No, I wasn’t; I don’t think that’s our issue here.
Let me try it this way. If you say “I’m going to roll a 4 on this six-sided die”, and then you roll a 4 on a six-sided die, and my observations of you are equally consistent with both of the following theories: Theory T1: You rolled the die exactly once, and it came up a 4 Theory T2: You rolled the die several times, and stopped rolling once it came up 4 ...I should choose T2, because the observed result is less surprising given T2 than T1.
Would you agree? (If you don’t agree, the rest of this comment is irrelevant: that’s an interesting point of disagreement I’d like to explore further. Stop reading here.)
OK, good. Just to have something to call it, let’s call that the Principle of Least Surprise.
Now, suppose that in all scenarios constants are set shortly after the creation of a world, and do not subsequently change, but that the value of a constant is indeterminate prior to being set. Suppose further that life-supporting values of constants are extremely unlikely. (I think that’s what we both have been supposing all along, I just want to say it explicitly.)
In scenario 1-3, we have multiple worlds with different constants. Constants that support life are unlikely, but because there are multiple worlds, it is not surprising that at least one world exists with constants that support life. We’d expect that, just like we’d expect a six-sided die to come up ‘4’ at least once if tossed ten times. We should not be surprised that there’s an observer in some world, and that world has constants that support life, in any of these cases.
In scenario 4, we have one world with one set of constants. It is surprising that that world has life-supporting constants. We ought not expect that, just like we ought not expect a six-sided die to come up ‘4’ if tossed only once. We should be surprised that there’s an observer in some world.
So. If I look around, and what I observe is equally consistent with scenarios 1-4, the Principle of Least Surprise tells me I should reject scenario 4 as an explanation.
Let me try it this way. If you say “I’m going to roll a 4 on this six-sided die”, and then you roll a 4 on a six-sided die, and my observations of you are equally consistent with both of the following theories: Theory T1: You rolled the die exactly once, and it came up a 4 Theory T2: You rolled the die several times, and stopped rolling once it came up 4 ...I should choose T2, because the observed result is less surprising given T2 than T1.
Would you agree? (If you don’t agree, the rest of this comment is irrelevant: that’s an interesting point of disagreement I’d like to explore further. Stop reading here.)
This bit is slightly ambiguous. I would agree if Theory T1 were replaced by “You decided to roll the die exactly once and then show me the result”, and Theory T2 were replaced by “You decided to roll the die until it comes up ‘4’, and then show me the result”, and the two theories have equal prior probability. I think this is probably what you meant, so I’ll move on.
In scenario 1-3, we have multiple worlds with different constants. Constants that support life are unlikely, but because there are multiple worlds, it is not surprising that at least one world exists with constants that support life. We’d expect that, just like we’d expect a six-sided die to come up ‘4’ at least once if tossed ten times. We should not be surprised that there’s an observer in some world, and that world has constants that support life, in any of these cases.
I agree that we should not be surprised. Although I have reservations about drawing this analogy, as I’ll explain below.
In scenario 4, we have one world with one set of constants. It is surprising that that world has life-supporting constants. We ought not expect that, just like we ought not expect a six-sided die to come up ‘4’ if tossed only once. We should be surprised that there’s an observer in some world.
If we take scenario 4 as I described it — there’s a scientific model where the constants are free parameters, and a straightforward parameterless modification of the model (of equal complexity) that posits one universe for every choice of constants — then I disagree; we should not be surprised. I disagree because I think the die-rolling scenario is not a good analogy for scenarios 1-4, and scenario 4 resembles Theory T2 at least as much as Theory T1.
Scenario 4 as I described it basically is scenario 3. The theory with free parameters isn’t a complete theory, and the parameterless theory sorta does talk about other universes which kind of exist, in the sense that a straightforward interpretation of the parameterless theory talks about other universes. So scenario 4 resembles Theory T2 at least as much as it resembles Theory T1.
You could ask why we can’t apply the same argument in the previous bullet point to the die-rolling scenario and conclude that Theory T1 is just as plausible as Theory T2. (If you don’t want to ask that, please ignore the rest of this bullet point, as it could spawn an even longer discussion.) We can’t because the scenarios differ in essential ways. To explain further I’ll have to talk about Solomonoff induction, which makes me uncomfortable. The die-rolling scenario comes with assumptions about a larger universe with a causal structure such that (Theory T1 plus the observation ‘4’) has greater K-complexity than (Theory T2 plus the observation ‘4’). But the hack that turns the theory in scenario 4 into a parameterless theory doesn’t require much additional K-complexity.
