Hamming, "Foundations of the Digital (Discrete) Revolution" (March 30, 1995)

Hamming, "Foundations of the Digital (Discrete) Revolution" (March 30, 1995) - https://www.youtube.com/watch?v=x2i5w9onAsY

This lecture is on the. Yeah, I turned to lecture two, hadn't I? It's on the foundations of the digital discrete revolution. We're approaching the end, or perhaps not quite the end of the conversion from analog to digital. Analog signals are what you are used to, although if I'm careful, the world is made out of molecules, so signals do come in discrete amounts. Still, we tend to think of time, your weight, density and so on as being a continuous variable. Particularly, the telephone company took the pressure on the microphone and translated electrical current, regarded as a continuously varying signal, and sent the signal at the other end, moved the diaphragm and you heard the voice. We're moving to digital where we sample high frequency very frequently at a high rate, equal space, and we convert it to digits. Now, the digits involves round off. I will not discuss round off in this course, but it's an important topic. It causes trouble in computing all the time. But I will talk about this effective sampling a good deal. Now, why are we doing this? Well, consider when the telephone company, when I arrived, they sent the voice analog across the continent. The gain was something like 10 to the 120. You say, my God, how can that be? Well, we do the back of envelope calculation. There were amplifiers about every 50 miles and the amplifiers had a gain of about 100 and across the continent, 3,000 miles. You see how one gets 10 to 120. That means that in the analog system, every bit of noise that got in early, whether it came through the wire or in the amplifier, was amplified to set on and on and on. Therefore the amplifiers had to be made very, very carefully and maintained very carefully. Well, digitally we do something else. We send the signal. We don't amplify it, we detect it and gate a new signal. We repeat repeaters, copy the original signal not with the noise, but strips it out and gives you back a nice clear pulse. So therefore we can send a pulse across the continent with almost no distortion. Furthermore, we'll take up error correcting codes which are widely used. So in case small errors do creep in, we know how to remove them if there are not too many. So the digital one is working out very well. It requires much simpler equipment, gets much higher accuracy. Now, I have to be careful and warn you that we are moving partly back to analog. We were, as you probably think, most of the time, signaling with pulses. We are actually now going to things called solitons, which are mysterious things. I don't want to get into it theory, but they are nice features and we are beginning to Analog, amplify them four or five stages. Then we build a repeater. So we do a sequence of analog amplifiers, then followed by a nice reshaping of a repeater. And again we get high accuracy and great reliability. That is what this revolution is about. And you've probably seen somewhere near the end of it, because more and more of the experiments you do, you get the stuff as numbers as soon as you can. And you go ahead there and at the last minute you may translate the numbers back to graphs. Well, why has it happened? I've given you the first reason that digits work better than analog. The second one is the transistor and the integrated circuit particularly. You may not have thought about the trouble of building, say, the Eniac with 10,000 vacuum tubes. Each vacuum tube had quite a few terminals which had to be soldered into the socket. There were a bunch of resistors and capacitors and such things connected with every vacuum tube. There were hundreds of thousands of solder joints. Now, solder joints require cleaning and there's some acid involved. And they will, in time, if the acid is left there too much, etch away and produce intermittent failures. So solder joints were a real curse. But they seldom mentioned it. Just something we lived with. Well integrated circus removed it. Fundamentally, you don't have the problem. And I gave you in the notes there some figures on costs. I got an estimate from somebody else, said on a chip it cost you about a thousandth of a cent to connect one part with another. Between chips it costs you about $0.01. Between circuit boards it costs you about $0.10. And between mainframes it cost you maybe like a dollar. It takes the time to put a cord from one mainframe to another. And a dollar is not a bad estimated cost. These are approximations. Now, the third reason why we are going digitally is that we are going from an manufacturing society to an information society much more rapidly. Most people think if you exclude the military from government, take all other government employees, there are more of them than there are people making things in the factories. We now have more people managing than we have doing back in the time of the American revolution. More than 90% of people were farmers. They were out there doing things. Now we have very few farmers. We have moved, although it's Washington and other people are reluctant to admit it, we have moved from a society which was dominated by making things to manufacturing and manipulating information. And it's going to go on, I would guess, by the time the peak of your career, which I am taking as being year 2020, it's a very nice convenient number. Most