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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: [mg19877] Re: [mg19811] Re: [mg19765] Re: [mg19677] Mathematica can't win against Tiger Woods
  • From: Leszek Sczaniecki <leszek2 at home.com>
  • Date: Sun, 19 Sep 1999 01:20:58 -0400
  • Sender: owner-wri-mathgroup at wolfram.com


David Withoff wrote:

> 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.
>

You are generously crediting me with statements, I never made.
I just pointed out an area for improvement. I never said that
the machine is useless. Perhaps, It would be more productive,
if you could tell us a TECHNICAL or any reason explaining why
mathematica cannot do better in the area of linear differential
equations with constant coefficients. Or perhaps, for what
technical reason it can do this simplification

In[1]:= FullSimplify[(Sqrt[2] 1/2))^2 Sin[x/2]^2]

Out[1]=
1/4 (1 - Cos[x])

but fails here

In[2]:= FullSimplify[(Sqrt[2] x/2))^2 Sin[x/2]^2]

Out[2]=
1/2 x^2 Sin[x/2]^2
?

>
> 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.
>

People are being prepared to solve whatever problems come their way by solving
old problems with known solutions. They are learning the same Newton equations
in physics, the same chain rule in calculus, the same Maxwell or Lagrange
equations for many dozens of years. Lectures, textbooks, problems and examples
have been fine-tuned for years. It is nothing wrong about repeating old good
stuff. It would be silly to reject that valuable heritage. I will try to
illustrate what consider the best approach to the education using the following
example. When learning about matrices for the first time, people should do the
first computations manually becuse they gain better insight to the subject this
way. However, later, when they study, say, the relativistic quantum mechanics
via Dirac equations, they should use computer for manipulating gamma matrices. I
hope you see the difference. In the first case, they benefit intellectually by
doing "manual" work, exercising their brains. In the second case, because they
already know well how to manipulate matrices, they would not significantly
benefit from doing that agaim. They should use computer algebra to eliminate the
tedious, mechanical  work, that does not enrich them intellectually. They can
then use the saved time to get deeper inside into the main subject. I used to do
computations involving quantum mechanics for more then fifteen year, but the
illustrations of solutions of two dimensional Shroedinger equations prepared by
TerryRobb helped me to gain new insight. On other hand, the overdose of computer
algebrain education can have decremental influence on people, who use it as a
magic blackbox to deliver solutions and an excuse for not thinking.


>
> 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.
>

That's really funny. Apart is an excellent illustration of one of my points. It
behaves exactly as defined the documentation, but it doesn't do what users
expect. Brian Evans, the principal author of "Signals and Systems", had to write
his own version of Apart named MyApart, that is available on MathSource
http://www.mathsource.com/MathSource/Enhancements/Algebraic/0202-071/MyApart.m
for many years. Here is an excerpt from the package header.
--
(* From: Brian Evans <evans at gauss.eedsp.gatech.edu>
To: mathgroup at smc.vnet.net
Subject: [mg19877] Re: Partial Fraction Decomposition with imaginary coeff.
Source-Info:  From (or Sender) name not authenticated.

          You just don't know how difficult Apart has made my life.
          It is crucial to the implementation of inverse linear
          transforms.  Under 1.2, it would not handle polynomials
          with rational coefficients expressed in decimal form.
          Under 1.2 and 2.0, Apart does not break up terms like
          1 / (x^2 + 1).  About two years ago, I had to write a general
          purpose routine to work around Apart's drawbacks.  I call it
          MyApart.  It is embedded in the signal processing packages
          for Mathematica and is used by the inverse z- and Laplace
          transforms when Apart doesn't complete the decomposition.
          MyApart is, of course, darn slow.

Brian L. Evans
Digital Signal Processing Laboratory
School of Electrical Engineering
Georgia Institute of Technology
Atlanta, GA  30332-0250

e-mail: evans at eedsp.gatech.edu
*)
--

Look at the dates. Brian wrote his package in 1988. For eleven (sic!) years
electric engineers have been using "home made", substandard extensions to
Mathematica. This is precisely what I meant asking for more sensitivity to
user's needs. I have been trying to promote Mathematica in my company.
Mathematica has here reputation of being "to difficult". I am doing my best. I
train my co-workers for free, I am writing notebooks to present the system in
its best to some wider audience. I am trying to help you guys.  I know that
others, such as a long term mathematica proponent Prof.MacDonald, who started
this thread, are doing the same. When I pointed out, what hurts your business, I
got in return lectures about computers and software engineering in general, some
philosophical opinions that I never expressed have been promptly straighten up,
I was advised on my career, told a personal success story, send a quote of a big
shot taken out of context, and my credibility has been questioned, but I heard
very little technical information. I didn't hear: "Yes, FullSimplify needs
improvement, we are going to work on it" or "Sorry, at this point we don't have
human resources to spend of FullSimplify".

>
> 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.
>

Sadly you chose to question my credibility rather than address technical issues.
I might have for you a better way to check my claims than organizing a public
vote. I advise you to consult Operations Committee of SIA (Security Industry
Association) ((212) 608-1500) regarding the standards for fixed income
instruments. For mortgage backed securities you can contact PBS (Public
Securities Associations)((212) 809-7000). For other instruments contact the
appropriate association. They regulate how many digits you must retain for
intermediate results, how many for the final result, when the result has to
rounded, when truncated, etc. I am talking about official business, privately
you can do whatever you want. Dave, if any one of these organizations happens to
accept the rounding to the nearest even number, I will send you a bottle of good
Bordeaux.:-) BTW, if you care about the finance community, where are filters for
spreadsheets? Like it or not, THE most common tool in business is spreadsheet.

If you would spend just a little time to look into this newsgroup archive, you
would certainly notice postings from users surprised by the behavior of Round.


There is a story, that I learned from Neil Soiffer. It is about NeWS (Network
Window System) developed by Gosling, who became later famous for his work on
Java. Thesystem was technologically very advanced, included number of leading
edge technologies, but people didn't use it. Desperate Sun organized events for
developers to promote NeWS. On one of such events, after couple hours of work
with no apparent success, hopeless Sun's employee asked the audience: "This
system has so many modern, exciting, great features. Why you don't use it?". One
developer from back rows stood up and said: "If you really want us to use it,
fix the shell first, so that it doesn't crash so often". We know the rest of
NeWS story. Here is my advice to Wolfram's developers. If you really want to
succeed, while chasing very advanced features don't forget about the fundamental
ones. Remember that customers can easily survive without Wolfram Research, but
Wolfram Research can hardly survive without customers.

Now, because this thread has been loosing the technical focus and getting
unnecessarily personal, I decided to terminate my participation in it. :-(

-- Leszek Sczaniecki


>
> Dave Withoff
> Wolfram Research


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