Re: Are there any non-gifted scientists?!?!?
From: Nick Landsberg (hukolau_at_NOSPAM.att.net)
Date: 04/30/04
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Date: Fri, 30 Apr 2004 15:57:21 GMT
Gregory L. Hansen wrote:
> 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.
Another great benefit of doing it this way (rather than just
punching numbers into a calculator), is that you can see
if one of the data points looks "wrong", e.g. 9 of 10 are
(alost) in a straight line, while one of them is way off.
Seeing this, you should then go and repeat that particular part
of the experiment. (If you have a decent graphing calculator
you can do the same thing, of course, but in my experience
few folks bother at first.)
>
> 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.
>
>
-- "It is impossible to make anything foolproof because fools are so ingenious" - A. Bloch
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