of you will be in your peak of your career about that time, and 2020 suggests 2020 foresight. By that time, I think that probably less than 25% of people who are working will be making anything. Now, when you make a movie or when you make a TV program or something, you're really manipulating information. Yes, there is a film in material form. Yes, when I write a book, there is a book. But the true content of a book or a film or such things is the information it contains and not the form in which it exists. So in the broad sense, we have moved from one to the other. So consequently we are not dealing with material things as much. Now, these three things together, the shifting analog to digital, the integrated chip, and the fact our society has changed is what is really behind this digital revolution which you are living through now. There are other ones as well. If you define a robot to be something which handles the material world, not what a child thinks, a robot looking like a human being. Robots are doing an increasing amount of our manufacturing, very much more. Now, don't think of robots necessarily being run by a von Neumann machine. It may well be run by neural net. It may be using fuzzy logic. It may be various other things for control. You have to take a reasonable view of what a computer could be. It doesn't have to be a von Neumann type machine. It might be a highly parallel one. Now we're using them in manufacturing for three reasons. First, they produce a better product with tighter control. If you think about taking some pills with a strong drug in it, I think you'd rather have a machine making those pills than human beings. The machine can operate more reliable moment after moment. And human beings will slip up, they will get careless, they will get bored. Machines do a better job, they do it cheaper. But one more important thing, most of the time they do a different job. And I have to emphasize this to you because upon that feature depends your success in using computers. When we first started using computers in accounting, when we moved the hand methods to machines, we had to change the accounting method somewhat. Mrs. Smith, who did the accounting, always knew that such and such happened. Well, it doesn't work well with machines. So we had to change the accounting slightly. When we went to numerical analysis by machines, we did it differently. We did by hand. Now we went from hand fabrication. In my childhood, hand fabrication involved screws and bolts and nuts. Now you have rivets and welding. You don't make the same thing. You make an equivalent one that change that imaginative Change, which shifts it from one thing to another is what is central to successful applications of computers. It's an equivalent product. Now, it's not only material, it's also social. When you want to build another organization, a different structure, if you try and incorporate machines and keep exactly the same structure you have now, you'll have trouble. What you need to do is ask, what are the fundamental things I'm trying to accomplish? How do I accomplish it with machines? The attempt to do what humans always did, the way humans did it, has produced any number of disasters. In the attempts to mechanize things, you must imagine. You must use your imagination to get the kind of results you want. A big success by using machines, an equivalent product. Now, the effects of computers on science have been very, very large. Somewhere in the 50s, I made a talk to the vice president and president, Bell labs on machines. And I said nine out of 10 experiments are now being done in the lab. One in 10 are on the machines. But before I leave, it'll be 9 out of 10 on the machines and 1 in 10 in the labs. They all knew I was a crazy theoretician for the math department and they didn't believe me. As a result, when they put up another building, they put a lot of labs in, you know, soapstone benches, hydrogen, oxygen, water, distilled water, frequency, everything else laid on. Before they got the doors on some of those labs, we moved in programmers. They spent an enormous sum of money because I could not hear that we are moving from experiment to simulating experiments on computers. Well, by now you know that something more like 99% of experiments are done on computers and 1 in the lab. Now, the reason why I knew that is quite simple. I was at Los Alamos. I was stuck with computing atomic bomb designs. You can't do a field test or laboratory test other than with a critical mass. There's no small scale experiment possible. There wasn't much alternate to compute. But I realized from that the laboratory work will enable me to compute things you can't do in the lab. For example, in simulating traveling wave tubes, we study the effect of the amount of charge on the beam going down. Now, the charge, of course, makes the beam disperse. I could solve the problem with no space charge by simply taking out one term. They could not do that in the lab. But I could nail down, if they made the thing finer and finer and finer, what was the ultimate. I could get that point. They could not. Many times the simulation in the laboratory will do what you cannot do in the lab. It will also frequently get you more accurate answers, Particularly in a rapidly changing experiment. It is very hard to catch what's happening on the fly, but the computer's got the numbers right there. But now let me remind you of what happened when you got your