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Research Article

Neither Digital Nor Analog: The Case of Graphical Monte Carlo

LEE Kwan Soo

Program in History and Philosophy of Science, Seoul National University

Published: January 1997 · Vol. 19 · pp. 20-42
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Abstract

In the first months of 1947, Stanislaw Ulam and John von Neumann conceived a way to estimate the behavior of neutrons. Their idea was to repeat many times tracing a neutron's path, using random numbers to mimic the stochastic nature of neutron reaction. This scheme had several traits inherited from the calculating activities during World War II at Los Alamos. A sphere or a circle was the shape of the modeled physical system in their scheme as was in many atomic bomb calculations. Its working procedure consisted of the numerical operations. This scheme got named "Monte Carlo" before long, underwent intricate development and diversification, and has acquired many faces. It is considered at least a (class of) widely applicable numerical method(s). Sometimes Monte Carlo simulations are practically regarded as the dealing with another Nature as Peter Galison showed recently. What I call 'graphical Monte Carlo' was a feeble but implicative thread of Monte Carlo activities. In the summer of 1947, Enrico Fermi visualized the operational procedure of Monte Carlo estimation. He replaced the numeral operation with line drawing. Marvin L. Goldberger, then a recent Ph.D. at Chicago used Fermi's graphical scheme to investigate neutron and proton scattering in nucleus, which could be easily represented by a sphere or a circle. Goldberger's paper in 1948 was the first published one that used the Monte Carlo method, though he never used the term, "Monte Carlo". His paper was severely criticized. However some others defended, improved and used the line-drawing scheme presented in Goldberger's paper well into the middle of the 1950s. These graphical Monte Carlo calculations did not fit into the received dichotomy between digital and analog. According to the contemporary authorities, digital calculations use numerals in various forms as the medium of calculation whereas the analog ones use continuous quantities. The lines drawn did not correspond to any numerals used in Ulam and von Neumann's scheme, the graphical Monte Carlo calculations' digital version. The length and direction of the lines corresponded to those numerals, but the length and direction of the lines were not the medium of calculation. They were the results of the working procedure. The graphical Monte Carlo evolved largely isolated from other Monte Carlo activities then growing in number and scope. Those who used "Goldberger-type Monte Carlo" method did not cite Monte Carlo other than what Goldberger had done, and their modifications of the method were not thoroughly reasoned. Their selection of the parameters of operations that obviously might have influenced the statistics of the results was not explicitly based on statistical consideration, though their works increasingly emphasized the statistical quality of the results in various settings. On the other hand, their verbal characterization of the method was often incompatible with that of the cited literature on which their explanation was allegedly grounded. These suggest that a peculiar form of calculation method can be transported separated from that method in general or from the previously attached meanings and justifications.