Re: Not Just the US With Education Problems

On Jun 8, 11:43�pm, John McKendry <jlastn...@xxxxxxxxxxxxxxx> wrote:
On Sun, 08 Jun 2008 23:27:54 +0000, Paul J Gans wrote:
tgdenn...@xxxxxxxxxxxxx wrote:
On Jun 8, 2:58�am, "Mike Dworetsky" <platinum...@xxxxxxxxxxxxxxxxxxxx>
wrote:
"Paul J Gans" <g...@xxxxxxxxx> wrote in
messagenews:g2f2bi$87q$4@xxxxxxxxxxxxxxxxxxxx

Walter Bushell <pr...@xxxxxxx> wrote:
In article <6ask8qF38sc6...@xxxxxxxxxxxxxxxxxx>,
"alwaysaskingquestions" <alwaysaskingquesti...@xxxxxxxxx> wrote:

Some of it may have to do with personal inclination - I have
always been fascinated with both puzzles in general and with
knowing how things work; in
my first job - just before the introduction of desktop calculators
- I had
to learn how to use a slide rule and was thought it was a
fantastic invention.

Just how old are you. Frieden calculators from the styling my
predate WWII and maybe I.

The Friden calculator was in major use up through 1970. �I recall
doing the calculations for a paper on one in that year.

Fridens had 10 digit keyboards and the high end models could
automatically extract square roots of 20 digit numbers.

See <http://www.oldcalculatormuseum.com/fridenstw.html> for a view
of a late model.

I was at an advanced summer school for teens in 1961 and we had to do
orbit calculations with calculators (!). �During the course of the
programme we took delivery of the latest Friden calculator that could
extract square roots. �For amusement one day we tried taking
concatenated square roots of a number several times then squared it
back up again. �And that's when we learned a practical lesson about
the meaning of precision and significant digits in computations.

An excellent example. By removing the time, tediousness, and human error
associated with doing monkey-work �by hand, a far more expansive lesson
can be delivered. And that was with technology from almost 50 years ago.

Carl Friderich Gauss, undoubtedly one of the most brilliant
mathematicians who ever lived, wasted three years of his live manually
calculating the orbit of the moon. �Given his productivity, we lost out
on a bunch of "Gauss's Theorems" and tons of insights.

�First of all, I'm having a hard time finding corroboration of
this story at all, so it may not even be true. One of Gauss' earliest
accomplishments was the calculation of the orbit of the asteroid
Ceres on the basis of three observations, but if that's the story
you're thinking of, it really seems to be more a counterexample
to the claim you seem to be making, because it was the sort of
creative mathematics that absolutely could not have been accomplished
with a calculator alone; it required a deep familiarity with
the geometry of conic sections. And it took three months.http://www.maa.org/mathland/mathtrek_4_19_99.html

�But if he had taken three years to calculate the orbit of the moon,
I still doubt that it would have been lost time. You make it sound
like grunt-work arithmetic, like calculating seven hundred digits
of pi. Calculating the orbit of Ceres meant inventing a new method
of calculating.

�The broader argument here seems to be about what counts as monkey
work, and I have to vote with Tim Norfolk overall. I agree that
calculating the sine of 39 degrees is monkey work, but writing out
an expression for the sine of 67.5 degrees is not. Anyone who
wants to do any level of creative work involving math should
recognize the latter as a couple of applications of basic trig
identities to the sine of 45 degrees (or better, 135 degrees).
I don't care if he/she looks in a book for the trig identities;
the important thing is to know they exist. You will never learn
the trig identities from a calculator. If all you care about
is the numeric answer, it doesn't matter, but if all you care
about is the numeric answer, you'll never learn what it is
to do math, either.

John- Hide quoted text -

- Show quoted text -

Thanks for at least one show of support.

As for the issue of Gauss, given today's computational tools, he might
have had a lot more useless digressions. I am by no means in his
league, but I have often been led astray by patterns that I saw thanks
to numerical work, or even Maple. A case in point is related to a
paper I am working on, in the zeros of complex polynomials. The actual
problem in question gives a nice distribution of same, but numerical
computation gives them all over the complex plane, as the problem is
extremely unstable.

.

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