I recently had the privilege of a 1-hour speaking slot at SPARC, a yearly two-week camp for top high school math students.
Here's the video: Wisdom for Smart Teens
Instead of picking a single topic, I indulged in a bunch of mini-topics that I feel passionate about:
- Original Sight
- "Emperor has no clothes" moments
- Epistemology is cool
- Think quantitatively
- Be specific / use examples
- Organizations are inefficient
- How I use Bayesianism
- Be empathizable
- Communication
- Simplify
- Startups
- What you want
Overall, enjoyed the talk! Thanks for posting it.
I'm not sure if I would have done the Emperor has no clothes bit the same way. In particular, I probably would have put it after the epistemology section; it's easier to say "yep, no God, move on" after saying what it means to know or prove something. (I'm not sure you do that all that well, though, and then the question at the end suggests that even if you had led with crossing off God in the epistemology section people's feathers may have been ruffled.)
As for the history of the lecture, it's right there in the name (well, if you know Latin). It's that books are too expensive for everyone to have one, and so the professor will read the one copy of the book aloud while all the students listen (and take notes). Yes, videos and textbooks are a superior technology given the modern economy.
I also feel like a talk for teens should expect a lot of snark, and it didn't look like you did. :P In particular, whenever you give the advice to be specific, you should be prepared to be specific.
I don't know Latin so I'm guessing "lecture" is Latin for "lost purpose"? That's great, thanks for educating me.