Re: [Phys-l] Sig figs

[John Denker <jsd@av8n.com>]

On 10/14/2010 10:28 AM, Rauber, Joel wrote:

> The article has an entire section entitled "A Modest Proposal",

A thousand apologies.  I was inadvertently looking at an abbreviated
version of the paper.

On 10/14/2010 09:12 AM, Rauber, Joel wrote:
> > John —  I am curious as to your opinions regarding the Journal of
> > Chemical Education
> >
> > http://pubs.acs.org/doi/pdfplus/10.1021/ed068p400
> >
> > article that you provided us.  Do you agree whole heartedly with the
> > proposal of what to teach in the article?  Agree with some
> > reservations?  Would change the proposal? Etc.

I have grave reservations about the "less modest proposal".
I could say it is better than the usual sig figs rules, but 
that would fall into the category of damning with faint praise.

For one thing, it assumes the "weakest datum" is known to ± 1
count in the last place, but this is not satisfactory.  In the 
quite common case where the datum results from roundoff, it is 
known to better than that.

For another thing, the proposal strongly implies that the same 
rules apply to all intermediate steps (not just the final answer)
... since otherwise there would be no way to know even approximately 
how much uncertainty attaches to the final answer.  Alas, applying 
such rules to the intermediate steps is a recipe for disaster if 
there are many steps.

Item (3) mixes terminology (precision versus uncertainty) without 
explanation and for no good reason.

Item (3) says that expressing the uncertainty "should be mentioned 
but not emphasized".  I don't know what that means.  Mentioned 
favorably?  Mentioned unfavorably?  I would have said almost the
opposite:  I emphasize that expressing the uncertainty separately
is /better/ and /easier/.  I would mention sig figs unfavorably 
and as briefly as possible.

Any proposal that involves digit-counting in any form (as opposed
to representing the uncertainty as a separate number) is guaranteed
to fail miserably.  At the most fundamental level, it confuses the 
issue of roundoff with the issue of uncertainty, which is not the 
same thing.  Furthermore, it represents the uncertainty in a very
crudely quantized way, which will rarely if ever be acceptable for 
serious applications.

Any proposal based on digit-counting is grossly incompatible with
electronic calculation, including hand calculators, spreadsheets,
c++ programs, or whatever (assuming any vestige of sanity remains).
Are you going to assume that they will never use any form of
calculator or computer in situations where they need to keep track
of the uncertainty?  I hope not.  Given that they need to learn to
keep track of the uncertainty separately and explicitly for computational
purposes, why not use that approach for everything?  Why learn an
additional technique that is ridiculous when implemented by hand 
and even more ridiculous when computerized?

The "modest proposal" comprises all the faults of the "less modest 
proposal" and more.

As previously mentioned:
 *) Students often do figure this out, sometimes in the first week 
  of class, sometimes later.
 *) This undermines the relationship of trust between student and 
  teacher.
 *) It puts students on notice that thinking about the material will
  just get them into trouble.