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MathGroup Archive 2005

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Re: Re: Language vs. Library why it matters

  • To: mathgroup at smc.vnet.net
  • Subject: [mg61428] Re: Re: Language vs. Library why it matters
  • From: "Steven T. Hatton" <hattons at globalsymmetry.com>
  • Date: Wed, 19 Oct 2005 02:16:07 -0400 (EDT)
  • References: <dipr57$hfl$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Jose Luis Gomez wrote:

> Richard Fateman, to my knowledge (I am not a Mathematician) the classic
> works of mathematician Kurt Goedel and computer scientist Alan Turing
> shows that both Mathematics and computer programs have this property:
> 
>> contrary to some comments
>>   here, it IS NOT nice to have a language so complicated that you
>> don't
>>   know what it will do, and use as an excuse that's ok because no one
>>   else knows either, and often it does the right thing.
> 
> That is, I think, the reason why Andrzej Kozlowski gave you that somehow
> ironic answer about Arithmetic. It might not be nice, but it is the way it
> is, it is a fundamental limitation of Mathematics, it is also a
> fundamental limitation of Computer Programs, it is Not a particular
> limitation of Mathematica.

I'm not sure Gödel's (anti-)proof is the core reason that Mathematica is
difficult to understand, though it certainly plays into the whole picture. 
In particular, Gödel's results tells us any sufficiently powerful language
necessarily leads to the possibility of formulating selfcontradictory
statements.  I'm not aware of Mathematica producing any such
selfcontradictions.  I am, however aware that there are a few places where
Mathematica will produce an incorrect result.  I can't provide a specific,
but the one case I remember has to do with powers of negative numbers,
IIRC.

> Let me recommend this beautiful book about the work of Goedel and the
> fundamental limitations of Mathematics:
> 
> Douglas R. Hofstadter, "Gödel, Escher, Bach: An Eternal Golden Braid"
>
http://www.amazon.com/gp/product/0465026567/103-1693629-0244650?v=glance&n=2
> 83155&s=books&v=glance
> 
> It is a beautiful book.

Indeed.  That book is very much in the same spirit as Mathematica.  I have
wanted to read it again, but every time I pick it up, I realize what a
chore it was the first time, and I simply haven't found time to commit to
the undertaking.
-- 
Hatton's Law: There is only One inviolable Law.


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