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Re: [Phys-l] J.D. uncertainty



On 08/22/2011 03:18 PM, Richard L. Bowman wrote:
I emphasize sig figs to my intro level students, both majors and
non-majors, so that they do not just blindly report all of the digits
their calculator gives them.

Are you sure that there are only two possibilities? Have you ever
considered that there might be other possibilities, other than
a) emphasis on sig figs, and
b) blindly reporting all of the digits their calculator gives them.


generally if one reports a measurement of 3.12 cm in the sig figs
method, then the usual implication is that due to rounding the
uncertainty is ± 0.005 cm

Alas, that is not "generally" or even "usually" true. I have here
a whole stack of textbooks that teach students to write down all
of the certain digits plus one uncertain digit ... in which case
3.12 has an uncertainty of /at least/ 0.01, possibly more, possibly
quite a bit more.

One of the many pernicious things about the sig figs rules is that
people seem to change the rules back and forth, again and again,
all while expecting students to memorize "the" rules.

Another pernicious thing is the blurring of two ideas, namely roundoff
error and uncertainty. In a well-designed experiment, roundoff error
is not "generally" or even "usually" the dominant contribution to the
uncertainty.

even on exams, we want them to think about uncertainties

Thinking about uncertainty using tools that don't make sense is
worse than nothing. It rewards rote learning and mindless application
of rules, and penalizes critical thinking.

Yet another pernicious thing about the sig figs doctrine is that it
means I cannot write down any number without -- allegedly -- being
forced to imply something about the uncertainty. I object! All day
every day, I need to be able to write down numbers without knowing
the uncertainty. It might be days or months or years before I figure
out the actual uncertainty of this-or-that number.

My advice: If you have a number, just write it down. Write it down
with plenty of guard digits. Write it down now. You can worry about
the uncertainty later, if at all.