Simple Bayes means that, if there is no longer any anthropic angle to your problem, you should be able to apply non-anthropic updating.
Equivalently-ish[1] it implies that it doesn’t matter when you started thinking anthropically; if you started doing it yesterday and then updated on one day’s observation, it would be the same as if you started doing it today, or twenty years ago and updated on twenty years of observations. And it also doesn’t matter that you could have been X, if you know that you’re not X.
Formally, this is anchor-free: there isn’t an anchor moment that defines the beginning of when you’re thinking anthropically[2].
Anchor-free is stronger than simple Bayes; simple Bayes is just the equivalent of anchor-free in situations where there is no anthropic uncertainty. Anchor-free is the real condition I want, but simple Bayes is enough for the impossibility result.
One needs to be careful here; technically, any method with a specified anchor is “anchor-free” in a certain sense if it says “whenever you actually started thinking anthropically, then go back to this moment in the past (or future) and anchor then”. If the specified anchor is part of the definition of the method, then it’s “anchor-free” in that it formally doesn’t matter when you started thinking anthropically, because in all cases you just go to a specified anchor[3] and role out everything backwards/forwards from that I don’t consider “anchor specified” to be anchor-free.
“Go to a specified anchor” is not actually that trivial to define. If the “anchor specified” truly behaves like “anchor-free” then it has to work from the very moment of first consciousness (as that’s certainly a place you could start anchoring from), when you could have been, potentially, any being in the universe. So there’s a universal anthropic probability that depends potentially on the details of all agents who ever were or ever could be.
Simple Bayes means that, if there is no longer any anthropic angle to your problem, you should be able to apply non-anthropic updating.
Equivalently-ish [1] it implies that it doesn’t matter when you started thinking anthropically; if you started doing it yesterday and then updated on one day’s observation, it would be the same as if you started doing it today, or twenty years ago and updated on twenty years of observations. And it also doesn’t matter that you could have been X, if you know that you’re not X.
Formally, this is anchor-free: there isn’t an anchor moment that defines the beginning of when you’re thinking anthropically [2] .
Anchor-free is stronger than simple Bayes; simple Bayes is just the equivalent of anchor-free in situations where there is no anthropic uncertainty. Anchor-free is the real condition I want, but simple Bayes is enough for the impossibility result.
One needs to be careful here; technically, any method with a specified anchor is “anchor-free” in a certain sense if it says “whenever you actually started thinking anthropically, then go back to this moment in the past (or future) and anchor then”. If the specified anchor is part of the definition of the method, then it’s “anchor-free” in that it formally doesn’t matter when you started thinking anthropically, because in all cases you just go to a specified anchor [3] and role out everything backwards/forwards from that I don’t consider “anchor specified” to be anchor-free.
“Go to a specified anchor” is not actually that trivial to define. If the “anchor specified” truly behaves like “anchor-free” then it has to work from the very moment of first consciousness (as that’s certainly a place you could start anchoring from), when you could have been, potentially, any being in the universe. So there’s a universal anthropic probability that depends potentially on the details of all agents who ever were or ever could be.