Challenge HN: Convince an ancient Greek that you are from the future

I'm writing a book about the scientific method targeted to a lay audience. As part of the dramatic narrative I came up with the following puzzle: imagine you have built a time machine and you want to go back to ancient Greece and try to convince someone that you are from the future. The time machine operates under Terminator rules: it can only transport your body, no artifacts. (Some provision is made for you to acquire period clothing once you arrive, but that's it.) So the only thing you can take back with you is information that you are able to memorize. You can study for as long as you want before you go (so, for example, you can, and probably should, learn to speak ancient Greek) but once you go there is no coming back.

Mark Twain used a similar scenario as a plot point in his book, "A Connecticut Yankee in King Arthur's Court." In that book the protagonist solves the problem by predicting an eclipse of the sun, but that isn't very interesting so I am adding the following two conditions to the puzzle:

1. There is some uncertainty about exactly when and where you will arrive. The time uncertainty is many decades, and the space uncertainty is many tens of kilometers.

2. You have to convince them within a small number of weeks, otherwise they will just decide you are crazy and throw you in the loony bin.

So predicting a solar eclipse doesn't work because solar eclipses are very rare at any particular point on the ground, so the odds of you appearing someplace where there will be a solar eclipse to predict are vanishingly small. Even if you did get lucky enough to end up somewhere that an eclipse would happen within a few weeks, you would have to either memorize the exact time and location of all of the solar eclipse events in Greece over a multi-decade period, or learn how to calculate them on the fly by hand. You would also have to somehow figure out exactly when and where you had arrived. You can't just go buy a newspaper and look at the masthead.

Some other things that won't work:

1. Predicting a lunar eclipse. The ancient Greeks knew how to do that so this would not impress them.

2. Predicting a historical event, for all of the same reasons that predicting a solar eclipse wouldn't work.

The puzzle is designed to nudge you towards an approach where you try to reproduce some scientific or technological advance towards which you can leverage the knowledge you bring with you from the future.

I have not been able to come up with a solution.

> Predictive power of Newtonian physics

The problem with that is that this predictive power only manifests itself when you can make precision measurements of celestial objects, and the Greeks could not because they didn't have telescopes. (Hm, inventing the telescope might be an answer. Did the Greeks have lens-making technology?)

> Euclidean geometry as a starting point would blow their minds.

Sure, but that wouldn't prove you were from the future any more than it proved that Euclid was from the future.

> Sure, but that wouldn't prove you were from the future any more than it proved that Euclid was from the future.

By that standard it doesn't seem like any scientific or technological knowledge could prove you're from the future, either.

The only way to show you're from the future that can't also be explained by being from the present and having great knowledge/intelligence is to predict the unpredictable. But, you've narrowed the time constraint (a few weeks) and widened the range (a few years) so that predicting the immediate and unknowable isn't an option. Seems to be what you're going for also. So, I don't think you're left with anything.

I'm pretty sure they didn't have lenses. Lenses need optically clear glass. Clear glass came along around 100AD, but it took another 1000 years before it was sufficiently clear that you could make good lenses with it.

Glassmaking would be a good one because the chemistry is based on available materials and with sufficient knowledge you would walk them through the history of glassmaking up to a simple lens and make eyeglasses.

Go with Archimedes and teach him calculus. He will understand https://en.wikipedia.org/wiki/Quadrature_of_the_Parabola