22 October 2005

Sculpture unveils fourth dimension

via Daily Science News
Artistic works traditionally carry significance beyond their physical beauty, but a new sculpture in the McAllister Building headquarters of the Penn State Department of Mathematics may carry that tradition to its limits. The stainless-steel work, a striking object of visual art, also is a mental portal to the fourth dimension, a teaching tool, a memorial to a graduate of the math department, and a reminder of the terrorist attacks of 11 September 2001. The sculpture itself measures about six feet in every direction and is mounted on a granite base about three feet high in order to bring its center approximately to eye level.

The sculpture, designed by Adrian Ocneanu, professor of mathematics at Penn State, presents a three-dimensional "shadow" of a four-dimensional solid object. Ocneanu's research involves mathematical models for quantum field theory based on symmetry. One aspect of his work is modeling regular solids, both mathematically and physically. In the three-dimensional world, there are five regular solids--tetrahedron, cube, octahedron, dodecahedron, and icosahedron--whose faces are composed of triangles, squares, or pentagons. In four dimensions, there are six regular solids, which can be built based on the symmetries of the three-dimensional solids. Unfortunately, humans cannot process information in four dimensions directly because we don't see the universe that way. Although mathematicians can work with a fourth dimension abstractly by adding a fourth coordinate to the three that we use to describe a point in space, a fourth spatial dimension is difficult to visualize. For that, we need models. "Four-dimensional models are useful for thinking about and finding new relationships and phenomena," says Ocneanu. "The process is actually quite simple--think in one dimension less." To explain this concept, he points to a map. While the Earth is a three-dimensional object, its surface can be represented on a flat two-dimensional map.

visit Penn State's site for more info
clck for an animation of the sculpture

3 comments:

Kylark said...

Oh how funny, I was just about to blog this.

Y'know, I was looking at the animation, trying to relate it to a four-D object the same way a shadow relates to a 3-D object, and I just couldn't. I wonder if anyone can truly understand what a 4-d object is; maybe the mathemeticians who study them all day long? I got the feeling that if I were able to comprehend it, my mind would break.

Fell said...

You can greatly begin to understand it with the a_ Zen riddles, or b_ deep meditations and/or out-of-body experienecs. Tesseracts and the such as the equivalent of mathematical koans.

It's akin to probability, from what I can tell from my own experiences. I prefer to refer to it as "sidereal."

Again, for this I highly suggest Astral Dynamics, by Robert Bruce. It's one of those things I don't even try to describe anymore. It's just something you need to experienec in order to wrap a semantic around it.

Fell said...

http://www.traipse.com/hypercube/
http://www.geocities.com/CapeCanaveral/7997/