PEOPLE

Metropolis, Monte Carlo, and t

MA N I A

In 1942 Nick Metropolis was work-ing with Edward Teller on the reac-tor project at the University of Chi-cago when J. Robert Oppenheimer

invited the young physicist to continue hiscollaboration with Teller, but at Los Ala-mos. There Metropolis joined the Manhat -tan Project as a member of the TheoreticalDivision, having been encouraged by Tellerto move from experimental to theoreticalphysics. His first assignment was to de-velop equations of stale for materials athigh temperatures, pressures, and densi-ties.

Over the years Metropolis turned in-creasingly to mathematics and computerdesign, and by 1948 he was leader of a LosAlamos team that designed and built theMANIAC, one of the first electronic digitalcomputers. Many of the country's foremostscientists were eager to try their experi-ments on the wonderful new machine andcame to the Laboratory to work withMetropolis. A few years later, together withTeller, John von Neumann, StanislawUlam, and Robert Richtmyer, Metropolisdeveloped techniques and algorithms for

using the Monte Carlo method (so namedby Metropolis) on the new computers.

The Monte Carlo method is an applica-tion of the laws of probability and statisticsto the natural sciences. The essence of themethod is to use various distributions ofrandom numbers, each distribution reflect-ing a particular process in a sequence ofprocesses such as the diffusion of neutronsin various materials, to calculate samplesthat approximate the real diffusion history.Statistical sampling had been known forsome time, but without computers the proc-ess of making the calculations was so la-borious that the method was seldom usedunless the need was compelling. The com-puter made the approach extremely usefulfor many physics problems.

Metropolis was also involved in the de-velopment of an importance-samplingscheme, called the Metropolis algorithm,that improves the effectiveness of the MonteCarlo method. In the past twenty years hiswork has included nonlinear problems andcombinatorial theory as well as MonteCarlo calculation. He was named aSenior Fellow of the Laboratory in 1980.

by Herbert L. Anderson

In September 1985 more than one hun-dred researchers from around the worldmet in Los Alamos for a four-day con-ference, in honor of Nick Metropolis, on thefrontiers of quantum Monte Carlo. One ofthe speakers was Herb Anderson, from theLaboratory Physics Division, Anderson'spresentation was a fascinating remi-niscence about the first modern calculatingmachines and the scientists who usedthem, about the intellectual ferment in thephysics community that began early in thiscentury and still continues, and about NickMetropolis and the MANIAC. This articleis adapted from Anderson's presentation.

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This story is about the MANIAC andabout Nick Metropolis, who conceived theMANIAC, built it, and saw how to use itfor a wide variety of problems. In theperiod just after World War II, other com-puters were being built, many of them, likethe MANIAC, modeled on the von Neu-mann principle, the principle of the storedprogram. Von Neumann organized agroup at the Institute for Advanced Studyand started building a computer based onthat principle. Other institutions got intothe act, too, because they all realized theimportance of building computers. Therewas one at Argonne called the AVIDACand one at Oak Ridge called the ORACLE.Then there were the SEAC at the NationalBureau of Standards and the ILLIAC atthe University of Illinois. But theMANIAC at Los Alamos was special.

You see, the circumstances in postwarLos Alamos were special. The war hadbrought together there an exceptionalgroup of scientists, with whom Nick hadestablished a close relationship. John vonNeumann, Enrico Fermi, Hans Bethe, Ed-ward Teller, Stan Ulam, Dick Feynman,George Gamow, Tony Turkevich, andRobert Richtmyer, among others, weredrawn to Nick because they enjoyed work-ing with him. When you went to Nick witha problem, he took a deep interest in it andworked hard on it with you, invariablymaking some essential contribution. Itwas a treat to work with Nick, and, if youunderstand that, you will understand a lotabout how this story evolved.

Those who returned to Los Alamosafter the war were drawn irresistibly toNick and his MANIAC, to what this won-derful electronic computer could do forthem. They went away enriched by theirnew experience and rewarded by newscientific results in their fields of interest.This is a happy tale of how one of the firstof the modern computers got its start andwhat it was able to do in its early years.

Fermi’s Brunsviga

Let’s go back about forty-five years to

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the beginning of World War 11. Nick wastwenty-five years old. In those days we hadno computers as we now know them. Weused slide rules and adding ma-chines—hand-operated machines. Ma-chines with electric motors were the excep-tion rather than the rule.

