The notion of dimension is valuable, I believe.

While I am neither a mathematician nor a physicist, it seems clear from
popular articles about string theory et. al. that scientists and theoretical
physicists have an explict, mathematical definition for dimension.
I suspect it is somewhere between
A: the notions of "point, line, and plane" that remain without definition
but have meaning from the consistent contexts of their use ( two lines meet
at one and only one point -- Euclidian geometry or two lines meet at two
points, etc -- Non-Euclidian geometry--but the meaning of point and line are
understood without (apparent) difficulty)
and
B: the physical measurements that allow us to determine if the new sofa will
fit in our living room.

Again, as I understand it, not being versed in the difficult mathematics,
that string theory (for example) theorizes additional *spatial* dimensions,
but of such a small order that they do not show themselves outside of the
circumference (so to speak) of a subatomic particle.

Certainly, if it is possible to write a single number (which can be
interpreted, given a reference point) a point on a line; if it is possible
to write two numbers (which can be interpreted as a point in on a plane or
in two-dimensional space); if it is possible to write three numbers (which
can be interpreted as a point on the surface of a cube or a point in three
dimensional space; then it is possible to do this with N-numbers
representing a position in N-dimensional space.

Now of course, that's just mathematics. Just a convention on the use of
sequences of numbers. N-dimensional mathematics is definately usefull (many
phenomena vary with respect to more than 3 variables) but does it map to
anything physically real? That's something that experimental physicists and
theoreticians get to fight over, and that's the beauty of science. When
Einstein asserted (mathematically) that distance and mass varied with
velocity, that seemed absurd, but ultimately experiements validated his
assertions. Those who assert that there are additional spatial dimensions
have concluded that such requires the existence of particular particles with
certain properties, but we have not yet (as I understand it) been able to
generate the energetic circumstances necessary to test those hypotheses.

I think the meaning of dimension clearly persists as valuable. I haven't
felt compelled to study enough mathematics to try to begin to understand
string theory. Now the use that science-fiction stories throw around
"another dimension" is just nonesense, but science fiction is not physics.

Speaking of which, there is the "many universes" theory of quantum mechanics
but that's a different issue.

That's my attempt to defend the notion of dimension--does that help you at
all, Lou?

>From: Lou Stone <digital_dumpster@...>
>To: sdfuturists@yahoogroups.com
>Subject: [sdfuturists] Santa's New Five Speed
>Date: Sat, 25 Dec 2004 00:22:42 -0800 (PST)
>
>You may have heard that Santa couldn't possibly deliver toys to all the
>children in the world, all in one night (tonight!), and all while obeying
>the laws of physics. But add a little secret sauce and presto!
>
>Four Norse scholars have figured out just how the old fellow does it. The
>team was put together by forskning.no (hopefully Yahoo! doesn't flag that
>as a swear word). The results are here:
>===== http://www.physorg.com/news2487.html
>
>Basically, throw in a couple of extra dimensions and everything works out.
> Far be it from me to tell Santa how to do it, but this seems like
>cheating. Part of the fun of figuring out Why Santa Couldn't Do It was
>because it was a puzzle, with real constraints, that you had to work out.
>They're basically saying "Santa can do it because... because he can,
>that's why."
>
>Can someone offer me one concise definition of "dimension"? If we say we
>live in a three dimensional universe, I can understand. Roughly: Up/Down,
>Left/Right, Forward/Backward. Add in the so-called fourth dimension,
>time, and it all goes to hell. What does it possibly mean to move in
>time? We don't walk to and fro in time, but we do in the other three. We
>can't measure this "time" thing by anything external to it, anything
>objective. But we can with any of the other three.
>
>And then all the pop physicists go talking about the fifth, sixth, and
>26th dimensions. What gives?
>
>I think "dimension", in the sense of the original three, is an outdated
>concept, like ether and phlogiston. Can any of you offer a good defense
>of this concept?
>
>"A brave little theory, and actually quite coherent for a system of five
>or seven dimensions--if only we lived in one."
> -- Academician Prokhor Zakharov
>
>-todd
>
>
>=====
>__________
>
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