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Re: Re: Mathematica 7.0.1.0 and some General Comments

  • To: mathgroup at smc.vnet.net
  • Subject: [mg97494] Re: [mg97429] Re: Mathematica 7.0.1.0 and some General Comments
  • From: "David Park" <djmpark at comcast.net>
  • Date: Sat, 14 Mar 2009 05:39:17 -0500 (EST)
  • References: <goqphr$lt2$1@smc.vnet.net> <gp5fou$9nr$1@smc.vnet.net> <13988171.1236942033280.JavaMail.root@m02>

From: Mariano Su=E1rez-Alvarez [mailto:mariano.suarezalvarez at gmail.com]

Of course, in my work as a mathematician I have seen (too!)
many papers in which I could not tell why something
followed from something, or why something was equal to
something else.
______

Ah yes! If it is a book, then for me this usually first occurs on page 3.

This all brings us back to the intent of my original posting. Instead of
just thinking of Mathematica as an ancillary tool to provide material for
some other purpose, we should think of it as a primary medium for technical
development and communication.

I would urge that all development and communication be done via active
dynamic Mathematica notebooks. Everything should be developed, derived,
proved or calculated ACTIVELY with no interludes of hand waving or 'word
processing'. (But there should be plenty of textual discussion.) This means
that all starting points should be gathered as definitions and rules, and
further definitions or rules will be developed and accumulated as the
exposition proceeds. This may seem to many as too much work, and some may
doubt that it can be done. It can almost always be done! It IS work, but the
payoffs from the work are enormous. One of the payoffs is that you will be
accumulating active rules and definitions that you can use in creating
graphics and other types of presentations, and for doing further exploration
of the subject matter. (The graphics, presentations, or further explorations
may be the first indication of errors.) You may even find it worthwhile to
turn these routines into a package. This is one of the main fruits of your
labor. Don't let it slip through your fingers. A second enormous payoff is
that Mathematica notebooks in the active style are largely self-proofing.
Yes, it is still possible to make errors or have a clumsy approach but,
nevertheless, such notebooks are of a far higher quality and integrity than
traditional media.

Many technical writers don't use active Mathematica notebooks because they
are just plain lazy. There is no other word to describe it. That is why
their work is often so difficult to follow, or sometimes wrong. (Sometimes
they rationalize this with: "If the reader can't follow it, he shouldn't be
working in the field anyway." Come on! Let's invite more people in.)

It is far easier for people to understand actions than to understand
'static' diagrams or equations. We evolved to detect actions and respond to
them with our own actions. That is why a derivation that is done actively is
easier to understand. We get from one expression to another expression by
actively applying some axiom or theorem. Gee, that might even cause a
student to actually think about the axiom and how it is used. These axioms
and theorems, in turn, are encapsulated as rules or routines. The reader of
an active notebook could see what rule or routine is used to get from point
to point in the derivation. He could use it himself. He could try it on
other cases. The reader is far less likely to get stuck at some point she
has no explanation for.

Fully active Mathematica notebooks: they are the path.

If we could only convince WRI to take it a little more seriously.


David Park
djmpark at comcast.net
http://home.comcast.net/~djmpark/ 



From: Mariano Su=E1rez-Alvarez [mailto:mariano.suarezalvarez at gmail.com]

Of course, in my work as a mathematician I have seen (too!)
many papers in which I could not tell why something
followed from something, or why something was equal to
something else.




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