I remember particularly the hand-oper-ated machine that Fermi used with re-markable deftness. It was made byBrunsviga, a German firm in the town ofthe same name, famous as the place whereGauss was born. This machine had a crankthat you rotated by hand. To multiply, forexample, you set the machine and thenrotated the crank the number of timescalled for by each digit of the multiplier,shifting the carnage for each successivedigit and turning the crank again. Fermihad one of those machines when he wasworking in Rome and brought it alongwith him when he came to Columbia Uni-versity in 1939. He was using it when Istarted working with him on the chainreaction, soon after his arrival. WheneverI used my slide rule to make a calculation,he started cranking his machine. By thetime I announced my result, he was wait-ing—and grinning. He could beat meevery time. But that situation changedwhen I got myself a Marchant. When itbecame clear that he couldn’t even keepup with me, let alone beat me. he gave upthe Brunsviga and got a Marchant of hisown. Fermi could never resist the op-portunity to calculate faster.

It seemed to me that Fermi was alwayscalculating something. It was Fermi’s viewthat Nature revealed itself through theexperiments you devised to test it. Youcan construct a theory to explain what isgoing on, but unless the numbers come outright, you can’t be sure the theory is right.So you have to do a lot of calculations.

Fermi Monte Carlo

You might be interested to know thatFermi was one of the first to use the MonteCarlo method—in a rather simple formand hand-calculated—long before it had a

name. I don’t know whether he was thevery first, but the story comes from EmilioSegre, who told me that Fermi used thatstatistical sampling technique as early as1934, when he was working on neutrondiffusion in Rome.

In 1933 Frederic Joliot and Irene Curiehad discovered the radioactivity inducedin light elements by bombardment withalpha particles. The neutron had been dis-covered just one year before. These twofacts gave Fermi the idea that neutrons,having no charge at all, would be muchmore effective than alpha particles inproducing nuclear transformations. Theywould not be repelled by the Coulombbarrier and could therefore penetrate thenuclei of all atoms, whatever their charge,whereas the alpha particles could only getinto the nuclei of light elements.

It was an exciting idea. He got a radon-beryllium neutron source and began aseries of experiments with some of hisyoung and enthusiastic collaborators:Amaldi, Segre, Pontecorvo, d’Augostino,and Rasetti. Early in the course of theirwork, they found they were getting somevery peculiar effects. The radioactivitythey obtained depended a whole lot onwhere the irradiation was carried out. Inparticular, the activity induced in silverwas much greater when they did the ir-radiation on a wooden table than whenthey did it on a table with a marble top.That was a great puzzle. They couldn’texplain it. Then Fermi began to tell themthat they didn’t know how to experimentvery well and that they didn’t really dothings properly. Of course this didn’tmake them very happy. To clear up thepuzzle, Fermi decided to try filtering theneutrons through various substances. Hisfirst idea was to use lead, but then at thelast minute, for no apparent reason, hesubstituted paraffin instead. The increasein the activity of the silver wasphenomenal. Everyone went home mys-tified.

Now, one of Fermi’s characteristics wasthat he liked to come into the lab early inthe morning and surprise his colleagues

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Nick Metropolis enjoying a break in the quantum Monte Carlo conference, Septem-

with the answer to whatever problem theyhad been worrying about the night before.Unlike—or like—the early bird whocatches the worm. Fermi had an afflictionthat helped him do this. He had insomnia,and he always got up at four in the morn-ing. Now what do you do if you are wideawake at four in the morning? Well, inFermi’s case he either did theory or he didcalculations. For making quick calcula-tions he had a whole bag of tricks, and thehand-calculated Monte Carlo method wasone of them.

On the morning following this greatpuzzlement in the lab he got up at four asusual, and in thinking about the problemhe decided he knew what might be hap-pening. Maybe the neutrons were beingslowed down as they went through varioussubstances, and if they were, then hydro-gen nuclei would be especially effective.And with a greater slowing, you couldexpect a higher level of induced activity inthe silver. Well, he came into the lab andmade this pronouncement, and everyonewas struck by the simplicity of it all andthe theory turned out to be quite plausible.

Then Fermi, in working out the detailedtheory, used Monte Carlo calculations togive him a physical insight and to help himchoose a su i table funct ional form,Gaussian, exponential, or o ther , forrepresenting the slowing down process.

The slowing down turned out to be amajor discovery. Slow neutrons have verylarge cross sections for nuclear reactions.

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and with them Fermi produced a largenumber of new radioactive isotopes. Thiswork won him the Nobel Prize in 1938. Itled directly to the chain reaction in Chi-cago in 1942 and to the establishment ofLos Alamos in 1943.

