I feel like this thought experiment is less about how to cleverly communicate to Archimedes all the things that he is obviously wrong about and that we are obviously right about, and more about how to try to recognize the potential mistakes within our own way of thinking, as Archimedes was as certain about his geocentric point of view as we are with our heliocentric one. While I think we’re right about heliocentrism at least, there may be other seemingly obvious facts that we take for granted, but that future generations will want to yell at us through a chronophone for, and whatever tricks we come up with to get Archimedes to question his beliefs (like giving nonobvious input) may help us to question our own beliefs. But maybe all that was just really really obvious in which case ahhhh I’m sorry.
But besides that, I remember doubting the power structure within my own familial unit as a child (parents are always right, children should always just listen until they turn 18 and become magically responsible) , could communicating that help Archimedes doubt some of the power structures withing Greek society? Maybe it would have him question the arbitrariness of slaves always having to defer to normal citizens, until the point at which they can buy themselves out of slavery and become magically worthy of politics like everyone else?
I have taken the survey.