Re: [Phys-L] Sig Figs homework from my 7th grader

[John Denker <jsd@av8n.com>]

On 10/09/2013 07:42 AM, Paul Nord wrote:
> For this exercise the student is intended to presume that these are
> scientific data where the uncertainty is indicated by the number of
> significant digits.

When real scientists do it, uncertainty is *not* indicated by
the number of digits!  People who care about their data do not 
use sig figs.  For details on how to do things right, see
  http://www.av8n.com/physics/uncertainty.htm

Real measurements have noise on them.  Very often the significant
signal is /below/ the noise, and must be extracted via signal
averaging, curve fitting, et cetera.  Sig-figs rules require 
rounding off to get rid of the noise.  That means everybody gets 
the same answer, with no noise ... but the baby has been thrown 
out with the bathwater.

This reminds me of wacko-bird politics.  That is, the important 
thing is for everybody to get the same answer.  Getting the wrong 
answer is perfectly fine, so long as everybody gets the /same/ 
answer.  This is just one example of the Kadavergehorsamkeit 
that is so very common in primary and secondary school.  I find
it nauseating.

Sig figs /requires/ people to keep rounding off until roundoff 
error becomes the dominant contribution to the overall uncertainty.
This is scientific malpractice.  In a well-designed experiment,
roundoff error is almost never the dominant contribution.

I've heard people say that sig figs rules are a "convenient" 
way of getting the wrong answer, but it's even worse than that,
because they are not even particularly convenient.  In most 
cases the simple rule "keep plenty of guard digits" is easier
and in every way better.

Sig figs are incompatible with any real understanding of the
decimal number system.

Sig figs are incompatible with any real understanding of what
probability is.  There is no such thing as an uncertain number.
If it's uncertain, it's not a number.  If it's a number, it's
not uncertain.  You can have an uncertain distribution over
numbers, but then the uncertainty is in the distribution, not
in any particular number drawn from the distribution.  Most
observations do *not* have error bars.

Sig figs are incompatible with any notion of /correlated/
uncertainties.  This is a Big Deal in numerical analysis,
even in familiar simple cases such as the quadratic formula.

To a good approximation, the only time anybody cares about sig
figs is on days when the the teacher requires them to do so.
You can confirm this using Google Trends.  Plot "significant
figures" against something people actually care about, such
as "fingernail polish" or "cardboard" or "shiitake" or even
something scientific like "lagrangian".  Sig figs have a huge
peak at the start of the fall semester and a subsidiary peak 
at the start of the second semester.  Things that people care 
about for non-trumped-up reasons are much less peaky.
  http://www.google.com/trends/explore?q=%22significant+figures%22#q=%22significant%20figures%22%2C%20shiitake

The sig-figs rules that are taught in high-school chemistry do
not work in practice.  Simple examples suffice to prove this.
Students know this!  They take it as evidence that the teacher 
cannot be trusted.

People complain that students do not exhibit critical thinking
in class.  Well, there's a reason for that.  They are perfectly
capable of critical thinking, but they have learned that it is
not tolerated on school grounds.