On November 16, 1974, the Arecibo Observatory transmitted 1,679 binary digits toward Messier 13, turning the problem of a common language between humans and extraterrestrial intelligence into a concrete engineering test. The Arecibo message used a number with two prime factors, 23 and 73, so that a receiver might arrange the bits into a rectangular image. That choice captured a central idea in interstellar communication: before meaning can exist…
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