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[Phys-L] Re: infinite sig. figs.



If a student gave an answer of 0.285714286 m/s, Robert Cohen said... "I
would remind the student that people typically interpret (correctly or
incorrectly) the uncertainty of such a number as being around +/-
0.0000000005 m/s."

John Denker responded... "Remember Feynman's motto, 'What do you care
what other people think.' I'm not responsible for what other people
'typically' do. I'm only responsible for what I do. If there are two
ways of doing something, i.e. "correctly or incorrectly", I choose to do
it correctly."

I find myself between these two stances. Mostly I try to do what is
right and mostly I don't care what the wrong people think. But I do
think it is our responsibility to warn students of pitfalls they might
fall into, or prejudices they might run up against.

Since the primary goal of using words and numbers is to communicate, we
ought to warn students of the miscommunication that might arise when
they are not careful with their words and numbers.

For example, I encourage students to use giga rather than billion, and I
encourage them to use tera rather than trillion. Part of this
encouragement includes my warning that in much of the world people
hearing billion will think 10^12 rather than 10^9, and those same people
will think 10^18 for trillion rather than 10^12.

Likewise, when I tell them the number 5.000 inches by itself does not
really mean 5 inches plus-or-minus 0.001 inch, I think it's okay (and
even wise) to warn them some people will think it means plus-or-minus
0.001 inch. Therefore, before writing down 5.000 inches, students might
want to think about why they are including so many zeroes, and if it
might be better to use fewer zeroes... or better yet, for them to
indicate an uncertainty or tolerance.

Even though 5.000 does not mean +/- 0.001 to me or the student, some
people will indeed infer that, and students ought to know that.

Above is my main message. Below is an example that happened to me in
grad school. It's about tolerances instead of uncertainties, but the
idea of good communication is the same.

I was involved in a large instrument-building project in graduate
school. In my first year I designed a vacuum chamber with several
ports. The ports and the flanges that fit into them were about 5-inches
diameter. At that time I had little experience in designing or
machining at the one-mil level, let alone the tenth-mil level the MSU
Cyclotron machinist were capable of. In my chamber drawing I labeled
the ports as 5.000 inches. In a separate drawing I labeled the flanges
as 5.000 inches.

Some on this list have said that errors like this are expensive errors.
Actually, this was not an expensive error because these machinist were
so good it didn't really take them any more effort to make the flange
5.000 +/- 0.001 inches than to make it 5.00 +/- 0.01 inches. However,
it was a good lesson in communication, and a good lesson in making
things fit. The expense was my pride.

The head machinist was a great teacher as well as a great machinist. He
knew exactly what was going on, and he intentionally made the ports and
the flanges within a tenth-mil of 5 inches. Of course when I picked up
the parts, the flanges would not fit into the ports. I accused him of
making the ports too small or else the flanges too big. He patiently
help me measure them, and of course we found they were both essentially
"right on" 5 inches.

He went on to explain two important things to me. (1) When something is
going to fit into something else, the inner piece has to be a little bit
smaller than the outer piece. (duh!!!) (2) There is a way to
communicate this to the machinist that will make clear what needs to
happen. Write the port size as 5.000 - 0/+0.002 and write the flange
size as 4.995 -0.002/+0. This sizing provides 5 mils clearance if the
machinist hits it "right on," and the notation also tells the machinist
it is okay to err 2 mils on the large side for the port, and okay to err
2 mils on the small side for the flange. In the best case I get 5 mils
clearance and in the worst case I get 9 mils clearance. If I want to
specify less slop, I can do so, but this is about right for a typical
5-inch flange for what I was doing.

He went on to say that if you don't specify a tolerance then the typical
machinist will assume +/- 1 in the last digit specified... but in this
case he actually did +/- 0.1 in my last digit because he wanted to show
me it was no sweat for him to do +/- tenth-mil, and he knew I'd be back
with a flange that didn't fit and he wanted to teach me a lesson. Over
a four-year period I learned a lot from this man.

I don't think it hurts, and I think it can be very positive, to warn
students how their words and numbers are going to be interpreted even if
the people making that interpretation are doing the wrong thing.

Michael D. Edmiston, Ph.D.
Professor of Physics and Chemistry
Bluffton University
Bluffton, OH 45817
(419)-358-3270
edmiston@bluffton.edu
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