PrimIntelekt comments on Archimedes's Chronophone - Less Wrong
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Really, the best advice would be "Get out of Syracuse before the Romans show up" but I suppose your infuriating machine would refuse to transmit that as well.
Perhaps "Get off of Earth before Nemesis sends some more comets our way"
Nemesis: http://en.wikipedia.org/wiki/Nemesis_%28star%29
Reasoning: The Roman invasion could have been predicted, but wouldn't have been well supported by evidence -- although foreign invasions were certainly a repeated (even cyclic) phenomenon. Of course, the Nemesis hypothesis rests on an unproven root cause of all major extinction events, whereas invasions came from various, known causes...