have to somehow correct for the fact that we know N is not zero, since we are hereThe anthropic principle is the correction. Observing ourselves is a prerequisite of analysis - independently of probabilities which can be any low! So it is not an "independent" observation.
Otherwise we could easily say from armchair, that:
1. Probability of civilization in a certain place is extremely low
2. Universe is huge, with plenty of places
3. https://en.wikipedia.org/wiki/Poisson_limit_theorem
4. Expected number of civilizations in universe (without noticing anthropic principle): 1 (at least!)
5. So take Poisson dist. with lambda=1, as a conservative estimate
6. Probability of more than 1 civilization, if we know that there is at least 1 (again without noticing anthropic principle):
P(X>1 | X>0) = P(X>1)/P(X>0) /Bayes/ = 0.718
So with around 72% probability there is a another civilization. ;)
The anthropic principle is the correction. Observing ourselves is a prerequisite of analysis - independently of probabilities which can be any low! So it is not an "independent" observation. Otherwise we could easily say from armchair, that:
1. Probability of civilization in a certain place is extremely low
2. Universe is huge, with plenty of places
3. https://en.wikipedia.org/wiki/Poisson_limit_theorem
4. Expected number of civilizations in universe (without noticing anthropic principle): 1 (at least!)
5. So take Poisson dist. with lambda=1, as a conservative estimate
6. Probability of more than 1 civilization, if we know that there is at least 1 (again without noticing anthropic principle): P(X>1 | X>0) = P(X>1)/P(X>0) /Bayes/ = 0.718
So with around 72% probability there is a another civilization. ;)