Q: I think that any method of computation would not be fruitful unless it would give a kind of provision on how to compose such devices or programs. I thought the Fredkin paper on conservative logic was very intriguing, but once I came to think of making a simple program using such devices I came to a halt because thinking out such a program is far more complex than the program itself. I think we could easily get into a kind of infinite regression because the process of making out a certain program would be more complex than the program itself and in trying to automate the process, the automating program would be much more complex and so on, especially in this case where the program is hard-wired rather than being separated as a software. I think it is fundamental to think of the ways of composition.
A: We have some different experiences. There is no infinite regression: It stops at a certain level of complexity. The machine that Fredkin ultimately is talking about and the one that I was talking about in the quantum mechanical case are both universal computers in the sense that they can be programmed to do various jobs. This is not a hard-wired program. They are no more hard-wired than an ordinary computer that you can put information in–the program is a part of the input–and the machine does the problem that it is assigned to do. It is hard-wired but it is universal like an ordinary computer. These things are very uncertain but I found an algorithm. If you have a program written for an irreversible machine, the ordinary program, then I can convert it to a reversible machine program by a direct translation scheme, which is very inefficient and uses many more steps. Then, in real situations, the number of steps can be much less. But at least I know that I can take a program with 2n steps where it is irreversible, convert it to 3n steps of a reversible machine. That is many more steps. I did it very inefficiently since I did not try to find the minimum–just one way of doing it. I don’t really think that we’ll find this regression that you speak of, but you might be right. I am uncertain.
Q: Won’t we be sacrificing many of the merits we were expecting of such devices, because those reversible machines run so slow? I am very pessimistic about this point.
A: They run slower, but they are very much smaller. I don’t make it reversible unless I need to. There is no point in making the machine reversible unless you are trying very hard to decrease the energy enormously, rather ridiculously, because with only 80 times kT the irreversible machine functions perfectly. That 80 is much less than the present-day 109 or 1010 kT, so I have at least 107 improvement in energy to make, and can still do it with irreversible machines! That’s true. That’s the right way to go, for the present. I entertain myself intellectually for fun, to ask how far could we go in principle, not in practice, and then I discover that I can go to a fraction of a kT of energy and make the machines microscopic, atomically microscopic. But to do so, I must use the reversible physical laws. Irreversibility comes because the heat is spread over a large number of atoms and can’t be gathered back again. When I make the machine very small, unless I allow a cooling element which is lots of atoms, I have to work reversibly. In practice there probably will never come a time when we will be unwilling to tie a little computer to a big piece of lead which contains 1010 atoms (which is still very small indeed), making it effectively irreversible. Therefore I agree with you that in practice, for a very long time and perhaps forever, we will use irreversible gates. On the other hand, it is a part of the adventure of science to try to find a limitation in all directions and to stretch the human imagination as far as possible everywhere. Although at every stage it has looked as if such an activity was absurd and useless, it often turns out at least not to be useless.
Q: Are there any limitations from the uncertainty principle? Are there any fundamental limitations on the energy and the clock time in your reversible machine scheme?
A: That was my exact point. There is no further limitation due to quantum mechanics. One must distinguish carefully between the energy lost or consumed irreversibly, the heat generated in the operation of the machine, and the energy content of the moving parts which might be extracted again. There is a relationship between the time and the energy which might be extracted again. But that energy which can be extracted again is not of any importance or concern. It would be like asking whether we should add the mc2, the rest energy, of all the atoms which are in the device. I only speak of the energy lost times the time, and then there is no limitation. However, it is true that if you want to make a calculation at a certain extremely high speed, you have to supply to the machine parts which move fast and have energy, but that energy is not necessarily lost at each step of the calculation; it coasts through by inertia.
