LISTSERV mailing list manager LISTSERV 16.0

Help for TSE Archives


TSE Archives

TSE Archives


TSE@PO.MISSOURI.EDU


View:

Message:

[

First

|

Previous

|

Next

|

Last

]

By Topic:

[

First

|

Previous

|

Next

|

Last

]

By Author:

[

First

|

Previous

|

Next

|

Last

]

Font:

Proportional Font

LISTSERV Archives

LISTSERV Archives

TSE Home

TSE Home

TSE  March 2001

TSE March 2001

Subject:

Re: OFF TOPIC - Map coloring

From:

[log in to unmask]

Date:

Mon, 12 Mar 2001 07:23:56 EST

Content-Type:

text/plain

Parts/Attachments:

Parts/Attachments

text/plain (166 lines)


--part1_e.a03beb1.27de19dc_boundary
Content-Type: text/plain; charset="US-ASCII"
Content-Transfer-Encoding: 7bit

In a message dated 3/11/01 7:27:31 PM Eastern Standard Time, 
[log in to unmask] writes:


> In Dublin I read part of the book on the history of the map-colouring 
> problem and how it was solved, which was really interesting to read - it 
> was one of the first proofs in which computers played a great part and 
> hence it was and still is very controversial. 

Arwin, 

What's the book? The reason the proof was controversial is that it isn't 
actually a "proof" in any logical or mathematical sense. Just a brute force 
examining of all examples the computer could think of, and no proof (or way 
of proving) that the program was actually sufficient to test "every" possible 
example. 

Personally, I think the map-coloring problem is a design problem, not a 
mathematical problem, and that's precisely why problems arose in trying to 
formulate a solution in mathematical terms. One question is whether there are 
criteria for identifying a mathematical problem as opposed to some other kind 
of problem. If these criteria exist, I sure don't see where they are, and the 
envelope can't be pushed to include any question with a numerical answer. 
There's no provable mathematical formula, for example, that allows anyone to 
determine what numbers are used on the license plate for my car. And the 
question isn't actually a mathematical question, even though the answer can 
be expressed in numbers. One can get an answer by checking the motor vehicle 
records. But looking up a number on a list isn't the same thing as 
constructing a mathematical proof...unless mathematicians are willing to 
broaden their standard of what constitutes a mathematical proof so that it 
includes all the "trivial" proofs that seem to be ignored at present.

I think Cantor developed some proof that there can't be any highest possible 
number or any end to the number series...which tends to validate the common 
sense observation that no matter how large a number is, one can always add 1 
to it. So why should we believe a computer that erroneously tells us that 
there actually is a highest possible number...this being the highest number 
that this particular computer can express given its limitations of memory and 
technology?

In any case, I'd like to see the actual program for supposedly "proving" the 
four color theorem, which I think came from U of Illinois. Was it reprinted 
in the book you read? It's supposed to be teribbly long, rather than a 
relatively short program that's used recursively. I'd like to see whether 
what made it so long is an attempt to define "every possible" situation.  

There was a period, you know, when an attempt was made to demonstrate that 
computers can do all kinds of things they aren't actually capable of doing. 
One engineer was claiming a computer could make Mondrian paintings, and 
another started that stupid "the Mona Lisa is Leonardo in drag" stuff. Here, 
the arguments were set forth in relatively brief articles. And when one 
finished reading the articles, one realized each was written by a person who 
didn't know a thing about art, and therefore didn't know how to interpret the 
data.

In the 4-color theorem, too, it seems to me from what I've read that the 
programmers skipped too many steps. Starting at square one, the first job is 
to program a computer to construct mathematical proofs. Until that's been 
accomplished, a computer isn't able to construct a mathematical proof of 
anything. And this of course is the borderline question that I hope is being 
considered in AI. What's the limit to what a computer can do? And what 
problems can only be solved by a sentient being?

