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From: kallis@pen.DEC
Newsgroups: net.astro,net.sci
Subject: Dimensions
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Date: Thu, 6-Jun-85 13:39:10 EDT
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Steve Aldrich asks if there's a clearcut definition of a "dimension."
There are many definitions.

Primarily, a dimension is a measurement.  Or something that can be
quantified.  Normally, we think of dimensions in terms of mutually
perpendicular space "vectors" [in quotes to illustrate that I know
the difference between vectors and scalars] we usually term length
breadth/width and height (or as my old 3rd-grade teacher was wont
to say, "heighth").  Once we determine an arbitrary location as a
reference ("origin"), we can extend lines in the appropriate direc-
tions to establish these measures.  These spatial dimensions we
measure in linear units such as inches, meters, furlongs, or light
years.

Time is a dimension, which we measure in seconds, minutes, hours, years, 
and so on.  Some models of the Universe make Time a "dimension" perpen-
dicular" to the space dimensions, but that's unnecessary for our discus-
sions.

Brightness or intensity is a dimension, usually measured in "magnitude."
At least in astronomical circles.  It is also measured in foot-candles.

Temperature is a dimension, measured in degrees Kelvin, Celsuis, Farenheit,
or Rankine.

"Color" is a dimension, measured in Angstrom Units.

In short, anything that can be measured in definable units is a dimension.

With that all cleared away, most people talking about "dimensions" are
generally implying spatial ones.  Discounting the time aspect, our uni-
verse appears to have three spatial dimensions that are curved, according
to some theories, in a fourth.  There is no reason why there might not be
an infinite number of spatial dimensions, all at right angles to each other,
but there's no proof that any of them exist (or don't, for that matter).
Representing higher dimensions (if any) in three-dimensional space is as or
more difficult than representing three-dimensional space on a sheet of
paper (essentially two-dimensional).

I hope this has helped.

regards,

Steve Kallis, Jr.