A (to no Q): Could I just say with regard to the question of useless ideas, I’d like to add one more. I waited, if you would ask me, but you didn’t. So I will answer it anyway. How would we make a machine of such small dimensions that we have to put the atoms in special places? Today we have no machinery with moving parts whose dimension is extremely small, at the scale of atoms or hundreds of atoms even, but there is no physical limitation in that direction either. There is no reason why, when we lay down the silicon even today, the pieces cannot be made into little islands so that they are movable. We could also arrange small jets so we could squirt the different chemicals on certain locations. We can make machinery which is extremely small. Such machinery will be easy to control by the same kind of computer circuits that we make. Ultimately, for fun again and intellectual pleasure, we could imagine machines as tiny as a few microns across, with wheels and cables all interconnected by wires, silicon connections, so that the thing as a whole, a very large device, moves not like the awkward motions of our present stiff machines but in the smooth way of the neck of a swan, which after all is a lot of little machines, the cells all interconnected and all controlled in a smooth way. Why can’t we do that ourselves?
______
*John von Neumann (1903–1957), a Hungarian-American mathematician who is credited as being one of the fathers of the computer. Ed.
*The jerky movements of particles caused by the constant random collisions of molecules, first noted in print in 1928 by botanist Robert Brown, and explained by Albert Einstein in a 1905 paper in Annalen der Physik. Ed.
*Sci. Am. July 1985; Japanese Transl.–SAIENSU, Sept. 1985. Ed.
3
LOS ALAMOS FROM BELOW
And now a little something on the lighter side—gems about wisecracker (not to mention safecracker) Feynman getting in and out of trouble at Los Alamos: getting his own private room by seeming to break the no-women-in-the-men’s-dormitory rule; outwitting the camp’s censors; rubbing shoulders with great men like Robert Oppenheimer, Niels Bohr, and Hans Bethe; and the awesome distinction of being the only man to stare straight at the first atomic blast without protective goggles, an experience that changed Feynman forever.
Professor Hirschfelder’s flattering introduction is quite inappropriate for my talk, which is “Los Alamos from Below.” What I mean from below is although in my field at the present time I’m a slightly famous man, at the time I was not anybody famous at all. I did not even have a degree when I started to work on my stuff associated with the Manhattan Project.* Many of the other people who tell you about Los Alamos knew somebody up in some higher echelon of governmental organization or something, people who were worried about some big decision. I worried about no big decisions. I was always flittering about underneath somewhere. I wasn’t the absolute bottom. As it turns out I did sort of get up a few steps, but I wasn’t one of the higher people. So I want you to put yourself in a different kind of condition than the introduction said and just imagine this young graduate student who hasn’t got his degree yet, who is working on his thesis. I’ll start by saying how I got into the project, and then what happened to me. That’s all, just what happened to me during the project.
I was working in my office* one day, when Bob Wilson† came in. I was working–[laughter] what the hell, I’ve got lots funnier yet; what are you laughing at?–Bob Wilson
came in and said that he had been funded to do a job that was a secret and he wasn’t supposed to tell anybody, but he was going to tell me because he knew that as soon as I knew what he was going to do, I’d see that I had to go along with it. So he told me about the problem of separating different isotopes of uranium. He had to ultimately make a bomb, a process for separating the isotopes of uranium, which was different from the one which was ultimately used, and he wanted to try to develop it. He told me about it and he said there’s a meeting. . . I said I didn’t want to do it. He said all right, there’s a meeting at three o’clock, I’ll see you there. I said it’s all right you told me the secret because I’m not going to tell anybody, but I’m not going to do it. So I went back to work on my thesis, for about three minutes. Then I began to pace the floor and think about this thing. The Germans had Hitler and the possibility of developing an atomic bomb was obvious, and the possibility that they would develop it before we did was very much of a fright. So I decided to go to the meeting at three o’clock. By four o’clock I already had a desk in a room and was trying to calculate whether this particular method was limited by the total amount of current that you can get in an ion beam, and so on. I won’t go into the details. But I had a desk, and I had paper, and I’m working hard as I could and as fast as I can. The fellows who were building the apparatus planned to do the experiment right there. And it was like those moving pictures where you see a piece of equipment go bruuuup, bruuuup, bruuuup. Every time I’d look up the thing was getting bigger. And what was happening, of course, was that all the boys had decided to work on this and to stop their research in science. All the science stopped during the war except the little bit that was done in Los Alamos. It was not much science; it was a lot of engineering. And they were robbing their equipment from their research, and all the equipment from different research was being put together to make the new apparatus to do the experiment, to try to separate the isotopes of uranium. I stopped my work also for the same reason. It is true that I did take a six-week vacation after a while from that job and finished writing my thesis. So I did get my degree just before I got to Los Alamos, so I wasn’t quite as far down as I led you to believe.
