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Re: Re: Replace and ReplaceAll -- simple application

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  • Subject: [mg106085] Re: [mg106033] Re: Replace and ReplaceAll -- simple application
  • From: "David Park" <djmpark at>
  • Date: Fri, 1 Jan 2010 05:33:54 -0500 (EST)
  • References: <> <hh72dp$kud$> <hh9vfo$1rk$> <> <hhf5kg$go6$> <11737724.1262250965477.JavaMail.root@n11>

Replying to your two emails Tony.

I agree with you that there are problems (or we might say challenges!) but I
disagree with you on the identification of the problems and the solutions.

You see the problem in WRI trying to do too much and Mathematica being too
difficult to learn with all its features. You see the solution in a pared
down Mathematica, perhaps something more like a super-graphical-calculator,
and better documentation.

I see the challenges differently. I'm really enthusiastic about Mathematica
because I see it as a revolutionary medium that allows one to write literate
mathematical documents with all the power of Mathematica behind the
document. Such documents have tremendous advantages over the present
practice. They have a large amount of self-proofing; they create generated
knowledge in the form of definitions and routines; they can be much more
expressive with all the active and dynamic capabilities of Mathematica. It
may take a while for this concept to be taken up by the majority of users
but I am certain it will eventually win through because of its great

Obviously, I wouldn't want a pared down Mathematica. That would destroy the
prospects. I really don't want an application that is just a
super-calculator or a programming language. I want to be able to write,
communicate AND do math with it.

I see the principal problem as being education and acceptance of the
application. One can't just buy Mathematica off the bit-server and start
using it productively. We didn't learn how to write literate essays in a
week. We actually had years of schooling in the use of our language. We
can't just add mathematics and the use of Mathematica in a week - especially
with graphics and dynamic presentations. Mathematica may have its quirks,
but most languages have their quirks also. We just have to learn about them
and practice. Students who might be headed toward technical careers should
really be starting in early secondary school. That's the real problem! It
isn't sufficient for students to get to university, illiterate in
mathematical writing, and just modify examples provided by the professor.
They have to be able to think with Mathematica on their own. It isn't
sufficient to do calculations without integrating them with textual
discussion. (Unless you're a super genius that is.)

By the time students get to university they should know the basic syntax and
usage of Mathematica. They should know how to use Help. They should know how
to write definitions and routines in good style. They should know how to do
reasonable graphics and some dynamics. They should know how to write
packages. They should have written a few mathematical essay notebooks using
sectional headings and textual discussion. 

A second major problem is that Mathematica notebooks should be able to be
read (but not written) by anyone. I think that WRI is not oblivious to the
problem and it might get solved.

Another problem is the cost and acceptance of Mathematica. Some people in
academia resent the commercial status of Mathematica. I think this is unfair
because there are LOTS of commercial products that have near monopolies in
various educational niches. But the WRI use restrictions, licensing
practices, and cost, do present barriers. I don't know what the answer to
these problems are, but surely there are answers. 

Finally, this whole discussion got started with the behavior of 1., -1., I
and -I, and pattern matching. Whether or not this behavior could be
improved, anyone who has had an even half-way good education in Mathematica
knows that looking at the FullForm is the way to diagnose pattern matching
problems. And students should learn early not to mix approximate numbers or
units into symbolic equations. And they should also learn early that
Conjugate and ComplexExpand is the general method for taking complex
conjugates. These are far more educational issues than they are Mathematica

David Park
djmpark at  

From: AES [mailto:siegman at] 

In article <hhf5kg$go6$1 at>,
 Murray Eisenberg <murray at> wrote:

[Re documentation issues and I->-I]
> Only gathering usage statistics, or having a focus group of users trying 
> stuff, might suffice to escalate some issues to the point of requiring
> more prominent warnings.

1)  Fully agree.  My understanding is that many software vendors (and 
hardware equipment vendors, for that matter), at least the larger ones, 
do exactly this, systematically and extensively, on their products, and 
especially the interfaces to their products.  I have no idea whether 
Wolfram does any of this or not.

2)  On this point let's note that, to many users, the _interface_ to 
Mathematica -- what the user has to (learn to) type in, to get useful 
results out -- is the most important (and sometimes frustrating?) part 
of the product.  

What Mathematica does or can do -- it's "capabilities" as contrasted to 
its interface -- is of course also of primary importance; and 
Mathematica seems to rank very highly on this criterion.  It's the user 
interface where many if not most of these problems arise.

3)  And let's note the explicit assertions by Conrad Wolfram (in the 
screencasts/video gallery on the Wolfram web site), and by others, that 
Mathematica is intended to be a program that does *all* tasks, for *all* 
users, in a *single* application (with 'all' and 'single' taken very 
broadly).  This means, necessarily:

a)  A *very* complex interface (with, in particular, a _huge_ 

b)  And at the same time, a very broad and diverse set of users, with 
very different levels of education and knowledge and experience.

And this may mean that this basic goal and approach of the Wolframs' for 
Mathematica may not be realistic or possible.   The "focus groups" you 
suggest will have to be very diverse in makeup, corresponding to the 
huge diversity of the proposed users; and each different group of users 
will have different interface (and documentation) needs, and want very 
different things.

If the Wolframs' are going to insist on following this path, then user 
documentation -- easily accessible, brilliantly designed documentation, 
readily available in different forms oriented to the needs of different 
users -- is the primary thing they have to focus on.  

Thus far, so far as I can see, Heikki Ruskeepaa may be the only person 
on the planet who recognizes this and does something about it.  
Mathematica's own documentation gets maybe a C- on this score.  And 
simply expecting ordinary users to learn ever more arcane CAS concepts 
and terminology in order to use Mathematica effectively seems as 
unrealistic as it is absurd.

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