Re: Are there any non-gifted scientists?!?!?

From: Gregory L. Hansen (glhansen_at_steel.ucs.indiana.edu)
Date: 04/30/04 

Date: Fri, 30 Apr 2004 14:15:18 +0000 (UTC)

In article <5f6b0df.0404291822.3a9bb341@posting.google.com>,
Der Fugue <bwvbabygotbach@netscape.net> wrote:
>Ken Pledger <Ken.Pledger@vuw.ac.nz> wrote in message
>news:<Ken.Pledger-2F3BD3.10234030042004@bats.mcs.vuw.ac.nz>...

>>
>> Don't overlook mathematical statistics. Many people (including
>> physicists) have a very shallow idea of what it is. After you know
>> enough basic calculus, a good introduction to statistical theory could
>> be a real eye-opener in many ways.
>
>Interesting... you're the second (third?) person to bring up
>mathematical statistics. Right now I'm taking AP stats at my high
>school, and I'm not too fond of the course. 89 first marking period
>:-/, although that *was* the 4th highest grade in the class. I've got
>the College Board examination for this class on Tuesday, which I
>should probably be studying for right now..
>
>My biggest qualm with the curriculum is that it is essentially based a
>combination of rote memorization and graphing calculator usage. We do
>linear regression on our calculators, for example, but never learn how
>to do it by hand. There are a number of rules and procedures that
>need to be memorized, but understanding the REASONS for them is
>unimportant in the eyes of the College Board. At one point I made it
>a priority to actually understand the concepts, but I realized that
>simply memorizing them was much more time effective and earned me
>better grades on the tests. I really can't blame my teacher (or my
>intro textbook) for this, because again, the College Board simply
>doesn't think understanding statistics from a mathematical point of
>view is important, and with time constraints and such it's just
>impractical to expect these concepts to be actually TAUGHT in a
>classroom environment.

Working out the formulas they're giving you requires calculus.

The big reason for the scientist to know something about statistics is the
analysis of data.

Before there were computers to crunch the numbers, it was common to use
graphical techniques. To take a very simple example, maybe you're trying
to find a spring constant, and you generate some extensions versus force
and graph x versus F. You expect a straight line, F=-kx. People have
literally taken a peice of thread to the graph and moved it around so that
as many points were above as below, and called that a best fit. And then
found the steepest and shallowest angles that would fit into the data and
called them the uncertainty of the measurement.

If they were looking at something like the distance an object falls versus
time, x=0.5*g*t^2, they would linearize it by plotting x versus sqrt(t).
Many types of graph paper were (and maybe still are) available with the
axes scaled in different ways. Log scales are still commonly used, with
the major ticks going e.g. by 0.1, 1, 10, 100, 1000...

That's basically what you're doing with your calculator. But it's a great
help for fitting to something like a periodic function, since it's hard to
fit a straight peice of thread to a sine wave. 

-- 
"Very well, he replied, I allow you cow's dung in place of human 
excrement; bake your bread on that." -- Ezekiel 4:15

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