education. You were told about medieval scholastics and how they read what happened according to Aristotle and said that was what was going to happen. And Galileo died, 1642 says, you know, you've got to look at the real world. Don't look at the books, look at reality. That is what's supposed to have made modern science possible. But what did I just say a few moments ago? We are doing the opposite. We are looking in the books, simulating and saying, that is what's going to happen. We are going back to medieval scholasticism. We will undoubtedly go too far more than a few times, and I advise you to consider that matter when you go on simulations. Are you going back to medieval scholastics? How far dare you go? It's a very serious problem because some people are going to go too far and fall back in the evils of believing whatever Aristotle said or whatever the books say. You won't find fundamentally new things that way. Very often, computers are affecting engineering too. Not only do we build more complex things, but more and more engineering jobs depend upon a computer somewhere running the thing. So you look at a handbook or you look at a catalog and you buy some chips off the shelf, you assemble them to do the job, and you write the program and you have the thing and you have your control now, not the way they were long ago by mechanical other devices, but rather your control is very directly by the computer. It enables you to do much more. And since I told you, engineering is coming closer to research, you have the problem that before you really know for sure a lot of the details, as, for example, atomic bomb. It was an engineering job, but we didn't have all the constants, and so we had to do further experiments to get constants. We had to design with some flexibility in it. Well, computers give you enormous flexibility. You can design and as the numbers become more known, you can get the appropriate formulas and write those programs instead. So the effects in society are also very large, and they're not always good. Managers tend to believe that if they only knew what was going on, they would know what to do. It's called micromanaging. And I think most of you have more or less had to endure a certain amount of micromanaging. The bosses tell you what about, for example, in the school here, department heads have Much less freedom than they did in my time. Their budgets are allocated in some detail by the deans and the provost. Well, the effect of this is bad. In the first place, the person who knows what's going on is often the person right on the ground doing the job. And the person at headquarters doesn't really know the details and really doesn't want to know the details, but makes decisions. Now, the evidence that this management is bad is first easily obtained by looking at the great Russian experiment of central management. It finally pretty much collapsed. You only look at our bureaucracy, which is now under serious attack, for the same reason that central planning is not so good. Local planning, however, has its faults. The local planner doesn't know what the whole company is trying to do, and so it's somewhat difficult. But of the two of them, it seems to me often top management micromanaging causes more trouble than local people doing things without knowing what corporate policy really is. But it's both ways go wrong. Now, the great evil of micromanagement is the following. Middle management never gets much chance to manage and make decisions because top management is always making them for you. So finally, when top management leaves, middle management finds themselves at top, never having made a bunch of decisions and learned to live with bad decisions. Top management by micromanagement is failing to bring forward people to replace them. That is the greatest evil of micromanagement. When you're at top, remember, leave the people at the bottom alone to make their mistakes and learn from those mistakes where it won't do so much harm. When they're at the top and they make mistakes, it can be very, very expensive. So that's one of the trends. Now, there's a trend against this. It came clear to me one day when a guy who had been in a brokerage firm called me up and asked me to have lunch with him and I made a date to have hamburgers with him. And he was forming his own brokerage company because he was tired of the big company where he'd been being told what to do. And he had found out there was a small company formed which would do bookkeeping for him and would also rent out legal talent so he could form his investment company and pay attention to investments. He did not have to spend time on record keeping. He did not have to worry about legal aspects. Those were taken for him so that he could concentrate on the main job and not make the mistakes of top management not knowing what's going on, because top management was disturbed by other things. I was quite impressed with the fact that that was the way they were doing things. And then I realized I had invested myself in a couple of biological companies. What we do is we can find a compound, we can develop it if we want, or we can hire out some other company loosely associated with us to do it at a later stage. We can either sell it or we can now make more detailed markets. We can carry it all the way through approval and final marketing and take the profit, or we can sell it to various stages along the way. In short, there are a whole bunch of