Fermi never wrote up his use of theMonte Carlo method, but he told the storyto Emilio Segre many years later whencomputers had made statistical samplingpractical and the technique was cominginto wide use. Segre mentions it in hisintroduction to the neutron papers in TheCollected Works of Enrico Fermi.

The Marchant Repairman

Now- let’s get back to Nick Metropolis.It is 1944, and the scene is Los Alamos.What is Nick doing? He is busily repairingMarchant calculators. And how did he getinto that business? Well it happened in thefollowing way. When Los Alamos was setup in 1943 there were no calculators.There was, however, an obvious and ur-gent need to carry out a lot of calculations,and the Lab went out and bought a wholelot of calculators-Marchants andFridens, which were the best mechanicalcalculators at the time—and set up a hand-computing facility. The machines wereheavily used and soon began to show signsof wear and tear. Too many were out forrepair, and it took too long to send them tothe manufacturer to be fixed. So Nick,together with Dick Feynman, set up a little

repair shop. They took the machines apartand traced the mechanical linkages to findthe sources of jams and slippage, and ofcourse they learned how the machinesworked, Pretty soon they could identifythe difficulty rapidly, and the machinessent to their shop were quickly repairedand returned to service.

When the administrators came acrossthis curious extracurricular activity, theyregarded it as a problem. They issuedsome sharp criticism and stopped the re-pair service. But not for long. The demandfor working machines was so great that theadministrators decided they had better notinterfere. and the service was soon re-instated.

In the fall of 1943 it became apparentthat large computational problems werestraining the capacity of the hand-calcu-lators. That’s where Dana Mitchell comesinto the picture. I mention his name withgreat fondness because he was the manwho got me into physics. He had come toLos Alamos to help with procurement.and he was familiar with the IBMpunched-card machine. Soon a whole setof those machines arrived at the Lab.Metropolis and Feynman immediatelydecided to see whether these punched-cardmachines were really faster than theirteam of Marchant hand-calculators. Theyset up a test in which the two groups wouldcalculate the same problem. For the firsttwo days the two teams were neck andneck—the hand-calculators were verygood. But it turned out that they tired andcouldn’t keep up their fast pace. Thepunched-card machines didn’t tire. and inthe next day or two they forged ahead.Finally everyone had to concede that thenew system was an improvement.

As the atomic-bomb project entered itsfinal phases in late 1944, the pressure forcomputation increased sharply. Nick be-c a m e m o r e a n d m o r e i n volved inpunched-card operations with Dick Feyn-man, who was put in charge. Their workcontinued at a frantic pace during 1945until the Japanese surrendered on August15, after which they began to relax a bit.

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The ENIAC

The great step forward in computingwas the introduction of’ electronics, andnow the ENIAC entered the scene. TheENIAC was the first electronic, digital,general-purpose, scientific computer. Itwas designed and built for the AberdeenProving Grounds by a group of engineersunder the direction of Pres Eckert andJohn Mauchly. It had 18,000 vacuumtubes and computed 1000 times as fast asits closest electromechanical competitor.The machine was built during wartime onthe promise that it would calculateballistic trajectories at least ten timesfaster than the mechanical differentialanalyzers then in use. As things frequentlyturn out, the machine was now working aspromised—but the war was over, and sud-denly no one cared that much about calcu-lating ballistic trajectories.

The connect ing l ink be tween theENIAC and Los A1amos was Johnny vonNeumann, who was a consultant both atthe Aberdeen Proving Grounds and at theLab. He was tremendously excited aboutthe ENIAC. He took a deep interest in itsdesign and thought a good deal about whatcould be done with it. When he came toLos Alamos early in 1945, he told Nick.Edward Teller, and Stan Frankel aboutwhat the Eckert and Mauchly team wasdoing. They were enchanted. You knowhow things sometimes work out if you arein the right place at the right time—andprepared for the opportunity. Well, vonNeumann suggested that perhaps Los Ala-mos had a problem that could be workedout on the ENIAC and invited Nick andStan to try the new machine. It was a greatopportunity, and they seized it eagerly.And so it turned out that the first seriousproblem the ENIAC solved was the oneMetropolis and Frankel put to it regardingthe “super,” the thermonuclear bomb.

