Re: Introducing CAS To Engineers (was Mathamatica vs MATLAB)

Richard Fateman disagrees with my suggestion that swelling Matlab
with symbolics could degrade its performance.

> In a dynamic type system that is reasonably constructed, the cost
> to provide a dispatch to a routine to handle yet another type should
> not be much. Since Matlab is (usually) interpreted, I find it
> surprising that allowing symbolic types would slow it down at
> all.

This assumes that the evaluation / dispatching /conversion etc.
are implemented efficiently and economically. But Matlab evolved
incrementally, it is not Python, OO since the beginning. OK, in
Matlab 7 the situation seems to have changed, I won't add more,
I feel incompetent (and I feel even less competent as a judge
of the psychics of the MathWorks team...).

But I am not sure I agree with your philosophy - as you express
it:

> Now, <<cui bono>>?
> [translated: who would it benefit?] Anyone who believes that
> computer programs, including Matlab, should do as much as possible
> to mimic what humans doing mathematics might do. I think it is a very
> small step from what is already in the program to what needs to be
> done. It is not a deep change. It is a very shallow change, distributed
> over each operator that currently does not know how to deal with a
> combination of sym and e.g. 34. Note that the number 34 is, to
> Matlab, a 1X1 array of double-float.

I am far from the idea that Matlab, or any CAS etc. should mimic my
*mathematics*! You know better than I that a computational tool is
not a mathematician. Wolfram advertized Mathematica as a "way of doing
mathematics"; the gurus of functional languages claim that Haskell etc.
is "close to mathematics". But what normal people want are tools to
solve concrete problems, where math plays *some* role... Why not
equip *all* the computer languages with CAS libraries?

> > What's wrong with specialized tools?
>
> Specialized tools restrict your vision. If all you have is a
> hammer, then every problem looks like a nail.

Now, I am sorry, Maestro RJF! You are one of the last people I would
offend, or even annoy, but this is simply unfair, if not a bit
demagogic. Every professional uses specialized tools. Many of them.
Who said *anything* about having *one tool*? Me? No, yourself! You
want -- apparently -- to have a super-package doing numerics and
symbolic algebra (and what else?), and everything FAST.

I refuse to have warm feelings towards a tool which combines a hammer
and a screwdriver. Or, getting back to my Jules Verne example, to
go to work on a vehicle which combines bike and space shuttle.
I prefer to have many efficient and portable tools.

About Maple and teaching of programming.

> I could guess why it wasn't successful, but if there is a discussion
> of this, please point us to it.

I wrote something in my previous posting.

> I know that at some institutions
> the Math department has used Maple, Mathematic, Mupad, etc for calculus
> "labs". The success of the language is highly correlated with
> the enthusiasm of the instructor for the language.

Absolutely right. And I used also CAS (concretely, Reduce) a looong
time ago in a "computational lab" for physics students. We *were* all
enthusiasts and it worked. But an enthusiasm will not replace a sound
methodology, when a taught topic is an *introduction*.

> If Maple turned out to be unpopular with students, and that is why
> it was cancelled, why don't we turn that same evaluation technique
> to other parts of their education.

What "same evaluation technique"? Who told you that the project turned
into vinegar because it was unpopular? It was simply hardly compatible
with the rest of the curriculum concerning *programming*.

> As Barbie (the Mattel doll) says, "Math class is hard". So why don't
> we just stop teaching Math?

I still hope we might discuss seriously, so I pretend that I haven't
read this last phrase.

Jerzy Karczmarczuk


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