I was assuming per Tegmark that we live in (at least one variety of) big world, and “I” denotes a set of entities indistinguishable with current information, but who live in different parts of the multiverse. But more prosaically, you could note that there is a nonzero albeit small probability that atoms on a lifeless Mars will arrange themselves into a life form between one visit and the next.
I grant that a big world provides an ensemble such that epsilon could make sense. I think that the prosaic explanation fails, though—a fully specified version of statement two refers either to an instant in time or an interval, and either way, in a small world there will be a fact of the matter.
Hmm, frequentist probability is most usually described in terms of, er, frequency; what fraction of the time we will get a given result when we run the test. But if you take it as referring to an instant of time (and you assume small world and no fuzziness) in that case I agree the epsilon would disappear.
It’s a minor point, but wackily enough, the above quote is a subtle equivocation on the word “time”. I can flip N exchangeable coins simultaneously and count the number of times I see “heads”, and this is perfectly sensible in the frequentist interpretation. Physical clock time is something else again.
I’m not sure why the frequentist would put an epsilon in P2. Surely there is a fact of the matter about statement 2 just as there is for statement 3.
I was assuming per Tegmark that we live in (at least one variety of) big world, and “I” denotes a set of entities indistinguishable with current information, but who live in different parts of the multiverse. But more prosaically, you could note that there is a nonzero albeit small probability that atoms on a lifeless Mars will arrange themselves into a life form between one visit and the next.
I grant that a big world provides an ensemble such that epsilon could make sense. I think that the prosaic explanation fails, though—a fully specified version of statement two refers either to an instant in time or an interval, and either way, in a small world there will be a fact of the matter.
Hmm, frequentist probability is most usually described in terms of, er, frequency; what fraction of the time we will get a given result when we run the test. But if you take it as referring to an instant of time (and you assume small world and no fuzziness) in that case I agree the epsilon would disappear.
It’s a minor point, but wackily enough, the above quote is a subtle equivocation on the word “time”. I can flip N exchangeable coins simultaneously and count the number of times I see “heads”, and this is perfectly sensible in the frequentist interpretation. Physical clock time is something else again.