One of the first experiences that was very interesting to me in this project at Princeton was to meet great men. I had never met very many great men before. But there was an evaluation committee that had to decide which way we were going and to try to help us along, and to help us ultimately decide which way we were going to separate the uranium. This evaluation committee had men like Tolman and Smyth and Urey and Rabi and Oppenheimer and so forth on it. And there was Compton, for example. One of the things I saw was a terrible shock. I would sit there because I understood the theory of the process of what we were doing, and so they’d ask me questions and then we’d discuss it. Then one man would make a point and then Compton, for example, would explain a different point of view, and he would be perfectly right, and it was the right idea, and he said it should be this way. Another guy would say well, maybe, there’s this possibility we have to consider against it. There’s another possibility we have to consider. I’m jumping! He should, Compton, he should say it again, he should say it again! So everybody is disagreeing, it went all the way around the table. So finally at the end Tolman, who’s the chairman, says, well, having heard all these arguments, I guess it’s true that Compton’s argument is the best of all and now we have to go ahead. And it was such a shock to me to see that a committee of men could present a whole lot of ideas, each one thinking of a new facet, and remembering what the other fellow said, having paid attention, and so that at the end the decision is made as to which idea was the best, summing it all together, without having to say it three times, you see? So that was a shock, and these were very great men indeed.
This project was ultimately decided not to be the way that they were going to separate uranium. We were told then that we were going to stop and that there would be starting in Los Alamos, New Mexico, the project that would actually make the bomb and that we would all go out there to make it. There would be experiments that we would have to do, and theoretical work to do. I was in the theoretical work; all the rest of the fellows were in experimental work. The question then was what to do, because we had this hiatus of time since we’d just been told to turn off and Los Alamos wasn’t ready yet. Bob Wilson tried to make use of his time by sending me to Chicago to find out all that I could about the bomb and the problems so that we could start to build in our laboratories equipment, counters of various kinds, and so on that would be useful when we got to Los Alamos. So no time was wasted. I was sent to Chicago with the instructions to go to each group, tell them I was going to work with them, have them tell me about a problem to the extent that I knew enough detail so that I could actually sit down and start to work on the problem, and as soon as I got that far go to another guy and ask for a problem, and that way I would understand the details of everything. It was a very good idea, although my conscience bothered me a little bit. But it turned out accidentally (I was very lucky) that as one of the guys explained a problem I said why don’t you do it that way and in a half an hour he had it solved, and they’d been working on it for three months. So, I did something! When I came back from Chicago I described the situation—how much energy was released, what the bomb was going to be like and so forth to these fellows. I remember a friend of mine who worked with me, Paul Olum, a mathematician, came up to me afterwards and said, “When they make a moving picture about this, they’ll have the guy coming back from Chicago telling the Princeton men all about the bomb, and he’ll be dressed in a suit and carry a briefcase and so on–and you’re in dirty shirtsleeves and just telling us all about it.” But it’s a very serious thing anyway and so he appreciated the difference between the real world and that in the movies.
