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Re: Types in Mathematica, a practical example

• To: mathgroup at smc.vnet.net
• Subject: [mg62940] Re: [mg62800] Types in Mathematica, a practical example
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Fri, 9 Dec 2005 05:10:20 -0500 (EST)
• References: <000f01c5fbf8$e3979330$996f1081@fy.chalmers.se>
• Sender: owner-wri-mathgroup at wolfram.com

On 8 Dec 2005, at 22:11, Ingolf Dahl wrote:

> I feel it as a round-about way to solve the problem.
> Andrzej Kozlowski, who suggests such a solution, thinks that I am  
> looking at
> Mathematica from the wrong view point. It is my strong belief that one
> should be able, especially when mathematics is involved, to observe  
> from as
> many different view points as possible. An item is not really  
> beautiful, or
> properly designed, if it is not beautiful from all view points. The  
> same
> should apply to Mathematica, and I have also understood that  
> Mathematica was
> intentionally designed to be well-behaved when seen from different  
> view
> points. Or?


About mathematics: it seems to me that almost all beautiful solutions  
of difficult problems involve finding the right "point of view".   
Often once the right point of view is found the problem is almost  
solved, while from the other "wrong" points of view the problem looks  
extremely hard  and often uninteresting - (usually because it appears  
that the only way to solve it is by a tedious computation or, in the  
case o finite problems, by an exhaustive examination of all possible  
cases).

About Mathematica: it is true that Mathematica allows many styles of  
programming and that this has many practical advantages, but it  
certainly is not true that all these styles are equally efficient,  
elegant and equally suitable to all types of problems. So if you mean  
that for any problem that one wants to tackle with Mathematica it  
should not matter whether you choose a functional approach, a  
procedural approach, a re-write rule based approach, a recursive  
approach etc,  well this definitely is not true and I do not think it  
is reasonable to expect otherwise. In a similar vein in mathematics  
certain problems are more suited to be tackled with algebraic  
techniques, certain with topological, others with analytic etc.

About  your concrete proposal : I personally do not think it would  
fit in well with the functional style of programming that is usually  
the most natural way to tackle problems involving lists, matrices etc  
in Mathematica and also I  do not feel any need for what you are  
proposing and hence do not see any benefit if something of this kind  
were to be implemented in Mathematica. But I am sure that this is  
just a matter of taste, exactly as my preferring certain areas of  
mathematics to others is only a matter of taste.

Andrzej Kozlowski