(June 4, 2011 at 5:05 am)diffidus Wrote: Firstly, on a technical point, the probability of guessing 10 numbers in sequence is not 10^10. It is in fact 10!, which is equal to ~ 1 in 3.6 million. Following the rest of your argument this would mean at least one and likely two people on the planet would guess the correct sequence.How did you come to 10! as the answer? For some reason, my memory seems to tell me you're correct, but in trying to look up the answer it I could only verify my calculation. The probability of you guessing one digit is 1/10. The probability of you guessing 2 digits is 1/10 * 1/10 both numbers is 1 in 100 or 1/10^2. The probability of you guessing 3 digits in a row is 1/10*1/10*1/10 or 1/10^3. Therefore the probability guessing a sequence of of digits is 1/10^n, where n is the number digits you have to guess in a row. So in trying to guess 10 digits correctly the probability is 1/10^10.
Regardless if the probability is 1 in 3.6 million or 1 in 10 billion, would you let someone accused of a crime go based on either of those odds, or would you say with certainty he/she is guilty?
diffidus Wrote:On the second point, it is true that I have said holding an open mind reflects the facts as they are, but I have never said that this means you are unenlightened if you don't. In fact, it is in the nature of an open mind to respect all peoples beliefs where that facts are not fully known.I never meant to say that you were doing it intentionally, but you have started two threads of a similar manner. In both of those you have inadvertently come off condescending towards anyone who believes differently.
Even if the open windows of science at first make us shiver after the cozy indoor warmth of traditional humanizing myths, in the end the fresh air brings vigor, and the great spaces have a splendor of their own - Bertrand Russell
