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The string theory landscape: a tale of two hydras

String theory is the leading theoretical approach to finding a consistent quantum theory that unifies gravity with the other three forces. However, the theory is only consistent in ten dimensions. In order for string theory to describe observable physics, the six extra dimensions must be sufficiently small to be unobservable. Originally it was hoped that there would only be one consistent way of doing this, but now it is realized that this problem may have as many as 10500 possible solutions. I describe where this number comes from and the approaches, both statistical and anthropic, taken in dealing with this superfluity of solutions.