Comments by "" (@TheDavidlloydjones) on "Essence of linear algebra preview" video.

  1. Boring reminder: when you throw a baseball the applicable law is Kepler's. Think ellipses, give or take air resistance. Earth is not flat, and there is no reason for teechers to tell kids that any parabolas are involved.
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  2. ***** Excellent! What you wrote there is exactly what I wish every physics teacher in the world would say first before going on to tell all those lies about parabolas. The lesson that we sometimes have to use an incorrect, but malleable, approxiamation instead of the real thing is much more valuable than the lesson about parabolas. Nobody cares about parabolas and ellipses in t the real world, and the Willie Mays Algorithm, keep the angle constant, for catching a fly ball doesn't involve either one. The judicious use of a good approximation, on the other hand, is something every kid is going to need all their life. Let the teaching be real. Your good post above is a fine example of how it should be done! Cheers, -dlj.
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  3. "Although parabolas have nothing to do with projectile motion, we can use them as an easy hack for small problems. "If your projectile is a baseball, a parabola will approximate it roughly, and the error from using the wrong math will only be a couple of microns -- much less than the error from air resistance. "On the other hand, if you try to use parabolas when your projectile is a Minuteman III, Moscow is not worried about you. 'Course San Francisco might be in trouble when you aim for Moscow..." The point is not knowing that a cannonball dropped off the Leaning Tower of Pisa takes 4.3 seconds, or whatever it is. Thep point is getting the ideas right. In this case, the whole point of teaching math to kids is to tell them that math is a bunch of tools, all of them approximate hacks, and you choose the one that comes closest -- being careful about it because there are a lot of people who get it wrong. Whaddya think? -dlj.
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  4. They haven't learned about Kepler, but they've learned about conic sections? Hunh? And no, I'm not suggesting an "everything... is a lie narrative." My idea is that we not tell them lies in the first place. -dlj.
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  5. OK, I guess we've pretty much come full circle -- although you seem to be getting a wee bit French-deconstructionist about things if you insist on calling the ordinary discourse of everyday life "necessary lies." Meet me at Deux Magots for Sunday morning coffee some time. My point is that things will go better if the "lie," since you insist, that you start with is as accurate as possible. "We're using parabolas because they're a good enough approximation" would seem to do the job, imho. Going along implicitly using parabolas as if they were the actual case is a dishonest lie. You've forced me to coin a phrase. :-) The Big Point, it seems to me, is that a lot of kids are turned off to science by the fact that it is taught as a The Truth, and they can see right away that this is horsefeathers. Cheers, -dlj.
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  6. If you had put the Roman numeral at the beginning of each title, rather than then end, several thousand people would have found it easier to arrange them in order.
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  7. You haven't answered my question a month later, so let me put it more directly. Above you say "One loses almost nothing in accuracy and gains a world of intuition and understanding from the vastly simpler equations. " How can you gain "a world of intuition" when your teacher is forcing you, over and over and over, to "intuit" something that is factually false? Far better than being brainwashed with falsehoods incorrectly called "intuitions," surely it's far better to learn "Sometimes we use convenient lies because they get us into the ballpark. (and in the ball park we put up with the air resistance to the furshlugginer ball because we breathe the stuff)." Doncha think? -dlj.
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  8. I'll be the guy at the corner table out front, reading Libération, espresso up, Pernod back.
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