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 (nobody)...and 108 guests Last 5 registered Oplandisks nothingstar N_loop yipe foxtrotromeo Browse members... |
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i have acquired a copy of "What Is Calculus About" By W. W. SaWyer, (c) 1961 in the hopes of finally "knowing" calculus. the introduction explains that this book will contain a lot of driving metaphors, and then uses a driving metaphor to explain its approach to explaining calculus: "How should calculus be taught then? Should we bother the beginner with warnings that only become important in more advanced work? If we do so, the beginner will be confused because he will not see any need for these warnings. If we do not, we shall be denounced by mathematicians for deceiving the young. I believe the correct approach is to do one thing at a time. When you take a student into a quiet road to drive a car for the first time, he has plenty to do in learning which is the brake and which is the accelerator, how to steer, and how to park. You do not discuss with him how to deal with heavy traffic which is not there, nor what he would do if it were winter and the road were covered with ice. But you might very well warn him that such conditions exist, so that he does not overestimate what he knows. If you try to tell him the whole truth, he probably cannot take it in all at once. AN even more important objection is -- we do not know the whole truth. Our student is young. Perhaps he will live to drive a car in the first Martian expedition. And who knows what difference in driving technique will be needed on Mars?" Mathematics is also an exploration. As we push out further, we meet new and unexpected situations and we have to revise our ideas. Rulse we have used, theorems we have proved turn out to have unforseen weaknesses. If I were asked to write on a sheet of paper all the statements that I was absolutely sure of, statements that would be true at every time and place, I should leave the paper blank." this is a good start |
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and this was only the start |
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and this was a good start |
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this was a good start |
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"Rulse" "We use rulse, ba samtaim, mang, da rulse turn out weak." |
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I remember talking to an old French mathematician. While I was staring at his rotting, yellow teeth and his pipe, he explained to me that (a) mathematical knowledge is unchaning and perfect, that (b) all things created by human beings are imperfect and that therefore (c) mathematics can't be a human construction but must expresses eternal strucutres which weren't created by human beings. ... It doesn't strike me as a good argument. But also not as an obviously bad one. ..I'm not sure what to think (....That "W. W. SaWyer"-person emphasises that he can't think of any mathematical rules which would apply in any context at any time, but that in itself isn't enough to undermine the idea that mathematical truths are eternally and absolutely true for a specific mathematical context) |
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Rulse was a typo. I capitalized the third W just for a laugh. god doesn't exist |
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