All that to-do about computers playing chess is far from persuasive, because 
chess has a finite number of possible moves.  What about programming a 
computer to write a recipe book, with some assurance that the receipes will 
be superior to those a human being might develop?  Here, it's a tougher 
problem, because more is involved than shuffling numbers, which is all 
computers can do. But, as above, I think the main problem with any 
computerized "mathematical proof" of the four-color theorem is that one can't 
skip the necessary step of developing a program capable of constructing 
mathematical proofs. 

pat




--part1_e.a03beb1.27de19dc_boundary
Content-Type: text/html; charset="US-ASCII"
Content-Transfer-Encoding: 7bit

<HTML><FONT FACE=arial,helvetica><FONT  SIZE=3 FAMILY="SANSSERIF" FACE="Arial Narrow" LANG="0"><B>In a message dated 3/11/01 7:27:31 PM Eastern Standard Time, 
<BR>[log in to unmask] writes:
<BR>
<BR></FONT><FONT  COLOR="#000000" SIZE=2 FAMILY="SANSSERIF" FACE="Arial" LANG="0"></B>
<BR></FONT><FONT  COLOR="#0000ff" SIZE=2 FAMILY="SANSSERIF" FACE="Arial" LANG="0"><BLOCKQUOTE TYPE=CITE style="BORDER-LEFT: #0000ff 2px solid; MARGIN-LEFT: 5px; MARGIN-RIGHT: 0px; PADDING-LEFT: 5px">In Dublin I read part of the book on the history of the map-colouring 
<BR>problem and how it was solved, which was really interesting to read - it 
<BR>was one of the first proofs in which computers played a great part and 
<BR>hence it was and still is very controversial. </FONT><FONT  COLOR="#000000" SIZE=3 FAMILY="SANSSERIF" FACE="Arial" LANG="0"></BLOCKQUOTE>
<BR></FONT><FONT  COLOR="#000000" SIZE=3 FAMILY="SANSSERIF" FACE="Arial Narrow" LANG="0"><B>
<BR>Arwin, 
<BR>
<BR>What's the book? The reason the proof was controversial is that it isn't 
<BR>actually a "proof" in any logical or mathematical sense. Just a brute force 
<BR>examining of all examples the computer could think of, and no proof (or way 
<BR>of proving) that the program was actually sufficient to test "every" possible 
<BR>example. 
<BR>
<BR>Personally, I think the map-coloring problem is a design problem, not a 
<BR>mathematical problem, and that's precisely why problems arose in trying to 
<BR>formulate a solution in mathematical terms. One question is whether there are 
<BR>criteria for identifying a mathematical problem as opposed to some other kind 
<BR>of problem. If these criteria exist, I sure don't see where they are, and the 
<BR>envelope can't be pushed to include any question with a numerical answer. 
<BR>There's no provable mathematical formula, for example, that allows anyone to 
<BR>determine what numbers are used on the license plate for my car. And the 
<BR>question isn't actually a mathematical question, even though the answer can 
<BR>be expressed in numbers. One can get an answer by checking the motor vehicle 
<BR>records. But looking up a number on a list isn't the same thing as 
<BR>constructing a mathematical proof...unless mathematicians are willing to 
<BR>broaden their standard of what constitutes a mathematical proof so that it 
<BR>includes all the "trivial" proofs that seem to be ignored at present.
<BR>
<BR>I think Cantor developed some proof that there can't be any highest possible 
<BR>number or any end to the number series...which tends to validate the common 
<BR>sense observation that no matter how large a number is, one can always add 1 
<BR>to it. So why should we believe a computer that erroneously tells us that 
<BR>there actually is a highest possible number...this being the highest number 
<BR>that this particular computer can express given its limitations of memory and 
<BR>technology?
<BR>
<BR>In any case, I'd like to see the actual program for supposedly "proving" the 
<BR>four color theorem, which I think came from U of Illinois. Was it reprinted 
<BR>in the book you read? It's supposed to be teribbly long, rather than a 
<BR>relatively short program that's used recursively. I'd like to see whether 
<BR>what made it so long is an attempt to define "every possible" situation. &nbsp;
<BR>
<BR>There was a period, you know, when an attempt was made to demonstrate that 
<BR>computers can do all kinds of things they aren't actually capable of doing. 
<BR>One engineer was claiming a computer could make Mondrian paintings, and 
<BR>another started that stupid "the Mona Lisa is Leonardo in drag" stuff. Here, 
<BR>the arguments were set forth in relatively brief articles. And when one 
<BR>finished reading the articles, one realized each was written by a person who 
<BR>didn't know a thing about art, and therefore didn't know how to interpret the 
<BR>data.
<BR>
<BR>In the 4-color theorem, too, it seems to me from what I've read that the 
<BR>programmers skipped too many steps. Starting at square one, the first job is 
<BR>to program a computer to construct mathematical proofs. Until that's been 
<BR>accomplished, a computer isn't able to construct a mathematical proof of 
<BR>anything. And this of course is the borderline question that I hope is being 
<BR>considered in AI. What's the limit to what a computer can do? And what 
<BR>problems can only be solved by a sentient being?
<BR>
<BR>All that to-do about computers playing chess is far from persuasive, because 
<BR>chess has a finite number of possible moves. &nbsp;What about programming a 
<BR>computer to write a recipe book, with some assurance that the receipes will 
<BR>be superior to those a human being might develop? &nbsp;Here, it's a tougher 
<BR>problem, because more is involved than shuffling numbers, which is all 
<BR>computers can do. But, as above, I think the main problem with any 
<BR>computerized "mathematical proof" of the four-color theorem is that one can't 
<BR>skip the necessary step of developing a program capable of constructing 
<BR>mathematical proofs. 
<BR>
<BR>pat
<BR>
<BR>
<BR></B></FONT></HTML>

