![]() Strogatz explains the infinite sum that deprived me of my slice of cake, ½ + ¼ + ⅛ . . ., by describing a hotel manager who has a finite amount of time to prepare rooms for new arrivals. In a voice-over by the mathematician Steven Strogatz, we learn that the hotel is occupied, yet it can always accommodate more guests-even an infinity of new guests. ![]() It includes, for example, a cartoon called “The Infinite Hotel,” based on a thought experiment by the twentieth-century German mathematician David Hilbert. “A Trip to Infinity” has moments of math magic. So is “The Proof” (1997), the popular “Nova” documentary that captured the excitement of Andrew Wiles’s proof of Fermat’s Last Theorem. ![]() Even if animated, “Mathmagic Land” is helpfully light on metaphor. Crucially, “Mathmagic Land” combines fun and fact without oversimplifying the math, and without speaking down to the viewer. In less than thirty minutes, the film takes the viewer-and Donald Duck-from ancient Greeks to futuristic astronauts, introducing such concepts as number theory and geometry. How do you illustrate a complicated concept without resorting to gimmicks and distractions, or limiting your film to a sequence of talking heads? One of the best answers to that question is “Donald in Mathmagic Land” (1959), which was part of a series of science-education documentaries that Disney produced in the fifties and sixties. Math documentaries always pose a challenge to filmmakers because mathematics does not exist in the realm of images but in the realm of ideas. Perhaps to make sense of infinity, even just a little, is a way to feel some control and comfort in the face of life’s big questions. Buzz Lightyear, in “Toy Story,” teaches kids that life is full of infinite possibilities Hamlet, as he laments the finitude of life, remembers Yorick as a man of infinite jest. Young people can think that life will last forever older people, realizing that it will not, might look for a semblance of immortality in their legacies. Why are we so intrigued by the infinite? Maybe it’s because of the tension between our finite lives and the seemingly unbounded range of our imagination, between the limits that we experience and the possibly infinite universe that we inhabit. In images and interviews, the film contemplates whether there are physical manifestations of infinity, and whether it is possible for a mortal person to experience endlessness. Populated by a diverse and engaging cast of mathematicians, physicists, and a stray philosopher or two, the film, by Jonathan Halperin and Drew Takahashi, explores the infinite, with its puzzles and paradoxes, 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. ![]() When I convinced them that it equalled ¼, I was pretty sure that their murmurs of “mmm” were not dreams of cake.Ī new documentary, “A Trip to Infinity,” tries to serve up this feeling of wonder to Netflix’s massive audience. Then we talked about a different infinite sum that had been making its way around the Internet: 1-2+3-4+ . . . ![]() We agreed that, eventually, if you kept writing numbers forever, they had to add up to one. Together, we wrote a sum on the board: ½ + ¼ + . . . How much cake would I have at the end of this? “None!” many of the fifth graders yelled. This happened again and again-in the story, I have a lot of friends-and my snack kept getting smaller. Before I could eat my half, another friend came by, so I split it again. In the story that I told them, I was preparing to eat a piece of cake when a friend walked in on me. Several years ago, I tried to explain infinity to a class of fifth graders. ![]()
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