companies, all of them small, all of them fairly specialized, who are working together to accomplish what normally is done by a big corporation. But it's avoiding the cost of top management and all the overhead and all the micromanagement they do. I don't know how far that's going to go, but I see that that is a defense and I believe that's what is happening. For example, my own experience when AT&T was broken up into a bunch of small companies, there was almost universal complaint of all the wickedness and evilness. There's going to be the government doing that. I said, well, you know, there's something to be said on the other side. And I waited for some years and I think you can say that there was good and bad. The breaking up of the central management so the separate companies could go their own ways has produced much more diversity and many more kinds of services than you would have had had it remained in control of AT&T. It's got its avenue and I think that may well be what will happen. But how you want to apply that your own business is something I don't want to get involved in. Now computers have also invaded the entertainment field. People spend more time watching television. They do eating and other things that are needed for life. Furthermore, many of the programs you see on television and the music is computer produced. I will talk about computer music one of these days as to how it's done. But a lot of those cartoons and so on are clearly nothing but computer produced things. Now, how far a computer will change society is a question which I would like to discuss with you, but I don't dare to. We live in a litigation society. I leave it to you individually, therefore, to think of how computers, microchips connect with a few servo mechanisms could operate in the areas of sex, family, sports, travel at home via virtual reality, in all the comforts of home, how much it will change the way we live. It's obvious it can do it. The difficulties are legal and other ones in many cases. Particularly when you come to the delicate subject of sex. There are great restraints on what can happen. But if you use your imagination at all, you can easily figure out for yourself what you think are possible futures. If you want to make a lot of money, I suggest there's a lot of money in that field. Now, computers began in the number crunching business. Atomic bomb. We were crunching numbers because those were the people who could pay the bill. As the price came down, we spread out into doing word processing and information retrieval and so on. When you only have 10 or 20 registers, you cannot do such big databases as we've got ability to do. So you find things like the airplane reservation system and so on, which would be almost impossible without modern computers. Now we've done other things. I will talk about them somewhat later. We can do analytic integration that you learned in the calcus. Cheaper, faster and more accurate than you can. Just that way. It's all it is. You stuck with it. We can do these kind of things with surprising success. Now in the military, it's easy to observe if you want. The Gulf War, the central role of information. Our failure to use information we had in our hands caused quite a few deaths. We had the information, we didn't use it fast enough. You saw there was basically tremendously a war of depriving the other person from information and you having it. Whether it's indicative of the future, I don't know. But it's a problem which I have again to leave to you. I can only suggest a sign. I once saw around here. The battlefield is no place for a human being. Not a bad rule. It's got all the things. Humans are slow. There are all kinds of things wrong. And furthermore, they can get hurt badly. And you have to do something about them. If you have robots aboard a ship and a robot gets hurt, you can kick them overboard. A human. You got to do something to take care of them. It's a very different situation. The machines have got great advantages, but they've got disadvantages. We take them up now. I want to talk about growth. I talked about it briefly last time. I want to do it again. The simplest model of growth is the rate of change is proportional to how much you've got. For example, bacteria growing or human beings unrestrained. They have a given rate of reproducing. Children are going to grow exponentially unless other factors come in. This is a very simple one and of course gives rise to the solution. You all know the exponential. Well, that goes out to infinity. And you don't believe Infinity. The current belief is the whole universe is finite. So you haven't got an infinite number of molecules. You haven't got anything like that. You're finite, so that can't be right. So the next model you pick is, well, I'm going to put a factor which is limiting as I get near the upper limit. This is going to bring the rate back down again. This is a reasonable model, which it starts exponentially grows, but then it's limited because of this factor. Now all I got to do is make some substitutions and I come down without the dimensions. The L and the K are removed. And I advise you always to do this. Get rid of the local constants and get the down equations free of those constants. It pays off. Now, this equation, all I got to do is separate variables, do partial fractions, and I'll come up with this solution. And you can see here, when X is very large, negative, this is very big. The quotient is