This Thursday, June 11, marks the 100th birthday of mathematician Nicholas Metropolis (1915-99). An early recruit to the Manhattan Project who became a mainstay at the Los Alamos National Laboratory, Metropolis was known for his work on the Monte Carlo method, initially used for problems of atomic physics too complicated for classical mechanics, but too particular for the broad solutions of calculus.
The Monte Carlo method reimagined such problems as sequences of events; by assigning each event a probability, one could mathematically simulate thousands of such sequences (a task well-suited to the newly invented digital computer) and note which solution came up most often. Stanislaw Ulam, who first conceived the method, likened it to determining the chance of winning at solitaire by playing a hundred games and seeing how many times you won. Ulam and Metropolis developed that insight into a valuable tool for physics, chemistry, economics, and music.
Yes, music. Mathematicians brainstorming musical applications for those early computers often utilized the Monte Carlo method: analyze a few dozen melodies, calculating how often certain pitches appeared, how often they led to certain other pitches, etc. — then have a computer output tunes following the same probability distribution. In 1950, Harry F. Olson and Herbert Belar produced computer-generated melodies based on a statistical profile of 12 Stephen Foster songs. Six years later, Martin Klein and Douglas Bolitho programmed a Burroughs 205 computer to randomly churn out pop-song melodies; with lyrics by Jack Owens, one became a serviceably quirky ditty called “Push Button Bertha.”
You also could have the computer create a corresponding score based on hypothetical probabilities. Lejaren Hiller — who, before turning to composition, learned Monte Carlo techniques as a research chemist — teamed up with programmer Leonard Isaacson to run four experiments on the University of Illinois’s ILLIAC I computer (at the time, one of the most powerful in the world), which became the four movements of the 1957 “Illiac Suite” for string quartet.
Ideas of randomness and chance were already current in experimental music, most famously via composer John Cage, who would later collaborate with Hiller. Statistical methods and the computer formalized such ideas. Composers like Iannis Xenakis, in Europe, and James Tenney, in America, further developed what Xenakis called stochastic music, filling in details of textures and trajectories with bespoke mathematical means.
It was an inspired approach to an art that has always been — to borrow one of Ulam and Metropolis’s descriptions of the Monte Carlo method — “a mixture of deterministic and stochastic processes.” By serendipity or design, music cherishes opportunities for happy accidents.