Frogwatch wrote:
JimH wrote:
"Short Wave Sportfishing" wrote in message
...
On Wed, 25 Oct 2006 18:24:46 -0400, Wayne.B
wrote:

On Wed, 25 Oct 2006 20:47:23 GMT, Short Wave Sportfishing
wrote:

By it's very definition
there is no way to orient a Klien Bottle so any single point or points
would have no value in reference to any other.

How do you drink from a Klien bottle

Carefully.

and how much does it hold?

Nothing - it has no inside or outside.

Well, that's not exactly true either.

The fourth dimension is all space that one can get to by traveling in
a direction perpendicular to three-dimensional space. Just for
laughs, let's build a universe of four dimensions follows a sequence
that starts with a "zero" dimension and progress up to the fourth
dimension ending in a hypercube.

The zero dimension would be a point. A point is a zero dimension
because it is infinitely small with no length, width or height. Thus
every point is exactly the same because it has no dimension.

The next dimension, first, would be taking any single point and
extruding it in any direction. It's called a "line segment" and is
one dimensional in that it extends only in one dimension - length -
everything else is still in the zero dimension.

A second dimension would take the line segment and extrude it in any
direction that is perpendicular to the first direction, creating a
square. All squares are two dimensional because they differ with each
other in size by two measurements, width and length. All the lines
have the same height.

Take the square and expand it adding height perpendicular to both of
the first two directions, creating a cube. That is the third
dimension.

So now we have a cube and if we take that cube and expand in a
direction perpendicular to the cube, we force it into tetraspace
building a tesseract. Tetraspace can be considered as the fourth
dimension. The three space cube is now a fourspace object.

If we define the square as planespace and the cube as realmspace
(where we live) you can consider the tesseract to exist in fourspace
and if there are individuals living in fourspace realm, then I suppose
that it could hold something that one could drink.

To us, however, nothing.

Clear now? :)
--

"What the hell's the deal with this newsgroup...
is there a computer terminal in the day room of
some looney bin somewhere?"

Bilgeman - circa 2004

Interesting discussion.

Another view on the Klein bottle: http://en.wikipedia.org/wiki/Klein_bottle

I gotta have one of these

http://www.kleinbottle.com/

The weird siphoning mug would be great for one of my beer drinking
friends, especially after he already had a few.

Here is something else that is cool but unrelated to navigation (even
bizarre mathematical worlds)
http://205.243.100.155/frames/interesting.html