By this time the idea of the stored pro-gram had already been conceived. prin-cipally by John von Neumann and hiscollaborators on the ENIAC. They hadalready begun to design the EDVAC, a

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computer that would have a stored pro-gram. The ENIAC was programmed byconnecting cables and wires and settingswitches on a huge plugboard that wasdistributed over the entire machine. Fig-ure 1 is a photograph showing youngwomen programming the ENIAC by inter-connecting the electron tube registers withcables inserted in plugboards, It was anawkward and tedious way to tell the ma-chine what to calculate and what to dowith the results. When von Neumann wasin Los A1amos, in about 1947. he de-scribed a suggestion made by RichardClippinger of the Ballistic Research Labo-ratory on how the ENIAC might be con-verted to a limited stored-program mode.The idea was to rearrange the so-calledfunction tables, normally used to store 300twelve-decimal-digit numbers set by man-ual switches. to store up to 1800 two-decimal-d ig i t numbers . each pai r ofnumbers corresponding to an instruction.A particular problem would correspond toa sequence of’ such instructions. This se-quence would be set on the functiontables. A background control would inter-rogate these instructions sequentially,including so-called loops of instructions.Changing from one problem to anotherwould be achieved by resetting theswitches of the function tables to cor-respond to the new sequence of instruc-tions. Figure 2 shows the function tables ofthe ENIAC.

This suggestion made a deep im-pression on Nick, but there was a missingelement—the background control. On avisit to the ENIAC in early 1948, Nick

learned that a new panel had been con-structed to augment one of the logicaloperations. It was a one-input, one-hun-dred-output matrix, and it occurred toNick that this matrix could be used in-stead to interpret the instruction pairs inthe control mode proposed by Clippinger.Such a panel would greatly simplify theimplementation of a background control.He told von Neumann about it and wasencouraged to go ahead and try-and sohe did. The scheme was implemented onthe ENIAC forthwith, and Nick’s set ofproblems-the first computerized MonteCarlo calculations—were run in the newmode.

The MANIAC

After the war Nick joined the faculty ofthe University of Chicago, to help set up amajor computing facility. When thatdidn’t materialize as quickly as he hadhoped , he began to th ink of o therpossibilities, and about that time he got acall from Carson Mark, head of the Theo-retical Division at Los Alamos. suggestingthat he set up a computing Facility here.Nick was ready, willing. and able. Themoral of my story is that fortune favorsthe prepared mind. Nick was right there.well prepared to do just what he was askedto do, and that’s how the MANIAC wasborn.

The Mathematical and Numerical Inte-grator and Computer—the MANIAC—was designed according to von Neumann’sprinciples. which had been set forth in aremarkable publication by Arthur Burks.

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Herman Goldstine, and Johnny von Neu-mann. The MANIAC borrowed heavilyfrom the IAS, the computer being built atthe Institute for Advanced Study undervon Neumann’s direction. But because theMANIAC came later, Nick was able toavoid many pitfalls that delayed the IAS.

As I have mentioned, many computerswere built in this outburst of activity’ afterthe end of the war. The ENIAC had starteda revolution that continues to this day,with no end yet in sight. But the unusualsuccess of the MANIAC was due primarilyto the personality and motivation of NickMetropolis and to the group of highlycapable engineers and programmers he as-sembled at Los Alamos to help him buildthe machine and make it run. The originalengineers were Dick Merwin, HowardParsons, Jim Richardson. Bud Demuth,Walter Orvedahl, and Ed Klein. The im-portance of programming aids was rec-ognized early on. About 1953 John Jack-son led a study of assembly languages, andan assembler was produced, Mark Wellsand others launched the development ofthe MADCAP, a high-level programming

language and compiler. This was a criticaldevelopment because it provided a conve-nient way to communicate with theMANIAC.

Fermi and Metropolis

Enrico Fermi had been at Los Alamosduring the war and liked it so much that heclaimed he would not have left if only theLab were a university. Since it wasn’t auniversity, he made the best possible com-promise by accepting a position at theUniversity of Chicago and spending hissummers at Los Alamos.

When he came to Los Alamos in thesummer of 1952, the MANIAC was upand running, and it would hate been veryhard to keep Enrico from that machine.He though the MANIAC was just wonder-ful. He could hardly wait to get his handson it. I’ve told you how he loved to calcu-late, the faster the better, and here was hisgood friend Nick Metropolis with thefastest machine in the world, offering tointroduce him to its mysteries and let himrun it himself.

Fig. 2. Function tables of the ENIAC.

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Nick must have been pleased by thepraise and interest shown by so many ofthe illustrious scientists he had workedwith in wartime Los Alamos, but thesupreme accolade came from EnricoFermi. When you build something. whatcould be more satisfying than to have oneof the world’s greatest physicists tell younot only that it’s a great machine but thathe wants to use it. Moreover, Fermi had aproblem that was ideally suited to themachine. He wanted to analyze the pion-proton scattering experiments he had beencarrying on in Chicago with his col-laborators at the new 450-MeV synchro-cyclotron.

