[Phys-L] Re: infinite sig. figs.

[John Denker <jsd@AV8N.COM>]

Folkerts, Timothy J wrote:
> > I don't understand any of what has been said about rounding off
> > "immediately prior to reporting" as opposed to rounding off
> > intermediate results.
>
> That seems like just a corollary of your own rules.=20

Oh.  That explains a few things.
  -- If the argument is that the same rules applied in different situations
   lead to different conclusions, then of course I agree.  In particular,
   copious insignificant digits in the registers of a computer are harmless,
   but written into a report (final or otherwise!) they would be a bother.
  -- If the argument is that final reports are governed by different rules,
   just because they are "final" or "reported", then I'm still confused and
   skeptical.

> I don't see the rationale that every report must be as precise as hum=
> anly possible or it is useless, which seems to be what you are saying=
> .  For example, from today's news: "In all, nearly 2 million people a=
> long the Texas and Louisiana coasts were urged to get out of the way =
> of Rita,

That's all fine ... but it represents a sharp change in topic.

It is, alas, all too common when discussing the dreaded "sig figs" for
there to be confusion as to whether the topic of discussion is uncertainty
or significance.  These are *not* the same notion.
  -- Bean counting may have very low significance, out of all proportion
   to the uncertainty.
  -- Signal averaging may render a signal significant, despite a huge amount
   of uncertainty in the raw signal.


Suppose the number of evacuees was known to be exactly 2,000,003.  The
newscaster would be within rights to round that off to 2 million, on
the basis that the details were not _significant_ in the context of
the news report.

In contrast, one of the major requirements of scientific work is to
evaluate and report the _uncertainty_ of results.  In some cases the
scientist may additionally opine as to the significance of the results,
but this does not lessen the responsibility to report the uncertainty
of the results.  In other cases, the result will have many disparate
applications, and what is significant in one application may be
insignificant in another.  From this we conclude that significance is
not an inherent property of a measured or calculated result (in
contrast to uncertainty, which is inherent).

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

It is scandalously ironic that students are asked to report the /uncertainty/
of their results using _significant_ figures.  Urk, what's next?  Shall we
ask them to report /significance/ using _uncertain_ figures?  :-)

No wonder the students are confused.
_______________________________________________
Phys-L mailing list
Phys-L@electron.physics.buffalo.edu
https://www.physics.buffalo.edu/mailman/listinfo/phys-l