Re: The 4th Dimension

From: Mark Fergerson (nunya_at_biz.ness)
Date: 09/05/04 

Date: Sun, 05 Sep 2004 16:28:49 -0700

Jack wrote:

> I saw an interesting documentary several years ago, and it explained
> the following:
>
> A dot, (without length, width, or breadth), moves along a straight
> line. This line formed, is the FIRST dimension.
>
> If the theoretical line were moved perpindicular to the first
> linear motion, then a plane is formed. The original dot would only
> see an edge of the plane, and therefore would not see the plane; it
> can only see 'length', but not breadth. this is the SECOND dimension.
>
> If the plane were moved upwards, it would form a cube, or the THIRD
> dimension. The original 2 dimensional plane would see the cubes
> length and width, but not it's height; therefore it would see the cube
> as a mere plane like itself.
>
> What direction does the cube move in, to form the 4th dimension?
> Is the 4th Dimension here around us, but are we unable to see it?

   One answer is to consider that the cube has duration, or extension in
the "time direction". Observe it (from some hypothetical
super-duperspace of five or so dimensions) long enough for its duration
to be equivalent to the length of a side (at 3x10E8 meters = 1 second)
and you have a hypercube.

   But that's not what most people mean when thinking of extra physical
dimensions, mainly because of the severely limited mobility
opportunities (time's arrow and all that).

   The nearest thing to a testable contention that physical dimensions
above the three we see is the Kaluza-Klein idea (and derivatives
thereof) that some dimensions are "curled up" rather like taking a slice
of your plane and rolling it into a cylinder. From a distance it would
look like a one-D line, but close up it would be revealed as two-D.
Stack a bunch of them and you'd see a plane, and close up it would look
a bit "thicker".

   Unfortunately, all tests done so far have eliminated the "reasonable"
rolled diameters of these putative dimensional structures.

   Mark L. Fergerson

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