zero. As I come in, as X gets, say to zero, I've got E. To zero is one one over one plus one over A. I have some value at the origin. As X gets large, this gets very small. This term drops out and I have one. So I have a curve come up like that. I'm saturating. And that's the typical growth curve. During the time I was running computers, I lived basically on that piece there. It was almost a straight line during all the years I was involved. But we're getting in trouble now. We'll discuss it more next time. But I'll simply say why you're in trouble. Given a single computer, you believe that the world is made out of molecules. They've got a given size. You believe, probably due to two theories of relativity. There's a maximum speed of signaling usefully from one place to another. And third, although they've talked about other things, you believe that heat is going to be generated, you've got to get rid of it. Those set limitations, what you can do on a single processor. And we're beginning quite definitely to see this here. That's why we're going to parallel computers. Well, instead of this model I picked here, I could pick one more general arbitrary A and arbitrary B positive quantities. And if I take the 1/2 and 1/2, I get a very interesting one which is finite in range. The curve starts out here, comes up and saturates. But it's got a finite range. You can play with various A's and B's. You can play also with not a hard upper Limit like L, but a logarithmic growth or something. And you can study growth. And you will find that these problems here have the following characteristic. This is a direction field. At every point I calculate the slope. But since T does not enter, the slopes along a given height are always the same. Give me the Z value and the slope is fixed. And due to the two limiting terms, they flatten out here towards zero and flatten out here towards zero. So you find the typical S curve where you look at the solution is moved across and back. But it's always the same solution. Just like the exponential is the same curve. Wherever you look, it's the same curve goes up like that, but it always looks locally exactly the same. So you can do those things and make studies as you want and find out quite a few things. Now, sometimes such a thing happens that a new invention comes along and you have another S curve on top of it. But an S curve of saturation is very common. And human population, for example, for a long, long while it was very small. We believe 100,000 humans on the earth for a long time gradually rose. We've had one. And we sort of believe that in the long haul the population can't go on the way it has. We'll be standing on each other's feet. There aren't that many molecules to make that many people, let alone running out of resources. So we see a future which is typically that you've seen it in many other places. Computers are certainly like this. I will talk about again. I said next lecture. I'll talk about the hardware, how long a start we had, how I lived on this and how for a single computer. But parallel computer is doing exactly that. It's producing another shift and there's no reason why you can't have two or three. But typically it requires a new technology to get there. Now, these simple models, while not great precise, give you a feeling for what has happened to you. And I was well aware that I was living here and I kept worrying in the early days how close was I to that saturation point. When was it going to be that I would not be able to continue increasing computing rate doubling every 18 months or so. Now I claim it is evident in electrical engineering, I said it before, I'll say it again, that it's going to be a matter of selecting chips to do the job you want, because there's going to be information almost all the time. GUN DIRECTOR the heart of it is the information you get from the radar and the information you put out to Aim the gun in all kinds of other things. It's information. Almost always, therefore, electrical engineering and much of other engineering is doing it. But when you do this, will you please, for heaven's sakes, think about field maintenance? The idea I'll make a design and then I'll graft on. Reliability later on does not work out well. You only think about your own home, the situation, how many devices you have at home. When they break, you say, throw it out, we'll get another one. Maintenance is too hard. If you got a little small transistor radio, would you ever try to have it repaired? New, well, more valuable things must be maintained. Putting maintenance as a last thing isn't very satisfactory. Although I do think, as I suggested a few moments ago with regard to robots, there comes a time when the robot is sufficiently busted due to accidents, you kick it overboard and forget it, start again. But maintenance of equipment will be vital. And I say again, you must begin to plan in the initial stages for field maintenance. It's very, very decisive. Now I want to go with another observation. Special purpose chips. Special purpose chips. You have one built, designed just for your job. It's enormously ego satisfying. I mean, you got a job so important, we got a special ship for it. Well, I advise you against it if you possibly can avoid it. Now you can't always, sometimes you do have to have a special chip. But a lot of times it is this ego satisfaction that controls it. Because if you have a general purpose ship as against a special purpose, for