Learning that “I am in the sleeping beauty problem” (call that E) when there are N people who aren’t is admittedly not the best scenario to illustrate how a normal update is factored into the SSA update, because E sounds “anthropicy”. But ultimately there is not really much difference between this kind of E and the more normal sounding E* = “I measured the CMB temperature to be 2.7K”. In both cases we have:
Some initial information about the possibilities for what the world could be: (a) sleeping beauty experiment happening, N + 1 or N + 2 observers in total; (b) temperature of CMB is either 2.7K or 3.1K (I am pretending that physics ruled out other values already).
The observation: (a) I see a sign by my bed saying “Good morning, you in the sleeping beauty room”; (b) I see a print-out from my CMB apparatus saying “Good evening, you are in the part of spacetime where the CMB photons hit the detector with energies corresponding to 3.1K ”.
In either case you can view the observation as anthropic or normal. The SSA procedure doesn’t care how we classify it, and I am not sure there is a standard classification. I tried to think of a possible way to draw the distinction, and the best I could come up with is:
Definition (?). A non-anthropic update is one based on an observation E that has no (or a negligible) bearing on how many observers in your reference class there are.
I wonder if that’s the definition you had in mind when you were asking about a normal update, or something like it. In that case, the observations in 2a and 2b above would both be non-anthropic, provided N is big and we don’t think that the temperature being 2.7K or 3.1K would affect how many observers there would be. If, on the other hand, N = 0 like in the original sleeping beauty problem, then 2a is anthropic.
Finally, the observation that you survived the Russian roulette game would, on this definition, similarly be anthropic or not depending on who you put in the reference class. If it’s just you it’s anthropic, if N others are included (with N big) then it’s not.
The definition in terms of “all else equal” wasn’t very informative for me here.
Agreed, that phrase sounds vague, I think it can simply be omitted. All SSA is trying to say really is that P(E|i), where i runs over all possibilities for what the world could be, is not just 1 or 0 (as it would be in naive Bayes), but is determined by assuming that you, the agent observing E, is selected randomly from the set of all agents in your reference class (which exist in possibility i). So for example if half such agents observe E in a given possibility i, then SSA instructs you to set the probability of observing E to 50%. And in the special case of a 0⁄0 indeterminacy it says to set P(E|i) = 0 (bizarre, right?). Other than that, you are just supposed to do normal Bayes.
What you said about leading to UDT sounds interesting but I wasn’t able to follow the connection you were making. And about using all possible observers as your reference class for SSA, that would be anathema to SSAers :)
Definition (?). A non-anthropic update is one based on an observation E that has no (or a negligible) bearing on how many observers in your reference class there are.
Not what I meant. I would say anthropic information tells you where in the world you are, and normal information tell you what the world is like. An anthropic update, then, reasons about where you would be, if the world were a certain way, to update on world-level probabilities from anthropic information. So sleeping beauty with N outsiders is a purely anthropic update by my count. Big worlds generally tend to make updates more anthropic.
What you said about leading to UDT sounds interesting but I wasn’t able to follow the connection you were making.
One way to interpret the SSA criterion is to have beliefs in such a way that in as many (weighed by your prior) worlds as possible, you would as right as possible in the position of an average member of your reference class. If you “control” the beliefs of members in your reference class, then we could also say to believe in such a way as to make them as right as possible in as many worlds as possible. “Agents which are born with my prior” (and maybe “and using this epistemology”, or some stronger kind of identicalness) is a class whichs beliefs are arguably controlled by you in the timeless sense. So if you use it, you will be doing a UDT-like optimizing. (Of course, it will be a UDT that believes in SSA.)
And about using all possible observers as your reference class for SSA, that would be anathema to SSAers :)
Maybe, but if there is a general form that can produce many kinds of anthropics based on how its free parameter is set, then calling the result of one particular value of the parameter SIA and the results of all others SSA does not seem to cleave reality at the joints.
Learning that “I am in the sleeping beauty problem” (call that E) when there are N people who aren’t is admittedly not the best scenario to illustrate how a normal update is factored into the SSA update, because E sounds “anthropicy”. But ultimately there is not really much difference between this kind of E and the more normal sounding E* = “I measured the CMB temperature to be 2.7K”. In both cases we have:
Some initial information about the possibilities for what the world could be: (a) sleeping beauty experiment happening, N + 1 or N + 2 observers in total; (b) temperature of CMB is either 2.7K or 3.1K (I am pretending that physics ruled out other values already).
The observation: (a) I see a sign by my bed saying “Good morning, you in the sleeping beauty room”; (b) I see a print-out from my CMB apparatus saying “Good evening, you are in the part of spacetime where the CMB photons hit the detector with energies corresponding to 3.1K ”.
In either case you can view the observation as anthropic or normal. The SSA procedure doesn’t care how we classify it, and I am not sure there is a standard classification. I tried to think of a possible way to draw the distinction, and the best I could come up with is:
Definition (?). A non-anthropic update is one based on an observation E that has no (or a negligible) bearing on how many observers in your reference class there are.
I wonder if that’s the definition you had in mind when you were asking about a normal update, or something like it. In that case, the observations in 2a and 2b above would both be non-anthropic, provided N is big and we don’t think that the temperature being 2.7K or 3.1K would affect how many observers there would be. If, on the other hand, N = 0 like in the original sleeping beauty problem, then 2a is anthropic.
Finally, the observation that you survived the Russian roulette game would, on this definition, similarly be anthropic or not depending on who you put in the reference class. If it’s just you it’s anthropic, if N others are included (with N big) then it’s not.
Agreed, that phrase sounds vague, I think it can simply be omitted. All SSA is trying to say really is that P(E|i), where i runs over all possibilities for what the world could be, is not just 1 or 0 (as it would be in naive Bayes), but is determined by assuming that you, the agent observing E, is selected randomly from the set of all agents in your reference class (which exist in possibility i). So for example if half such agents observe E in a given possibility i, then SSA instructs you to set the probability of observing E to 50%. And in the special case of a 0⁄0 indeterminacy it says to set P(E|i) = 0 (bizarre, right?). Other than that, you are just supposed to do normal Bayes.
What you said about leading to UDT sounds interesting but I wasn’t able to follow the connection you were making. And about using all possible observers as your reference class for SSA, that would be anathema to SSAers :)
Not what I meant. I would say anthropic information tells you where in the world you are, and normal information tell you what the world is like. An anthropic update, then, reasons about where you would be, if the world were a certain way, to update on world-level probabilities from anthropic information. So sleeping beauty with N outsiders is a purely anthropic update by my count. Big worlds generally tend to make updates more anthropic.
One way to interpret the SSA criterion is to have beliefs in such a way that in as many (weighed by your prior) worlds as possible, you would as right as possible in the position of an average member of your reference class. If you “control” the beliefs of members in your reference class, then we could also say to believe in such a way as to make them as right as possible in as many worlds as possible. “Agents which are born with my prior” (and maybe “and using this epistemology”, or some stronger kind of identicalness) is a class whichs beliefs are arguably controlled by you in the timeless sense. So if you use it, you will be doing a UDT-like optimizing. (Of course, it will be a UDT that believes in SSA.)
Maybe, but if there is a general form that can produce many kinds of anthropics based on how its free parameter is set, then calling the result of one particular value of the parameter SIA and the results of all others SSA does not seem to cleave reality at the joints.