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Re: Re: Re: Language vs. Library why it matters

• To: mathgroup at smc.vnet.net
• Subject: [mg61311] Re: [mg61245] Re: [mg61230] Re: Language vs. Library why it matters
• From: "Jose Luis Gomez" <jose.luis.gomez at itesm.mx>
• Date: Fri, 14 Oct 2005 22:22:50 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

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. 

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.

Best regards!

José Luis


----Mensaje original-----
De: Andrzej Kozlowski [mailto:andrzej at yhc.att.ne.jp] 
Enviado el: Viernes, 14 de Octubre de 2005 04:54 a.m.
Para: mathgroup at smc.vnet.net
Asunto: [mg61245] Re: [mg61230] Re: Language vs. Library why it matters


On 13 Oct 2005, at 14:39, Richard J. Fateman wrote:

> 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.


Actually, a "language" need not be terribly complicated for that. It  
only needs to contain the axioms of arithmetic...

Andrzej Kozlowski
Tokyo, Japan