Theory is elegant and rock solid but complicated and long winded because
they deal with all possible situations.  Practical solutions are quick and
useful in most situations, but prone to failure when one extrapolates
predicting what will happen in an unusual situation from what always happens
in normal situations.  For example the physics of Newton & Einstein.  Both
work on normal (not nearing the speed of light) situations, though Newton's
formulas are a lot easier to work with (just force, mass, & acceleration).
For driving a car, the quick easy and practical Newtonian physics are just
fine, but for particles traveling near the speed of light the practical
assumptions don't work & one needs the more obscure theories of Einstein.


	-----Original Message-----
	From:	Arwin van Arum [SMTP:[log in to unmask]]
	Sent:	Monday, March 12, 2001 3:27 PM
	To:	[log in to unmask]
	Subject:	RE: OFF TOPIC - Map coloring

	I'm of course exaggerating ... . Theory is nothing to gloss over and
can be very very useful, elegant and quick. But it's a theory, and theories
have a history of being overturned in practice. People are often blinded by
the beauty of an elegant theory, but often the real test for a theory is
when we apply them to the world; that's usually where things start going
wrong. And therefore I think there is definitely something to say for being
able to prove something 'uitputtend' as we say in Dutch, exhaustive. It's
not always necessary, it's not always elegant, but it's rock solid. You also
often really need it when applying a theory to the world, because when you
use a theory in practice you also have an impure domain to cover; practical
situations do not always meet a theoretical domain.

		-----Oorspronkelijk bericht-----
		Van: [log in to unmask]
[mailto:[log in to unmask]]Namens Richard Seddon
		Verzonden: dinsdag 13 maart 2001 0:01
		Aan: [log in to unmask]
		Onderwerp: Re: OFF TOPIC - Map coloring
		Didn't Kant maintain precisely the opposite?  
		Still trying to understrand Kant but can't
		Rick Seddon
		McIntosh, NM, USA

			-----Original Message-----
			From: Arwin van Arum < [log in to unmask]
<mailto:[log in to unmask]> >
			To: [log in to unmask]
<mailto:[log in to unmask]>  < [log in to unmask]
<mailto:[log in to unmask]> >
			Date: Monday, March 12, 2001 3:52 PM
			Subject: RE: OFF TOPIC - Map coloring
			With which you only illustrate that a theoretical
proof is only better when a practical proof is impossible.

				-----Oorspronkelijk bericht-----
				Van: [log in to unmask]
[mailto:[log in to unmask]]Namens [log in to unmask]
				Verzonden: maandag 12 maart 2001 23:39
				Aan: [log in to unmask]
				Onderwerp: Re: OFF TOPIC - Map coloring
				In a message dated 3/12/01 2:47:08 PM
Eastern Standard Time, 
				[log in to unmask] writes: 

				. Usually once the practical proof has been
achieved, this is stronger proof 
				than theoretical proof, because to be
one-hundred percent certain of a 
				theoretical proof you just have to be sure
that the theory will correctly 
				predict any given situation that lies within
its domain, and the least 
				doubtful way of doing so is to test it with
every possible situation within 
				its domain. 

				It seems to me a mathematician would
disagree with your definition of proof, 
				and I'm inclined to agree with the
mathematical assumption that the 
				theoretical proof is stronger, which is
precisely why we learned to do all 
				those geometrical proofs in high school.
With a geometrical proof in hand 
				that certain relationships can be found in a
right angle triangle, one no 
				longer needs to check every right angle
triangle in the universe to see if it 
				works every time.