Re: PHYS-L Digest - 26 Feb 2000 to 27 Feb 2000 (#2000-64)

["Glenn A. Carlson" <gcarlson@MAIL.WIN.ORG>]

Regarding mathematics and computer science, perhaps, I'm trying to
have it both ways.  We should not fail to recognize phlogiston or
ether theorists as scientists any more than we should fail to
recognize Java or Pascal programmers as scientists.  I.e., just
because the language (or theory) used to describe nature is outmoded
(or wrong) doesn't mean those who used those languages were any less
scientists.

As for mathematics, it is distinguished from science in that it does
not follow the scientific method.  Computer proofs are no more
experiments than paper proofs.  (Though consider that if computer
proofs are the empirical component of the science of mathematics,
then, perhaps, mathematics is nothing more than computer science.)

The scientific method is a process by which we describe the true
nature of the universe (whatever "true" means, and whatever "universe"
means) through a process of observation, statement of a falsifiable
hypothesis, deductive testing of the hypothesis by experimentation,
etc.

But the important element of the scientific method which
distinguishes, for example, physics and math is that while both may
seek to test hypotheses, in physics hypotheses are tested against the
objective universe; in math hypotheses are tested against a logical
structure based on arbitrarily chosen axioms.  Physicists cannot
change the universe in which they live, but mathematicians can create
new mathematical worlds simply by adding or deleting one axiom.  E.g.,
non-Euclidean geometry was created by deleting Euclid's axiom that
given a line and a point off the line, there is only one coplanar line
parallel to the given line.  If we accept Euclid's axioms, there is
only one parallel line; if we don't accept Euclid's axioms, there may
more or less than one parallel line.  Whether our universe is
Euclidean or non-Euclidean is a question for scientists not
mathematicians.  (I don't in any way suggest by this that scientists
are superior or more important than mathematicians or that
mathematicians are excluded from such investigations.)

Glenn A. Carlson, P.E.
gcarlson@mail.win.org


> Subject: Re: PSEUDO-SCIENCE ?
> Date: Sat, 26 Feb 2000 08:29:58 -0500
> From: Ludwik Kowalski <KowalskiL@MAIL.MONTCLAIR.EDU>
>
> "Glenn A. Carlson" wrote:
>
> > What about all those chemists who "mastered" the phlogiston
> > theory? Or those physicists who "mastered" the ether theory?
> >
> > Also, I don't consider geometry or algebra to be sciences,
> > because mathematicians don't use the scientific method.
>
> The last sentence can be challenged by those who believe that
> "proving theorems with computers" is an experimental component
> of mathematics. And by those who observe how mathematicians
> actually work, not how they present the products of their work in
> textbooks. I read recently that proofs were often produced after the
> discoveries. Numerical and graphical experimentation was always
> part of mathematics.
>
> If I recall correctly, the ether model was actually used by Maxwell
> to derive his equations. They were modified later to reflect better
> models. And alchemists were the best chemists; they discovered
> and described many chemical properties of matter. In practical
> terms many of them new chemistry much better than some of
> us (myself included) know it today.
> Ludwik Kowalski
>
>   ----------------------------------------------------------------------
>
> Subject: Re: PSEUDO-SCIENCE ?
> Date: Sat, 26 Feb 2000 07:38:33 -0600
> From: Jack Uretsky <jlu@HEP.ANL.GOV>
>
>         I think that I am a working scientist.  What, pray tell, is the
> "scientific method"?
>                                 Regards,
>                                                 Jack
>
> Adam was by constitution and proclivity a scientist; I was the same, and
> we loved to call ourselves by that great name...Our first memorable
> scientific discovery was the law that water and like fluids run downhill,
> not up.
>                           Mark Twain, <Extract from Eve's Autobiography>
>
> On Sat, 26 Feb 2000, Glenn A. Carlson wrote:
>
> > What about all those chemists who "mastered" the phlogiston theory? Or
> > those physicists who "mastered" the ether theory?
> >
> > Also, I don't consider geometry or algebra to be sciences, because
> > mathematicians don't use the scientific method.
> >
> > Regards,
> >
> > Glenn A. Carlson, P.E.
> > St. Peters, MO