Friday, December 24, 2010

Animals and math

Stories keep coming along about animals being better at mathematical computation than humans are. Many such stories at least are of scientific interest (with exceptions, such as the story about octopuses' knowledge of soccer), but they generally can be explained in other ways.

For instance, bees that seem to find the shortest path between many flowers in a meadow are said to have powers of calculation that far surpass our own. This is nothing more than a guess. To determine if a bee's path is optimal, you would have to measure all possible paths. Nobody's done that, or likely ever will. To suggest that bees have invented a general algorithm for picking the shortest path is a bit ridiculous - such tasks are so complex that they fall into a class of virtually unsolvable problems called NP-hard. Bees have evolved to be good at what they do, but they surely aren't doing math.

Another story asserts that pigeons are better than humans at "getting" our old friend the Monte Hall Problem. (Recall that a prize hides behind one of three doors. The contestant picks one door, and thus has a one-third chance of winning the prize. The game host then opens one of the remaining two doors, revealing no prize. Should the contestant switch to the remaining closed door? Yes. While his first choice still has that one-third chance, the remaining closed door now has a two-thirds chance of winning the prize.)

People are bad at this. In a recent study, even after playing multiple times (ample time to see that switching doubles one's chance of winning), most people switched only two-thirds of the time. It took only a few tries for pigeons to learn to switch every time.

Does this mean that pigeons are making some kind of statistical analysis? Are they thinking about the odds? Nope. They're just good observers who follow the evidence.

People, on the contrary, think too much. They overanalze, and get themselves all confused.

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