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Re: Mathematica Programmer vs. Programming in Mathematica

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  • Subject: [mg63129] Re: Mathematica Programmer vs. Programming in Mathematica
  • From: Andrzej Kozlowski <akoz at>
  • Date: Thu, 15 Dec 2005 03:06:37 -0500 (EST)
  • References: <> <dnopbs$2g9$> <>
  • Sender: owner-wri-mathgroup at

On 15 Dec 2005, at 07:22, Steven T. Hatton wrote:

> He also says: " It is to be hoped that there will soon be a
> hard-wired version in the underlying Mathematica C code."

It seems prety obvious now it is not going to happen. I for one do  
not regret it.
>> Both volumes of "The Mathematica Programmer" are very different from
>> "Programing in Mathematica". The latter book is actually devoted
>> entirely to writing Mathematica packages and isn't a particularly
>> good guide to other aspects of Mathematica programming (it was the
>> first book on Mathematica programming I ever read and I don't think I
>> learnt very much from it).
> I have read from several different books on Mathematica over the  
> years.
> None of them provide a very good introduction.  I believe part of the
> problem is that the authors tend to avoid explaining what makes  
> Mathematica
> "functions" different from functions in languages such as C.   
> Instead, they
> seem to focus on the similarities.  A few diagrams such as are  
> found in
> _Interpretation of Computer Programs_ by Abelson and Sussman, and an
> accompanying general description of the process of evaluation would  
> have
> been of great value to me.

I wonder what value there would be in trying to explain what makes  
Mathematica "functions" different from functions in languages such as  
C in a book addressed to readers most of whom have no knowledge of C  
and are not particualry interested in getting it?
The "Structure and INterpretation of Computer Programs" is a good  
book; I actaully learnt a lot about Mathematica form it ;-) One good  
thing about it is that it leaves all mention of C to the fotnotes and  
the exercies (see in particualrl page 610) for those who are  
interested only.

> I have gained a lot from _Programming in Mathematica_.  I don't  
> agree that
> it is devoted entirely to writing Mathematica Packages.  To me that is
> similar to saying something like '_The C++ Programming Language,  
> Special
> Edition_" is entirely about creating namespaces'.  Packages are  
> merely a
> (good) means of organizing code in Mathematica. Most of what Maeder
> presents could easily be done in the Global` context.

O.K., I guess I exaggerated somewhat. In fact Programming in  
Mathematica is a very elegantly written book that gives a good idea  
of the possibilities of Mathematica programming. Since I have bought  
three editions of it (for Mathematica versions 1, 2 and 4) obviously  
I must have found something of value in it. Nevertheless I still do  
not think this is a good book to start learning Mathematica  
programming form. On the other after I read Wagner's book I could  
easily read Programming in Mathematica and other Mathematica books  
and although I found useful things in them I don't think I ever  
discovered any more fundamental principles I that were somehow missed  
by Wagner.

> [...]
>> The
>> explanation is pretty compressed: less than one page long.
> I'm hoping there is sufficient development in the preceding  
> chapters to
> explain his implementation.  I have a used copy on order.

As I and others have already explained: each chapter is on a totally  
different topic. They are unrelated and and do not naturally lead  
from one to another.

>> The package is used again in Maeder's book "Computer Science with
>> Mathematica" in the chapter on object oriented programming but again
>> Maeder writes that the exact way how is works is irrelevant and
>> refers the interested reader to the Mathematica Programmer.
> He actually says it is "unimportant for our applications of object  
> oriented
> programming."  _Computer Science with Mathematica_ was one of the  
> books I
> read without much depth of understanding due to my lack of a solid  
> grasp of
> how Mathematica works differently from traditional procedural and
> functional languages.

I don't understand you here, though I suspect that is because our  
background and interests are quite different.
  I have never had much interest in "how Mathematica works  
differently from traditional procedural and functional languages" and  
honestly do not have much now either. I don't think not knowing that  
was ever any obstacle to my understanding of Mathematica. I knew a  
bit of Lisp at the time when I started learning Mathematica (and that  
was entirely due to reading Chaitin's "algorithmic Information  
Theory" , which of course does not give you any knowledge of  
"practical" Lisp) and as a result I made the mistake of trying to  
program in too Lisp like style, before I realised how dreadfully  
inefficient such programs are in Mathematica (due to the sort of  
things mentioned by Jon Harrop). I guess if I had known even less  
Lisp my progress would have been faster ;-)

In fact my approach was entirely different from yours. I had been  
using Mathematica for a number of years without any programming but  
then I got an idea about a specific project I wanted to implement for  
the classes I was teaching. I found that I had to learn to program to  
do that. I could not find any information that I needed in the  
Mathematica book (it was of course all there, but the problem was I  
did not know  how to look for it).
After reading "Programming in Mathematica"  I was not much closer.  
But after I read David Wagner's book it became almost trivial to  
implement my project; the whole program turned out to be less than a  
page long. Since then I have read or at least looked at lots of  
Mathematica books  and I learnt many interesting tricks (although not  
as many as I learnt from the MathGroup, particularly from Allan  
Hayes, Carl Woll and Hartmut Wolf not to mention WRI employees). I  
also read "The Structure and Interpretation of Computer Programs"  
following a suggestion by Richard Fateman (I am grateful for  
that ;-)). That was, I think, the only books on programing  other  
than Mathematica programing  that I have fully read or want to read  
(I am not counting books on algorithmic algebra, like Mishra,  
Akritas,  etc, which I consider part of mathematics , or general  
books on algorithms like those by Knuth, Sedgewick, etc). I enjoyed  
it and it gave me some insight but that is enough. I think I know now  
as much about this subject as I need or want to know.
It's a bit like with research in mathematics: there is a point at  
which you have to stop enlarging your "general knowledge",most of  
which you won't be able to use and which is always affected by the  
"The more I study the more I know. The more I know the more I forget.  
The more I forget the less I know. " syndrome, and start working on  
your own specific problems.

Andrzej Kozlowski

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