My connect ion wi th th is s tory i sanalogous to Nick’s except that in this caseI had built the cyclotron. I also helpedbuild the apparatus and carry out themeasurements. The other collaboratorswere Darragh Nagle and Earl Long. on thefaculty and my graduate students. RonaldMartin, Gaurang Yodh, and MauriceGlicksman.

The results of our pion-proton scatter-ing experiments had been as striking asthey were surprising. The large scatteringcross section at a specific energy indicatedthe presence of a resonance. It was a majordiscovery, an excited state of the proton.We had uncovered a new particle nowknown as the delta. and it attracted theattention of the entire high-energy physicscommunity. In order to extract the ap-propriate quantum numbers of the delta,Fermi wanted to do what he called phase-shift analysis, which tells you which quan-tum states have the biggest scatteringamplitudes and which have the smallest.

I should mention that Fermi had aknack of coming up with problems whosecomputation matched the means avail-able. Some years before, when thepunched-card machines were the principalmeans for computing, Fermi posed theproblem of calculating a table of atomicmasses using a semiempirical mass for-mula he had devised on the vonWeizsacker model. Nick organized the cal-culation and the preparation of the tables.

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The tables turned out to be very useful andwere widely used. I still have my copy.

So anyway, Fermi came to Nick with hisphase-shift problem. As always, Nick wasextremely helpful, and they carried out thework. I learned all about it when Fermireturned to Chicago in the fall of 1952, sosteamed up about computers and theMANIAC that he announced he wouldgive a series of lectures on digital comput-ing. We were treated to a magnificentcourse—Fermi at his best. We learned forthe first time about binary and and hexa-decimal arithmetic, Boolean algebra, andlinear programming. With this kind ofintroduction, we were easy converts to thecause of computers in science, and weeven began to go out to Argonne, wherebythat time the AVIDAC was running, tolearn how to program and run that ma-chine. The gospel according to NickMetropolis was taking effect.

There’s an amusing story about EdwardTeller that fits in here. Remember thatNick had been a member of Teller’s groupwhen they were working on the “super.”Now, Teller was not one to let Fermi leavehim behind. Anything Fermi could do, hecould do too. So Teller also became astudent of Nick’s and learned how to pro-gram the MANIAC. When he came backto Chicago—he was on the facultythen—not to be outdone by Fermi he an-nounced that he would give a colloquiumon the subject of computers. But when thecolloquium notice appeared, it didn’t con-vey exactly the impression he had in-tended. It read,

Edward Teller

The MANIAC

To show how closely Fermi inter-acted with the MANIAC, I want you to seesome of his programming efforts, done inhis own hand. Remember, these were thedays before FORTRAN. Programmingwas done at the lowest level, in machine

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Fig. 3. A subprogram written by Fermi for converting data in memory from hex-adecimal to decimal form and printing the results.

language. Figure 3 is a subprogram Fermiwrote to convert the data in memory intodecimals and to print the results. Figure 4is a block diagram of the program forcalculating the phase shifts by finding aminimum chi-squared in a fit to the data.And Figure 5 is a printout of the programfrom the MANIAC. Note the use of hexa-decimal numbers. The comments are writ-ten in Fermi’s hand.

Phase-Shift Analysis

In this period, 1953 and 1954, phase-shift analysis was such a hot subject that itoccupied center stage in the elementaryparticle physics community. At the

Rochester Conferences held in those andsubsequent years, you could talk aboutalpha three three and alpha three one, andeveryone understood that these were thephase shifts of the pion-proton scattering.The physics was important-the delta wasa new particle.

In working with the phase-shift analysisprogram, we encountered, for the firsttime, solutions in hyperspace, many-func-tional space. You had to get used to thefact that this kind of space has its ownproblems of minimization, that you couldeasily fall into the wrong minimum andend up with wrong solutions. The vir-tuosity of the computer almost made uslose sight of the discovery of the proton

Fall 1986 LOS ALAMOS SCIENCE

Fig. 4. A subprogram written by Fermi for calculating phase shifts by finding aminimum chi-squared in a fit to the data.

Fig. 5. A portion of the printout of the program containing the subprograms describedin Figs. 3 and 4. The program is written in machine language in hexadecimalnumbers.

