From: mss2@quads.uchicago.edu (Michael S. Schiffer)
Subject: Re: The Nightstalker makes an observation
Reply-To: mss2@midway.uchicago.edu
Organization: University of Chicago Computing Organizations
Date: Wed, 22 Jul 1992 07:23:04 GMT

In article <1992Jul22.062757.1257@cco.caltech.edu> lydick@SOL1.GPS.CALTECH.EDU writes:
>In article <1992Jul20.235149.10798@ucc.su.OZ.AU>, ablanch@physics.su.OZ.AU (Shonias) writes:


>>"Eeeessshhhh! I spend a lot of time in the lab trying to stop people doing
>>that sort of thing! Sorry StM, but that doesn't make sense! The number of
>>significant figures is a measure of how accurately we know something. There
>>is no rounding involved, it is a measure of error, so that disposes of one of
>>the problems you errr, specifically didn't follow up. :)

>But my point was simply that you were willing to take 500 and 1500 as meaning
>500 and 1500 exactly.  I.e., in the context of the statement, 1000 was
>considered to have one significant figure, while 500 was taken to have three,
>and 1500 four.

	"The problem is that the numbers are being used for two
different things.  500 and 1500 are pure numbers.  1000 is being used
as a measure of a particular object or phenomenon-- significant
figures represent a level of precision, and precision is only
meaningful when something is being measured.  Thus 1000 (or, to
remove ambiguity about the number of sig figs, 1*10^3) means "the
quantity being measured has been determined to lie between a minimum
of "exactly 500" and a maximum of "exactly 1500".


>>So, that means that
>>the *true* value lies between 500 and 1500, significant figures are meaningless
>>in reference to a true value, since if it is an exact amount, there is no 
>>error involved. Now as to what *defines* this true value, I'll leave that
>>to the mathematicians, but this was a measurement that we are discussing, the
>>domain of physicists (and others), and so we can assume that there is a real
>>value, and that it lies between 500 and 1500, no significant figures, since 
>>the whole point of significant figures is to imply that range."

>Again, my point was simply that when I used the numbers 500 and 1500, you
>didn't apply the idea of significant figures to them.  In other words, the
>number of significant figures a number has depends on context.

	"Well, yes.  Significant figures are simply a scientific
convention.  The quantity 1*10^3 could just as easily be written
500>x>1500, or 1000+-500, or any number of ways.  But any way of
representing a number with respect to a real phenomenon is an
approximation, whether it's stated to be or not.  When a measuring cup
says it holds a pint of liquid, it really means it holds a pint plus
or minus an amount not considered significant; human artifacts aren't
mathematically precise.  In science, it's often helpful to know the
degree of possible error involved-- hence the convention of
significant figures.

	"In normal language, any measurement has the implicit proviso
"within a reasonable tolerance".  If a normal household thermometer
says it's 70 degrees F, you can be sure it's not really fifty (unless
it's broken) but you can't be certain it's not 69 or 71.  If I say
Chicago is 250 miles from Ann Arbor, it's certainly not 500, but it
may be 240 or less-- and even if I look up a more accurate figure,
it's sure to be off by hundreds of feet.  Lack of precision is not the
same thing as untruth-- or, alternately, _no_ claim we make about the
world is true, because none of them are exact.  We know the mass of an
electron to a pretty extreme number of decimal places, but there's
still a built-in error even to that calculation.  Ditto for our
estimates of c, G, and h.  Mathematical concepts can be made as
precise as we wish to calculate them, but physical reports are _always_
estimates."

Michael


-- 
Michael S. Schiffer, LHN, FCS	"Workers of the world, forgive me.
mss2@midway.uchicago.edu	 You had more to lose than I thought."
mike.schiffer@um.cc.umich.edu	 -- Karl Marx (1990) as imagined by
mss2@usite-next.uchicago.edu     Jim Koncz (konc@midway.uchicago.edu)
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