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MathGroup Archive 2002

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RE: Re: re: Accuracy and Precision

  • To: mathgroup at smc.vnet.net
  • Subject: [mg37221] RE: Re: re: Accuracy and Precision
  • From: "DrBob" <drbob at bigfoot.com>
  • Date: Thu, 17 Oct 2002 00:08:49 -0400 (EDT)
  • Reply-to: <drbob at bigfoot.com>
  • Sender: owner-wri-mathgroup at wolfram.com

Sorry, but that's not as profound as it sounds.  The speed of light is
indeed a very specific number, but that doesn't mean we can measure it
precisely.  Instead, like E or Pi or 2 or Sqrt[7], it's a defined
constant and -- unlike E or Pi or Sqrt[7] -- the definition doesn't
allow us to compute it with arbitrary precision.  Yes, it's defined now
so that it can pretend to unlimited precision -- but that only means
meters (or seconds, take your pick) aren't defined precisely.

For anything we can measure (or even COUNT, in the real world), I
suspect 16-digit machine precision is more than enough.

Bobby

-----Original Message-----
From: Kevin J. McCann [mailto:kjm@KevinMcCann] 
To: mathgroup at smc.vnet.net
Subject: [mg37221]  Re: re: Accuracy and Precision


In the "real world" of physics there are several subatomic level
processes
which can only be distinguished by small changes in the n-th decimal
place.
But there is one example which is fairly easy to comprehend, and that is
the
constancy of the speed of light in a vacuum regardless of reference
frame,
as proposed in Einstein's special theory of relativity. If this were
true
"only" to the 9th or 10th decimal place, or, for that matter, to the
50th
place, then whoever managed to show that it was not really a constant
would
certainly be in Nobel Prize territory, and much of modern physics would
need
a rewrite.

Kevin

> "Mark Coleman" <mark at markscoleman.com> wrote in message
> news:aobg22$hrn$1 at smc.vnet.net...
> > Greetings,
> >
> > I have read with great interest this lively debate on numerical
prcesion
> and
> > accuracy. As I work in the fields of finance and economics, where we
feel
> > ourselves blessed if we get three digits of accuracy, I'm curious as
to
> what
> > scientific endeavors require 50+ digits of precision? As I recall
there
> are
> > some areas, such as high energy physics and some elements of
astronomy,
> that
> > might require so many digits in some circumstances. Are there
others?
> >
> > Thanks
> >
> > -Mark






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