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Re: How to write a "proper" math document

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  • Subject: [mg120088] Re: How to write a "proper" math document
  • From: AES <siegman at>
  • Date: Fri, 8 Jul 2011 04:51:33 -0400 (EDT)
  • References: <> <iuukk8$epi$> <15944200.6757.1309943765495.JavaMail.root@m06> <iv45b8$es8$>

In article <iv45b8$es8$1 at>,
 "David Park" <djmpark at> wrote:

> The "two document" approach has both feet planted in the past. The first
> "document" is really a "programmable super graphical calculator" planted in
> the recent past. The second document is a static "text, equations, diagram"
> document planted in 3000 year old technology.
> . . .  the second of the current "two documents" nearly completely throws
> away all of the benefits of an active and dynamic mathematical medium. Such
> as: . . . 
> AES, I sometimes wonder if you have ever tried to write such a document or
> ever read one. You seem to be unaware of the advantages.

I'll refer you once again to an article I wrote two decades ago (when 
the Mac was just 5 years old, and Mathematica had just appeared):


It's opening sentence reads:

   "As I began preparing the talk on which this article is based its 
   subject matter began to evolve, moving from the original topic 
   of computer display tools for optics education toward the more
   general topic of  personal computers in higher education, 
   especially in science and engineering; and so this article will 
   be directed more broadly to that topic."

I've also voiced on this forum my very high opinion of Manipulate and 
its dynamic capabilities as providing a major and highly valuable 
contribution to these broad objectives.

But I believe there are still multiple methods and needs for the 
creation and the distribution of information and knowledge, including 
dynamic mathematical tools that individuals can use by themselves to 
explore all kinds of knowledge; dynamic tools for group presentations 
(seminars, lectures, dynamic web sites]; and, still very important and 
necessary, printed books, journal articles, manuals, and other 
manuscripts for individual use.

If I'm trying to understand and puzzle out the physical implications of 
some involved mathematical analysis of a physical problem, I very much 
want to have the equations and their derivation, along with other 
reference material, in a printed article or memo or book on the desktop 
beside me -- maybe several such items -- so I can flip through this 
material, or scrawl notes on it, or just stare at the derivations to see 
if some insight will leap out at me, AND at the same time have a dynamic 
mathematical tool available and running on the large monitor in front of 

Similarly, if I'm trying to program something using a new tool, I need 
to have one or more systematically organized manuals or collections of 
reference material on the desktop beside me, AND at the same time have 
that tool itself running on the large monitor in front of me. 

Trying to carry out all the activities involved in either of these two 
situations using only a monitor and no printed materials, so that one is 
continuously jumping back and forth and navigating between the active 
computation and the reference materials, all on a single screen (even a 
large one) is an exercise in frustration and inefficiency.  

And, trying to insist that all of this be done not only on a single 
screen but within a single tool or a single program, like Mathematica, 
with all the documentation for that tool available only on that same 
screen, is also an absolutely prime way to suppress the creativity of 
all the innumerable other people in the world who might write other 
better tools, or might write better documentation for some aspect of 

So:  We basically agree on some things -- but, I guess, substantially 
disagree on others.

You further add:

> The solution is simple. Every technically literate person should have
> Mathematica. A price of $295 (for the Home edition) is not unreasonable for
> people who might at first be casual users or readers. 

I absolutely agree with your second sentence -- except I'd broaden it to 
say something like "Every intellectually active individual . . .", at 
almost any age from intermediate school level to senility, and in almost 
any field, 'technical' or not.

The problem is, this is absolutely incompatible with your third 
sentence.  For the average family in this world a stripped down "Family 
Edition" in the $40 range (fully usable by mom, dad, and all the kids) 
would be more like it; $295 is at the upper level of what I'll willingly 
pay for a more or less full-bore edition of Mathematica to use in my own 
post-retirement technical consulting and scholarly explorations (and 
that's for something with at least a 4 or 5-year lifetime before I have 
to pay for any upgrades).

Mathematica needs more competition from other open-source or 
lower-priced or freeware tools that can do some of the things it does 
equally well.  It also needs some form of modular restructuring, so that 
different grades and levels of users can be served with different levels 
or subsets of the capabilities built into the complete system (I 
appreciate this may not be easy; but that doesn't make it any less 

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