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resonance because the computer wouldfind solutions that we didn’t expect werethere. We would put a program into themachine fully expecting the quantum stateof the resonance to emerge. But no. Acomputer doesn’t pay any attention towhat Nature would like the solution to be;it has its own way of finding solutions.And all of a sudden it began to find solu-tions, many of them—six of them—thathad nothing to do with the resonance. Itfound many sets of phase shifts that gavegood fits to the data, leaving open thequestion whether the resonant solutionwas the correct one. The resonant solutionwas appealing in that it accounted for all ofthe unusual features found in the experi-ments, but the nonresonant solutions werenot easy to rule out.

I won’t say that this confusedFermi—that would be a little tooharsh—but the result of all this was that hecouldn’t claim with certainty that we haddiscovered a resonance in our experi-ments. As long as the computer was turn-ing out solutions, good fits of the data,good chi-squareds, that were nonresonantsolutions, he was always forced to con-clude that the result was ambiguous.

Now Hans Bethe, who had been head ofthe Theoretical Division at Los Alamosduring the war, decided to get into the act.He made himself a great expert in phase-shift analysis. He wasn’t satisfied with theway Fermi was handling the problem, andhe went in with the idea that he wasn’tgoing to be that naive and that he could do

better by including additional physicsarguments. So he enlisted Nick’s aid and,with Fred deHoffmann to help him,mounted a second program in phase-shiftanalysis. So here we had Nick on bothsides of the competition, an odd situationthat only someone like Nick could handle.In matters of science, Nick had nofavorites. In the end, I think, the problemwas handled best by two of my graduatestudents, Ronald Martin and MauriceGlicksman, working separately. Theydidn’t have a fancy computer and there-fore had to use much simpler approaches

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to the problem. By using graphical meth-ods with simplified but plausible assump-tions, they came up with the resonantsolution that turned out to be the correctone. It was a lesson in the use of computersthat should be a caution to us all.

Scientific Triumphs

The nice thing about having the firstcomputing machine is that almost any-thing you do on it is new and important. InFig. 6 I have listed ten of the many scien-tific uses of the MANIAC. I chose these toemphasize the distinction of the men whocame to work with Nick and the varietyand importance of what they were able toaccomplish. These projects are also exam-ples of how the computer opened newpossibilities for scientific investigation,sometimes with surprising results.

Nonlinear Oscillators. I have already dis-cussed the first two calculations listed inFig. 6. The third, the Fermi, Pasta. andUlam study, turned out to be extra-ordinarily important. In the summer of1953 Fermi raised the question of thenature of the approach to equilibrium of avibrating, nonlinear string, initially in asingle oscillatory mode. He thought itwould be fun to use the MANIAC for thisexperiment, so he and Stan Ulam andJohn Pasta set up a test problem and beganto run it. As they expected, the computa-tions showed that the initial vibrationalenergy gradually transferred into neigh-boring modes and eventually achievedequilibrium, the time taken being the so-called relaxation time. Everybody was re-ally quite happy with the result.

But the completely unexpected hap-pened one day when they were computinga typical problem. While the machine wasgrinding away at this problem, they be-came engrossed in a heated discussion andlet the computer go beyond its usual turn-off point. When they finally got around tolooking at it, they found that the vibra-tional energy had returned to within a fewpercent of its initial state. Well, that was

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Pion-proton phase-shift analysis (Fermi, Metropolis; 1952)

Phase-shift analysis (Bethe, deHoffman, Metropolis; 1954)

Nonlinear coupled oscillators (Fermi, Pasta, Ulam; 1953)

Genetic code (Gamow, Metropolis; 1954)

Equation of state: Importance sampling (Metropolis, Teller; 1953)

Two-dimensional hydrodynamics (Metropolis, von Neumann; 1954)

Universalities of iterative functions (Metropolis, Stein, Stein; 1973)

Nuclear cascades using Monte Carlo (Metropolis, Turkevich; 1954)

Anti-clerical chess (Wells; 1956)

The lucky numbers (Metropolis, Ulam; 1956)

Fig. 6. Scientific triumphs achieved with the MANIAC. Nick Metropolis was a co-author of the publications resulting from these studies except for the ones onnonlinear coupled oscillators and anti-clerical chess.

Fig. 7. Mr. Tomplins Iears how the MANIAC works in an illustration from Mr. TompkinsLearns the Facts of Life by George Gamow. (Copyright 1953 by Cambridge UniversityPress; reprinted with permission.)

