🚀 go-pugleaf

Note: this posting may look like a flame. Unfortunately it is not. It is
a dire and stern warning. Think over it over and over again if you think
you have reason to disagree.

On 5 Dec 90 02:23:02 GMT, mroussel@alchemy.chem.utoronto.ca (Marc
Roussel) said:

mroussel> Fortran has a relatively simple relation to mathematical
mroussel> formulae.

Hahahahahahahahaha! If only it were that easy. Ever heard of problems
with associativity for example? I am very sure that the relation of
Fortran to mathematical formulae is a very difficult and subtle and
highly counterintuitive one, and that a lot of research has gone into
the past to map some of its simpler aspects, or to work around the more
difficult ones that are too difficult for us to understand.

mroussel> You write the formula on paper and then transcribe it more or
mroussel> less directly into your program; this is especially true of
mroussel> Fortran 77 with it's intelligent type conversions and
mroussel> intrinsic function selection.

This is 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).

I hope that people like the guy above read the famous (evidently not
enough!) paper on how to find the real roots of 2nd order polynomial
equations (ax^2+bx+c=0) by computer (I cannot remember the author now --
Dekker maybe -- but I remember the paper is looong and difficult) and be
ashamed (yes, ashamed) for ever having thought that the resemblance of
Fortran's notation with maths is anything more than a honey trap for the
unwary.


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.

I'd venture to say that as things stand probably Scheme is currently the
best language for numerical analysis (if you think I am joking, think it
over again *very* carefully), or some of the newer language with
abstraction facilities, like C++.
--
Piercarlo Grandi                   | ARPA: pcg%uk.ac.aber.cs@nsfnet-relay.ac.uk
Dept of CS, UCW Aberystwyth        | UUCP: ...!mcsun!ukc!aber-cs!pcg
Penglais, Aberystwyth SY23 3BZ, UK | INET: pcg@cs.aber.ac.uk