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Jay Daigle
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Mathematician at The George Washington University. I write about teaching, epistemology, math, and metascience, and how hidden assumptions shape our decisions and beliefs.
@austin This will definitely make me leave the server. I don't want to be on social media where the administrator is trying to enforce "quality" in posts.
But most of the examples we actually study, and pretty much all the computations we do, are looking at removable discontinuities, where there's just one missing or misplaced point. And that idea tends to sound artificial and made-up: "We took this reasonable pattern and then changed a point to mess with you."
But the p-value chart and the crack chart are both perfect examples of removable discontinuities, so I can use them to illustrate that point.
I organize the course around the idea of approximation. With limits, we're asking if knowing f(a) gives us a good estimate of f(x) for x~a.
In continuous functions, which include most reasonable algebraic formulas, it does, but in lots of real-world functions it doesn't—I use that same graph of car prices. (I.e. knowing a car has "about" 40k miles isn't enough information, if you don't know whether it's just above or just below.)
@danluu I'm going to steal a couple examples from that post for my next calc 1 class. (If I'd seen it three weeks ago, I'd have stolen them for this one.)
@danluu I wonder how much of this is people using "exponential" to just mean "very fast"?
Like, I don't know anything about car tires, but I doubt that they are ten or a hundred times better than they were in 2000. Whereas phones and computers obviously are, and AI image generation is like infinity percent better than it was in 2000.
@danluu I really notice the huge hit to efficiency I take when a post gets too large to hold the whole thing in my head at once. One of the hardest things about my attempts to write a full book!
@danluu I feel like this makes sense given some assumptions about goals.
So like, if one of your friends practices and studies strategy and you don't, the two of you can't have a chill night of playing with friend any more.
My impression was that the nationally-competitive board games do in fact take it seriously; but the expectation at Game Night is that you're not doing that.
cf this Penny Arcade: https://www.penny-arcade.com/comic/2009/07/24/escalation-part-one
@danluu I desperately want a small-ish android phone with a physical keyboard.
But when they discontinued the Droid line, I remember reading an interview with I think a Verizon product veep, who said something like "yeah, I think the keyboard is great. I like it. But we just can't sell them."
I really want it but that doesn't mean it would be a money-maker.
@danluu A major contributor to me majoring in math and not economics is that the math department was great about letting me move ahead, and the econ department was not. So I took advanced econ coursework, but never took like intermediate micro or anything, and didn't wind up with a minor.
(There are definitely requirements that would have been useful to take in there, too, but I didn't want to deal with them if I had to go through too many intro courses I already knew.)