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MathGroup Archive 1999

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Re: Re: Mathematica can't win against Tiger Woods

  • To: mathgroup at smc.vnet.net
  • Subject: [mg19794] Re: [mg19765] Re: [mg19677] Mathematica can't win against Tiger Woods
  • From: David Withoff <withoff at wolfram.com>
  • Date: Fri, 17 Sep 1999 01:36:47 -0400
  • Sender: owner-wri-mathgroup at wolfram.com

Leszek Sczaniecki <leszek2 at home.com> wrote:

> To many times I tried to replicate simple computations done by hand with
> Mathematica and was not able to get results that would justify the use of an
> expensive computer algebra system. Therefore, I understand very well the
> frustration of Prof. MacDonald. Here is a recent example.
>
> ...
>
> Here is my point. Mathematica can certainly do plenty of problems much
> better than human. But, it is very, very frustrating, that in trivial
> cases the system often produces results worse then those delivered by a
> human. I see this as the challenge for Mathematica developers. The system
> should always produce better results than human. Presently, Mathematica
> is a tool for some kind of "scientific lower middle class". It is way to
> weak for people, who do serious mathematics or theoretical physics, and
> way to complicated for pedestrians. If Wolfram Research Inc. truly intents
> to reach "masses", it has to be more sensitive to their needs.

Although the examples that led to your closing generalizations are
justified, those generalizations are wrong, for two important reasons:

First, the highest priority in developing almost any tool, including
Mathematica, is to enable you to do new things, not to provide yet another
way of solving problems that have already been solved.  The computer and
your brain operate on fundamentally different principles, so it should
come as no surprise that they are good at different things.  Although it
is sometimes useful, such as for checking your work, or as an academic
exercise, to duplicate calculations on a computer, the best practical
advice is to use Mathematica for things that Mathematica is good at,
and to use your brain for things that your brain is good at.  Anything
else is a misuse of both tools.

A second misunderstanding is this notion that if something that we all
want to do is difficult to do in Mathematica, it must be because the
people who wrote the program need to be "more sensitive to [our] needs".
The truth is that if some useful problem hasn't been solved in Mathematica
it is usually because it is a really hard problem, or because no one quite
knows how to solve it.

The examples reported by Prof. MacDonald regarding the aesthetics of
results from DSolve are good examples of this.  The people who are
responsible for this part of Mathematica are acutely aware of these
examples, and have struggled on a number of occasions with possible
solutions.  It turns out, however, that there almost certainly is no
general solution.  There is no algorithm to make an expression
aesthetically pleasing.  Probably the only viable approach will be to
hack in a collection of heuristics and special cases to give improved
results most of the time, and to do so with sufficient care so as not
to significantly interfere with the performance of other examples.
In other words, it is a really hard problem.

The best advice is to choose the right tool for the right job.  You
will only be stuck in a "scientific lower middle class" if you spend
your career trying to coax a machine to do things that are best done
by hand, or wasting time doing by hand all of those laborious
calculations that the rest of us do using Mathematica.

Dave Withoff
Wolfram Research


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