LEWISTON – It was fun and games and it was all about the shape of space as freelance mathematician Jeff Weeks took a Bates College audience on a mind-boggling excursion through the ins and outs of our universe.

Infinite or finite? Boundaries or unbounded? Using computer games and interactive 3-D graphics of tic-tac-toe and chess projected on a large screen, Weeks demonstrated concepts that represent present thinking and study in cosmology. His presentation Thursday night favored no particular conclusion, but he said he likes the concept of a finite universe.

At the end of the talk, Weeks was asked whether we are possibly “mapping out the contents of our own brains” in attempts to explain the universe.

“My response would be no,'” Weeks said.

However, he continued, “The questions we ask about nature depend very much on our own brain. We can answer only the questions we choose to ask.”

He noted that, “There are places where we probe the boundary of this, for example with quantum mechanics, where I think we got some answers that nobody was expecting.”

And, he was asked, what are the implications for a multi-universe concept?

“There’s no reason why there can’t be other universes,” he said, but added, “Those other universes would be totally unrelated to ours.”

Weeks started his talk with computer games that suggested how space in the total universe might wrap around and allow movement off one side and simultaneously on the other side.

He helped the audience visualize possibilities by illustrating torus and Klein bottle constructions in two dimensions and three dimensions. A torus is a doughnut shape in which an object could move over the top, down through the hole, and back up to the outside starting point, or it could go around the outside or the inside, in all cases winding up where it started.

“You can think of yourself as looking ahead through a torus and seeing yourself from behind,” Weeks explained.

From there, he talked about the twists and turns of a universe shaped like a Klein bottle, a mathematical structure with no inside or outside that’s constructed by gluing both pairs of opposite edges of a rectangle together, giving one pair a half-twist. It can be physically realized only in four dimensions, since it must pass through itself without the presence of a hole.

With ever-increasing complexity, Weeks suggested a universe of interlocking dodecahedrons, which are like spheres with 12 flattened five-sided surfaces.

Some of the concepts taxed the limits of comprehension of the trained mathematicians at the lecture, although Weeks pointed out how even a fourth-grader had once shown him new ways to look at things.

In a discussion of one dimension – a line – Weeks said the youngster had seen a way to get past obstacles that block movement along the line by saying you go in the opposite direction and get there by “looking at the chalk and ignoring the chalkboard.”

Weeks, a resident of Canton, N.Y., was guest lecturer for the Bates College mathematics department’s annual Richard W. Sampson Lecture, which is set up to honor the late Bates professor.

Weeks is the author of a book titled “The Shape of Space” and the recipient of a MacArthur Foundation “genius” fellowship in 1999. His present research centers on a collaboration with cosmologists to test the shape of the universe using satellite data.