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Re: How to write a "proper" math document
*To*: mathgroup at smc.vnet.net
*Subject*: [mg120088] Re: How to write a "proper" math document
*From*: AES <siegman at stanford.edu>
*Date*: Fri, 8 Jul 2011 04:51:33 -0400 (EDT)
*References*: <201107041044.GAA02461@smc.vnet.net> <iuukk8$epi$1@smc.vnet.net> <15944200.6757.1309943765495.JavaMail.root@m06> <iv45b8$es8$1@smc.vnet.net>
In article <iv45b8$es8$1 at smc.vnet.net>,
"David Park" <djmpark at comcast.net> 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):
<http://spie.org/etop/1991/338_1.pdf>
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
me.
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
Mathematica.
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
needed).
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