Neat is the idea of playing chess with distant civilizations. Perhaps beam your first move toward a galaxy or galaxy cluster hoping someone will respond. Millions if not billions of years between moves.
Better would be to communicate not individual moves but chess programs. (This part is not an original idea.) This is the radio equivalent of teleporting an ambassador to play the game there. The aliens then are challenged to respond back with a stronger program.
Tricky is defining and communicating the model of computation upon which the chess program runs, and specifying the rules of the game. Go 囲碁 would probably be easier to specify.
The converse problem is to look specifically for computer programs when examining radio signals for SETI.
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