apples and oranges

["JACK L. URETSKY (C)1998; HEP DIVISION, ARGONNE NATIONAL LAB ARGONNE, IL 60439" <JLU@hep.anl.gov>]

From:	ANLHEP::JLU          "JACK L. URETSKY (C)1998; HEP DIVISION, ARGONNE NATIONAL LAB ARGONNE, IL 60439"  2-NOV-1998 13:34:25.10
To:	SMTP%"trebor@velocity.net"
CC:	JLU
Subj:	Re: apples and oranges

Hi Bob-
	I don't understand what you mean  by "the same question".  An operative
condition in my question is "non-trivial" meaning, it's got to be capable
of extension.
	While the statement "abs(Q) = -1" is, grammatically, a complete
sentence, I don't see that it goes anywhere except to make the definition
of "abs" logically inconsistent.  That is, sum of non-zero abs > 0
(property of "abs").  But with your definition, abs(Q)+abs(1)=0.
	The same question about i would have to do with abs(i)=1, which
causes no problems at all.
			Regards,
				Jack
*************************************************************
Jack,
You could ask (as many do) the same question about i = sqr(-1)  ;  ie
i^2 = -1 .
Just define the quantity Q with:
abs(Q) = -1
Why not?

Bob Sciamanda
Physics, Edinboro Univ of PA (ret)
trebor@velocity.net
http://www.velocity.net/~trebor

-----Original Message-----
From: JACK L. URETSKY (C)1998; HEP DIVISION, ARGONNE NATIONAL LAB
ARGONNE, IL 60439 <JLU@hep.anl.gov>
To: phys-l@atlantis.uwf.edu <phys-l@atlantis.uwf.edu>
Cc: JLU@hep.anl.gov <JLU@hep.anl.gov>
Date: Sunday, November 01, 1998 2:47 PM
Subject: Re: apples and oranges


> Hi all-
> OK.  I've never been a friend of apocryphal stories because, in
> my experience, they (a) never happened, (b) could not have happened, and
> (c) are usually invented by people who don't know what they are talking
> about.  So here is my challenge: give a non-trivial definition of
> "absolute value" that makes sense out of this story.
> ****************************************************************
> Second, in answer to Richard Grandy's question: "Perhaps you could give
> an example of what other choices we might have made in inventing the
> negative or irrational numbers." I'll report a story I heard about a
> mathematics student who followed up the classroom introduction to
> complex numbers by asking about "the number whose absolute value is
> -1."  The professor, I'm told, followed it up by working with the class
> to invent a number system based on this new number.
******************************


	"I scored the next great triumph for science myself,
to wit, how the milk gets into the cow.  Both of us
had marveled over that mystery a long time.  We had
followed the cows around for years - that is, in the
daytime - but had never caught them drinking fluid of
that color."
		Mark Twain, Extract from Eve's
		Autobiography

	"I scored the next great triumph for science myself,
to wit, how the milk gets into the cow.  Both of us
had marveled over that mystery a long time.  We had
followed the cows around for years - that is, in the
daytime - but had never caught them drinking fluid of
that color."
		Mark Twain, Extract from Eve's
		Autobiography