This is a multi-part message in MIME format. ------=_NextPart_000_003E_01C0AB54.4765A460 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 7bit 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]> To: [log in to unmask] <[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 ------=_NextPart_000_003E_01C0AB54.4765A460 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable <!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN"> <HTML><HEAD> <META content=3Dtext/html;charset=3Diso-8859-1 = http-equiv=3DContent-Type><!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 = Transitional//EN"> <META content=3D"MSHTML 5.00.2920.0" name=3DGENERATOR></HEAD> <BODY bgColor=3D#ffffff> <DIV><FONT color=3D#0000ff face=3DArial size=3D2><SPAN = class=3D144531623-12032001>I'm of=20 course exaggerating ... . Theory is nothing to gloss over and can = be=20 very very useful, elegant and quick. But it's a theory, and = theories have a=20 history of being overturned in practice. People are often blinded by the = beauty=20 of an elegant theory, but often the real test for a theory is when we = apply them=20 to the world; that's usually where things start going wrong. And = therefore I=20 think there is definitely something to say for being able to prove = something=20 'uitputtend' as we say in Dutch, exhaustive. It's not always necessary, = it's not=20 always elegant, but it's rock solid. You also often really need it when = applying=20 a theory to the world, because when you use a theory in practice you = also have=20 an impure domain to cover; practical situations do not always meet a = theoretical=20 domain.</SPAN></FONT></DIV> <DIV><FONT color=3D#0000ff face=3DArial size=3D2><SPAN=20 class=3D144531623-12032001></SPAN></FONT> </DIV> <DIV><FONT color=3D#0000ff face=3DArial size=3D2><SPAN=20 class=3D144531623-12032001>A.</SPAN></FONT></DIV> <BLOCKQUOTE=20 style=3D"BORDER-LEFT: #0000ff 2px solid; MARGIN-LEFT: 5px; MARGIN-RIGHT: = 0px; PADDING-LEFT: 5px"> <DIV align=3Dleft class=3DOutlookMessageHeader dir=3Dltr><FONT = face=3DTahoma=20 size=3D2>-----Oorspronkelijk bericht-----<BR><B>Van:</B>=20 [log in to unmask] = [mailto:[log in to unmask]]<B>Namens=20 </B>Richard Seddon<BR><B>Verzonden:</B> dinsdag 13 maart 2001=20 0:01<BR><B>Aan:</B> [log in to unmask]<BR><B>Onderwerp:</B> Re: = OFF TOPIC=20 - Map coloring<BR><BR></DIV></FONT> <DIV><FONT color=3D#000000 size=3D2>Arwin:</FONT></DIV> <DIV><FONT color=3D#000000 size=3D2></FONT> </DIV> <DIV><FONT size=3D2>Didn't Kant maintain precisely the opposite? = </FONT></DIV> <DIV><FONT size=3D2></FONT> </DIV> <DIV><FONT color=3D#000000 size=3D2>Still trying to understrand Kant = but=20 can't</FONT></DIV> <DIV><FONT size=3D2>Rick Seddon</FONT></DIV> <DIV><FONT size=3D2>McIntosh, NM, USA</FONT></DIV> <DIV><FONT size=3D2></FONT> </DIV> <BLOCKQUOTE=20 style=3D"BORDER-LEFT: #000000 2px solid; MARGIN-LEFT: 5px; = PADDING-LEFT: 5px"> <DIV><FONT face=3DArial size=3D2><B>-----Original = Message-----</B><BR><B>From:=20 </B>Arwin van Arum <<A=20 = href=3D"mailto:[log in to unmask]">[log in to unmask]</A>><BR><B>To:= =20 </B><A = href=3D"mailto:[log in to unmask]">[log in to unmask]</A>=20 <<A=20 = href=3D"mailto:[log in to unmask]">[log in to unmask]</A>><BR>= <B>Date:=20 </B>Monday, March 12, 2001 3:52 PM<BR><B>Subject: </B>RE: OFF TOPIC = - Map=20 coloring<BR><BR></DIV></FONT> <DIV><FONT color=3D#0000ff face=3DArial size=3D2><SPAN=20 class=3D361415622-12032001>With which you only illustrate that a = theoretical=20 proof is only better when a practical proof is=20 impossible.</SPAN></FONT></DIV> <DIV><FONT color=3D#0000ff face=3DArial size=3D2><SPAN=20 class=3D361415622-12032001></SPAN></FONT> </DIV> <DIV><FONT color=3D#0000ff face=3DArial size=3D2><SPAN=20 class=3D361415622-12032001>A.</SPAN></FONT></DIV> <BLOCKQUOTE=20 style=3D"BORDER-LEFT: #0000ff 2px solid; MARGIN-LEFT: 5px; = PADDING-LEFT: 5px"> <DIV align=3Dleft class=3DOutlookMessageHeader dir=3Dltr><FONT = face=3DTahoma=20 size=3D2>-----Oorspronkelijk bericht-----<BR><B>Van:</B>=20 [log in to unmask] [mailto:[log in to unmask]]<B>Namens=20 </B>[log in to unmask]<BR><B>Verzonden:</B> maandag 12 maart 2001=20 23:39<BR><B>Aan:</B> [log in to unmask]<BR><B>Onderwerp:</B> = Re: OFF=20 TOPIC - Map coloring<BR><BR></DIV></FONT><FONT = face=3Darial,helvetica><FONT=20 face=3D"Arial Narrow" lang=3D0 size=3D3 FAMILY=3D"SANSSERIF"><B>In = a message dated=20 3/12/01 2:47:08 PM Eastern Standard Time, <BR>[log in to unmask] = writes:=20 <BR><BR></FONT><FONT color=3D#000000 face=3DArial lang=3D0 = size=3D2=20 FAMILY=3D"SANSSERIF"></B><BR></FONT><FONT color=3D#0000ff = face=3DArial lang=3D0=20 size=3D2 FAMILY=3D"SANSSERIF"> <BLOCKQUOTE=20 style=3D"BORDER-LEFT: #0000ff 2px solid; MARGIN-LEFT: 5px; = MARGIN-RIGHT: 0px; PADDING-LEFT: 5px"=20 TYPE=3D"CITE">. Usually once the practical proof has been = achieved, this=20 is stronger proof <BR>than theoretical proof, because to be = one-hundred=20 percent certain of a <BR>theoretical proof you just have to be = sure that=20 the theory will correctly <BR>predict any given situation that = lies=20 within its domain, and the least <BR>doubtful way of doing so is = to test=20 it with every possible situation within <BR>its domain. = </FONT><FONT=20 color=3D#000000 face=3DArial lang=3D0 size=3D2=20 FAMILY=3D"SANSSERIF"><BR></BLOCKQUOTE><BR></FONT><FONT = color=3D#000000=20 face=3D"Arial Narrow" lang=3D0 size=3D3 = FAMILY=3D"SANSSERIF"><B><BR>It seems to me=20 a mathematician would disagree with your definition of proof, = <BR>and I'm=20 inclined to agree with the mathematical assumption that the=20 <BR>theoretical proof is stronger, which is precisely why we = learned to do=20 all <BR>those geometrical proofs in high school. With a = geometrical proof=20 in hand <BR>that certain relationships can be found in a right = angle=20 triangle, one no <BR>longer needs to check every right angle = triangle in=20 the universe to see if it <BR>works every time. <BR><BR>pat=20 = <BR></BLOCKQUOTE></B></FONT></FONT></BLOCKQUOTE></BLOCKQUOTE></BODY></HTM= L> ------=_NextPart_000_003E_01C0AB54.4765A460--