How about a slightly more mathematical, but really hand wavy answer. Note I am not a mathematician or anything really relevant, but I do use bayesian stats a bit. Feel free to critique it.
If we assume there are 10^21 stars in the universe, and 10^21 universes. Let us also say that our prior probability for intelligent life around 1 star (P) is a uniform distribution bounded by 10^-2 and 10^-100.
We then take our 1 observation, there exists 1 universe with at least 1 star with intelligent life. How does this change our knowledge of the probability function? It reduces our estimate of the probability at P = 10^-100, because at that level the probability of our observation happening is 10^-58 (I think). However it does not say anything about the relative probabilities of P = 10^-27 (1 intelligent life per 1,000,000 universes) and P = 10^-15 (1,000,000 intelligent lives per universe) because the probability of our observation under both these conditions ~ 1.
Therefore I believe that the observation that life exists on earth does not do much to inform us on the chance of meeting ET.
If we assume there are 10^21 stars in the universe, and 10^21 universes. Let us also say that our prior probability for intelligent life around 1 star (P) is a uniform distribution bounded by 10^-2 and 10^-100.
We then take our 1 observation, there exists 1 universe with at least 1 star with intelligent life. How does this change our knowledge of the probability function? It reduces our estimate of the probability at P = 10^-100, because at that level the probability of our observation happening is 10^-58 (I think). However it does not say anything about the relative probabilities of P = 10^-27 (1 intelligent life per 1,000,000 universes) and P = 10^-15 (1,000,000 intelligent lives per universe) because the probability of our observation under both these conditions ~ 1.
Therefore I believe that the observation that life exists on earth does not do much to inform us on the chance of meeting ET.
I do not think this is true, but it is really getting into maths I only know about through osmosis from real mathmaticians I know socially. Even if there are infinite planets with life on them, this does not mean that every form of life possible exists somewhere. As an explaination, consider there are an infinite number of integers, and there are an infinite number of real numbers. Does that mean that if I take one real number for every integer, eventually I will pick an integer? No, because there are aleph-naught integers but aleph-one real numbers, and aleph-one is infinitely larger than aleph-naught. Equally if there are aleph-naught stars in the multiverse, but aleph-one (or aleph-two, or aleph-42) configurations of life, then you will not get another warpus.The inconceivable size of the multiverse means it is near-certain there is another warpus out there somehwere.
Last edited: