In 1974, the astronomer Frank Drake sent a mathematically-based binary message to the stars (specifically the M13 globular cluster), using a radio telescope. What was the message, and how was it constructed?

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(L) The Arecibo Message string, arranged in 73 rows and 23 columns. Even in text, your eye can see patterns emerging. © The same message shown as a shaded grid, making the patterns more clear. ® The same image colorized for discussion. [Images by S. Larson; R image from Wikimedia Commons]