of x He would write something like this Integral from 0 to a Now where is the tip? Where is the upper end of the strip? g of x Correct, where is the lower end of the strip at y equal to 0 plus Integral from a to b now, where is the upper end of the strip on the circle? Yes or no Circle is f of x minus 0 So unnecessarily you will have to take two integrals to solve this problem Whereas in this case you could have solved this question in just one integral correct So guys you have to be very very judicious in taking a call Whether you need a vertical strip or a horizontal strip or a combination of both in order to get your area Are you getting this point and those two and finally the last step is You would have to be very very careful in integration right Though the integrations involved will not be of very high level Because we are dealing with some standard functions like circle ellipse parabola hyperbola No, we'll be dealing with straight lines. We'll be dealing with modulus function We'll be dealing with gif So you have to be very very careful in performing the integration If these three steps are taken care of then you'll find this chapter super easy Okay


Personal notice, dangerous by stock and trade. If the job's too tough for you to handle, you got a job for me, George Valentine. Write full details. Why the frown, pal? Worried about that lawnmower you lent the guy next door two years ago? Not just because he lost his memory when he went ten rounds with Lewis is no reason to get yourself in a snit. My advice to you is let George do it. You know George Valentine. Take your problems to him. Everybody else does. You'll find him in the phone book. That's where Abner found him. Only Brooksie got him first. Brooksie fronts for George. And even over the phone, you'd know she's perfect for the job. But not our Abner. All he could do was confuse the issue. Hello? I would, but I can't, you see. It's a great ad. I've seen it lots of times. Oh, a great ad, I said to myself. There's a kind of a guy that when a guy's in a pinch can... Just a minute, Mr. Valentine. Hello? Hello? I haven't got much time. Yeah, I'm right here. I got it. No time to write, but who are you? What's your problem? Now, this is a real pleasure, sir. If you'll permit me, my name is Abner. And I'm in jail. You what? Only don't get me wrong. The reason I can't write is because I can't write.  Wait a minute, wait a minute. You said you were... That's right. I'm in jail. And let me tell you a more unjust thing has never happened to me. There ain't no justice. Mr. Abner, slow down a little. I'm trying to write. It's important, that's all. And there wouldn't be time to write either, I guess, for that matter. But the main thing is it's important. That's what I've got to make you understand, see? You get me? Oh, sure, you make it so easy. Yeah, well, I'm kind of excited. Because you see, the jail burned down. What? Oh, oh, yeah. And you burned down with it. Now, hold on. I mean the jail over in Melody. That's where I'm calling from. Melody? Over in the valley? Yes, sir, that's the one. And a beautiful little town it is for tarantulas. That old jail, let me tell you, was the biggest I saw it. Hold it, hold it, would you? Now say something sensible or hang up. But I am. I mean, just because I can't write.  They moved us out, that's all. Now we're locked up in the sheriff's office. That's how I could get to the phone. Ah, clear as a bell. Listen to me. I got out of the fire, understand? Only one of the guys in the big cell, he didn't. He's dead. And if I tell what I know about it, I'll be dead too. What? It's a rough deal. Get over here, will you? If you don't help me, if they make me tell what I know, they'll burn me. I wonder if this Abner's telling the truth. Could be he's taking George on a wild goose chase. Well, all I know is my friend here won't lead you astray because what he has to say is straight into the point. Lead on, McDuff. You made every word live, son. Now let's see if George and Bruxy can do as much for Abner. Well, that's them pulling up in front of the sheriff's office. Well, that's the sheriff's office, George. Yeah. Sure needs a coat of paint, all right. But I guess this is the place that don't be guy on the telephone... Hey, that's you, Valentine. Yeah. Only where in the name... The alley, George. Here. Right here. Hurry up. Don't let anybody see you. Okay.  But I thought you said you were locked up. That's right, lady. Transferred all of us here when the jail burned down. Only now I'm... I'm not, see? Well, how did you get out? They turned us loose. I just dropped into town for a little game. A slight flutter of the pasteboards and wham.  