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MathGroup Archive 1999

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

  • To: mathgroup at smc.vnet.net
  • Subject: [mg19869] Re: [mg19811] Re: [mg19765] Re: [mg19677] Mathematica can't win against Tiger Woods
  • From: David Withoff <withoff at wolfram.com>
  • Date: Sun, 19 Sep 1999 01:20:51 -0400
  • Sender: owner-wri-mathgroup at wolfram.com

Leszek Sczaniecki <leszek2 at home.com> wrote:
> 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.
>
> Think about the education which is precisely about solving again and
> again old problems. How you are going to justify the usefulness of
> Mathematica in education, if it can't easily replicate known results?

These sentiments are variants of the same mistake: starting with a
common frustration -- difficulty coaxing a machine to do things that
can be done by hand -- and extrapolating to the incorrect conclusion
that the machine is therefore useless, or at least seriously diminished
(useful only to a "scientific lower middle class") because of it.

No one ever claimed that being able to reproduce hand calculations on
a computer was a Bad Thing.  In particular, Prof. MacDonald, in the
message that introduced this thread, is entirely justified in being
disappointed that DSolve sometimes returns results in an awkward form.
To the extent that there is a practical way to do it, it is obviously
desirable to address this concern.

It is in extrapolating beyond this point that this sentiment becomes
a serious and self-defeating error.

It is not realistic to expect a computer to always give better results
than a human, any more than it is realistic to expect any human to
always give better results than a computer.  As Andrzej Kozlowski
pointed out, computers are not intelligent beings, and you should not
expect them to behave that way.

And no, education is not about solving old problems again and again.
It is about preparing people to solve whatever problems come their way,
and about showing them how to choose the right tool for the right job.
Being able to reproduce hand calculations on a computer is not
essential to this task.

For example: using a computer to demonstrate all of the algebra that
would be used to do partial fraction decomposition by hand would be
difficult.  It would also be a waste of time.  Just use Apart.

Another example:  using a computer to demonstrate all of the steps
for calculating a square root by hand would also be difficult, and
it would again be a waste of time.  Just use Sqrt.

The most brilliant uses of Mathematica in education involve carefully
identifying which topics are still best illustrated using hand
calculations, which topics are best illustrated using the computer,
which topics (such as calculating square roots by hand) are obsolete
because of computers, and which topics can now be added because computers
are available to handle the otherwise prohibitive calculations.

And the poorest uses of computers in education involve using them to
solve the same old problems, using exactly the same calculations that
were done by hand before computers.

And finally:

> Here is an example of what I meant by insufficient sensitivity to
> user's needs. It is absolutely critical for finance applications to
> have fixed point display of numbers with trailing zeros and Round that
> rounds x.5 up and not toward the nearest even integer. They are easy to
> implement on the kernel level. In past Round was rounding x.5 up so the
> code should be somewhere. Why Round cannot have an option Method with
> values IEEE, Up, etc.? I brought these issues many times.  The only
> answer was: "Write your own functions". I wrote the functions, but
> others just abandoned the system. Wolfram lost.

this seems like nonsense to me.  I happen to know quite a few people
in the financial industry, all of whom couldn't care less what Round
does with x.5.  Perhaps we could test your credibility on this point
with an informal poll of mathgroup readership.  Is there anyone reading
this message who seriously believes that this aspect of Round "is
absolutely critical for finance applications"?  If there is any demand
I am sure this feature will be added.  

Dave Withoff
Wolfram Research


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