example, you designed a Pentium yourself. If you have a general purpose chip, other people will find the bugs for you. If you don't, other people will help write instruction manuals, other people will make upgrades. The manufacturer himself will come around and say, hey, we got a new model. It's got all these new features on it, it runs 10 times faster. You won't have to do much, you won't even have to have a big inventory. But if you have a special purpose chip, you make the production run. How many do you put in inventory? Furthermore, when a change in philosophy occurs, all those special purpose chips are dead and the inventory is dead too. And I'm telling you regularly, things are going to change more rapidly in the future than they did in the past. And they change awful rapidly. For me, they're going to change more rapidly for you. Things are not going to be stable. We're going to get to the point where we are on the edge of what people can stand. And I point out to you several well known things. Old People don't learn so well. And there's a very famous saying, children can run VCRs but old people can't. I don't know how your age is. I suspect most of you probably can run one, but probably some of you may already reach the point where your children run VCR and you don't know quite how well. We will get to a rate of change where the populace cannot stand more rapid change. You can't change everything every day. That's the role of habits. You get up in the morning. For example, I found I put my right sock on before my left sock normally. But when I put my shoes on, I put the left shoe on before the right shoe. I don't think I just put my shoes on. When I stopped to look what I did, I found I had habits. And that's how you get by. You get up in the morning and you by and large go through a large number of things with habits. You don't really think. You just do it. You take a shower. You don't think what you're going to do. You do the things you always do in that order. That's what saves you to be able to do something else. Humans have habits in order to avoid thinking. But if I'm going to change what you do every day, you aren't going to be able to do anything useful. You're going to be busy adjusting all the time. So the rate of change in society will be limited to a great extent by the ability of people to respond to the change. And that applies not only to material goods, it applies to the organization. If you try and change the organization of a corporation every six months, you'll tend to produce chaos. And if you make a change, you can't go back. That's one of the terrible things about many things. If you try this out, let's try it out. This new organization doesn't work. It isn't really possible to go back to the old one. That's why we do simulations. We say, well, if you do that, we think this is what you will see. If you do that, we think that's what you'll see. We don't know, but then we think so we try to anticipate what's going to happen. And one of the things you want to watch is that change is painful to human beings. Computers. I told you the other day, I just put a new program in. It's changed. But humans can't learn that. You have habits. That's what makes you possible. So don't Sneer at habits. They're essential, but also they have to be changed at times. Now, I want to say beware of special purpose chips. Beware of them. They are a dead end. You may have to have them. I'm not saying you don't, but by and large when you get a chip, you are down a dead end and you are there by yourself. And to give a simple example, when I was in charge of computers and ordering other ones, I did not want to get a machine which was a dead end of a line. I wanted a machine in the mainstream. In fact, I argued with manager one time of two different machines. I wanted one which had the most people using it, the one with the biggest sales. It might not be the best temporarily, but I've got a large number of people who know how to use it. I can learn from them. And quite a few times, several of the machines, early ones users learned how to get 10 times more out of the machines than the manufacturer ever thought they could do. The users did it well. If you've got one machine of a kind or there's only two or three people, you don't have that support. Now I know there are things which make it difficult for corporations to cooperate, but we've done this quite successfully. And I will mention one which I always find very amusing and that is the airframe company. In the early days, the airframe companies, as you well imagine, are competitive. What the presidents did not know was that the people in the computing groups had formed an organization which they swapped information and traded programs. If that had ever come to the attention of the lawyers, there'd been lawsuits every place. But we couldn't cope with the machines without cooperation. They were too big and too gigantic. And even to this day a whole new chip is a big problem. It wasn't easy for anybody to find that there was an error in the Pentium chip. It wasn't a serious one, but there'll be these things. If you get special purpose chips, you have no such help. If you will go out and use a general purpose chip, you may pay a little bit more, but it's more flexible. You can evolve with time. Other people will be helping you. As I said, the manufacturers come around and say, hey, we got a 10 times faster chip doing the same job, it only costs $2 