You have oversimplified vision on rationality of humanity. You see decisions that are harmful for humanity and conclude that they are irrational. But this logic only works under the assumption that humanity is one individual. Decisions that are harmful for humanity are in most cases beneficial to the decision-making person, and therefore they are not irrational - they are selfish. This gives us much more hope, because persuading a rational selfish person with logic is totally possible.
Oh look, if we definitely the complexity as "the date when hypothesis was published", then I can say that the prior probability that our earth stands on top of a whale, on top of a turtle on top of an elephant is the highest, because this hypothesis is the oldest. And the Occam's razor becomes "don't propose new hypotheses". Trinitrotrololol)
I find it funny, that it works even in continuous case: suppose that we have probability density defined in R^n (or any other set). Then whatever bijection F:R <--> R^n we apply, the integral of probability density on that path should converge, therefore p(F(x)) goes to zero faster than 1/x. :)
Also, look: suppose the "real" universe is a random point x from some infinite set X. Let's say we are considering finite set of hypotheses "H". Probability that random hypothesis h € H is closest to x is 1/|H|. So the larger H is, the less likely it is that a
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Good point. Mathematically I'd say this: there are actually a lot of competing alternative theories. "almost nothing ever happens" - is also a competing theory. From Solomonoff's induction we know that
P(event|history) = integral_{all_theories} P(event|theory)*P(history|theory)P(theory) d theory
it basically means, that we should weight each theory by the factor P(history|theory) - probability of our entire history of past observations given the theory.
What you're saying, is that if a theory is very precise, then P(history|theory) will only be high if ... (read more)