johnlawrenceaspden comments on Archimedes's Chronophone - Less Wrong
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I think probability theory would have been very accessible to the Greeks, had they only thought to think about games of chance, which they certainly played. I bet if you'd asked Archimedes 'What odds should you offer on a bet that two dice get seven?', then the whole thing would have come crashing out within a hundred years or so.
So you might want to put him in touch with a modern philosopher trying to take a mathematical approach to something mysterious, say Dennett.