But the way they treat you in this town, you'd think you'd murdered a whole city block. We got in the way and they turned us loose. I don't blame them. Kicked me out and told me to get out of town without even giving me a free meal. Can you imagine? There ain't no justice. Oh, now listen, Buster. I drove four hours just so I could try to make sense out of what you said on the phone. Sure, sure, sure. So let me tell you just what... Oh, no, you don't. I'll tell you. We stopped at the scene of the fire on our way in. You weren't lying. There was a fire. Well, that's what I... Furthermore, a man, a prisoner who was hauled in last night, another big gentleman like yourself, didn't get out. He died in that fire. It's plain to see you got the facts. But I don't know his name. Nobody knows his name. Sure, sure. But it was a plain simple death so far as anybody knows. So, Abner, whatever you know had better before... He was dead before the fire. What?  Conditions are terrible here, I tell you.  How do you know? Because when the fire started, I tried to rescue him. That's why... Because I put my hands on him and shook him and practically got frozen for my trouble. Body cold as ice, I tell you. All right. All right. We get the idea. Why didn't you tell the police? Because they're mixed up in it. That's why. In some way. I tell you in this town, they got a chief of police. Oh, no. Wait a minute. Abner and his crew are crooked as a cactus. For instance, you know what? He beats me, hauls me into his office and beats me. You don't believe me. Ask Hank. Hank, come over here. Hank? He was there. He knows. Hello, everybody. Hank, huh? I beg your pardon. Whiskers do not measure a man. Know the patches in his pants. How do you do? Pleasure, young lady. Pleasure, indeed. Now listen, Mr. Valentine. Hank here was visiting my humble abode. Humble abode? A small place. Not too elegant. As for that big guy, the guy who died, we did entertain him. Hank and I invited him to share our diggings a couple of days ago. Don't exaggerate, Abner. Your room is a dump. And you didn't even know the guy's name.  What do you know about his death, Hank?  It's no skin off my neck. I don't like people who won't talk. I doubt if even he said three words to the cop who threw him in. You mean when he was arrested?  Guess they do it every Saturday night in this town. That's the cross we have to bear. And I may say a draft deal jail sale. Now listen, that guy didn't die of no cold. He didn't look any too well. I wouldn't be surprised if the fright and the excitement of the fire. It was a treatment, he got, I'm telling you. The rough way that they had. What rough treatment? What kind of stuff are you guys trying to pull? Beature. That's what they do.  Say, change your clothes and into the tank you go. No chance to argue or nothing.  Oh, get off the soapbox, Abner. Live and let live. Take it easy. There's no excitement. Okay, Abner, okay. Where do I find this chief of police? Oh, no. Oh, no, you don't. I'm not going to come within five miles of that. I wouldn't ask you to. Hey, you, Hank, come on, lead the way. How did I get dragged into this? Quit kicking, friend. I could ask the same question myself. So they say he died somehow before the fire. Is that right? Yes, chief. They said... Now, wait just a minute how you use that word they. It's Abner who said... Oh, get out of here. Go on, beat it. Look out, chief. Don't hit me. What? What did you say? Well, I haven't done anything. And when you talk like that, Abner will say... Go on, Hank. Go on. We don't need you. Well, sure, if you say so. I didn't mean any harm.  There's a wreck of a man. Big words, little work. What are you looking at me like that for? I suppose you expect me to hit people too. All right, now just take it easy, chief, will you? I know what kind of a guy Abner is. But I also saw that jail had burned. And it wasn't exactly a model one for as big a town as this. Sure, sure, my fault. Blame it on the chief. Wouldn't have anything to do with how much money the town gives me to run this force, would it? Skip it, would you? There was no connection between the fire and that other bomb's death. Unless somebody set the fire in order to get rid of some evidence, like a blow or a bullet, just in case that death wasn't natural, I mean. Oh, well, George, that doesn't make any sense. All that trouble just to get rid of some unknown man nobody cared about? Now look, both of you, I want to... Get out of here, Sergeant. I thought you ought to see that dead guy's clothes. You know what? Well, here, for the wing of the jail it wasn't burned. Where they changed. You mean what he was wearing when he was thrown in? Let me see that. I'll do that, Mr. 11 cents change, yeah? Big man. Typical vagrant, I tell ya. He was just... Oh, here, Chief, piece of paper. So many on a Saturday night. We don't really have time to go over them. Let me see that. Mr. Walter F. Smith. Who? Yeah, Mr. Esau, Chief. That's his name, apparently. I suggest you stick pretty closely to plenty of milk. Leave out too much starch. Be careful of pepper or any seasoning. What? What's that? That's all. Some doctor's name came to the city. Yeah, diet list, Chief. So he was just a nobody, huh? Oh, no. Well, what's the matter? I should think that would help... Chief just realizes he might be in a worse spot than ever, right, McNabb? Very smart, Valentine. You catch on real quick. Negligence, Angel. If there was anything wrong with this guy, then the police should have found out about it. Maybe he needed help instead of a cell.  