The Listening Monks in Mort have amazing powers to distinguish things by the sound they make. As I recall the final entrance exam included being able to tell what colour a coin is merely by hearing it fall at 100m. In a maths lecture recently, I was told about a problem put forward in the 1930s, nicknamed "Hearing the shape of a drum" which seemed highly appropriate.
If you define everything about a
drum - surface area, tension and so on - in terms of a matrix M, you
can use the equation Mx=kx to find k, a family of solutions which are
the frequencies which the drum will produce. One clever mathematician
decided to pose the problem the other way around: given k, all the
frequencies the drum produces, can you find M? Or, can you hear the
shape of the drum?
The problem was a lot harder than it may sound, and wasn't actually solved until the 1980s. It turns out that while you can "hear" some properties of the drum, like its perimeter length, it's impossible to find the precise shape. Two drums, which are identical except for the shape, will sound exactly alike. I suppose this puts a fundamental limit on what the Listening Monks could actually hear of the universe. Of course, they were trying to filter out the rest of the universe so they could hear the words of the Creator. This sort of thing always seems to involve running up against fundamental limits - ask any cosmologist.
Rachel Coleman
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December 1997
