A new documentary, “A Trip to Infinity,” explores the infinite, not only as a mathematical construct but also as an idea that helps us calibrate the vastness of the universe and grasp what it would mean for something to go on forever, and ever, and ever.
and geometry. Crucially, “Mathmagic Land” combines fun and fact without oversimplifying the math, and without speaking down to the viewer. Even if animated, “Mathmagic Land” is helpfully light on metaphor. So is “The Proof” , the popular “Nova” documentary that captured the excitement of Andrew Wiles’s proof of Fermat’s Last Theorem.
“A Trip to Infinity” has moments of math magic. It includes, for example, a cartoon called “The Infinite Hotel,” based on a thought experiment by the twentieth-century German mathematician David Hilbert. In a voice-over by the mathematician, we learn that the hotel is occupied, yet it can always accommodate more guests—even an infinity of new guests. Strogatz explains the infinite sum that deprived me of my slice of cake, ½ + ¼ + ⅛ . . .
The film goes wrong, I think, when it attempts to dress up the mathematics in psychedelic animations, and when it asks experts on math and science to engage in armchair philosophy. As a viewer, I often felt as if I had been invited on an epistemological fishing expedition. In one awkward sequence, participants are handed a small black orb to contemplate, and then instructed, “Tell me what it makes you think about with infinity.
Is the universe as infinite as we might imagine it to be? We may never know, but the reasons for that are fascinating in themselves. The surprise, the film points out, is that even a finite universe can seem infinite to its inhabitants. To explain, the viewer goes on a journey to a four-dimensional world.
When I was a freshman in college, I had the kind of epiphany that “A Trip to Infinity” hopes to inspire. My life, at the time, felt limited; I was unhappy with university and uninspired by the chemistry labs that I had planned to spend my time on. One day, I wandered into my campus bookstore and pulled a math book off the shelf. I found it so transfixing that I sat down in the aisle, oblivious to the shoppers who had to shuffle their way around me.
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