ABSTRACT
Mathematical ideas seem to inevitably find applications that were undreamed of when they were originally discovered. This chapter details how modular arithmetic and logarithms helped the Allies win World War II. Speech that is scrambled in the manner of the A-3 Scrambler can be reconstructed using a sound spectrograph, which simply involves plotting the tones and reassembling them like a jigsaw puzzle. The vocoder used by SIGSALY broke the speech into ten channels, and another channel represented pitch. Some sources describe the pitch as being represented by a pair of channels. The digitized speech was sampled 50 times per second, so to separately encipher all of the channels, the record had to be simultaneously playing twelve tones at different frequencies, and these tones had to change every fiftieth of a second.
