Comments by "" (@TheDavidlloydjones) on "3Blue1Brown" channel.

  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.  @mohammedsamir5142  Um. Survival of the fittest. "Nature red in tooth and claw." God provided the mayhem maybe.
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  4. "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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  5. 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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  6. 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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  7. "The first thing we do, let's kill all the lawyers". William Shakespeare's Henry VI, Part 2, Act IV, Scene 2.
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  8. "Momentarily" means for a moment, not in a moment. "He was momentarily insane, saying briefly when he meant soon."
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  9. . Guest Informant RH may be undecidable? ..which is exactly why it's the obvious answer to the question posed, shurely?
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  10. At 2:00, a line is one dimensional, a square is two-dimensional? Agreed. But then "The space we live in is three-dimensional, and so on..."? Hunh? People are always saying "You can go up and down and front and back, and sideways, so that's three." But I can go sideways in a whole bunch of different directions. Left and right, and east and west are all directios. Down is a pointer in my local gravity field, and up is a wavy moving line which varies with the phases of the local Moon, mostly. We face great puzzles (and huge wastes of money) in academic physics, and it seems to me this is largely because we don't talk sense to ourselves in the most elementary ways. Keeping mathematical degrees of freedom from getting confused with physical dimensions, and physical dimensions and directions from getting confused with each other might be a start, wouldn't it?
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  11. I don't see why front-and-back is more important than "off at 45 degrees." More generally, I think that a bunch of different ideas have been linked together without justification by sticking them all under the word "dimension." But the fact that you don't see my point seems to me your problem, not mine. When I look back at my original post it seems pretty clear to me. What is your problem, Raphael?
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  12. Raphael, You make the popular claim that " you can describe every point in space with just 3 numbers." This is not true. Three numbers will identify a point's relationship to a framework -- which requires three orthogonal lines -- how many numbers is that? -- to define. Ninety-degree angles are utterly unstable, so what sense does it make to claim that they are any foundation for dimensions? There are in fact no ninety-degree angles in nature, so it seems pretty clear it is merely a human notion, not anything foundational of reality. Cheers, -dlj.
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  13. By Nature I mean the real world, "the space we live in" in the words of the YouTube. Sure you can choose your own framework, and then use three numbers to put a point somewhere in your framework. There: you've got your framework and your three numbers. That's rather more than "3 numbers." It's plus a whole framework. Of yours. Which may take just a wee bit of specification to distinguish it from other frameworks. And it still won't be the real world, will it? Keep on practising, Raphael. -dlj.
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  14. Fermat -- pronounced fer' matt, not "fermah.". It's a good joke when Steven Colbert does it, but for the rest of you guys it's a mistake. Now then, about these Bay-zhing guys. Sorry, folks, Beijing is Bay jing. No phoney French soft palate called for.
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  15. Bruct Fer shure. Pariss- Paree. -dlj.
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  16. 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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  17. 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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  18. I'll be the guy at the corner table out front, reading Libération, espresso up, Pernod back.
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  19. Strogatz is wrong. In fact this claim is just crazy. Totally out of touch. Differential equations don't express laws, they express questions. If they expressed laws, why would we need to "solve" them? Wigner's "unreasonable effectiveness of mathematics" is another version of the same error. Mathematics appears everywhere because you can ask a question anywhere: mathematics is asking questions, and sometimes turns up in the expressions of the answers.
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  20. "Coordinates" is a plural noun. The coordinates are a pair of numbers. It's OK for a plual subject to verb something singluar.
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  21. It would have made more sense to title these with the "Chapter #n" at the beginning, so that our computers could get them into the right order automagically.
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  22. Um, maybe make up your mind. Are you going to approach the problem head-on? Or give us a sneaky back-door way of looking at it? Those two are not any paradox: they're a contradiction. On the other hand, it's difficult to see why Bishop Berkley should have objected. He was in the business of forgiving sinners, wasn't he?
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  23. That's a pure A except in Cleveland. The Cleveland Philharmonic tunes to an A of 444. I can't help suspecting that this is why the Rock and Roll Hall of Fame is in Cleveland.
