3 ms·
He is making a really long winded point I'm not sure I completely understand, so feel free to correct me if I am off here, but I could not really disagree more.
by JohnMakin 2y ago
He is making a really long winded point I'm not sure I completely understand, so feel free to correct me if I am off here, but I could not really disagree more.
While there is value in emphasizing things like defining/abstracting a problem rather than calculating the result of it, things like the "algorithm" typically taught to elementary schoolers to do long division is pretty much how you would naively/algorithmically program a division operator that can give a remainder. The multiplication "algorithm" given to me at a young age was what first gave me the insight into the connection between addition and multiplication. Abstracting this away in education could not possibly be doing society, math, or computation any service whatsoever, at least not in the way (I think?) he is imagining.
I do think there is value to asking whether a problem needs to be solved or redefined or abstracted in a different manner. I had a calculus teacher in college a long time ago that had a really hilarious way of emphasizing this - he'd often bury "trap" questions into his tests that looked really simple but would test your knowledge of a simple algebraic or trigonometric trick he'd only covered during lecture, and lack of knowledge of this trick would lead one down a hopeless 20+ page response to the problem, to the point where if you found yourself going off the rails with a complex solution, you knew you messed up somewhere. This forced me to look at the problem from a variety angles to see if I could solve it in a more clever, general, or simpler way, or if it could be rewritten (this was usually the correct way to solve it). I really valued that, even years and years later, but maybe that's not the kind of thing Wolfram is getting after in this interview.
- lordnacho 2y agoThis is why I think we'd be better off doing a load of olympiad questions. Those are exactly the kind of thing where you can practice the flash-of-insight type thing that often gives an elegant solution.