One thing that's never been explained to me is how large the space is. Does everyone have one big swirl on their thumb that goes clockwise or counter-clockwise? Could you have two swirls? What is the space of potential fingerprints?
Fingerprint scanners compile a small set of identifying features (typically where ridges end or split). They don't characterize the entire fingerprint. The higher quality the scanning system, the more identifying features they use -- so the size of the search space is both smaller than most people think, and varies depending on the quality of the system.