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Re: Using Mathematica results in publications


  • To: mathgroup@smc.vnet.net
  • Subject: [mg11788] Re: Using Mathematica results in publications
  • From: gwinn@xyz.ma.ultranet.com (Joe Gwinn)
  • Date: Sat, 28 Mar 1998 00:25:23 -0500
  • Organization: Gwinn Instruments
  • References: <6fd5i8$6ba@smc.vnet.net>

I suspect that even if one had full access to the source code of
Mathematica, it wouldn't solve the problem of belief or non-belief,
because it would be in practice impossible to prove that it's correct
given the sheer bulk of Mathematica.  In fact, the existence of bugs
proves that it isn't correct in the strict mathematical sense. 
Therfore, I would submit that the "solve it twice, by two different
methods, and compare the results" approach is the only practical
solution.  This is true regardless of the use or non use of
Mathematica, or any other tool, of any kind.

As for use in publication, I don't see how this differs from use of
printed table of integrals.  Such tables can be wrong, and people can
mis-apply them, etc.  The cross-check is still required if the result
is to be believed.

There is a parallel in Quantum Mechanics, the Correspondence Principle,
which holds that because Newtonian Mechanics well describes centuries
or millennia of experimental results, it is in a very strong sense
correct, so Quantum Mechanics had better reduce to Newtonian Mechanics
when Planck's Constant is set to zero.  Likewise, Relativity had better
reduce to Newtonian Mechanics when the speed of light is set to
infinity.  In practice, this is a very powerful mistake detector.

Joe Gwinn


In article <6fd5i8$6ba@smc.vnet.net>,
"=?iso-8859-1?B?TeFyaW8gU2FuY2hvIEdyYedh?="
<mario_sancho.graca@virgin.net> wrote:

> It's a problem of scientific method, in my view. The fact that the
> internals are not public is irrelevant, just as most people do not care
> about the availability of the Windows operating system source code. I
> do base some of my research on Mathematica output, but so far I have
> always compared results given by two different algorithms (possibly
> both accomplished via Mathematica, why not?), in some cases one giving
> analytical results and the other numerical. What I will not do is
> believe the result of an integral extending through 100 pages with no
> further cross-checking.
> 
> 
> -----Original Message-----
> From: Linc Davis <l_davis@ix.netcom.com> To: mathgroup@smc.vnet.net
To: mathgroup@smc.vnet.net
> Subject: [mg11788] [mg11699] Using Mathematica results in publications
> 
> 
> >Given that the internals of Mathematica are not public, are there any
> >practical or philosophical problems involved in using the results of
> >its computations in published research? Obviously this has to be done
> >with proper attribution, but aren't you just taking Wolfram's word for
> >it that the results are accurate? Just wondering. Thanks for replies.
> >
> >--
> >Lincoln R. Davis
> >(e-mail address is valid)
> >
> >

-- 
Remove "xyz." to get a usable address.



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