Suppose, for a moment, that you are the super-villain in a James Bond movie. You want to make 007 suffer from prolonged dramatic tension before ultimately killing him. How would you do it?
In the following 15-minute Numberphile video, Matt Henderson explains how the dumbest way to solve a maze might be your ticket. Particularly if that maze involves flooding poison gas into one part, which then has to make its way to where Bond is tied up in another part of the maze to succeed. [To be fair, Henderson uses the example of poison gas killing a canary rather than James Bond, but the hypothetical outcome would be the same and we might as well raise the stakes for what's really a discussion about coding a simulation to solve a maze!...]
The path the "winning" poison gas molecule takes is determined by a random walk, or Brownian motion, in which it can change direction at any time.
Believe it or not, there are real world applications that utilize what Henderson calls the dumbest way to solve a maze. Labyrinth seals use maze-like structures called tortuous paths designed to either minimize the leaking of something you don't want to get out or to minimize potential contamination from something you don't want to get in.
But our favorite application is the Labyrinth Security Door Chain. Imagine being a Bond villain who puts those on every door in their secret lair!
Labels: math
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