It seems to follow from what you’re saying that the assertions “a world containing an observer exists in scenario 4” and “a world containing an observer doesn’t exist in scenario 4″ don’t make meaningful different claims about scenario 4, since we can switch from a model that justifies the first to a model that justifies the second without any cost worth considering.
If that’s right, then I guess it follows from the fact that I should be surprised to observe an environment in scenario 4 that I should not be surprised to observe an environment in scenario 4, and vice-versa, and there’s not much else I can think of to say on the subject.
No, I wasn’t; I don’t think that’s our issue here.
Let me try it this way. If you say “I’m going to roll a 4 on this six-sided die”, and then you roll a 4 on a six-sided die, and my observations of you are equally consistent with both of the following theories:
Theory T1: You rolled the die exactly once, and it came up a 4
Theory T2: You rolled the die several times, and stopped rolling once it came up 4
...I should choose T2, because the observed result is less surprising given T2 than T1.
Would you agree? (If you don’t agree, the rest of this comment is irrelevant: that’s an interesting point of disagreement I’d like to explore further. Stop reading here.)
OK, good. Just to have something to call it, let’s call that the Principle of Least Surprise.
Now, suppose that in all scenarios constants are set shortly after the creation of a world, and do not subsequently change, but that the value of a constant is indeterminate prior to being set. Suppose further that life-supporting values of constants are extremely unlikely. (I think that’s what we both have been supposing all along, I just want to say it explicitly.)
In scenario 1-3, we have multiple worlds with different constants. Constants that support life are unlikely, but because there are multiple worlds, it is not surprising that at least one world exists with constants that support life. We’d expect that, just like we’d expect a six-sided die to come up ‘4’ at least once if tossed ten times. We should not be surprised that there’s an observer in some world, and that world has constants that support life, in any of these cases.
In scenario 4, we have one world with one set of constants. It is surprising that that world has life-supporting constants. We ought not expect that, just like we ought not expect a six-sided die to come up ‘4’ if tossed only once. We should be surprised that there’s an observer in some world.
So. If I look around, and what I observe is equally consistent with scenarios 1-4, the Principle of Least Surprise tells me I should reject scenario 4 as an explanation.
Would you agree?
This bit is slightly ambiguous. I would agree if Theory T1 were replaced by “You decided to roll the die exactly once and then show me the result”, and Theory T2 were replaced by “You decided to roll the die until it comes up ‘4’, and then show me the result”, and the two theories have equal prior probability. I think this is probably what you meant, so I’ll move on.
I agree that we should not be surprised. Although I have reservations about drawing this analogy, as I’ll explain below.
If we take scenario 4 as I described it — there’s a scientific model where the constants are free parameters, and a straightforward parameterless modification of the model (of equal complexity) that posits one universe for every choice of constants — then I disagree; we should not be surprised. I disagree because I think the die-rolling scenario is not a good analogy for scenarios 1-4, and scenario 4 resembles Theory T2 at least as much as Theory T1.
Scenario 4 as I described it basically is scenario 3. The theory with free parameters isn’t a complete theory, and the parameterless theory sorta does talk about other universes which kind of exist, in the sense that a straightforward interpretation of the parameterless theory talks about other universes. So scenario 4 resembles Theory T2 at least as much as it resembles Theory T1.
You could ask why we can’t apply the same argument in the previous bullet point to the die-rolling scenario and conclude that Theory T1 is just as plausible as Theory T2. (If you don’t want to ask that, please ignore the rest of this bullet point, as it could spawn an even longer discussion.) We can’t because the scenarios differ in essential ways. To explain further I’ll have to talk about Solomonoff induction, which makes me uncomfortable. The die-rolling scenario comes with assumptions about a larger universe with a causal structure such that (Theory T1 plus the observation ‘4’) has greater K-complexity than (Theory T2 plus the observation ‘4’). But the hack that turns the theory in scenario 4 into a parameterless theory doesn’t require much additional K-complexity.
I didn’t really follow this, I’m afraid.
It seems to follow from what you’re saying that the assertions “a world containing an observer exists in scenario 4” and “a world containing an observer doesn’t exist in scenario 4″ don’t make meaningful different claims about scenario 4, since we can switch from a model that justifies the first to a model that justifies the second without any cost worth considering.
If that’s right, then I guess it follows from the fact that I should be surprised to observe an environment in scenario 4 that I should not be surprised to observe an environment in scenario 4, and vice-versa, and there’s not much else I can think of to say on the subject.