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MathGroup Archive 2005

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Re: Types in Mathematica

  • To: mathgroup at smc.vnet.net
  • Subject: [mg62329] Re: Types in Mathematica
  • From: "Steven T. Hatton" <hattons at globalsymmetry.com>
  • Date: Sun, 20 Nov 2005 04:50:32 -0500 (EST)
  • References: <200511191053.FAA16418@smc.vnet.net> <dlp2ci$le$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Andrzej Kozlowski wrote:

> 
> 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.

The comment "forget C++" was in response to my giving an example of how I
might try to create a boolean "type" in Mathematica.  I stated that my
example was not something I was likely to do in C++.

Mathematica is not a "strongly typed" language, but there are some aspect of
it which do represent a kind of "type system".  People in this newsgroup
have suggested that I am making a mistake by thinking in terms of data
types when working with Mathematica.  This, however, is not consistent with
the expositions of Steven Wolfram, Roman Mæder and Michael Trott.

>> 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". 

By telling me to "forget C++", you are suggesting that I am incapable of
understanding the differences between Mathematica and C++.  You are also
making assumptions about my level of understanding with respect to both
Mathematica, and C++.  It seems to me it would be more productive to focus
on the point I was making about Mathematica than it is to focus on an aside
comment about C++.

> 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.  

It is generally acknowledged in the computer science field that a person
with experience in several programming languages is typically a better
programmer than a person who has an equivalent number of hours of
experience in one programming language. I mean to say both programmers have
the same total number of hours spent programming.


> 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

I agree that most attempts to use the equations of QM to "explain" what is
actually happening at the subatomic scale amount to intellectual absurdity.
Schrödinger's cat is alive and well.

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