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Fig. 8. Paul Stein (left), Nick Metropolis, the MANIAC, and the 6-by-6 “anti-clerical”chess board.

such a tremendous surprise that at firstthey thought the machine had gone awry.They ran the problem again, and 10 andbehold, given enough time, the amplitudesall went back to the initial state, and thenmore new and surprising things happened.The rest is history-nonlinear systemswere shown to have many fascinatingaspects. The ideas of soliton theoryemerged, and the subsequent outpouringof papers became a minor industry. Todaythis classic work is known as the FPU(Fermi-Pasta-Ulam) problem.

The Genetic Code and Mr. Tompkins.The Metropolis circle of famous scientistsincluded George Gamow. At the timeGamow was introduced to the MANIAC.his interest had turned to biology, and sohe got Nick to help him work on someproblems of the genetic code. He was oneof the first to have the idea that the geneticcode was vested in four nucleic acids.which somehow were able to code for thetwenty amino acids from which proteinsare made. So some of these early studies ofthe genetic code were carried out on theMANIAC.

On the lighter side Gamow was writinga book called Mr. Tompkins Learns theFacts of Life. Gamow was so fascinated bythe MANIAC that he decided to include

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the machine in his book. So when Mr.Tompkins is to learn how the brain works,Gamow introduces him to MANIAC andhas the computer explain how his elec-tronic brain works. Figure 7 is an in-imitable Gamow cartoon from this de-lightful book: notice how appealingly theessentials are presented.

Importance Sampling. A significant ad-vance in the use of the Monte Carlomethod came out of Nick’s collaborationwith Edward Teller. Teller, obviously de-l ighted a t ga in ing access to such amarvelous toy , p r o p o s e d t h a t t h eMANIAC, and the Monte Carlo method,be used to carry out calculations on theequation of state in two dimensions forhard spheres. These calculations in-troduced the idea of what is now known asimportance sampling, also referred to asthe Metropolis algorithm. The scheme.which reduces the statistical error andthereby greatly improves the effectivenessof the Monte Carlo method, is widely usedtoday, as participants in this conferencehave made evident.

Two-Dimensional Hydrodynamics. Iwon’t say too much about two-dimen-sional hydrodynamics because it wasalways a major problem at the Lab-and

still is. But Johnny von Neumann was oneof the great experts in the field, and heshowed how to attack the two-dimen-sional flow of two incompressible fluidsunder gravitational and hydrodynamicforces.

Iterative Functions. A striking thingabout these early computer experiments isthat in some cases the importance of thework wasn’t recognized at the time thework was done. It was immediately ob-vious that the pion-proton phase-shiftanalysis was going to be important. Butwhen Paul Stein, Myron Stein, and NickMetropolis began to look into the problemof iterative functions, it was mainly tosatisfy their curiosity. Quite some timelater, this problem unexpectedly turnedout to be very important.

One of the surprising consequences ofthese early studies of iterative transforma-tions was the discovery of their universalproperties. This work was an inspirationto Mitchell Feigenbaum, who took it up afew years ago and used it to show how suchfunctions lead to a theory of the onset ofturbulence and chaotic behavior. Thissubject has turned out to be as importantas it is exciting. It has fired the imagina-tions of many who are intrigued by thecurious aspects of nonlinear behavior. It iscurrently being widely developed, a goodexample of computer-driven mathe-matics.

A Few Others. Another noteworthy studywas the classic study of the nuclearcascades induced by bombarding heavynuclei with high-energy particles. Nick didthis study with Tony Turkevich, usingMonte Carlo techniques.

Then Mark Wells and others preparedthe first program to develop a strategy for“anti-clerical” chess . This game wasplayed on a 6-by-6 board with bishopsremoved. It was a highly amusing ex-perience and had many implications forsubsequent games of strategy. Figure 8shows MANIAC I. Paul Stein. NickMetropolis, and the chessboard.

105

Metropolis

Finally, I must mention some interest-ing work in number theory in which StanUlam and others introduced the notion of“lucky numbers,” a generalization of theordinary pr ime numbers wi th manysimilar properties. That was an attractivepiece of work.

This list often is just a small sample of’the many scientific uses of the MANIAC,and it includes only the most prominentnames associated with Nick on those proj-ects. These I think were the most impor-tant works—or at any rate the most inter-esting.

Death of MANIAC

Before closing, let me make clear howthe MANIAC evolved over the years.MANIAC 11 succeeded MANIAC I in LosAlamos in 1956. The second MANIACwas more powerful than the first and, be-cause it included floating-point arithme-tic, was easier to use. MANIAC III, withthe latest in solid-state circuitry, was de-veloped at the University of Chicago whenNick returned there to head the newlyformed Institute for Computer Research.

