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Re: Definitions



I'm not claiming that the rotation operator can't be generalized. I
am claiming that, if one claims to be generalizing the rotation
operator, one is obligated to state which of the many concepts or
principles associated with rotation is being generalized.

Your dictionary definitions of "rotation" mention returning an object
to its original orientation on one complete turn. Is this the only
property of your "generalized rotation operator"? Your dictionary
definitions did not mention the length-preserving property of
rotations. Does this mean your generalized rotation operator need not
preserve length (except for one complete turn)? Perhaps, you are
claiming it doesn't matter which, if any, of these properties your
generalized rotation operator has? I think it matters a lot.

We all know what an elephant is, but if I started talking about a
"generalized elephant," I would expect someone to ask (with more or
less diplomacy) what concept or principle of an elephant I am
generalizing. Replying "It won't do to claim that the elephant can't
be generalized" is not responsive. Replying that anteaters and jack
rabbits are examples of generalized elephants is only somewhat
responsive since it begs the question which concept or principle is
being derived from the particulars of elephants, anteaters, and jack
rabbits.

Glenn A. Carlson, P.E.
gcarlson@mail.win.org

Subject: Re: Definitions
Date: Sat, 28 Oct 2000 12:39:24 -0400
From: John Denker <jsd@MONMOUTH.COM>

Why does it not suffice to use the dictionary definition of "rotation"
http://www.m-w.com/cgi-bin/dictionary?va=rotation
and of "generalize" (in the transitive sense)
http://www.m-w.com/cgi-bin/dictionary?va=generalize
especially definition 2a:
"to derive or induce (a general conception or principle) from particulars"

It won't do to claim that the rotation operator can't be generalized; spin
and isospin are well-known examples of generalized rotations.