Whenever we're tempted to believe computers are superior to humans, perhaps we could consider fingerprints. It's not at all a trivial job for computers to work out how to generate random numbers, and yet, with billions of people on the planet, no two sets of fingerprints are identical. Simple human fingerprints display the kind of randomness of which computers can only dream (if computers dreamed, that is).
Even identical twins have unique fingerprints, because development of fingerprints is both genetically and environmentally influenced. All people are born with fingerprints -- we evolved the nifty grooves and swirls on our fingers so it would be easier to grip things. But the way the prints turn out for each person is entirely unique, thanks to a lot of random occurrences, such as a fetus's position in the womb and the disposition of the amniotic fluid; such random factors determine how each ridge on a fingerprint will form.
Unique fingerprints, along with their being just a neat thing to think about, have practical benefits as well. They've proved to be a pretty reliable form of identification, fitting well within the broader area of biometric security (which includes systems based on fingerprints, iris recognition and facial recognition, to name a few). Presenting human, physical evidence of who you are tends to make for a much more reliable security system. After all, it's relatively easy to get a fake ID card, but it's extremely hard to fake a physical trait such as a fingerprint. Similarly, you can guess someone's password, but you can't guess somebody's fingerprint, much less present it as your own. Furthermore, your physical characteristics are always with you, while you could lose an ID card. And, finally, while passwords are easy to forget, you can't really forget to bring your fingerprints.
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