The Penn State Department of Mathematics will host an open house of its extensively renovated McAllister Building, featuring a dedication ceremony for a unique sculpture with deep mathematical significance on 21 October 2005 at the Penn State University Park campus…..No good rendering of any 4-dimensional object existed anywhere in the world before the Octacube, either in solid or virtual form, according to Adrian Ocneanu, the Penn State professor of mathematics who designed the sculpture.
The sculpture….presents a three-dimensional “shadow” of a four-dimensional solid object. There is a link at the press release page to a detailed description of the whole representation.
The sculpture is a gift from Jill Grashof Anderson, a mathematics alumna of Penn State as a memorial for her husband, Kermit C. Anderson, also a Penn State mathematics graduate, who was killed in the terrorist attack on the World Trade Center in New York City on 11 September 2001. The dedication ceremony for the sculpture will include an explanation of its mathematical meaning by its designer, Adrian Ocneanu, professor of mathematics. The stainless-steel Octacube is a striking object of visual art and also a mental portal to the fourth dimension, a teaching tool, and a research object bringing together many branches of mathematics and physics connected to the structure of symmetry.
There is a striking animation of the sculpture here.
I can NOT see, and i fail to understand the explanation. Can someone enlighten me?
It’s kind of hard to explain.
Um–the sculpture is a projection on 3-space of a 4D object, where the 4th dimension is time?
That’s my guess…
Neither can I Movi. I do see what seems to be a very well crafted piece from a design that is likely beyond my grasp of physics. What might make this work really special is that it is a collaboration with the potential to be hyped to previously unexplored realms of the bullshitasphere, a designer that really understands physics, actual craftsmen that have mastered their foundry or fabrication skills ( I can’t tell if it was cast or welded or both) and a sponsor with probably good intentions and a worthy objective.
It might not stand up to critical analysis by art historians, if one could be found that has even a miniscule apprehension of the concept the work represents. The chances of that happening are too small to be measured with existing technology.
I’m somewhat of a “visual arts Quaker” in that my personal preference is that the less that comes between my perception of the art and the work itself, the better. I like anecdotes about the artist or the work, but don’t care much for the interpretations that always seem to attach themselves. This is the reason for my obviously cynical reaction to the project. I still like the piece, think it was nicely executed and hope that it serves to preserve the memory of the life that inspired it. Still, I suspect anyone looking to “zen up an art appreciation moment” with this piece had better bring earplugs, waders and a set of blinders.
And be careful! Don’t stare at it for too long… you may get sucked in and squirted back out as a mirror image of yourself.
Great sculpture but they should attach it to the pedestal so that it does not fall off, disapeer as a prank or end up on the lawn of Old Main during the next Arts Festival riot.
What’s not to understand? If you look at the shadow of a clear, plastic cube, you have a 2D shadow of a 3D reality. (Y’know, the two overlapped suares with lines connecting the corners that you always see in management retreats.)
This is just a 3D shadow of a 4D object (physical dimensions, not time). Don’t try to visualize it, you can’t.
Anyway beats the crappy brainless smear-paintings that pass for art hanging in the coffee shops I go to.
One thought exercise is to start with our three dimensional world. If you pass a sphere through a two dimensional plane you get a point that becomes a circle, the circle expands then contracts until it is a point again and finally disappears.
So a four-dimensional ‘sphere’ passing through our three-dimensional space would start as a point, grow into a solid sphere, expand and then contract back into a point and then finally disappear.
I wonder if this will create the cube that summons the zenobites…
There are two or three threads that come together in order to understand that sculpture:
Platonic Solids:
A Platonic solid is one for which every angle, edge, and face are (respectively) congruent to each other. The three dimensional Platonic solids are the tetrahedron (equilateral triangular pyramid), cube, octahedron, dodecahedron (pentagonal sides), and octahedron. They have lots of neat properties; mathematicians like to do things like construct the dual of a Platonic solid by constructing the midpoint of each edge of the original, and then connecting all of these new points. Turns out that this always yields another Platonic solid.
The ten, 30, and hundred sided dice (of which only the ten is pictured here) are NOT Platonic solids, but Dragon Dice give physical models of each of the actual solids: http://www.pirorin.org/DungeonsAndDragons/DragonDice.jpg
Projective Geometry:
Projective geometry maps one geometric system onto another. It is commonly (for some value of commonly) used to represent hyperbolic geometry in a Euclidean space, for instance by using the Half Plane model or the Poincare Disk (both of which have decent demos built into Geometer’s Sketchpad, and representations which are available via Google). At one point in time I also had a neat program for the TI-92 that would use matrix multiplication to project two dimensions onto two dimensions (but perhaps with a change of axes — instead of having the point (1,0) be “one to the right”, it might change to “one to the right and down a little”) or more familiarly three dimensions onto two dimensions, where the points (1,0,0), (0,1,0) and (0,0,1) would map to (1,0), (0,1), and (sqrt(3)/2, 1/2) respectively. The latter transformation will map a three-dimensional cube onto a two-dimensional monitor or piece of paper. Think of it as the shadow cast by a glass cube.
This kind of transformation is commonly (again, for some value of commonly) used to represent the tesseract (aka hypercube) onto two dimensions. A decent illustration is available on http://www.maa.org/editorial/knot/tesseract.html . This is not (I don’t think — haven’t looked that closely) the particular four-dimensional hypersolid that is represented by the sculpture, but playing with a tesseract may have a chance of building your four-dimensional imagination so that you might be able to maybe recognize, from its shadow, the hypersolid that is so depicted.