Aliens are here to destroy Earth 
But first, we’re allowed to send a 1-page letter back in time to some historical figure, which will then create a new timeline + trajectory for our species.
For maximum positive impact, who should we contact and what should we tell them?
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Scientific method, basics of calculus, germ theory of disease, and recipe for gunpowder to Archimedes.
This answer is so on point 
After reading @Meaningness’s critical take on the notion of “the scientific method” (https://meaningness.com/metablog/upgrade-your-cargo-cult …), I’d be curious to hear what he would say to Archimedes (if anything) re science.
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I think it’s fair to assume Archimedes had the scientific attitude and knew how to discover new truths. And yet I imagine he didn’t have crisp ideas around what we now consider the Scientific Method. Would he benefit from some of those ideas? Would he be able to transmit them?
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Scientific method cannot really function without the requisite sociopolitical structures. Science requires participation of a large number of groups separated by space and time equipped with freedom of speech and writing. Archimedes "knowing" SM wouldn't have changed much.
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