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From: crm@duke.UUCP (Charlie Martin)
Newsgroups: net.astro.expert
Subject: Re: What Constitutes A "DIMENSION"? {Question From a Novice}
Message-ID: <5900@duke.UUCP>
Date: Thu, 6-Jun-85 13:12:09 EDT
Article-I.D.: duke.5900
Posted: Thu Jun  6 13:12:09 1985
Date-Received: Mon, 10-Jun-85 06:47:56 EDT
References: <293@ihlpa.UUCP>
Reply-To: crm@duke.UUCP (Charlie Martin)
Distribution: net
Organization: Duke University
Lines: 37
Summary: 

In article <293@ihlpa.UUCP> amra@ihlpa.UUCP (s. aldrich) writes:
>{Your Traveling Through Another Dimension......}
>
>With all the recent discussion on the "Center of the {Known} Universe,"
>and/or 3D(+) Space-Time, I thought I'd pose a question of my own.
>
> Namely WHAT, to the best of current knowledge, exactly is a dimension?

Oh boy, another chance to play Isaac Asimov -- but take this with a
grain of salt, as it is certainly possible that someone else understands
this better than I.

When we talk about the number of dimensions of space, those "dimensions"
are things at all, in the sense that you can pick on up and hold it in
your hand.  They are instead a sort of conventional was of talking about
the way we deal with a location mathematically.

Essentially, when we talk about space having three dimensions, what we
mean is that we cannot locate a point uniquely with fewer than three
real numbers.  This can also be thought of as the number of lines that
can be put together so that each line is perpendicular to all the other
lines.  In the space that we talk about, this number is (usually) three.
(If you've had linear algebra, this is the same as saying that a basis
for our space must contain three vectors.)

When we talk about four (or more) dimensions, we are really talking
about making some kind of model that has these many dimensions, then
using it to handle a problem.  If we choose our model well, it may make
it easier to handle some problem.  When Einstein starting talking about
time as the fourth dimension, he did so because that made the math work
out better. 

Hope that helps.
-- 

			Charlie Martin
			(...mcnc!duke!crm)