--part1_e.a03beb1.27de19dc_boundary--

Top of Message | Previous Page | Permalink

Advanced Options


Options

Log In

Log In

Get Password

Get Password


Search Archives

Search Archives


Subscribe or Unsubscribe

Subscribe or Unsubscribe


Archives

November 2019
October 2019
September 2019
August 2019
July 2019
June 2019
May 2019
April 2019
March 2019
February 2019
January 2019
December 2018
November 2018
October 2018
September 2018
August 2018
July 2018
June 2018
May 2018
April 2018
March 2018
February 2018
January 2018
December 2017
November 2017
October 2017
September 2017
August 2017
July 2017
June 2017
May 2017
April 2017
March 2017
February 2017
January 2017
December 2016
November 2016
October 2016
September 2016
August 2016
July 2016
June 2016
May 2016
April 2016
March 2016
February 2016
January 2016
December 2015
November 2015
October 2015
September 2015
August 2015
July 2015
June 2015
May 2015
April 2015
March 2015
February 2015
January 2015
December 2014
November 2014
October 2014
September 2014
August 2014
July 2014
June 2014
May 2014
April 2014
March 2014
February 2014
January 2014
December 2013
November 2013
October 2013
September 2013
August 2013
July 2013
June 2013
May 2013
April 2013
March 2013
February 2013
January 2013
December 2012
November 2012
October 2012
September 2012
August 2012
July 2012
June 2012
May 2012
April 2012
March 2012
February 2012
January 2012
December 2011
November 2011
October 2011
September 2011
August 2011
July 2011
June 2011
May 2011
April 2011
March 2011
February 2011
January 2011
December 2010
November 2010
October 2010
September 2010
August 2010
July 2010
June 2010
May 2010
April 2010
March 2010
February 2010
January 2010
December 2009
November 2009
October 2009
September 2009
August 2009
July 2009
June 2009
May 2009
April 2009
March 2009
February 2009
January 2009
December 2008
November 2008
October 2008
September 2008
August 2008
July 2008
June 2008
May 2008
April 2008
March 2008
February 2008
January 2008
December 2007
November 2007
October 2007
September 2007
August 2007
July 2007
June 2007
May 2007
April 2007
March 2007
February 2007
January 2007
December 2006
November 2006
October 2006
September 2006
August 2006
July 2006
June 2006
May 2006
April 2006
March 2006
February 2006
January 2006
December 2005
November 2005
October 2005
September 2005
August 2005
July 2005
June 2005
May 2005
April 2005
March 2005
February 2005
January 2005
December 2004
November 2004
October 2004
September 2004
August 2004
July 2004
June 2004
May 2004
April 2004
March 2004
February 2004
January 2004
December 2003
November 2003
October 2003
September 2003
August 2003
July 2003
June 2003
May 2003
April 2003
March 2003
February 2003
January 2003
December 2002
November 2002
October 2002
September 2002
August 2002
July 2002
June 2002
May 2002
April 2002
March 2002
February 2002
January 2002
December 2001
November 2001
October 2001
September 2001
August 2001
July 2001
June 2001
May 2001
April 2001
March 2001
February 2001
January 2001
March 1996
February 1996
January 1996
December 1995
November 1995

ATOM RSS1 RSS2



PO.MISSOURI.EDU

Secured by F-Secure Anti-Virus CataList Email List Search Powered by the LISTSERV Email List Manager