Posted by You can imagine my dismay upon discovering that I had forgotten to deposit my latest Netflix offerings in the mail. Bereft of quality home entertainment to take my mind off the looming return of the students, I hopped into the Jasonmobile and sallied forth to the local Blockbuster Video.
Typically I rent back episodes of television shows. If I have the attention span for a movie, I simply go to a movie, you see. Nonetheless, I browsed the new releases and discovered an intriguing little film called Fermat’s Room.
So I picked up the box, noticed the first two words of the plot description were “Four mathematicians…” and read no further. I rented it at once.
(Warning, some minor spoilers ahead).
The story involves four mathematicians who are lured to a room on an island in the middle of nowhere. They have been enticed by the allure of solving some great, but unspecified problem. Sadly, the whole thing turns out to be a trap. They are locked in their room, with their mysterious host feeding them a series of mathematical brainteasers they must solve within a specified amount of time. If they do not, the walls to the room begin collapsing in on each other. The story revolves around them trying to solve the brainteasers before the walls crush them to death. Inevitably, information about the four comes dribbling out, until finally it becomes clear what is really going on.
Pretty farfetched, I grant you. But the mathematics is impeccable; the movie opens with an admirably clear explanation of Goldbach’s conjecture, for example.
If you are the kind of person who is intrigued by a movie about four mathematicians trapped in a shrinking room, then it is likely you are already familiar with the brainteasers in the movie. Here are three of them, for your solving pleasure:
- You have three boxes of candy, one containiing choclates, one containing peppermints, and one containing a mixture of both. Each box contains a sign announcing its contents. Alas, all of the boxes are labelled incorrectly. You are permitted to remove candies one at a time from any of the boxes. What is the fewest number of candies you must examine to determine for certain which box is which?
- There are three switches on the wall in front of you. One of them controls a lightbulb in a neighboring room, while the other two are not connected to anything. You are allowed to flip the switches in any manner you want. You can then enter the room to see what effect your moves had. What is the fewest number of times you will need to enter the room to determine which switch is connected to the bulb?
- You have a four minute hourglass and a seven minute hourglass. How can you use them to time a period of exactly nine minutes?
You may protest at this point that there is something implausible in the image of studly, professional mathematicians struggling over such problems, but here I think we can grant the writers some dramatic license. The viewer, after all, needs to be able to follow what they are doing. This really isn’t the time for a problem about Frobenious algebras or bifurcation theory.
A fourth puzzle, involving a sequence of numbers, had its amusing elements. The problem was to determine the next number in the sequence. I had paused the film at this point to try to solve it for myself. One possibility I considered was that the numbers were written in alphabetical order, but it was easy to verify that was not the case. Eventually I gave up. Alas, I had forgotten that this was a Spanish movie (with English subtitles). When the digits were written in Spanish, they were, indeed, in alphabetical order. D’oh!
The movie also played in to another of my favorite things in fiction: fair-play detective stories. This is definitely one of those films where seemingly insignificant details from early in the film get referred to later.
In addition to the suspense and generlaly good acting, there are also some impressive visuals. I was almost inclined to ignore the sheer physical impossibility of all four walls of the room closing in on each other simultaneously because the overhead shots of the room were so striking. There is also an impressive and strangely moving car accident, which I will not try to describe.
It may seem an odd thing to say about a movie with so much mathematics in it, but it’s very enjoyable so long as you don’t think too hard about it. There is definitely a James Bond villain aspect to the proceedings. If you are close enough to lure your enemy into an elaborate and very expensive death trap, you are close enough to shoot him. But what can you do? Definitely worth seeing.
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(they can’t expect atomic clock accuracy from a hourglass measurement anyway)
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January 9, 2012
