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Re: Re: Simplifying and Rearranging Expressions

From: AES [mailto:siegman at] 

3)  Instead, if what you're doing is a complex analysis and/or 
exposition, tackle the analysis portion initially with paper, pencil, 
and a good soft eraser, the way God intended analysis to be done.

And perhaps using only integers, since I read that's all that God invented?

It reminds me of a story I read somewhere, I can't recall the exact book,
about the history of modern physics. Robert Serber was an important
physicist on the Manhattan project. He would tell the story that one night
he dreamed he had died and gone to heaven. Saint Peter issued him in to see
God and God said: "You probably don't remember me but I audited your course
on quantum mechanics at Berkeley." That is probably the best witness we have
that God did use paper, pencil and a good soft eraser! There were no CASs in
those days.

And to strengthen your case further we know there are good mathematicians
who would never touch a computer. Not to speak of the great mathematicians
of the past.

Nevertheless, I would still argue that users should be encouraged to do
derivations completely ACTIVELY using Mathematica. They may think about the
principles, strategy and tactics of a derivation when they are away from
Mathematica. But implementing a derivation or proof actively on Mathematica
has many advantages.

1) You have to gather explicitly the definitions and rules used in the
derivation. Knowing the starting point is often half the problem.
2) These definitions and rules are active knowledge that you not only use in
the specific derivation or proof but may be useful elsewhere. The same goes
for intermediate and final results. They are not just inert equations on a
piece of paper but active tools. They are the fruit of your labor. You can
use these tools in further derivations or in producing graphics or dynamic
3) Active derivation has a great deal of self-proofing in it. Things have to
work. It is not totally foolproof, but it does impose a fair amount of
4) One can try out ideas, and see their results much faster.
5) An interactive and dynamic medium of expression is just much better than
a static document.

A may seem like a lot of work, but in 99.99% of the cases Mathematica users
deal with it is entirely possible. The results will be well worth it. It is
no more work than writing any good paper without Mathematica. Any good
product requires work.

It also requires learning how to use the tools, and it requires that WRI
keep working on adapting Mathematica to the working requirements of
mathematicians, scientists and engineers. They haven't done that badly, and
we are still at the beginning of a technology and not at the end of it.
Remember what the Greeks said: The past is in front of you and the future is
behind you, because what you see is the past.

David Park
djmpark at  

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