Re: [Phys-l] Significant figures -- again

[John Denker <jsd@av8n.com>]

On 03/07/2012 06:56 AM, Philip Keller wrote:
> To make this work, we now have to agree to add up all the quantities 
> that were measured with the same device first before adding 
> quantities that were measured with different devices.  In math
> class, order of addition never mattered.  In this strange case, it
> does.
>
> So does this scheme rescue the sig fig notion?

Nope.

It's like putting a band-aid over a melanoma.  It's like rearranging
the deck chairs on the Titanic.

Proof #1:  Consider the case where there are many devices.

Proof #2:  The sig fig method fails miserably when there are many 
readings all from the same device, all with the same number of
sig figs.  An example is discussed at
  http://www.av8n.com/physics/uncertainty.htm#sec-extracting

===

The students are not facing a logic problem or a math problem, so the
problem cannot be solved using logic or math.  It is a politics and psychology 
problem.  The best the students can hope for is to find a way to survive 
school without going crazy.  They need to find a way to give answers they 
know to be wrong, without compromising their moral principles.

Intentionally giving wrong answers offends me, and if the students are
offended, I say "good for them".

The only way I can explain it is to say that tests in school are a game.
They are not real.  They are a foolish game played by foolish rules.
By way of analogy, in football you are not allowed to throw a forward
lateral ... even though the physics allows you to throw the ball in 
any direction.  It's not physics, it's just some silly rule.  So it is 
with the test:  It isn't about physics or math or logic;  it's psychology.
It's about getting inside the head of the person who wrote the test, and 
giving them the answer they are expecting.

In contrast, the real world does not play by these rules.  In the real
world, you get paid extra if you can come up with answers different from
what was expected.



On 03/07/2012 08:44 AM, Richard L. Bowman wrote:

> > As to the way that I teach the concept, or have had it taught to be
> > in chemistry and physics classes, is that the rules only apply to the
> > final results. One should not apply it to intermediate results on the
> > way to a final answer. 

We agree that rounding off intermediate results is a disaster.

However, sorry, that doesn't solve the problem.  Not even close.  For 
starters, rounding only the "final" results is just another rule that 
only works in the classroom, where the assignment was artificial busywork 
to begin with, and nobody really cares about the answer.

In the real world, one person's "final" result is starting point for
some other person's work.

Stating the uncertainty separately and explicitly is *easier* and in
all ways better.  For details, see
  http://www.av8n.com/physics/uncertainty.htm