Fwd: WAS-- Re: Hanson 2006, Mortimer, Baeker response

[Andreas Johansson <andreasj@gmail.com>]

On 6/24/06, don ohmes <d_ohmes@yahoo.com> wrote:
> I never suspected that this was debatable, but here goes--
>
> The historical context of "math" is lost or ignored here. Mathematical phenomena (eg, 
> natural numbers, pi, the formulas for areas and volumes of various geometrical shapes) were 
> explored through use of the "tangible universe" by early mathematicians. A person 
> qualifying and quantifying pi with string and various round-ish objects, or exploring division and 
> fractions with piles of beads was gathering _data_, and _testing_ that data against reality.

Assuming, for the sake of the argument, that early mathematicians were
doing science, it doesn't follow that mathematics today is a science.

> The tools of scientific methodology were first formalized by early 
> mathematicians, and used to establish the congruence of mathematical concepts 
> to the tangible universe. After practical problems (eg, measurement error) were 
> overcome by the use of theoretical concepts (eg, Euclid's axioms), robust 
> mathematical systems became capable of exploring the tangible universe, rather 
> than vice versa.

Euclidean geometry was arrived at by studying the tangible universe,
but does not logically depend on it. Euclidean geometry did not become
falsified when the curvature of space-time was discovered; the
*physical* hypothesis that space obeys Euclidean geometry was
falsified.


> For those who insist that numbers are simply a figment of the human 
> imagination, I suggest a career in sales, or leftist politics. Now, stop being 
> so ungrateful, and get back to dinosaurs before Mickey gets mad...

I'm not insisting that numbers are a figument of the human
imagination; I'm asserting that mathematics is not a science.  Those
are different claims. The suggestion I'm being somehow "ungrateful"
would be insulting if it weren't so ridiculous.

--
Andreas Johansson

Why can't you be a non-conformist just like everybody else?