Absence of proof is not proof of absence. In logic, A->B, "A implies B", is not equivalent to ~A->~B, "not-A implies not-B".
But in probability theory, absence of evidence is always evidence of absence. If E is a binary event and P(H|E) > P(H), "seeing E increases the probability of H"; then P(H|~E) < P(H), "failure to observe E decreases the probability of H". P(H) is a weighted mix of P(H|E) and P(H|~E), and necessarily lies between the two.
"Absence of evidence is not evidence of absence."
- Carl Sagan
Yes it is:
A lack of sabotage doesn't prove that no Fifth Column exists. Absence of proof is not proof of absence. In logic, A->B, "A implies B", is not equivalent to ~A->~B, "not-A implies not-B".
But in probability theory, absence of evidence is always evidence of absence. If E is a binary event and P(H|E) > P(H), "seeing E increases the probability of H"; then P(H|~E) < P(H), "failure to observe E decreases the probability of H". P(H) is a weighted mix of P(H|E) and P(H|~E), and necessarily lies between the two.
Similarly, look at the amount of information each piece of data gives you. Knowing the month narrows down the possible times by 1/12, and knowing the day narrows it by (about) 1/30. How much knowing the year narrows it is trickier; perhaps you could expect it to be in a given x-year range, and so use 1/x. If x > 30, then 1/12 > 1/30 > 1/x, and so month/day/year would give you the most information first, and progress downward. There's a certain logic to that.
"I think people should have a right to be stupid and, if they have that right, the market's going to respond by supplying as much stupidity as can be sold."
Slashdot Mirror
Try holding down ctrl-w while closing the dialog. Works much of the time.
Sounds a lot like Julian Barbour's The End Of Time.
Similarly, look at the amount of information each piece of data gives you. Knowing the month narrows down the possible times by 1/12, and knowing the day narrows it by (about) 1/30. How much knowing the year narrows it is trickier; perhaps you could expect it to be in a given x-year range, and so use 1/x. If x > 30, then 1/12 > 1/30 > 1/x, and so month/day/year would give you the most information first, and progress downward. There's a certain logic to that.
"I think people should have a right to be stupid and, if they have that right, the market's going to respond by supplying as much stupidity as can be sold."
One interesting scheme that allows a form of verification without allowing vote selling is Ronald Rivest's ThreeBallot Voting System.