My favorite problems are simple but not easy. The difference hasn’t always been apparent. I’m talking about clear, minimal constraints which require complicated, comprehensive thought. These problems are rare, but some lucky days they arise from a single image, like the one up there, like the one today.
If that table tennis ball is the Earth:
- how big is the Sun?
- how far away is the Sun?
You take bets. Is the sun a tennis ball? A beach ball? (A: something closer to a weather balloon.) If you miniaturized the solar system, what solar body would focus the Earth’s orbit? (A: the taqueria down the road.) You pick their pockets with these bets, getting them to buy into the problem unwittingly.
Maybe you put them into groups and wait until they requisition data. (eg. the radius of the Earth, the tennis ball, and the Sun; the mean distance from the Earth to the Sun.) Maybe you give them all laptops and let them scour the ‘tubes for the same data.
And I Wonder Constantly:
- do these simple-but-not-easy questions exist for every math standard on the books?
- who has them?
- are these people easily extorted?