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April 16, 2004
The Shape of Things
Folks have been trying to figure out the shape of the universe for a long time. Early answers included "a big tree" and "flat, supported by elephants on the back of a turtle". One of the latest ideas is a Picard topology, sort of a horn shape with a really long end.
I notice that the term "pringle" has replaced "saddle" when describing areas of negative curvature...
Posted by Chris at April 16, 2004 09:11 AMComments
Not necessarily. It's the difference between "finite" and "bounded". Finite means that the area is a defined number, while bounded means the area has edges. For instance, the surface of the Earth is finite in 2 dimensions, but no matter how far you travel you'll never find the "edge" -- it's unbounded.
The illustration with the article isn't very helpful, because it makes the Picard topology look like a 3-dimensional horn. The actual shape is a 4-dimensional volume, so it connects to itself in ways that can't be shown on the 3-dimensional figure. They tried to note that (with the space ship description) but it's hard to visualize when it looks like there are hard edges.
We have a pretty decent book by Rudy Rucker about this, Spacetime and the Fourth Dimension. It's his master's thesis, actually, but still a good description (if I remember correctly.) He has another one called just The Fourth Dimension which is longer but more entertaining.
Posted by: Chris at April 16, 2004 02:10 PMThe universe is not a Pringle. It's a Ruffles - they have ridges.
Posted by: Deana at April 17, 2004 08:47 PMI've changed my mind. After looking at that image, it's obviously a Bugle, not a Ruffles or a Pringle.
http://theimaginaryworld.com/crk10.jpg
Posted by: Deana at April 17, 2004 09:14 PM
Okay, call me unimaginative, but I don't understand how the universe could be finite. Wouldn't that indicate an "outside" as well as an "inside"?
Posted by: karen at April 16, 2004 01:49 PM