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. Robert -----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. A. -----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 Arwin: 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. A. -----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. pat