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From: marcoj@ai.rl.af.mil (James D. Marco)
Subject: Re: Stapp, PK & Physics Today
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References: <3vv3q6$2h4@ixnews7.ix.netcom.com> <41a9g5$70r@gap.cco.caltech.edu> <41btu8$8mq@net.auckland.ac.nz> <NEWTNews.809103968.6053.richard.caldwell@oufan.oklaosf.state.ok.us>  <41cq12$sar@csnews.cs.colorado.edu> <cas.155.00186781@ops1.bwi.wec.com> <41hsqb$35f@lastactionhero.rs.itd.umich.edu>
Date: Fri, 25 Aug 1995 12:09:41 GMT
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Xref: glinda.oz.cs.cmu.edu sci.skeptic:122538 sci.physics:136740 sci.math:115587 comp.ai:32833

In article <41hsqb$35f@lastactionhero.rs.itd.umich.edu>, gregs@umich.edu
(Gregory T Stevens) wrote:

> In <NEWTNews.809116926.30963.richard.caldwell@oufan.oklaosf.state.ok.us> 
> Richard Caldwell <richard.caldwell@mhs.oklaosf.state.ok.us> writes:
> >In <41cq12$sar@csnews.cs.colorado.edu>, 
> ><juola@suod.cs.colorado.edu> writes:
> >> Richard Caldwell  <richard.caldwell@mhs.oklaosf.state.ok.us> wrote:
> 
> >>>Fine.  I have a bucket of marbles.  I will reach in a pull out exactly 2 
> >>>marbles.  You reach in a pull out exactly Pi marbles.  Let's see how exact 
> >>>you can be with that one ;-)
> 
> >> Neat trick.  Now, without using any extra marbles, pull out and hand me
> >> -3 marbles.  As soon as you do that, I'll see what I can do with pi.
> 
> >So, you give up on my challenge and answer it by stating an equally
impossible 
> >one.  I agree that I, nor you, can pull -3 marbles from the bucket. 
That just 
> >means that -3 is another abstract mathematical concept, like Pi.
> 
> But your original statement which spurred on this debate was that pi
> is "inexact" whereas 2 is "exact."  Whether pi is "an abstract mathematical
> concept" is an entirely different debate.  People have been trying to tell
> you that pi is just as *exact* as two, even if we can't write it out
> on paper exactly.  You have as "evidence" that it is not exact that you can't
> draw pi marbles out of a bag.  The response was intended to show that by
> your reasoning, -3 is also "inexact."  Now, either you must support
> the conclusion that -3 is "inexact" or you must give a *different* explanation
> for why you consider pi less "exact" than 2.
> 
> --
> Greg Stevens     
> gregs@umich.edu   
>  

Just my (int)two (real)cents.  
   Pi is an exact value based on the relationship between 2 other exact
values (derived geometrically from a circle, in this case). One of the
properties of real numbers is the ability to describe/quantify a relation,
hence, can be considered as singular complex objects composed of discrete
unary objects and some relation between them, an n-tuple. Integers on the
other hand, describe/quantify individual discrete events, unary
descriptors if you will.
   To my thinking (rarely exact and often skewed): 
   1) The value of pi is exact within the reals, but clearly inexact
within the ints. You are having trouble trying to put the relation - pi -
in the bucket, as well you should. 
   2) The integer value 2 is exact and is used to quantify objects, i.e.
it is a property of some descrete object/event/relation/etc. Hence, the
statement 2(pi), "two pi", has meaning, similar to 2(marbles). Like an
adjective without a noun,  I cannot put the integer 2 in the bucket for
you, either.   
   3) Since ints and reals are, clearly, used to denote DIFFERENT logical
concepts, the property of exactness needs to be evaluated within their
respective universes.
   >>->You seem to be mixing apples and oranges, to my thinking
(admittedly skewed).

   Oh, yeah.  Negative/Positive values imply direction, or, the vector of
a quantity along the proverbial number line.  When you can put *direction*
in your bucket, *I* will pull it out (joke).  
   
   Unfortunatly, the mathematical world is filled with exact relations
that cannot be evaluated exactly with current mathematics (pi, sqrt( -1 ),
1/3,  etc.), actually there are more of these that cannot be evaluated,
than there are  ones that CAN be evaluated exactly. 

Just my (int)two (real)1/100 dollar.
