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RE: Re: General--Difficulties in Understanding Mathematica Syntax

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  • Subject: [mg69074] RE: [mg69033] Re: General--Difficulties in Understanding Mathematica Syntax
  • From: robert.prince-wright at
  • Date: Tue, 29 Aug 2006 03:26:21 -0400 (EDT)
  • Sender: owner-wri-mathgroup at

This thread is an important one for the folks at Wolfram who are after all going to work to make a living by selling licenses. I was talking with another engineer last week about the kinds of work we did. I have stuck with Mathematica and resisted the path to other maths packages despite the fact that the vast majority of engineers have taken the 'easy' route. This has left me stranded in some ways since there is now a huge inventory of competent Math utilities - e.g. Roark and Young. Others have also increased the sophistication of their maths packages so that they can be used as a web integrated solution engine, much like webMathematica.

One of the key benefits of the alternatives (I am told) is that they are easier to understand and there is more commonality with the normal Windows environment. I have to say after using Mathematica for research and having used it to teach the Applicable Mathematics course at The University of Glasgow (1990) I can easily say I hated using the well know alternative when I returned to Industry - unfortunately I was the only one in the office.

I would guess that Wolfram would argue that Mathematica is aimed at a different market and there is some truth in that, however, having spent some time this morning looking at the competition I wonder if Wolfram are on a risky path since it's starting to look like Apple vs. Microsoft in the 90s.  

I think most would accept that David is correct in that the functional programming approach in Mathematica can result in code that is very difficult to read first time over. I end up having to unwrap the experts code when ever I'm looking to tap into Mathsource. Every now and then I am amused at how crafty some of you are when compacting code. The problem is not their code, nor the syntax, it's the fact that Mathematica makes it difficult to understand what's actually happening as, for example, we MapAll, MapThread, etc. a function onto a list, or list of lists. The current front end is still rather clunky and seems very underinvested. One simple way of helping people up the learning curve (or reminding occasional users like me) would be to have an optional window which dynamically shows a Short version of the effect of what were typing in. This would save people like me from having to repeatedly evaluate the complete expression in order to understand exactly what the outcom!
 e !
will be. Something akin to the Java applet that animates Map, Apply etc. 

We all know that Mathematica 6.0 is coming and one can only imagine that the next quantum step in Mathematica is being delayed to align with Windows Vista - I'm just hoping that the 'next step' (bad pun for oldies!) is going to provide better support for the next generation of Mathematica users. Let's hope the fact my current job is being implemented near a place called Dinosaur is not my fate. 


-----Original Message-----
From: David Bailey [mailto:dave at]
To: mathgroup at
Subject: [mg69074] [mg69033] Re: General--Difficulties in Understanding
Mathematica Syntax

AES wrote:
> In article <ecmgpr$9b3$1 at>,
>  Jean-Marc Gulliet <jeanmarc.gulliet at> wrote:
>> Now, it is utterly better to use high-level constructs such as Map, 
>> Thread, Apply, ... when you code in Mathematica.
> I don't exactly quarrel with this -- but I sure don't fully accept it 
> either.
> Concepts like Map[ ], Thread[ ], Apply[ ] are thoroughly understood by 
> adepts, and marginally understood by some of the rest of us.  They're 
> not concepts, or terms, commonly used in everyday speech.  And they may 
> have some hidden subtleties in their operation, even some "gotchas", in 
> how they apply to what's inside the [ ]s.
> Constructs like Do[] , If[ ], While[ ] are fairly likely to be 
> understood not just by adepts, but by anyone who's ever done even very 
> elementary programming in (horrors!) BASIC.  Their programming use 
> matches up pretty well with the same terms in everyday speech.  They 
> make the flow of the program logic more obviously visible (at least to 
> us non-adepts).  And I suspect they have fewer hidden gotchas.
> Writing complex Mathematica expressions as dense, deeply nested, 
> sometimes lengthy expressions full of arcane shorthands ("\\@", etc) is 
> akin to writing dense, arcane, possible lengthy prose sentences full of 
> arcane terminology.  Writing them as short, crisp, clear constructs, one 
> task at a time, is like writing short, crisp, clear prose sentences.  
> The people who construct "readability indexes" for prose have some 
> opinions about this.
> [We all, of course, fondly remember APL:  "Code once, read or modify 
> never".]
> What is it that's actually **better** (for the "ordinaryt user") about 
> these more sophisticated constructs?  
> *  Readability? -- except for adepts, I don't think so.  
> *  Faster, more efficient execution? -- perhaps so, but in the vast 
> majority of cases, who cares?!?
> *  More accurate execution?  -- I sure hope not.
> *  Shorter code (fewer characters)? -- again, who cares?!?
> *  Bragging rights (I can accomplish the task with fewer characters than 
> anyone around)? -- Well, that was a very salable skill, in magnetic core 
> and assembly language days.
> Again, to each his own.  Part of the genius of Mathematica is that it 
> serves the novice user and the sophisticated adept.  But "better"?
I agree with AES on this 100%. One problem with functional programming 
is that it reduces easy problems to one line but leaves a novice with 
little idea how to tackle a slightly more substantial problem - say one 
with boundary conditions which mean the edges of an array need to be 
treated differently. Of course there are ways to solve these problems 
functionally as well, but they take a lot more experience and are not as 
elegant. I teach both functional and non-functional approaches and point 
out the advantages of each.

Yes, explicit loops are less efficient in Mathematica, but you can do 
very sophisticated work with Mathematica without ever being troubled by 
speed of execution.

David Bailey

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