I got work to do. No, wait a minute, sir. There's something else. Look, Sergeant, you've caused enough trouble yourself for one day. I'm sorry, Chief, but over at the morgue, there's a woman. She says she's Mrs. Walter F. Smith. His wife? Well, I guess, or used to be. Anyway, she's been looking for him several months, read about this in the newspaper, just flew into town on a hunch to look at the body. Flew in? The wife of a typical nobody?   Of course there's nothing I can tell you. What could I tell you?  I'm going back to my hotel. Look, I know how you feel, Mrs. Smith. I don't know whether he was ill or not. I don't know anything about him lately. But the chief of police asked me, I'm sorry, I've been through enough seeing Walter there like that. Mrs. Smith, if you don't... My taxi's waiting. I'm sorry. Which hotel? Let her go. Leave her alone. Sure, where's a mink coat? The wife of a bum. Well, we ask her to stay until you die. I wanted to see what the teletype check said on his name, that's all. Well... Walter F. Smith is wanted by the law. What? Embezzlement. Wow. All right, what are you so sour about? If his death was the police's fault anyway, it's better for you than if he was a respectable citizen. Hold still, I'll give you the facts. Have fun with him. In addition to Smith, his loot of $200,000 is also wanted.  There you go, having fun already. Take it easy, Chief. At least you're off the hook. So now everybody else is up to something. That's all. As Abner puts it, there ain't no justice.  And he's right. Where's the body he always stumbles on along about now? This could ruin his reputation. You know, I'd ask my friend here to drop dead, except I know he has something pretty good to tell you. Now let's get back and see if George's temper has improved. Not that I blame him. Abner would make anybody see red. If you remember, Abner is the old coot that accused Chief of Police McNabb of barbecuing a fellow prisoner by burning down the pokey. As an added touch, Abner swears the victim was dead before he got the hot foot. Then to make matters more complicated, the Chief discovers the body belonged to a Walter Smith who was wanted for taking 200 grand that didn't belong to him. Complicated? You bet. But George hasn't figured. He says it's murder. Even so, I think I better lend our boy a hand as he starts asking questions around town. I have a landlady, George. Walter Smith came to town a couple of days ago. You must have noticed something about him or you must have had some baggage that you... I'm a working woman, Mac. I don't have time to sit around and gab with a guest. I just thought he was a drifter like the rest of them. That's all. And he had no baggage. I can tell you that in one word. No baggage. Two words. But you notice baggage, huh? Keep your eye out for that sort of thing? I gotta protect it, you know. Don't want nothing stolen from the guest. Uh-huh. Nothing in his bureau? Oh, spare shirt maybe. How should I know? I'm telling you like I told McNabb. Smith was here, but I didn't notice him until he wasn't here last night. And somebody said he was in jail. Who said? Guy named Abner. Seemed all upset. Oh, yeah. They're rounding up Abner again. Ain't that interesting.  Here's your newspaper. Huh? Yeah, it's today's newspaper. Rome hasn't been occupied since yesterday. And I don't know who else would read the fashion page around here. Thanks. Now you've been going through this, Rome. What did you find? Nothing. Gee, 200,000 bucks they say he's got someplace. But I'm telling you, not a thing. Not any baggage, not nothing. Expect me to believe that? George. Yeah, in here, Bruxy. George, I can't find you. Oh, if you're looking for me, dairy. Mrs. Smith, his wife. I tried every hotel in town. That taxi driver who drove her away from the morgue? No, the police had already located the driver. He says he dropped her off downtown here in the business section. What are you two talking about? You know something I don't? I doubt it. Come on, Angel. I've learned all I need to. So it wasn't the fault of the big, bad police, Valentine. I just talked long distance to that doctor in Kansas City, the one whose name was on the diet chart. What did you find