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In a message dated 3/12/01 8:19:34 AM Eastern Standard Time, 
[log in to unmask] writes:


> However
> it does indicate that there can be no possibility of a computer program ever
> correctly claiming that it has found a proof that differs from a 
> mathematiocal
> proof. 

Where does this leave the computer "proof" of the 4 color theorem? Doesn't 
the absence of a mathematical proof  indicate that the computer proof 
"differs" from the (non-existant) mathematical proof?


Indeed the concept of program as a set of steps to produce a result comes
> from mathematics.

Why mathematics? Couldn't it as easily have come from brick-laying? I can't 
think of any productive human activity that isn't a series of steps to 
produce a result.

pat



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<HTML><FONT FACE=arial,helvetica><FONT  SIZE=3 FAMILY="SANSSERIF" FACE="Arial Narrow" LANG="0"><B>In a message dated 3/12/01 8:19:34 AM 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><BLOCKQUOTE TYPE=CITE style="BORDER-LEFT: #0000ff 2px solid; MARGIN-LEFT: 5px; MARGIN-RIGHT: 0px; PADDING-LEFT: 5px">However
<BR>it does indicate that there can be no possibility of a computer program ever
<BR>correctly claiming that it has found a proof that differs from a 
<BR>mathematiocal
<BR>proof. </FONT><FONT  COLOR="#000000" SIZE=3 FAMILY="SANSSERIF" FACE="Arial" LANG="0"></BLOCKQUOTE>
<BR>
<BR></FONT><FONT  COLOR="#000000" SIZE=2 FAMILY="SANSSERIF" FACE="Arial" LANG="0">Where does this leave the computer "proof" of the 4 color theorem? Doesn't 
<BR>the absence of a mathematical proof &nbsp;indicate that the computer proof 
<BR>"differs" from the (non-existant) mathematical proof?
<BR>
<BR>
<BR>Indeed the concept of program as a set of steps to produce a result comes</FONT><FONT  COLOR="#000000" SIZE=3 FAMILY="SANSSERIF" FACE="Arial" LANG="0">
<BR></FONT><FONT  COLOR="#000000" 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">from mathematics.</FONT><FONT  COLOR="#000000" SIZE=3 FAMILY="SANSSERIF" FACE="Arial" LANG="0"></BLOCKQUOTE>
<BR>
<BR>Why mathematics? Couldn't it as easily have come from brick-laying? I can't 
<BR>think of any productive human activity that isn't a series of steps to 
<BR>produce a result.
<BR>
<BR>pat
<BR></FONT><FONT  COLOR="#000000" SIZE=3 FAMILY="SANSSERIF" FACE="Arial Narrow" LANG="0"><B>
<BR></B></FONT></HTML>

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