Re: Introducing CAS To Engineers (was Mathamatica vs MATLAB)
- From: JohnCreighton_@xxxxxxxxxxx
- Date: 9 May 2005 21:12:14 -0700
Jerzy Karczmarczuk wrote:
>
> 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*!
The goal or a lot of technology is to improve the efficiency of labor.
This goal can be seen every where from factories to the assembly line.
In terms of software this means getting the maximum results for the
minim human input. In the terminology of artificial intelligence this
is referred to as the A to I ratio. If a CAS can do you're
mathematics then you can move on to more general abstract and higher
level concepts while the CAS
mechanizes what you or may of not considered mechanical.
>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?
I can see your point here in that mimicking a typical perception of
mathematics may not always be the most effect way to solve a problem.
Haskell, is your best example because it is often difficult for some
people to solve problems in a non imperative fashion. Anyway, it is not
so important what is included with a computer language or a software
system but rather how well they work with other tools. If you have a
problem that mixes symbolic and numeric computation then without
considerable work at building a bride you are forced to use a system
that excels in one but not the other. It is like trying to farm two
fields on opposite sides of the river but having a plow on one side of
the river and a planting machine on the other side of the river. The
specialized tools are great but what is really needed is a sturdy
bridge.
> > > 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.
The comparison is kind of silly because software is developed largely
in a modular fashion. The key is how data is exchanged between the
modules and represented in each module and manipulated within each
module. If we want to use a tool analogy let CAS be the nut and
numerical systems be the bolt. You can have lots of nuts and lots of
bolts but if none of them fit each other then they are all pretty
useless.
.
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