Where did those neutrons go? (Monte Carlo method, part 2)

By Brian Clegg

This is the second of four posts on the mathematical approach known as the Monte Carlo method, following ‘Breaking the bank…’

Moving from the bank being broken at a casino to a mathematical method occurred as the Second World War came to a close. A number of scientists on the US nuclear programme were attempting to model neutron diffusion from a nuclear bomb. This was because a conventional nuclear explosion is effectively the trigger for the (then theoretical) thermonuclear explosion of a fusion bomb – and a major factor in its effectiveness is how neutrons travel out from the primary fission stage.

Like his colleague John von Neumann, the Polish-American physicist Stanislaw Ulam had an interest in the game of poker and the probabilistic nature of games. The new possibility of electronic calculation using the ENIAC computer made it possible to consider a novel approach to modelling neutron diffusion. At the heart of nuclear fission is the idea of a chain reaction. A neutron hits a nucleus, which splits, giving off more than one neutron. Each of these then has the opportunity to do the same. But predicting how such a process would occur, given the probabilistic nature of particle interactions, was a problem.

The idea behind the Monte Carlo method is to use the output of a (pseudo-) random number generator combined with known distributions of the chance of various interactions taking place to effectively simulate what is happening. By making many multiple runs of the model, an an accurate probability-driven picture is built up. This approach became widely used in a whole range of simulation applications – for instance predicting what would happen over time in complex queuing systems.

Ulam claimed to have come up with the idea while recovering from a serious illness, playing a variant of the card game solitaire (patience). He realised that it would take considerable mental effort to work out the chances of succeeding in any particular attempt. But if, instead, the game was repeatedly played – say 100 times – the percentage of successful plays would converge on the actual probability. He described this idea to von Neumann and began work on it with him.

Perhaps surprisingly, neither of these enthusiastic game players thought up the name. Greek-American physicist Nicholas Metropolis claimed to be responsible, writing ‘It was at that time [early 1947] that I suggested an obvious name for the statistical method – a suggestion not unrelated to the fact that Stan had an uncle who would borrow money from relatives because he “just had to go to Monte Carlo.” The name seems to have endured.’ Initially it was a code name, but it became one of mathematics’ more entertainingly named methods.

To make such simulations effective there needs to be a source of random(ish) numbers – but how was that to be achieved? We will look into those in more detail in the next, penultimate post.

Main source The Beginning of the Monte Carlo method by Nicholas Metropolis in the 1987 Los Alamos Science special issue.

Image from Unsplash by Hal Gatewood

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Now Appearing is the blog of science writer Brian Clegg (www.brianclegg.net), author of Inflight Science, Before the Big Bang and The God Effect.