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