Re: [Phys-l] formatting uncertainties

[John Denker <jsd@av8n.com>]

On 01/23/2008 01:34 PM, Savinainen Antti wrote:

> Here is how I do it. The level of discussion regarding uncertainty
> analysis depends on the group.  I have two presentations on
> propagating error/uncertainty: 

OK.

> the first one is required by the IB
> exams and contains typical HS rules of thumb. 

Sigh.

> The second presentation
> is introduced if I feel that my students are up to it. It makes use 
> of partial derivatives and discusses assuptions underlying the Least
> Square Fit and so on (still elementary but a bit more demanding than
> the first take). 

I think you might be skipping a step there.  Early in the process
(not on Day One, but long before going anywhere near partial
derivatives) you should teach numerical, iterative methods for
dealing with uncertainties
 -- Start with "crank three times"
  http://www.av8n.com/physics/uncertainty.htm#sec-crank3
 -- You can extend that in various ways with progressively
  fancier spreadsheets.
 -- Eventually that segues to full-blown Monte Carlo.
  http://www.av8n.com/physics/uncertainty.htm#sec-mg-mass

Such numerical methods require very little sophistication ... yet
give *better* results than anything you could do with partial
derivatives, in most cases.  In particular, if there are
constraints or correlations (as there usually are), the partial
derivative method gets quite nasty, while the Monte Carlo just
perks along.
  http://www.av8n.com/physics/uncertainty.htm#sec-mg-mass



=====================================



On 01/23/2008 02:48 PM, Rauber, Joel wrote:

> > Do you find any merit in discussing significant figure rules for the
> > simple silly but practical reason that students may be tested on them?

1) Agreed, silly. 

2) The California Science Framework
  http://www.cde.ca.gov/re/pn/fd/documents/scienceframework.pdf
has only one passing mention of significant digits.  That's on
page 202, in the chemistry section.  The science Standard doesn't
mention sig figs at all AFAICT.  So I reckon a California high 
school physics teacher could duck the issue without fear of 
serious repercussions.

3) The Framework says  "they should learn the rules of significant 
digits when reporting measurements and the results of calculations."
However, it doesn't say what the rules are.  I'm quite sure I
don't know what the sig figs rules are.  All evidence indicates
there is a raging lack of consensus on this list, and in the
literature.  Therefore it is unlikely that the test will have 
any very incisive questions about sig figs.

4) Folks should agitate at every opportunity to get sig figs
entirely removed from the standard and the framework.

5) Detailed instructions on how to survive an attack of the sig
figs can be found at
  http://www.av8n.com/physics/uncertainty.htm#sec-survival

Disclaimer:  Nothing I say is to be construed as an endorsement 
of using sig figs for any practical purpose.

> > Also, for the reason that they may have to communicate with folks who
> > talk about those rules?

What's next?  Are we going to teach Intelligent Design so
students can "communicate with folks" using ID terminology?


Sure, I'll /mention/ sig figs ... on the same day that I mention
homeopathy and magnetic copper anti-arthritis bracelets and DRE
(direct recording electronic) voting machines and filled Lewis 
"octets" in molecules and sending .doc format files and Intelligent 
Design and shared passwords and various other things you really 
ought to be avoiding.