Re: Epistemology 201: The Science of Science

From: robert j. kolker (nowhere_at_nowhere.net)
Date: 03/07/05 

Date: Mon, 07 Mar 2005 12:46:05 -0500

Albert Wagner wrote:
>
>
> An algorithm is an algorithm and data is data. So *** you and your
> 'mathematicians stock and trade'.

And a postulate is a postulate and a theorem is is theorem. Why are you
so hostile to what mathematicians do?

In point of fact it is mathematical analysis that has produced the
numerical methods frequently implimented as programs. Long before the
first computing machine was ever designed, algorithms for solving
differential equations (ordinary and partial) were developed and show to
converge to the correct solutions. Algorithms for find roots of
equations existed long before computers. Isaac Newton himself made the
earliest contributions to the application and solution of finite
difference equations. Effective methods of finding definite integrals
with definite limits were developed long before computers. For example,
Simposon's Rule.

Computers and programming have been more of a force multiplier to
mathematical algorithms than a replacement. The only area in which
computers and programming techniques have constituted breakthoughs is in
the area of graphics and other visual representations and real time
control. Ray graphics cannot really be done effectively except with a
computer. Bitmapped graphics along with dithering and aliasing tricks
have produced dazzling displays and motion picture fx would be very
backward without computers. Computerized realtime control has made
fly-by-wire and hands off flying possible and safe.

Even so, the underlying theory of these dazzling techniques were
developed well in advance of and distinct from programs. Bellman and
Wiener developed cypernetical applications on a purely mathematicatial
basis for example.

Bob Kolker