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  24. If you put the Roman number at the left hand side of your titles, our computers will put your stuff in order automagically.
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  25. At 6:45: Kolmogorov was very much not a 19th-century mathematician. He lived 1903-98 and his career spans, exemplifies, and affected both modern hyper-industrialism and the triumphs and disasters of the Soviet experiment and its failure. One of the key events of the 20th century. There are many good Kolmogorov stories around, but my favourite is the one, perhaps apocryphal, about steel industries. At one point in the 1940s, when he was working on linear programming, he conjured up a model for a steel industry. Some Russian bureaucrat is supposed to have looked at it admiringly, with an air of Yess, Kamerade, ve vill adopt zis right away, but asked "But what is this vector over here." "Those, Comrade Director, are the prices," said Kolmogorov.
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  26. And the video on how to get a ball to cast a shadow the same size as its cross-section is...? 😎🤣😂
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  27.  @masonkane5884  How about a nice impartial F?
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  28. That horrible median score on the Putnam? No big deal. The median number of errors found in a Microsoft operating system by its pre-release reviewers is zero. The top few reviewers, however, tend to turn in numbers like 160, 90, 68, 55,... lots of twos, lots of ones, and then about 200,000 people who just wandered in clueless. They're zeroes -- and that's the number of improvements they come up with, too. Hmmm. How about a video on Zipf's Law, power distributions, and maybe a few of the other fun ones. All the economists out there deserve to find out more about heteroscedasticity, for instance, doncha think?
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  29. Each anything is singular.
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  30. The claim that this puzzle is worthwhile because it makes us better at math is bogus because it's circular. I agree with the conclusion; my claim is only that the reason given is illogical. Clearly it assumes its conclusion because understanding math is worthwhile. But if it weren't then it wouldn't be. And if it wasn't then neither would math be. QED.
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  31. Uncomfortable moment: when you try to tile all of infinite space by making a spiral of little squares each of which contains a Hilbert Curve, haven't you just fallen into the problem that the snake curve had, back earlier in the video? Haven't you made a jumping, discontinuous, mess out of all those pleasantly well-proven-out little Hilbert-curves squares? It would be nice if somebody could post a reassuring No, 't'ain't so. Alternately, is there a better way of tiling-out the plane with a Hilbert Curve of little Hilbert-curve-squares instead of that dumb* spiral? I think the answer is yes to the first, it's a mess, but then yes to the second (whew!), it can be made to work, but I'm not sure. _____________________________________ * For once "dumb" as stupid is the same thing as dumb having lost the power of sound.
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  32. The handle, you mugs! (Spoiler, they get to it...) And Merry Christmas, folks. A pleasure to see you all together!
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  33. Grant, Damn but your expressive little blue Pi's are intelligently done! I think maybe you should be in the running for a Pulitzer in cartooning for them! I also think your Einstein quote, to the effect that the cultic "math and reality are identical" is ver-ree apropos. When I first read Eugene Wigner's paper, https://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences, I thought it must be a bad translation from the Hungarian. It turns out he was serious. Ugh! There are a whole slew of things wrong with it, among other things that for every mathematical construct suggesting a reality there a bunch of other ones with different implications. I think the Big One, though, is that most of the mathematics Wigner celebrates takes the form of differential equations, and these are hypotheses, not conclusions. Even their solutions are mere suggestions, not statements about reality. The Wiki entry on Wigner's paper does him a great favour, suggesting a tentativeness that I don't see in the original; to my mind, the paper is emphatically wrong, and your Einstein quote gets it right.
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  34. Once you've figgered out the percentages, 91.7, 94.2 and 92,6, the question arises, is 1.6%, the difference between the two big ones, even a difference? My rule, purely emotional I believe, is yes since 48 and 186 are "big numbers," a big number being completely arbitrarily defined as anything over about 17 and "about" being an undefined element, like a point or a line. FWIW, the long run feels like a time period where you can feel the difference between 1% and 3% compounded annually, so maybe five years. Alternatives welcome. Anybody got any real science on these? How can 17 be big while a mere five is long? I dunno.
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  35. Peek outside Flatland. Obviously, if you ever had a peak anywhere, it wouldn't be flat, would it?
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