[Phys-l] uncertainty +- error (was: misconceptions)

[John Denker <jsd@av8n.com>]

On 09/30/2011 10:28 AM, Bill Nettles wrote:
> I think it's more important for high schoolers (and all of us) to
> honestly look for sources of error before taking  measurements and
> getting to the nitty-gritty of calculating errors.

That's for sure.  It does no good to carefully calculate one
contribution to the uncertainty while ignoring other contributions.
  http://www.av8n.com/physics/uncertainty.htm#sec-all-contributions


That is part of a rather detailed writeup on how to handle uncertainty:
  http://www.av8n.com/physics/uncertainty.htm

I recently revised it, including a new emphasis on the distinction 
between the /indicated value/ and the corresponding range of /true values/.
  http://www.av8n.com/physics/uncertainty.htm#sec-indicated-true

Also, a suggestion:  It may be helpful to emphasize the word "uncertainty"
rather than "error".

Gross misunderstanding of what we mean by "error" has got to be high
on any list of misconceptions ... affecting students and everybody else.

A lot of people think "error" always means mistake or blunder.  Some
people think that an error is Wrong with a capital W, in the same way 
that lying and stealing are Wrong i.e. sinful.  This is absolutely 
not what we mean by "error" in this context.  

One good example to illustrate what we *do* mean is a comparator that 
shows a green light when the voltage is between -12 and +12 volts,
and a red light otherwise.  There is a wide range of voltages that
correspond to the "green" indication, so we will always be uncertain
about the true voltage ... but this is not a blunder.  That range
was carefully designed, and serves a useful purpose.  See also
  http://www.av8n.com/physics/uncertainty.htm#sec-error-mistake

There is also some discussion of the many reasons why no matter
what you are trying to do, sig figs are the wrong way to do it:
  http://www.av8n.com/physics/uncertainty.htm#sec-execsum-sigfig

Any student with one iota of critical thinking ability has already 
figured out that the sig figs rules don't make sense.  Teaching
sig figs just puts everybody on notice that  critical thinking is 
not tolerated in school.

I don't actually care very much either way about sig figs per se 
... but I do think critical thinking is kinda important.  If you 
want to promote critical thinking, one of the first steps is to 
stop requiring students to learn stuff that cannot possibly be 
true.

This is not easy, but it needs to be done.