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Unrelated problems share a core
Fire control is the study of hitting moving targets: planes, rockets, ballistics. Picture a gun the size of a two-story house, mounted on a moving Navy ship in the middle of the ocean, trying to shoot down an enemy fighter moving at 350 mph. The math for that shot is the challenge.
Claude Shannon worked on it at Bell Labs during the war, and he saw close, valid analogies between the fire control prediction problem and basic problems in communications engineering. The speed and quality of information mattered to both phone systems and fire control systems. A phone call reaching its recipient was a struggle against noise, and an anti-aircraft missile hitting its target presented the same conceptual challenge. Both required high-level statistical inference, and both meant building machines that translate math accurately into action.
Nothing he worked on went to waste. He turned the work into abstractions and analogies and carried them into later projects, including the information theory paper he was writing on and off over about eight years alongside these other jobs.
How do guns aim at a moving plane?
A shell takes seconds to reach a fast plane, so the gun has to aim at the point where the plane will be when the shell arrives. A predictor estimates the target's speed and heading from radar readings, then calculates its future position and the gun angle. Wartime systems such as the Bell Labs M9 director did this with electrical analog circuits and fed the result to radar-guided guns. Evasive turns by pilots add randomness, so the prediction has to be statistical.
How did Norbert Wiener link guns and signals?
In 1942 the MIT mathematician Norbert Wiener wrote a classified report on predicting an aircraft's path from noisy radar tracks. Its yellow cover earned it the nickname the Yellow Peril, and it was published openly in 1949 as Extrapolation, Interpolation, and Smoothing of Stationary Time Series. The method it describes, now called the Wiener filter, extracts a signal from noise by using the statistics of both. The Soviet mathematician Andrey Kolmogorov had reached similar results independently.
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