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Re: Re: Mathematica 7.0.1.0 and some General Comments

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  • Subject: [mg97491] Re: [mg97448] Re: Mathematica 7.0.1.0 and some General Comments
  • From: David Bakin <davidbak at gmail.com>
  • Date: Sat, 14 Mar 2009 05:38:44 -0500 (EST)
  • References: <goqphr$lt2$1@smc.vnet.net> <gp5fou$9nr$1@smc.vnet.net>

Absolutely true.  I would say that the way to start "believing" a proof that
is justified by software is to replicate the results, which is what
physicists and other scientists do.  A different team in a different
laboratory using different equipment tries the same experiment.  Or,
preferably, a different experiment.

In the case of mathematical proofs, additional confidence could be gained by
using a different program.  And by different program I mean not only the
CAS, but also the code written on top of the CAS that performs the
calculation.

In any event I would think that the code that led to the proof should be
made available to anyone who wishes to check the results.  (Note that the
Climate Audit blog is full of discussion and controversy over the fact that
a lot of results used in making policy decisions in the "global warming"
debate are based on computer models where the actual computer code is not
made available to people attempting to replicate the results, so that even
if the data sets are made available, the reported results can't be
duplicated.)

I'm not saying this will lead to computer-aided proofs being believed in
general, nor am I saying that it will lead to a level of confidence that
current non-computer-aided proofs have, just that in the case of any
particular computer-aided proof a result replicated using different software
will gain credibility.
On Fri, Mar 13, 2009 at 2:52 AM, Szabolcs Horv=E1t <szhorvat at gmail.com> wrote:

> This is a very misleading argument---a nasty sophism, I should say.  And
> it's quoted way too much.  A piece of software is not any less buggy by
> virtue of being open source.
>
> The sane approach is to accept that software are buggy, and check the
> results with different methods rather than e.g. learning the theory of
> indefinite integration, and start reading open source system X's source
> code.  (Unless your field of research happens to be indefinite
> integration, of course.)
>
> Blindly trusting open source programs leads to just as bad mistakes as
> blindly trusting commercial software (expect that with the current state
> of scientific software, it is likely to take longer and be more painful
> to obtain those bad results with open source programs than with the
> popular commercial choices).
>
>



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