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MathGroup Archive 2002

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Re: RE: Re: re: Accuracy and Precision

  • To: mathgroup at smc.vnet.net
  • Subject: [mg37247] Re: [mg37221] RE: Re: re: Accuracy and Precision
  • From: "Marko Vojinovic" <vojinovi at panet.co.yu>
  • Date: Fri, 18 Oct 2002 05:17:26 -0400 (EDT)
  • References: <200210170408.AAA14657@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Just two small (maybe relevant) notes:

----- Original Message -----
From: "DrBob" <drbob at bigfoot.com>
To: mathgroup at smc.vnet.net

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

Some data from 1983:

One of the millisecond pulsars, namely "PSR 1937+21", is measured to have
the period:

T=1.55780644887275 (3) ms

14 usefull digits !! In general, time intervals are the most precisely
measureable today, up to (as far as I know, at least) 18 digits. In doing
calculations with these (experimental) input, it may be important to have
even some more than just today's machine precision.

> 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.

The speed of light is *postulated* (rather then defined) constant, and
(since 1983.) in the international metric (aka "SI") system of units one
meter is *defined* to be the distance traveled by light during (exactely) 1
/ 299792458 seconds (second is defined some other way). So it follows that
the (exact) value for the speed of light is 299792458 m / s. However, the
problem is not in the correctness of this particular value (it is actually
just a convinient convention), but in the postulate that this value is the
same for all observers. To be specific, if there are two observers moving
relative to eachother and measuring the speed of light using two (in
principle) _identical_ experimental devices, the question is whether they
get the same result, ie. c' = c. Experimentally speaking, one wihses to know
how much (if at all) the quantity (c'-c)/c differs from zero. If someone
measures a nonzero value, that _would_ actually be for a Nobel...

Regards,
                 Marko

> -----Original Message-----
> From: Kevin J. McCann [mailto:kjm@KevinMcCann]
To: mathgroup at smc.vnet.net
> To: mathgroup at smc.vnet.net
> Subject: [mg37247] [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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