more. Of course you got a brand new one, but what the hell, you can go the other way. You cannot. Now I warn you, these computers are invading all of our society. It's not only management has to be coped with it's everyone else. They're involved in our society and are basically digital. But don't forget analog. Just today I was talking to Barbara Head and he and I agree that analog computers are being badly neglected at times. For example, take the float in your bathroom or toilet. You flush the toilet, the water goes down, the float comes up. It's an analog device for integrating the amount of water in that tank comes up. Now there's a digital part as it comes up. At last the modern ones have a snap which snaps off so it doesn't trickle down to a very slow. It goes up and snaps off. So it's a combined analog digital. And I don't expect to find a totally digital toilet system running in my near future. Analog devices are too easy. Your thermostat goes across until it makes a contact, turns on the furnace and when it gets hot enough comes back, it turns the furnace off. Right. Nice simple analog device combined with. Yes, no closing contact. That combination of analog digital is very powerful. When I inherited big analog computer, the first thing I did was put on some, those kind of switches on it. The old people who designed it and the maintenance man all screamed and hollered and I said, I'm in charge. You're putting them on. So they put them on. They were very, very useful to get a combination of digital analog. We are now far, far down the digital one. And you should think about the usefulness of analog at times it works very well, but it does not work when there's deep computation, many layers deep, or does not work when it's supreme accuracy. The machine we had at old gun director parts was one part in 2000. To get one part in 10,000 would have cost us 50 to 100 times as much more money. You just can't do it. One part in 2000 was better. We could buy commercial ones at one in 1000 for a tenth what it cost us to build a new one. But that one binary digit. Viewing the problems I was having to do for Bell Labs, I didn't think I'd give up one binary digit in each component and emerge with accurate answers. So we arranged to get some more gun directors condemned. We took the parts, built them into a standard patch port of 1 megohm and had another computer. Because the gun directors were beautifully designed, unlike the commercial ones. They had gone through the arctic tropics and they were well temperature compensated and they had been debugged and they were really robust. They were very nifty and long computers. Just old gun directors and I can't dwell too much on the problem of reliability of answers. If you cannot get the right answer, you're in a bad way. You know that recently an awful lot of equipment in the military has not been functional at any one moment. In fact, it has been less functional, usually reported, because people don't like to admit that the airplane there really isn't ready to fly. It's right there alive, and you could fly if you had to. But really that wasn't. Now you may say Hamming is a nut on the subject because Hamming worried about it all his life. That's why he invented error correcting codes, which will take up one of these days. How to get reliable results out of unreliable parts. Part of this earlier talk was exactly the same thing. How we went from analog to digital to get reliable results. Pulses could be gated and repeated. Analog ones could only be amplified. So there's a vast difference between these. Now I'll give you a clue where we're headed for. I'm not going to talk about machine computers, the history of them, hardware, software, applications. And then I will turn to future applications, which means really the field of artificial intelligence. And when we cover two lectures of those, the next one is you. You are going to have to discuss what you think machines can and cannot do and what they can do in your business. I will only shiver you. And I will remind you what I said in the first lecture. It is not my business what you believe. It is my business that you do believe. And I put it one way. You must be responsible for your own beliefs. A quotation I like. It's in translation. Obviously. The Buddha 500 BC said to his disciples, I don't care where you read it, I don't care who you said it. Even if I said it, if it doesn't fit with what you believe and your common sense, then it's not so. You are responsible for what you believe. Quoting professors, saying, professor said so and so and so and so is not so good. You are responsible for your beliefs. That's the one thing I've got to do. I've got to get you to believe these things. It's nice that I said these. You must go through the things and say yourself, do I believe that guy or not? After all, he's a famous. But how many famous people have been wrong? Almost all famous people have been wrong. Sometime or other is bound to me. Furthermore, I told you that what works in one generation does not work in the next. And of course, my feet are in the past. You have got to face the future. In the year 20, 20 is the number you can think about. What will be society like? How will you make your decisions? What things I'm saying will be relevant? Which ones will not be relevant? You are responsible for your decisions and that's the main message I want in this chapter. So I see you tomorrow at 3 o'clock, right? Same room.