I’m confused by your use of “priors”. On a Tegmark IV sort of view, all meaningful sentences are true (in some universe). So the usefulness of the term “prior probability” turns on one’s having at least some doubt about Tegmark IV, yes? I’m not accusing you of making any mistake over this; I just want reassurance or correction about my (mis)understanding of your probability talk.
It’s priors over logical states of affairs. Consider the following sentence: “There is a cellular automaton that can be described in at most 10 KB in programming language X, plus a computable function f() which can be described in another 10 KB in the same programming language, such that f() returns a space/time location within the cellular automaton corresponding to Earth as we know it in early 2014.” This could be false even if Tegmark IV is true, and prior probability (i.e., probability without trying to do an anthropic update of the form “I observe this, so it’s probably simple”) says it’s probably false.
Thanks. But how can I even think the concept “corresponding to Earth as we know it” without relying on a large body of empirical knowledge that influences my probability assignments? I’m having trouble understanding what the prior is prior to. Of course I can refrain from explicitly calculating the K-complexity, say, of the theory in a physics textbook. But even without doing such a calculation, I still have some gut level sense of the simplicity/complexity of physics, very much based on my concrete experiences. Does that not count as anthropic?
I’m confused by your use of “priors”. On a Tegmark IV sort of view, all meaningful sentences are true (in some universe). So the usefulness of the term “prior probability” turns on one’s having at least some doubt about Tegmark IV, yes? I’m not accusing you of making any mistake over this; I just want reassurance or correction about my (mis)understanding of your probability talk.
It’s priors over logical states of affairs. Consider the following sentence: “There is a cellular automaton that can be described in at most 10 KB in programming language X, plus a computable function f() which can be described in another 10 KB in the same programming language, such that f() returns a space/time location within the cellular automaton corresponding to Earth as we know it in early 2014.” This could be false even if Tegmark IV is true, and prior probability (i.e., probability without trying to do an anthropic update of the form “I observe this, so it’s probably simple”) says it’s probably false.
Thanks. But how can I even think the concept “corresponding to Earth as we know it” without relying on a large body of empirical knowledge that influences my probability assignments? I’m having trouble understanding what the prior is prior to. Of course I can refrain from explicitly calculating the K-complexity, say, of the theory in a physics textbook. But even without doing such a calculation, I still have some gut level sense of the simplicity/complexity of physics, very much based on my concrete experiences. Does that not count as anthropic?