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[science] calculus

offline EpicMegatrax from Greatest Hits on 2017-10-12 20:41 [#02533870]
Points: 9869 Status: Regular

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


offline mohamed on 2017-10-12 22:10 [#02533905]
Points: 25582 Status: Addict | Show recordbag

and this was only the start


offline EpicMegatrax from Greatest Hits on 2017-10-12 22:15 [#02533907]
Points: 9869 Status: Regular

and this was a good start


offline EpicMegatrax from Greatest Hits on 2017-10-12 22:15 [#02533908]
Points: 9869 Status: Regular

this was a good start


offline jnasato from (Antarctica) on 2017-10-13 08:46 [#02533946]
Points: 3375 Status: Lurker | Show recordbag


"We use rulse, ba samtaim, mang, da rulse turn out weak."


offline welt on 2017-10-13 12:58 [#02533955]
Points: 1855 Status: Lurker

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)


offline EpicMegatrax from Greatest Hits on 2017-10-13 16:48 [#02533969]
Points: 9869 Status: Regular

Rulse was a typo. I capitalized the third W just for a
laugh. god doesn't exist


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