out, Chief? There was nothing really wrong with Smith's health. He was one of them hypochondriacs. You know, warriors, pill takers. Doc finally booted him out. All right, all right. So the police are pure. Did you locate that abner for me? I haven't done anything for you. But I'll take you down to a garage if you want. A garage? Smith's wife. She went down to this garage and rented a car. Only now the car's back and she's disappeared. I don't know where she went when she took the car. But didn't you see Mrs. Smith when she came back to your garage? She was gone about an hour, I guess. Anyways, I didn't notice the car. It'll just a few minutes go parked here in the alley. Yeah, it's been someplace with a lot of dust. And I got the sergeant around combing the town for her. She's back. She's got to be around someplace. You sure about that? Why not? Well, I didn't have much luck. And I must have been looking after she came back. 22 miles. What? Well, you set the speedometer back to zero when you hire a car out, don't you? Well, that's right. So wherever she went, it was 11 miles out and 11 miles back. With all that dust, too.  What's ticking in your head? Most of the roads around here are paved. There's only a couple. This is Grape Country, irrigated most of it. So how did that sagebrush get there? Come on, hop in my car. I'll show you. This is the third and last road. Ten and a half miles. Yeah, plenty of sagebrush on this one. Yeah, a whole double A place. Sold out and cut the water off. Wait a minute. What's that building over there? Abandoned winery, only the mileage. Wait a minute, hold it. Stop tracks, right there. See him turning off? Yeah. Only there's two cars. Yeah, there's one right there. What? An old pickup truck, see? Beyond the building. Hey, hey you! It's Abner and Hank, George. Hey! Look out, Steve! Abner! Wait for me, Abner. I didn't do anything. Stop! Both of you! Get away from that truck! Wait, Abner! We haven't done anything, my boy! Stop or I'll shoot! Hey, slow down, Hank. I'm not doing anything. Okay, Hank. Your friend left you. That's all. Oh, cut it out, McNab. He got away. Let him go. But if I don't get after him right now... Abner was just looking for you, Mr. Valentine. We just got here.  Skip it. Radio the Highway Patrol, McNab. They'll get him. And take Miss Brooks into town for me. What? Who do you think is chief of police in this town? I've told her what I want. Help me, Ab. It hurts my foot a little. Okay, okay. I'll take care of Hank here. I want to get your car away from here, McNab. Quick! All right, cool off, Hank. We'll just wait in the shade if we can find anything. How long are we going to wait, Mr. Valentine? Oh, relax. Relax, Hank. The sun'll set in a couple of hours. A couple of hours? Then it'll be just as bad. It gets real cold out here in the evening. It goes through your bones. I don't know how I got into this great deal. Yeah, sure I know.  Abner got me into this because he already had a little idea who Smith really was. Does that check? I guess so, Mr. Valentine. I don't know. Sure, sure. You were all in jail together. Abner thought maybe I could help point him toward the monies, all right? I guess he thought that because Mrs. Smith came out here. Well, then the money was out here, too. Yeah, yeah. It might be. You really think so? Well, in that case, while everybody's gone, maybe you and I... Oh, no, no, it's too hot. Now we'd never fight it, Hank. Let the police worry. Abner doesn't trust McNam.  I know it. But he'll be back looking for the money. Look, Mr. Valentine, was this guy Smith murdered? I don't know. Holy smoke. Maybe he killed himself. Well, it could have happened. Only it doesn't tie with anything very well. Come on, we're losing our shade. Let's move. Maybe Smith was just not in too good health and kicked off. A man has to take care of himself. Yeah, you're right. Here's a good place. The winery? There. Oh, to be cool inside here, don't you think? Okay. Boy, it's dark. What's in the neighbor? Dave, what happened? Did you fall? I'm all right. Look. I crit. Mrs. Smith. The body of Mrs. Smith. Thank goodness, a last of body. Too bad it had to be Mrs. Smith. But you know the old saying, here today in ghoul tomorrow. Anyway, while George is getting to the bottom of this, I want my friend here to dish a little off the top. You know there's an ironic twist to this story. It all takes place in a town called Melody. As far as I can see, it's been one discord after another. And this fellow Hank isn't helping matters with his off-key baritone. Look, I don't like it around here, and it's cold even in here.  Quiet. Well, you don't make so much noise. But she's been dead a long time.  Yeah, I can see for myself. Somebody else drove the car back.  