PEOPLE Metropolis, Monte Carlo, and t MA N I A by Herbert L. Anderson n 1942 Nick Metropolis was work- using the Monte Carlo method (so named In September 1985 more than one hun- ing with Edward Teller on the reac- by Metropolis) on the new computers. dred researchers from around the world tor project at the University of Chi- The Monte Carlo method is an applica- met in Los Alamos for a four-day con- I cago when J. Robert Oppenheimer tion of the laws of probability and statistics ference, in honor of Nick Metropolis, on the invited the young physicist to continue his to the natural sciences. The essence of the frontiers of quantum Monte Carlo. One of collaboration with Teller, but at Los Ala- method is to use various distributions of the speakers was Herb Anderson, from the mos. There Metropolis joined the Manhat - random numbers, each distribution reflect- Laboratory Physics Division, Anderson's tan Project as a member of the Theoretical ing a particular process in a sequence of presentation was a fascinating remi- Division, having been encouraged by Teller processes such as the diffusion of neutrons niscence about the first modern calculating to move from experimental to theoretical in various materials, to calculate samples machines and the scientists who used physics. His first assignment was to de- that approximate the real diffusion history. them, about the intellectual ferment in the velop equations of stale for materials at Statistical sampling had been known for physics community that began early in this high temperatures, pressures, and densi- some time, but without computers the proc- century and still continues, and about Nick ties. ess of making the calculations was so la- Metropolis and the MANIAC. This article Over the years Metropolis turned in- borious that the method was seldom used is adapted from Anderson's presentation. creasingly to mathematics and computer unless the need was compelling. The com- design, and by 1948 he was leader of a Los puter made the approach extremely useful Alamos team that designed and built the for many physics problems. MANIAC, one of the first electronic digital Metropolis was also involved in the de- computers. Many of the country's foremost velopment of an importance-sampling scientists were eager to try their experi- scheme, called the Metropolis algorithm, ments on the wonderful new machine and that improves the effectiveness of the Monte came to the Laboratory to work with Carlo method. In the past twenty years his Metropolis. A few years later, together with work has included nonlinear problems and Teller, John von Neumann, Stanislaw combinatorial theory as well as Monte Ulam, and Robert Richtmyer, Metropolis Carlo calculation. He was named a developed techniques and algorithms for Senior Fellow of the Laboratory in 1980. 96 97 Metropolis This story is about the MANIAC and the beginning of World War 11. Nick was name. I don’t know whether he was the about Nick Metropolis, who conceived the twenty-five years old. In those days we had very first, but the story comes from Emilio MANIAC, built it, and saw how to use it no computers as we now know them. We Segre, who told me that Fermi used that for a wide variety of problems. In the used slide rules and adding ma- statistical sampling technique as early as period just after World War II, other com- chines—hand-operated machines. Ma- 1934, when he was working on neutron puters were being built, many of them, like chines with electric motors were the excep- diffusion in Rome. the MANIAC, modeled on the von Neu- tion rather than the rule. In 1933 Frederic Joliot and Irene Curie mann principle, the principle of the stored I remember particularly the hand-oper- had discovered the radioactivity induced program. Von Neumann organized a ated machine that Fermi used with re- in light elements by bombardment with group at the Institute for Advanced Study markable deftness. It was made by alpha particles. The neutron had been dis- and started building a computer based on Brunsviga, a German firm in the town of covered just one year before. These two that principle. Other institutions got into the same name, famous as the place where facts gave Fermi the idea that neutrons, the act, too, because they all realized the Gauss was born. This machine had a crank having no charge at all, would be much importance of building computers. There that you rotated by hand. To multiply, for more effective than alpha particles in was one at Argonne called the AVIDAC example, you set the machine and then producing nuclear transformations. They and one at Oak Ridge called the ORACLE. rotated the crank the number of times would not be repelled by the Coulomb Then there were the SEAC at the National called for by each digit of the multiplier, barrier and could therefore penetrate the Bureau of Standards and the ILLIAC at shifting the carnage for each successive nuclei of all atoms, whatever their charge, the University of Illinois. But the digit and turning the crank again. Fermi whereas the alpha particles could only get MANIAC at Los Alamos was special. had one of those machines when he was into the nuclei of light elements. You see, the circumstances in postwar working in Rome and brought it along It was an exciting idea. He got a radon- Los Alamos were special. The war had with him when he came to Columbia Uni- beryllium neutron source and began a brought together there an exceptional versity in 1939. He was using it when I series of experiments with some of his group of scientists, with whom Nick had started working with him on the chain young and enthusiastic collaborators: established a close relationship. John von reaction, soon after his arrival. Whenever Amaldi, Segre, Pontecorvo, d’Augostino, Neumann, Enrico Fermi, Hans Bethe, Ed- I used my slide rule to make a calculation, and Rasetti. Early in the course of their ward Teller, Stan Ulam, Dick Feynman, he started cranking his machine. By the work, they found they were getting some George Gamow, Tony Turkevich, and time I announced my result, he was wait- very peculiar effects. The radioactivity Robert Richtmyer, among others, were ing—and grinning. He could beat me they obtained depended a whole lot on drawn to Nick because they enjoyed work- every time. But that situation changed where the irradiation was carried out. In ing with him. When you went to Nick with when I got myself a Marchant. When it particular, the activity induced in silver a problem, he took a deep interest in it and became clear that he couldn’t even keep was much greater when they did the ir- worked hard on it with you, invariably up with me, let alone beat me. he gave up radiation on a wooden table than when making some essential contribution. It the Brunsviga and got a Marchant of his they did it on a table with a marble top. was a treat to work with Nick, and, if you own. Fermi could never resist the op- That was a great puzzle. They couldn’t understand that, you will understand a lot portunity to calculate faster. explain it. Then Fermi began to tell them about how this story evolved. It seemed to me that Fermi was always that they didn’t know how to experiment Those who returned to Los Alamos calculating something. It was Fermi’s view very well and that they didn’t really do after the war were drawn irresistibly to that Nature revealed itself through the things properly. Of course this didn’t Nick and his MANIAC, to what this won- experiments you devised to test it. You make them very happy. To clear up the derful electronic computer could do for can construct a theory to explain what is puzzle, Fermi decided to try filtering the them. They went away enriched by their going on, but unless the numbers come out neutrons through various substances. His new experience and rewarded by new right, you can’t be sure the theory is right. first idea was to use lead, but then at the scientific results in their fields of interest. So you have to do a lot of calculations. last minute, for no apparent reason, he This is a happy tale of how one of the first substituted paraffin instead. The increase of the modern computers got its start and Fermi Monte Carlo in the activity of the silver was what it was able to do in its early years. phenomenal. Everyone went home mys- You might be interested to know that tified. Fermi’s Brunsviga Fermi was one of the first to use the Monte Now, one of Fermi’s characteristics was Carlo method—in a rather simple form that he liked to come into the lab early in Let’s go back about forty-five years to and hand-calculated—long before it had a the morning and surprise his colleagues 98 Fall 1986 LOS ALAMOS SCIENCE Metropolis repair shop. They took the machines apart and traced the mechanical linkages to find the sources of jams and slippage, and of course they learned how the machines worked, Pretty soon they could identify the difficulty rapidly, and the machines sent to their shop were quickly repaired and returned to service. When the administrators came across this curious extracurricular activity, they regarded it as a problem. They issued some sharp criticism and stopped the re- Nick Metropolis enjoying a break in the quantum Monte Carlo conference, Septem- pair service.