Originally posted by DA Morgan:
Count Iblis wrote:
"I have a Ph.D. in physics"
and
"Sample size is not relevant here."
Ok I am going to hold back my gut instinct to just break out in hysterical laughter and ask you to provide a reference that supports the the following two statements you made which were:
"It is more probable to find yourself in a world where most people believe in God than in an atheistic world"
juxtaposed with your statement:
"Sample size is not relevant here."
Yes. I want you to address your claim that sample size is not relevant to a discussion of probability.
And then I will either nominate you for a Nobel Prize or laugh hysterically until I turn purple and my colleagues call the paramedics.
I use probability in a Bayesian sense, not a frequentist one. You won't win a Nobel prize for inventing Bayesian probability theory any more than for proving that 1 + 1 = 2. It's well established part of probability theory that you seem to be unaware of.
I argued for the statement "It is more probable to find yourself in a world where most people believe in God than in an atheistic world" on theoretical grounds. Sample size isn't relevant here. You can criticise the validity of the (implicit) assumptions made but that is another matter.
Compare the above statement with this one:
"It is more probable to find yourself in a galaxy in which there are many other planets than in a galaxy where there are just 20"
Suppose that this statement was made by an anstrophysicist 20 years ago on the basis of simulatons of planet formations. Thoise simulatons would be based on the known laws of physics. If accurate enough there wouldn't be much grounds to dispute the results.
So, based on these simulatations you would be able to estimate the number of planets in our galaxy, without ever having observed a single extra solar planet. Then you could calculate the probability that our galaxy contains no other planets besides the ones in our solar system. That would, of course, yield a very small probability.
What is the interpretation of this probability? It means that it is very unlikely that no extrasolar planets would be detected in the future. Of course you can only verify this once. There are either extrasolar planets or there aren't (we now know there are). But that's not a valid objection, because in principle you could imagine an ensemble of civilizations in different galaxies testing the same hypothesis.
If you insist on a frequentist definition of the probability then you have to invoke this ensemble. This is exactly how most physics textbooks define probabilities when you can measure the system only once. You invoke an ensemble of identically prepaired systems. But in the Bayesuian sense the probability is always defined and can be related to the knowledge you have about the system, e.g. via the Shannon entropy.
