Ah, so you meant: No physically possible series of Bayesian updates can promote a hypothesis to prominence if its prior probability is that low. And Peter meant: It is decision-theoretically useless to include a subroutine for tracking probability increments of 1/3^^^^^3 in your algorithm.
But the non-Bayesian source of your Bayesian prior might output 1/3^^^^^3 as the prior probability of an event—as surely for the coin flip example as for Robin Hanson’s anthropic one.
To be precise, it’s impossible to describe any sense event with a prior probability that low. You can describe hypotheses conditional on which a macro-event has a probability that low. For example, conditional on the hypothesis that a coin is fixed to have a 1/3^^^3 probability of coming up heads, the probability of seeing heads is 1/3^^^3. But barring the specific and single case of Hanson’s hypothesized anthropic penalty being rational, I know of no way to describe, in words, any hypothesis which could justly be assigned so low a prior probability as 1/3^^^3. Including the hypothesis that purple is falling upstairs, that my socks are white and not white, or that 2 + 2 = 5 is a consistent theorem of Peano arithmetic.
Ah, so you meant: No physically possible series of Bayesian updates can promote a hypothesis to prominence if its prior probability is that low. And Peter meant: It is decision-theoretically useless to include a subroutine for tracking probability increments of 1/3^^^^^3 in your algorithm.
But the non-Bayesian source of your Bayesian prior might output 1/3^^^^^3 as the prior probability of an event—as surely for the coin flip example as for Robin Hanson’s anthropic one.
To be precise, it’s impossible to describe any sense event with a prior probability that low. You can describe hypotheses conditional on which a macro-event has a probability that low. For example, conditional on the hypothesis that a coin is fixed to have a 1/3^^^3 probability of coming up heads, the probability of seeing heads is 1/3^^^3. But barring the specific and single case of Hanson’s hypothesized anthropic penalty being rational, I know of no way to describe, in words, any hypothesis which could justly be assigned so low a prior probability as 1/3^^^3. Including the hypothesis that purple is falling upstairs, that my socks are white and not white, or that 2 + 2 = 5 is a consistent theorem of Peano arithmetic.