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MathGroup Archive 2005

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Re: Re: Re: Re: Types in Mathematica

  • To: mathgroup at smc.vnet.net
  • Subject: [mg62303] Re: [mg62277] Re: [mg62273] Re: [mg62258] Re: [mg62245] Types in Mathematica
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Sat, 19 Nov 2005 23:18:30 -0500 (EST)
  • References: <200511191053.FAA16418@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

On 19 Nov 2005, at 19:53, Virgilio, Vincent - SSD wrote:

>
> Well now it's getting philosophical.  I did say "in trying to
> understand", not "in trying to use".

Yes, indeed. But in my understanding of the preceding discussion the  
advice "forget C++" referred to the attitude one should adopt when  
programming in Mathematica. At least that certainly was my meaning.  
Again, I will repeat what I meant: thinking in terms of C++ or Lisp  
will be no help and most likely will be a hindrance in writing good  
Mathematica programs. This is all I have been trying to say in this  
thread and no more.
>
> Anyway, it is always helpful to revisit first principles, novice or  
> not.
> And since nothing is understood in a vacuum, so the suggested
> comparisons.

"Understanding" is a difficult "philosophical" concept. It is true  
that usually people "understand" new things by trying to form  
analogies with other things that they consider as "already  
understood". But once they reach a certain level of understanding  
these analogies usually turn out to be a ballast that needs to be  
ejected in order to be able to move to a higher level of  
"understanding". There is a vast supply of examples to illustrate  
this but perhaps the one that most vividly illustrates the point is  
the Bohr's "planetary" model of the atom.
It is certainly not true that someone with no knowledge of other  
programming languages  cannot be a better Mathematica programmer  
than  someone who knows lots of them.  the idea that the latter  
person (the worse programmer who knows other languages)may have a  
"better understanding" of Mathematica seems to me unimportant and  
perhaps even meaningless.  Actually, I would argue that there is  
another way of "understanding" that is quite different form the one  
based on making analogy with the already familiar approach. Instead  
it comes from developing "intuition" through practice. This is  
exactly how one acquires understanding of the more abstract branches  
of mathematics: abstract algebra, category theory, algebraic topology  
etc. In fact, something like that is also true in quantum physics,  
where "analogy with the already familiar" is a very unreliable sort  
of "understanding". So, to conclude, it seems to me  that either  
somethings can indeed be understood "in vacuum" or perhaps that the  
role of  "understanding" in science, mathematics and programming is  
rather overrated

Andrzej Kozlowski


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