assumption that my current observer moment is a random sample from all observer moments throughout time
Well, it kinda makes sense? Like, if you can’t distinguish when and where are you, you should have uniform ish distributed credences over those indistinguishable circumstances?
E.g. one motivating problem:
You are given an emerald. You are told that it’s a lottery, 10 random people are given emerald and then 1000 random people are given an emerald 100 years later. In what batch do you expect to be, before they tell you?
Well, it kinda makes sense? Like, if you can’t distinguish when and where are you, you should have uniform ish distributed credences over those indistinguishable circumstances?
You are supposed to apply principle of indifference representing your lack of knowledge—that’s true. The tricky part here which systematically leads people astray in anthropic scenarious is this:
What are these “indistinguishable circumstances” which we are supposed to be indifferent between?
Are those the observer moments, most of which alledgedly belong to boltzman brains?
Or are those the two hypothesises: “I’m a boltzman brain” and “I’m not a boltzman brain”?
In other words, what is the kind of probability experiment that we are dealing with? The one where my observer moment is randomply sampled between all the observer moment or the one where it’s randomly sampled between two categories of such moments.
And in case we know nothing about it, we once again have to be indifferent between these possibilities. Half the credence goes to 1. and half to 2. So at first there is 50% chance that I’m almostly certainly boltzman brain and 50% chance that I have only 50% chance of being a boltzman brain.
But then, as we accumulate evidence that my observations are stable and ordered it simultaneously priviledges 2. over 1. and makes us being boltzman brain conditionally on 2. less likely. As a result we lawfully become pretty confident that we are not randomly sampled throughout all the observer moments and that we are not boltzman brains. And so mere fact of our existence doesn’t give us any precognitive powers to know with high confidence what happens to the universe in billions of years.
But then, as we accumulate evidence that my observations are stable and ordered
Well, like, the whole point of Boltzman brain possibility is that your memory is unreliable, and could be created wholesale. You just remember it, there is no like verified history you can rely on.
(to clarify on high level, I’m not pro BB particularly, just looking at the arguments)
Well, like, the whole point of Boltzman brain possibility is that your memory is unreliable, and could be created wholesale. You just remember it, there is no like verified history you can rely on
That’s beside the point, really.
Whether you are created wholesale with all your memories or you accumulate experiences during you life, the fact that these memories appear to be ordered, lawful and from the same body—unlike being Canaletto at moment t1 and Jeff Bezos at monent t2, for example - is evidence against you being a boltzman brain and evidence against being randomly sampled among people.
That’s not how evidence works, you have two theories, and you have some observation. Is this observation expected on H1? Yes. On H2? Yes. So, it’s not evidence either way.
The point that Eliezer (cited from Feynman) makes, is that given Boltzman brains, you would expect partially unordered instantiations to be more frequent. Partially unordered as a part of momentary experience.
Not, “first me, then Bezos”, this point still uses reliable history as a primitive.
That’s not how evidence works, you have two theories, and you have some observation. Is this observation expected on H1? Yes. On H2? Yes. So, it’s not evidence either way.
How does reflecting on your memories and noticing that they correspond to living in consistent and lawful universe is expected on BB?
You reflect on your memories. You notice that they point to living in a consistent universe. This is expected on living in a consistent universe. This is not expected on being a BB. Therefore you update in favor of not being a BB.
And the same applies for whether you should be indifferent between observer moments or theories.
Well, then you take that consistent universe at face value and notice it should (maybe) produce shitton of BBs. That’s the point of discussion of this post, I guess.
We started from considering two types of probability experiments:
Sample between all the observer moments
Sample between being and not being BB
P(BB|1) ~ 1
P(BB|2) = 1⁄2
By the principle of uncertainty we are indifferent between the two.
P(1) = P(2) = 1⁄2
Therefore
P(BB) = P(BB|1)P(1) + P(BB|2)P(2) ~ 3⁄4
And only then we account for the evidence, reflecting on our stable memories. Which simultaneously update us in favor of 2. and against being BB in general
P(SM|2) >>P(SM|1)
P(SM|BB) << P(SM|not BB)
Therefore
P(1|SM) ~ 0
P(2|SM) ~ 1
Which very quickly updates us to near certainty that we are not BBs.