Well, there still seemed to be a delay and Wilson went to Los Alamos to find out what was holding things up and how they were progressing. When he got there he found that the construction company was working very hard and had finished the theater, and a few other buildings because they understood how, but they hadn’t gotten instructions clear on how to build a laboratory–how many pipes for gas, how much for water–so he simply stood around and decided how much water, how much gas and so on, and told them to start building the laboratories. And he came back to us–we were all ready to go, you see–and Oppenheimer was having some difficulties in discussing some problems with Groves and we were getting impatient. As far as I understand it from the position I was in, Wilson then called Manley in Chicago and they all got together and decided we’d go out there anyway, even if it wasn’t ready. So we all went out to Los Alamos before it was ready. We were recruited, by the way, by Oppenheimer and other people and he was very patient with everybody; he paid attention to everybody’s problems. He worried about my wife, who had TB, and whether there would be a hospital out there and everything, and it was the first time I met him in such a personal way and he was such a wonderful man. We were told among other things, for example, to be careful. Not to buy our train ticket in Princeton. Because Princeton was a very small train station, and if everybody bought train tickets to Albuquerque, New Mexico, there would be suspicion that something was up. And so everybody bought their tickets somewhere else, except me, because I figured if everybody bought their tickets somewhere else. . . . So when I went to the train station and I said I want to go to Albuquerque, New Mexico, he says, oh, he says, so all this stuff is for you! We had been shipping out crates full of counters for weeks and expecting they didn’t notice that the address was Albuquerque. So at least I explained why it was that we were shipping out crates–I was going out to Albuquerque.
Well, when we arrived we were ahead of time and the houses for the dormitories and things like that were not ready. In fact, the laboratories weren’t quite ready. We were pushing them, we were driving them by coming down ahead of time. They went crazy at the other end and they rented ranch houses all around in the neighborhood. And we st
ayed at first in a ranch house and would drive in in the morning. The first morning I drove in was tremendously impressive; the beauty of the scenery, for a person from the East who didn’t travel much, was sensational. There are the great cliffs; you’ve probably seen the pictures, I won’t go into it in much detail. These things were high on a mesa and you’d come up from below and see these great cliffs and we were very surprised. The most impressive thing to me was that as I was going up, I said that maybe there were Indians even living here, and the guy who was driving the car just stopped; he stopped the car and walked around the corner and there were Indian caves that you could inspect. So it was really very exciting, in that respect.
When I got to the site the first time, I saw at the gate—you see there was a technical area that was supposed to have a fence around it ultimately, but because they were still building, it was still open. Then there was supposed to be a town and then a big fence further out, around the town–my friend Paul Olum, who was my assistant, standing with a clipboard checking the trucks coming in and out and telling them which way to go to deliver the materials in different places. When I went into the laboratory I would meet men I had heard of by seeing their papers in the Physical Review and so on. I had never met them before. This is John Williams, they said. A guy comes standing up from a desk which is covered with blueprints, his sleeves all rolled up, and he’s standing there by some windows at one of the buildings ordering trucks and things going in different directions to build the things. In other words, we took over the construction company and finished the job. The physicists, in the beginning the experimental physicists particularly, had nothing to do until their buildings were ready, and apparatus was ready, so they just built the buildings, or assisted in building the buildings. The theoretical physicists, on the other hand, it was decided that they wouldn’t live in the ranch houses, but they would live up at the site because they could start working right away. So we started working immediately, and that meant that we would each get a roll blackboard, you know, on wheels that you’d roll around, and we’d roll it around and Serber would explain to us all the things that they’d thought of in Berkeley about the atomic bomb, and nuclear physics and all these things, and I didn’t know very much about it. I had been doing other kinds of things. And so I had to do an awful lot of work. Every day I would study and read, study and read, and it was a very hectic time. I had some luck. All the big shots had by some kind of accident–everybody but Hans Bethe–happened to have left at the same time; like Weisskopf had to go back to fix something at MIT, and Teller was away, just at a certain moment, and what Bethe needed was someone to talk to, to push his ideas against. Well, he came to this little squirt in an office and he starts to argue, to explain his idea. I said, “No, no, you’re crazy, it’ll go like this.” And he said, “Just a moment,” and he explained how he’s not crazy, that I’m crazy, and we keep on going like this. It turned out that, although I–you see, when I hear about physics I just think about physics and I don’t know who I’m talking to and I say the dopiest things like no, no, you’re wrong or you’re crazy–but it turned out that’s exactly what he needed. So I got a notch up on account of that and I ended up as a group leader with four guys under me, which is underneath Bethe.
The Pleasure of Finding Things Out Page 6