In 1965 Nick returned to Los Alamos

from Chicago, but by this time the com-puting needs of the Laboratory had in-creased dramatically and were being sup-plied by commercial machines. Unfor-tunately, in this climate the decision waseventually made to abandon the kind oforiginal research that was special to thecomputer project, and in 1977 MANIACII was turned off.

To conclude this story on a happiernote. I remind you that it’s Nick’s birth-day. I’ve always had the idea that whenthere is a birthday there ought to be apoem. Here is my own modest offering.

Monte Carlo Metropolis

Nick, you’ll remember those halcyon days;The Monte Carlo method was in its earliest phase.You went to the ENIAC and got it to loadProblems you wanted in a stored-program mode.The Monte Carlos you gave it opened a crackThat helped you decide to build MANIAC.MANIAC came out as a marvelous toy,A machine you could work with and really enjoy.

You called on your friends to, join in the fun,And it wasn‘t too long before they‘d begun.There was Teller, Gamow, Turkevich too.Of others not mentioned there were quite a few.But these in particular knew that their goalWas through Monte Carlo in the MANIAC's soul.Those were seminal papers, seeds had been sown;That how Monte Carlo came into its own

106 Fall 1986 LOS ALAMOS SCIENCE

Metropolis

Further Reading

Metropolis, N., Hewlett, J.. and Rota, Gian-Carlo. eds. 1980. History of Computing in the TwentiethCentury. New York: Academic Press.

Burks, Arthur W., Goldstine, Herman H.. and von Neumann, John. 1946. Preliminary Discussion ofthe Logical Design of an Electronic Computing Instrument. Princeton:Institute for Advanced Study.

Segre E., ed. 1965. The Collected Works of Enrico Fermi. Chicago:The University of Chicago Press.

Metropolis, Nicholas, Rosenbluth, Arianna W., Rosenbluth, Marshall N., Teller. Augusta H.. andTeller, Edward. 1953. “Equation of State Calculations by Fast Computing Machines.” Journal ofChemical Physics 21:1087.

Metropolis, Nicholas, and Ulam, S. 1949. ‘“The Monte Carlo Method.” Journal of the AmericanStatistical Association 44:335.

Historical illustrations for this article were published by N. Metropolis.

Herbert L. Anderson received his Ph.D. in physics from ColumbiaUniversity in 1940. As a graduate student he assisted in the constructionof a 37-inch cyclotron at Columbia. He also began a close association withEnrico Fermi that lasted until Fermi’s death in 1954. Anderson was thefirst in the United States to demonstrate the energy release in the fissionof uranium in an ionization chamber/linear amplifier combination. Heparticipated in the original experiments on neutron reproduction inuranium. which led directly to the development of the nuclear chainreaction. These experiments included the early studies on the fission ofuranium. the emission of neutrons by uranium. the slowing down ofneutrons in carbon, and neutron reproduction in a lattice of uranium andgraphite. During 1942-44 he had a major role in the design and construc-tion of the first chain reacting pile, in Chicago, the second (CP-2) pile atArgonne, and the Hanford piles. At Los Alamos his experiments at theOmega reactor helped establish the critical size for nuclear explosions inuranium-235. His measurements at Alamogordo, New Mexico, in whichhe used fission-product analysis, established the field of the first nuclearexplosion in 1945. The method, adapted to air sampling, became aprincipal means for detecting and analyzing nuclear testing carried out byforeign countries. He returned to Chicago in 1945 as a member of thenewly formed Institute for Nuclear Studies. He served as Director of theEnrico Fermi Institute from 1958-62. He was appointed GuggenheimFellow in 1955-57 and Fulbright Lecturer in Italy in 1956-57. He waselected to the National Academy of Sciences in 1960 and to the AmericanAcademy of Arts and Sciences in 1978. In 1982 he received the EnricoFermi Award. During the years in Chicago, he was a consultant andVisiting Fellow at Los Alamos, and in 1978 he joined the Laboratory as astaff member. He was appointed a Los Alamos National LaboratorySenior Fellow in 1981 and Distinguished Service Professor Emeritus atthe University of Chicago in 1982. In the Physics Division at Los Alamos,he is currently working with an instrument of his own design to analyzethe proteins made by living cells. The proteins are separated by two-dimensional electrophoresis, and the protein analyzer measures them bydirect beta-ray counting. In a collaboration with biologist Theodore T.Puck, he is trying to identify the proteins specific to three humanchromosomes.

LOS ALAMOS SCIENCE Fall 1986 107

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