Well, it kinda makes sense? Like, if you can’t distinguish when and where are you, you should have uniform ish distributed credences over those indistinguishable circumstances?
E.g. one motivating problem:
You are given an emerald. You are told that it’s a lottery, 10 random people are given emerald and then 1000 random people are given an emerald 100 years later. In what batch do you expect to be, before they tell you?
You are supposed to apply principle of indifference representing your lack of knowledge—that’s true. The tricky part here which systematically leads people astray in anthropic scenarious is this:
What are these “indistinguishable circumstances” which we are supposed to be indifferent between?
Are those the observer moments, most of which alledgedly belong to boltzman brains?
Or are those the two hypothesises: “I’m a boltzman brain” and “I’m not a boltzman brain”?
In other words, what is the kind of probability experiment that we are dealing with? The one where my observer moment is randomply sampled between all the observer moment or the one where it’s randomly sampled between two categories of such moments.
And in case we know nothing about it, we once again have to be indifferent between these possibilities. Half the credence goes to 1. and half to 2. So at first there is 50% chance that I’m almostly certainly boltzman brain and 50% chance that I have only 50% chance of being a boltzman brain.
But then, as we accumulate evidence that my observations are stable and ordered it simultaneously priviledges 2. over 1. and makes us being boltzman brain conditionally on 2. less likely. As a result we lawfully become pretty confident that we are not randomly sampled throughout all the observer moments and that we are not boltzman brains. And so mere fact of our existence doesn’t give us any precognitive powers to know with high confidence what happens to the universe in billions of years.
Well, like, the whole point of Boltzman brain possibility is that your memory is unreliable, and could be created wholesale. You just remember it, there is no like verified history you can rely on.
(to clarify on high level, I’m not pro BB particularly, just looking at the arguments)
That’s beside the point, really.
Whether you are created wholesale with all your memories or you accumulate experiences during you life, the fact that these memories appear to be ordered, lawful and from the same body—unlike being Canaletto at moment t1 and Jeff Bezos at monent t2, for example - is evidence against you being a boltzman brain and evidence against being randomly sampled among people.
That’s not how evidence works, you have two theories, and you have some observation. Is this observation expected on H1? Yes. On H2? Yes. So, it’s not evidence either way.
The point that Eliezer (cited from Feynman) makes, is that given Boltzman brains, you would expect partially unordered instantiations to be more frequent. Partially unordered as a part of momentary experience.
Not, “first me, then Bezos”, this point still uses reliable history as a primitive.
How does reflecting on your memories and noticing that they correspond to living in consistent and lawful universe is expected on BB?
Yeah, it doesn’t, but not through your argument.
That is my argument.
You reflect on your memories. You notice that they point to living in a consistent universe. This is expected on living in a consistent universe. This is not expected on being a BB. Therefore you update in favor of not being a BB.
And the same applies for whether you should be indifferent between observer moments or theories.
Well, then you take that consistent universe at face value and notice it should (maybe) produce shitton of BBs. That’s the point of discussion of this post, I guess.
We already did it.
We started from considering two types of probability experiments:
Sample between all the observer moments
Sample between being and not being BB
P(BB|1) ~ 1
P(BB|2) = 1⁄2
By the principle of uncertainty we are indifferent between the two.
P(1) = P(2) = 1⁄2
Therefore
P(BB) = P(BB|1)P(1) + P(BB|2)P(2) ~ 3⁄4
And only then we account for the evidence, reflecting on our stable memories. Which simultaneously update us in favor of 2. and against being BB in general
P(SM|2) >>P(SM|1)
P(SM|BB) << P(SM|not BB)
Therefore
P(1|SM) ~ 0
P(2|SM) ~ 1
Which very quickly updates us to near certainty that we are not BBs.
P(BB|SM) ~ 0