By Shasta Webb

Clad in a bright turquoise polo t-shirt, mathematician Jeff Weeks attempted to answer the question: “is space infinite or finite?” for the annual Math and Society Lecture hosted by the math department Wednesday, Nov. 11 in the crowded JBD lecture hall.

As a generally non-mathematical person, I was admittedly a little worried that I wouldn’t understand a word Weeks said. However, to my relief and to the relief of the audience members attending for extra credit in their math classes, Weeks used simple ways of discussing incredibly complex phenomena.

To begin his analysis of the problem at hand, Weeks presented a series of very simple tools, or computer games, that he developed. His first game, which displayed a flounder and some shells, represented a two-dimensional torus universe. A torus is a geometric figure made when a circle wraps around an axis. A common torus is basically a donut shape. Weeks explained that in any torus universe, movement is cyclical. That is, if we “leave” one the side of it, we will immediately appear on opposite side of it and see the back of ourselves. Weeks tested our understanding of the concept by having us imagine that JBD was its own tiny universe. This thought was alarming to say the least, and I began imagining living the rest of my life in the basement lecture hall. Weeks continued using this metaphor, asking us what we would see if we could somehow float through the walls. I noticed some audience members looking behind them.

Weeks then explained a three-dimensional torus universe again using the flounder model. However this time when the flounder left one side of the universe and appeared on the other side, it appeared as the mirror image of itself, yet it would still be able to see itself. Weeks then created models that included Earth in a digital version of a finite universe, where Earth repeated infinitely. Weeks explained that in finite universes, the entities within repeat, but in infinite universes they do not.
It seems logical that looking through the Hubble space telescope for repeating images or patterns could determine whether the earth is infinite or finite. However, Weeks explained that the universe is so big, home to 100 billion galaxies each containing 100 billion stars, and it takes time for light to travel from past to present that any far away images humans might receive would essentially be looking back in time. The telescope images would only display light reflection from ancient times. Weeks went on to explain that since the universe is constantly expanding and changing shape, the ancient records of the galaxies would be far outdated. So, we can’t simply look out into space and expect to see ourselves in a finite, cylindrical universe.
At this point in the lecture the material was getting so dense that most of audience was struggling to keep up, despite Weeks’ skills in simplifying enormously complex topics. He admitted that some of the material would be simply out of reach for those unfamiliar with astronomy. He also referenced several more advanced astronomical concepts, but comforted the majority of the audience by saying that we need not worry about the complicated terms.
When he returned to generally less scientific terms, he simply explained that we do not know whether the universe is finite or infinte. This came as a surprise to most in attendance, because some, including myself, had come to find out a definite answer. Weeks was a hit all the same, and for quite a while after the lecture ended, he was bombarded with questions from curious faculty, students and community members. Despite the fact that he is Macarthur Fellow and is among the top of his field, I never once sensed condescension from the speaker. In fact, he seemed incredibly friendly and willing to speak about a wide variety of topics, when answering the questions fired at him.
Finally Weeks encouraged even the least scientific members of the audience to check out his Web site geometrygames.org, which uses games to help people understand the concepts of the universe’s shape, and to explore the concepts further.

I initially attended the lecture simply because my reward would be a few extra points in math, which is not a strongpoint of mine. However, I realized how important these types of lectures are for any type of student or community member. It is more than convenient to remain within our comfortable realms of knowledge and hesitate to branch out to subjects that seem far out of our reach. But when the math department offers events that are accessible to even the most non-mathematical individuals, it reminds us to dabble in some of the most complicated questions that affect our existence. I left the lecture feeling genuinely smarter than I had upon entering, and I realized that these types of talks are actually perfect for the non-mathematical type.