As the FBI helps a 14-year-old victim who escaped from a dangerous polygamist self-proclaimed prophet, it is faced with the question of how to search 2200 square miles of mountain desert.
“How rough is the terrain? Because the rougher the terrain, the more likely she was forced into a Lévy flight type movement. I can create a viable search pattern,” says Charlie Eppes, the mathematical genius.
“It's like when you lose your keys,” explains Amita Ramanujan, his girlfriend and former doctoral student. “You don't methodically search every inch of your house from front to back. You look like crazy in one area, and then jump to the next most likely area and look there.”
The preceding dialogue, from the American television series Numb3rs, shows how far the theory of Lévy flight foraging has penetrated mainstream science. Although the term foraging has a biological connotation, in fact, biological foraging is a special case of random searches. Michael Shlesinger, for instance, has pointed out the relevance of random searches to operations research in World War II, involving the hunt for enemy submarines.
There are intriguing aspects of the random search problem that are peculiar to biological foraging. Why should the movements of freely moving animals follow any natural law at all? This is a fascinating question, and we find it remarkable that animals – and even humans – that possess a degree of “free will” actually move in a manner that can be described quantitatively by physical principles.