How should mathematics be taught to non-mathematicians? (original) (raw)

I’ll add some problems, these might be somewhat similar to already existing ones, but they are interesting:

Imagine a hypothetical experiment where scientists are testing for precognition. A supposed psychic correctly predicts only 100 out of 1000 coin tosses. What does this suggest?

Interesting extensions of this problem include: What if they get 500 correct, but in alternating order? If we are statistically analysing the psychic’s guesses xored with 00000… or 11111… or 10101010…, does it make sense to analyse them xored with a random sequence? What about xoring the psychic’s guesses with a doctored sequence so that we always conclude that there is some psi phenomenon going on, even when there isn’t. That shouldn’t be allowed, but why?

If an outcomes with less than 500 correct guesses, and outcomes with more than 500 correct guesses both suggest a supernatural phenomenon, then why do we conclude in real life that these phenomena don’t exist? What if we are dealing with a die which has six outcomes instead of a coin’s two? Is there a general rule for making sense of all this?

Also: Tapei 101 has a giant metal ball in it. Why is this a good idea, and how does one decide on the design of the pendulum for a given tower?

In terms of geometry, a discussion of drawing in perspective could be interesting.

I can’t think of anything good for trigonometry other than triangulating the positions of stars which was already brought up. I know that navigating at sea used to require lots of trig. Probably still does, but computers do it all.

I hope that this course gets made, it’s a great idea.

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