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

[Jack Uretsky <jlu@HEP.ANL.GOV>]

        Simply repeating the seemingly nonsensical statement:

>  The contention that the result of a calculation, with
> numbers obtained from measurements, is to be interpreted as a
> significant number is practically certain to deceive...

        does nothing to aid my understanding.  I gave, in my posting, a
current example involving the "result of a calculation, with numbers
obtained from measurements."  The community is debating whether an
experimental result that lies outside of the uncertainty of the computed
result possibly signals evidence for "new physics".  See my paper in
Physics Letters, B523:299-303,2001. [hep-ph/0106145], for a flavor of the
discussion. Note that I am talking about uncertainty - NOT sig digs.

                                        Regards,
                                                Jack

On Thu, 22 Sep 2005, Strickert, Rick wrote:

> > I totally don't understand Delury (as quoted).
>
> In his paper, "Computations with approximate numbers", _The Mathematics
> Teacher_, Vol. LI, No. 7, Nov., 1958, pp.521-30, Daniel Delury states:
>
> "In any event, the theory of errors provides us with the only usable
> tool we have for dealing with errors of measurement.  This tells us,
> among other things, that the treatment of errors cannot be undertaken as
> an exercise in arithmetic.  The basic requirement is that the program of
> measurement be so arranged as to permit the estimation of a standard
> deviation, in terms of which the precision of the measuring process can
> be stated."  (p.525)
>
> "Above all, we must scotch the notion that the precision of an average
> or of a single measurement can be judged from the way in which it is
> written." (p. 528)
>
> "And after all, what difference does it make if one person runs his
> calculations out to, say, two more decimal places than another? As long
> as they have not stopped too soon, the basis for a preference between
> them is largely aesthetic.  Of course, before we can adopt this
> indulgent view, we must get rid of the notion, to which we never had any
> right, that we are dealing with significant numbers.  It is this notion
> that has led to the view that too many decimals in the answer imply
> deception.  As far as deception is concerned, the shoe is entirely on
> the other foot. The contention that the result of a calculation, with
i> numbers obtained from measurements, is to be interpreted as a
> significant number is practically certain to deceive...
>
> "To sum up, then let us keep the significant number where it belongs, as
> a convenient convention for writing answers in pure arithmetic.  It has
> no other use."  (p.530)
>
> Rick Strickert
> Austin, TX

--
"Trust me.  I have a lot of experience at this."
                General Custer's unremembered message to his men,
                just before leading them into the Little Big Horn Valley
_______________________________________________
Phys-L mailing list
Phys-L@electron.physics.buffalo.edu
https://www.physics.buffalo.edu/mailman/listinfo/phys-l