Yeah, you're right. All we know about her is that her husband left her. He was hiding out, posing as a bum. So she came after him to get the money. Do you mean to say the money was here? I mean, I've caught on to this case. That's all. Mrs. Smith didn't know where her husband was. How could she know where the money was if he was dead before she got to town? Oh, for the love of me. Okay, okay. I'll stop talking, Reynolds. You hear that? Yeah. We'll get company. Get back in here. He can't see. McNabb. Valentine? Yeah, right here, Chief. Holy smoke, Chief. We thought you might be somebody else. Where's Miss Brooks? Out in the car. We haven't located Abnery yet. Did you two find what I told Brooksie about? Yeah, pills, medicines, a small drugstore. Okay, where was it? First place he suggested. But I doubt if it'll do much good as evidence. I know it, but I got a better idea. Go on back to the car. Okay, sure. See, what's the idea? What's your funny? Well, you might not see the jail can't. Sit down. We're going to wait some more. For days if we have to. Wait. What more? A confession. What? Yeah, a man named Smith was a fugitive from the law and from his wife, too. Had money and plenty of trouble. And worst of all, he was sure he was sick. So the money couldn't give him much fun, could it? And result? And he got an idea. Why not die? Look, I'm cold. And I'm dying of rigidity. He did. He did. He did just that. He died of murder. And afterwards set fire to the jail he was in so his body couldn't be examined too closely. He what? And it all worked beautifully until his wife showed up.  But afterwards must have spotted Smith himself and so he brought her out here and he killed her. Probably told her the money was here when really I suppose it stashed away in Kansas City and I'll say you don't know anything.  I found Smith's room had no baggage. That's where the pill taker's private drugstore should have been.  They were with your stuff. Walter F. Smith. That's where McNabb found it. Oh, is that so?  A man you knew hardly ever opened his mouth. No one knew anything up bottom. He never been missed. I knocked him over the head, I suppose, when all the rest of the men were asleep. I don't know what you're talking about, Mr. Valin. And then you put that diet chart in his clothes. Oh, not a bad stunt. Make the police think they might have done a pretty terrible thing. Make them want to cover it up and keep it quiet. I won't admit any of it. There's nothing you could do.  Oh, you're cold? Oh, well, come on, let's have a brandy. You know, I remember the items on that diet list. Milk, no pepper, just bland stuff. So the guy it was written for must have been worried about his stomach. Come on, Hank, have a brandy. Little sharp, maybe kind of strong for some stomachs, maybe, but for you it'll... Hey, don't watch it. Too bad you didn't have the sense to stay away from here. Just curious, I guess, now. Look, Mr. Smith, if all I've said isn't true, well, go ahead, have a drink. There's nothing wrong with you. The diet chart wasn't yours. And after you're really hungry, we'll go in for a nice spicy Mexican dinner, maybe. There'll be no excuse for you not to eat it, will there be? After all, you're okay. You can eat anything. Go on, have a drink. All right, come on, Mr. Smith. Mr. Brooks will take it down in shorthand. And then we're going back to town and find Abner, and see how he can take some gentle persuasion. Abner, I want you to get out of melody and keep going. And right now... Hey, look out!  Oh, I've never hit you. Nobody on my force has ever... Hey, Abner, listen, will you? The Chief here is all right. With a little publicity on this case, maybe the town will wake up and give him the money his department needs. But, uh, Abner, I am not a cop. I'd be glad to hit you. No, no, you wouldn't. That's what you think. I don't like being played for a sucker, so start moving. No, look, I mean, I know I did a lot of lying to get you into the case. I figured we could make some dough together. There it goes. No, no, no! Thanks, friend, thanks. That guy sure was a headache. Don't mention it. Okay, Brooksy, let's go. All right, George. So long, McNam. So long. Well, where you been, Angel? Seems to me you kind of dropped out of things. Missed me? Hmm. Oh, well, I was busy with the case. Never mind. As Abner used to say, there ain't no justice. Say, did you ever see a dream walking? Maybe not, but you just saw a bell burning, Brooksy. And if she'd be good enough to hold that torch she's carrying a little closer, I'll be able to read that Robert Bailey plays George Valentine with Virginia Greg as Brooksy. Don Clark directed the script by David Victor and Jackson Gillis, and Eddie Dunsteader's music kept things blazing. I'd like you to make a mental note right now to save a half hour for us next time when you will hear what happens when you let George do it.