Pearl Harbor Day – Mathematics of Cryptography and Surprise

The attack on Pearl Harbor (1941) was a surprise. The mathematics of surprise: entropy and information theory. Surprise = –log₂(p), where p is probability. The US had broken Japanese codes (Purple) but failed to anticipate the attack – a failure of signal processing and human analysis. Pearl Harbor led to the creation of the NSA and massive investment in cryptanalysis. Mathematics of intelligence: Bayesian updating, prior probabilities, and the challenge of distinguishing signal from noise.