MathGroup Archive 2005

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: Types in Mathematica

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

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.

The Mathematica Wiki:
Math for Comp Sci
Math for the WWW:

  • Prev by Date: Re: Newbie with simple questions (take 2)
  • Next by Date: DNS for the Wiki site?
  • Previous by thread: Re: Re: Re: Re: Types in Mathematica
  • Next by thread: Re: Re: Types in Mathematica