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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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