🚀 go-pugleaf

In article <PCG.90Dec7150237@odin.cs.aber.ac.uk> pcg@cs.aber.ac.uk (Piercarlo Grandi) writes:
>
>   ...one of the tragedies of Fortran, that it traps people that do
>not understand about computers to think they do. Anybody who is good at
>maths thinks he/she is by God'a gift a good numerical analyst too.
>
>Doesn't Fortran give you real numbers, mathematical formulas, and
>familiar looking syntax? Fortran == maths!
>
>Frankly, a lot of mathematical research with computers is entirely
>meaningless because of this ridiculous delusion. Me, I am not a
>numerical analyst, but I know enough about computers to understand that
>numerical computing is a minefield of very difficult problems, and that
>the least of them is having a familiar notation that is utterly
>misleading (a+b in Fortran has completely different semantics from, only
>very remotely similar to, the semantics of a+b in maths).
>

Well, I AM a numerical analyst and while not minimizing the difficulty
of some numerical techniques, this paragraph is a wild exaggeration.  How
about some supporting evidence instead of just opinion?  As far
as Fortran's relationship to mathematical notation, I don't think
this has anything to do with why people fail to comprehend numerical methods.
In fact, the problem people have in misusing numerical methods is not
their programming for god's sake, it is their MATHEMATICS.  An example,
people in the flow in porous media community routinely apply finite difference
techniques to solve PDE's using extremely long and skinny cells (in 2d).
I have seen alot of 2 dimensional calculations with cells of 1 cm tall 
and 1 km wide.  Yet the finite difference schemes are only accurate
to some order of the largest cell dimension (in that community, they
are usually only 1st order to boot - ugh!).  That means the kilometer
size dominates the error, except in circumstances where the flow is
actually one dimensional.  Now, people don't seem to appreciate this fact.
Are you telling me it is because Fortran misled them?  


>
>What are the good languages for numerical research then? Sadly, Fortran
>is so preminent, precisely because it deceives the unwary about the
>immense chasm between maths and numerical computing, that I cannot think
>of any other similar low level language.
>

A bold claim from a non-numerical analyst.  And I suppose if some
hydrologist codes the same finite difference scheme I just referred to
in C (or Scheme or whatever) instead of Fortran, divine elightenment
will happen and he will see that he is making serious mathematical
mistakes?

Come on, this argument is ridiculous.  And if you aren't a numerical
analyst, why the sense of outrage?

John Prentice
Amparo Corporation
Albuquerque, NM   
USA