Jeff Weeks, a freelance mathematician and MacArthur Fellow, presented a lecture titled "The Shape of Space on March 31 at Hamilton College.
Weeks began his lecture by showing the audience a picture taken by the Hubble space telescope. The picture, which included several different colored shapes on a black background, was of a dime-sized patch of sky located near the big dipper; before the Hubble took such pictures nothing was seen in that area. However, the pictures conveyed many different galaxies. Weeks said there are over 100 billion galaxies in our sky, each galaxy including over 100 billion stars. "For sure, the universe is very big," he joked.
"When we look out on a clear night, the universe seems infinite but this may be an illusion," Weeks said. The true question, he explained is, "is the universe finite, does an edge of the universe exists, or is there a limitless volume of space?"
Weeks illustrated this idea, as well as the distinction between infinite and having no boundaries, by using a "toy 2-dimensional universe." He used computer images to create the 2-d torus (flat) universe. This universe wraps around like a cylinder both side to side and top to bottom.
Audience members were able to understand the elements of the 2-d torus universe by playing various computer games with a torus twist; games included tic-tac-toe, crossword, and even chess. (These games can be found on the internet at www.geometrygames.org.) Weeks was able to convey that although the "board" looked infinite, in reality it was finite.
Weeks then applied this concept to a 3-dimensional universe. He explained via computer simulation and games how 3-dimensional spaces work, and how patterns can help us understand how different topologies work.
"How can we tell if the real universe is like this," Weeks asked his audience. "The answer is harder than you may think." He explained how, although patters are easily found on a computer simulation, they are oftentimes harder to find in the universe because everything is so far away. Therefore, by the time light reaches the earth, we may be seeing an image of the past, not of the present. Therefore, because of the long delay, it is difficult to find patterns in the sky.
Weeks also explained that many galaxies do not emit light waves, but rather microwaves, which are invisible to the human eye, and therefore very difficult to follow.
However, this does not mean that such patters are totally impossible to find. In June 2001, NASA launched the Wilkinson Microwave Anisotropy Probe, otherwise known as WMAP. The WMAP found that the universe lacks broad fluctuations intrinsic to an infinite universe, thus suggesting that the universe may be finite after all.
The best candidate for the universe's shape, Weeks explained, would not be a 3-torus but a poincare dodecahedral space. This is not possible in a flat space; therefore, we may be living in a hypersphere, he said. Therefore, space as we know it may be finite and having a slight curvature.
There is no way to know for sure right now, Weeks concluded. These strange alignments could be from measurement error or some sort of new evolving physical process. However, as measurements continue to be recorded, the 3 torus shape may come back into the running.
Weeks earned a bachelor's degree from Dartmouth College and a master's and a Ph.D. from Princeton University. He is the author of the book The Shape of Space and Exploring the Shape of Space. He was awarded a MacArthur fellowship in 1999. MacArthur fellowships are "unrestricted fellowships to exceptionally talented and promising individuals who have shown evidence of originality, dedication to creative pursuits, and capacity for self-direction for his research." Weeks was awarded the MacArthur for his work on describing the topology of knots and hyperbolic structures, as well as for his collaboration with astronomers to help understand the universe.
Weeks' lecture was sponsored by Sophomore Seminar class 218 and the Physics Department.
-- by Emily Lemanczyk '05
