Science And Math

[Boris Borcic]

Gonçalo Rodrigues wrote:

> On Mon, 22 Apr 2002 13:49:00 -0400, Lulu of the Lotus-Eaters
> 
>>It is obvious from my other little note in the thread that I feel
>>sympathy with the Intuitionist idea about mathematics.  Of course, this
>>sympathy is somewhat forclosed by my attachment to the Axiom of Choice.
> 
> If it were just the axiom of choice... 
> 
> These came about because these non-constructive proofs can yield some
> really hair-raising examples (an orange can be split and reassembled in
> such a way to yield two oranges, etc.)


BTW, I recently had a debate on Archimedes' Principle, that I started by 
focussing on it as "an example of a physics statement that can be 
entirely formulated without any maths" only to be attacked by a 
physicist implying that no word of it could be properly defined without 
math, and also implied that stronger results/principles/theorems should 
base weaker results. The whole with a lawyer-like booby-trapped rhetoric.

AC and the Banach-Tarski paradox (the strange consequence of AC you 
allude to in terms of "oranges") thus came in handy to win the debate 
(because it refuted the primacy of math in the way claimed by my 
contradictor, showing math did not per force provide an ultimate 
understanding of the concept of volume that is central to Archimedes' 
Principle).

And strangely enough, the name of "Banach-Tarski" admitted a parse that 
described the role I found for it : ((ban (act arse)) key)... I am still 
very much intrigued by that coincidence, and finding it suggests that 
what I called "booby-trapped lawyer-like rethoric" might show a 
structural similarity with the belief in AC. Even though this would not 
explain the coincidence away, but make it richer.

Regards, Boris Borcic
--
filter(lambda W : W not in "ILLITERATE","BULLSHIT")