[Beowulf] Threaded code (& Fortran)

[Robert G. Brown]

On Wed, 18 Aug 2004, Josip Loncaric wrote:

> P.S.  Real physicists (and control theorists and mathematicians) 
> *routinely* use complex numbers: generic real polynomials have complex 
> roots.  Computing roots (or eigenvalues) using only real numbers is 
> possible, but needlessly complicated and prone to coding errors. 
> Pre-C99 extensions for complex arithmetic in C are a royal pain.
> 
> Quaternions are rarely used.  Equivalent matrix representations are 
> often easier to work with anyway.

I was mostly tongue in cheek there, of course.  Although quaternions are
in once sense used all the time -- it is just that Hamilton and his
followers lost the battle to Heaviside and Gibbs, so we do dot products
and cross products independently in a 3d space rather than by viewing
them as components of a quaternionic product.

Geometric algebra is still relatively rarely used, but I think this is
largely due to history and inertia -- its fully consistent formulation
is relatively new (it wasn't really known at all back when I was in
graduate school) and still isn't taught at all at most places.  I
suspect that in a decade or two IF graduate schools start teaching it it
will lead to a revolution in the way lots of disparate algebras are
currently treated in physics, and may even lead to the discovery of new
physics -- having a clean mathematical formulation of even well-known
relations can often lead to new insight.

But this is getting a wee bit off topic for the list.  I actually agree
that having intrinsic complex arithmetic is a lovely thing, and that F90
has snitched a lot of the better features of C (where C is obviously
SLOWLY doing a bit of snitching of its own).  This is fine and part of
the natural genetic optimization process -- the languages are just
having sex and generating stronger offspring that look like their
parents (in a metaphorical sense).

It would be indelicate to try to figure out which language was on top
during the process...;-)

   rgb

-- 
Robert G. Brown	                       http://www.phy.duke.edu/~rgb/
Duke University Dept. of Physics, Box 90305
Durham, N.C. 27708-0305
Phone: 1-919-660-2567  Fax: 919-660-2525     email:rgb at phy.duke.edu