But I couldn’t resist this small math nitpick: “But if the chance that one person can save the world is one in a million, then there had better be a million people trying.” → That’s a great quote, but we can be more precise:
If these probabilities were indeed independent (which they can’t possibly be, but still), and a million people tried with a chance of 1 in a million each, then the chance P that the world is saved is only P=1-(999999/1000000)^1000000=63.2%. If we want the world to be saved with probability P, we need x people trying, where x =ln(1-P)/ln(0.999999). For instance, to achieve 99% (which isn’t good enough), we need 4.6 million people; to get 99.99%, we need 9.2 million people, and so on.
I liked this series a lot. Thanks for writing it.
But I couldn’t resist this small math nitpick: “But if the chance that one person can save the world is one in a million, then there had better be a million people trying.” → That’s a great quote, but we can be more precise:
If these probabilities were indeed independent (which they can’t possibly be, but still), and a million people tried with a chance of 1 in a million each, then the chance P that the world is saved is only P=1-(999999/1000000)^1000000=63.2%. If we want the world to be saved with probability P, we need x people trying, where x =ln(1-P)/ln(0.999999). For instance, to achieve 99% (which isn’t good enough), we need 4.6 million people; to get 99.99%, we need 9.2 million people, and so on.
I was amused to note that Nate’s site (click “More »”) now reads: