Time travelling teacher

I would teach them the Arabic numbering system and as much of calculus as possible. If they understood that very quickly I would next try to teach them some of the foundations of real analysis. Realistically I don't think I could teach much more than that. Long term this would give them the tools to make a lot of other advances.

Not that this is necessarily the most important thing to share, but it's something I understood well enough that I could explain very clearly and yet still teach a lot of useful knowledge.

Also printing would be incredibly valuable, but I'm not sure I understand it well enough to teach it.
 
Sure you understand it. It's perfectly possible to print using a potato.

Ah, no. The Ancients Greeks didn't have potatoes. I'm stumped.
 
A basic talk on scientific method, touching on the idea of something along the lines of the royal society. With suggestions to look into and work out for themselves the printing press, zero and indeed some sane set of standards around a universal base. A base twelve metric as it were. And suggestions to have their own look into crop rotation, germs and how cool the potential of water and windmills could be if that logic were expanded. And a warning about the potential neuro-toxicity of lead, lest it all go wrong a while down the line.
 
Printing press might actually be key here. We might give a lot of ideas and knowledge to these guys, but without proper dissemination its all for naught. Additionally I'd probably throw in a few tidbits about astronomy.
 
If you went with printing, you would have to teach them all to read. What was written was copied by specialist. The results were read to the masses by specialist. The printing press was maybe the first mass production technique that put a lot of humans out of work. But until every one was afforded an education (which actually took away another "class" of labor. Or pushed it off until after education was completed.) it would be useless to have stuff to read, but no one who could read.

Having pointed that out though. The reality of a less tedious way to mass produce media was the catalyst that opened up education for more people and may have contributed to length of life. It allowed adolescents to forgo the workforce and early grave and in exchange there were more educated people which gave birth to a larger pool of thinkers adding more to life than just working and dying.
 
If you're going to go with inventing machines for mass production, keep in mind that the ancient Greeks, Romans, Egyptians, etc. were slave-owning societies, and if you invent machines to do certain kinds of labor, you need to have already figured out what's going to happen to the slaves who do that work. If you neglect this, the results could be catastrophic to the economy and could cause civil disorder. And unlike a game of Civ, you can't just convert people into Entertainers to cure it.
 
I guess teach with a focus things which are easy to understand, but which have historically taken a long time to figure out. (Sanitation, pasteurization, Human health, empirical skepticism, microscopic life, evolution, electricity, radio, atomic/molecular chemistry, Newtonian physics, gunpowder, compass/sextant navigation, etc.)

I'm sure convincing them would be simple if they're the best minds of the day, I've never had a situation where non-idiots haven't been convinced by me telling them the truth.
 
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