I don’t think I understand what you mean here. Can you elaborate? I’m talking about the difference in causal graphs.
I mean that different branches are casually connected—there is some level of interference between them. In practice you would be approximating it differently—coin toss causing all branches as opposed to Monday causing Tuesday, yes. But it’s basically the same causal graph as if we copy Beauty instead of reawakening, so I don’t get why such causality matters. You said in another comment, that copying changes things, but I assume (from the OP) that you still would say that Elga’s model is not allowed, because both rooms exist simultaneously? Well, branches also exist simultaneously.
The math stays the same, regardless. That’s the whole point.
It doesn’t—if all branches exist, then P of everything is 1. Even if you believe in Born probabilities, they are probably indexical too.
“Objective statistics” shows that all the sheets are spread among students and all the questions are asked. And yet there is a meaningful way to say that to a particular student there is a specific probability to receive a particular question in the exam.
...or do you accept Elga’s model for copies and it is really all about awakenings being sequential? Why the same arguments about changing probability of questions wouldn’t apply here? Or “if two models are claiming that you get different amount of knowledge while observing the same data one is definitely wrong”?
I mean that different branches are casually connected—there is some level of interference between them.
Can’t we model interference as separate branches? My QM is a bit rusty, what kind of casual behaviour is implied? It’s not that we can actually jump from one branch to the other.
You said in another comment, that copying changes things, but I assume (from the OP) that you still would say that Elga’s model is not allowed, because both rooms exist simultaneously? Well, branches also exist simultaneously.
Simultaneous of existence has nothing to do with it. Elga’s model is wrong here because unlike the Sleeping Beauty, learning that you are in Room 1 is evidence for Heads, as you could not be sure to find yourself in Room 1 no matter what. Here Lewis’ model seems a better fit.
..or do you accept Elga’s model for copies and it is really all about awakenings being sequential?
I think some cloning arrangement can work according to Elga’s model, it fully depends on the specific of the cloning procedure. Whether the process that led to your existence can be correctly approximated as random sampling or not. Though, I need to think more about it as these cases still feel a bit confusing to me. There definitely are settings where SIA-like reasoning is valid, like when there is a limited set of souls that a randomly picked to be instantiated in bodies, it just doesn’t really seem to be the way our universe works.
Can’t we model interference as separate branches? My QM is a bit rusty, what kind of casual behaviour is implied? It’s not that we can actually jump from one branch to the other.
Don’t know specifics, as usual, but as far as I know, amplitudes of the branch would be slightly different from what you get by evolving this branch in isolation, because other branch would also spread everywhere. The point is just that they all exist, so, as you say, why use imperfect approximation?
Simultaneous of existence has nothing to do with it. Elga’s model is wrong here because unlike the Sleeping Beauty, learning that you are in Room 1 is evidence for Heads, as you could not be sure to find yourself in Room 1 no matter what. Here Lewis’ model seems a better fit.
I meant the experiment where you don’t know which room it is, but anyway—wouldn’t Lewis’ model fail statistical test, because it doesn’t generate both rooms on Tails? I don’t get why modeling coexistence in one timeline is necessary, but coexistence in space is not.
What do you mean by “can be correctly approximated as random sampling”? If all souls are instantiated, then Elga’s model still wouldn’t pass statistical test.
Don’t know specifics, as usual, but as far as I know, amplitudes of the branch would be slightly different from what you get by evolving this branch in isolation, because other branch would also spread everywhere.
I’m afraid I won’t be able to address your concerns without the specifics. Currently I’m not even sure that they are true. According to Wei Dai in one of a previous comments our current best theory claims that Everett branches are causally disconnected and I’m more than happy to stick to that until our theories change.
wouldn’t Lewis’ model fail statistical test, because it doesn’t generate both rooms on Tails?
If you participate in a Fissure experiment you do not experience being at two rooms on Tails. You are in only one of the rooms in any case, and another version of you is in another room when it’s Tails. You can participate in a thousand fissure experiment in a row and accumulate a list of rooms and coin outcomes corresponding to your experience and I expect them to fit Lewis’s model. 75% of time you find yourself in room 1, 50% of time the coin is Heads.
I don’t get why modeling coexistence in one timeline is necessary, but coexistence in space is not.
Because coexistence in space happens separately to different people who are not causally connected, while coexistence in one timeline happen to the same person, whose past and future are causally connected. I really don’t understand why everyone seem to have so much trouble with such an obvious point.
Suppose in a Sleeping Beauty it’s Tails and the participant eats a big meal on Monday. On Tuesday they will likely need to visit the toilet as a result. But in Fissure on Tails if a person in one room eats a big meal it doesn’t affect in any way the person in the other room.
What do you mean by “can be correctly approximated as random sampling”?
Probability is in the map. And this map may or may not correspond to the territory. When someone throws a coin it can usually be treated as a random sample from two outcomes. But it’s not some inherent law of the universe about coin tossing. Its possible to make a robot arm that throws coins in such a way to always produce Tails.
I’m afraid I won’t be able to address your concerns without the specifics. Currently I’m not even sure that they are true. According to Wei Dai in one of a previous comments our current best theory claims that Everett branches are causally disconnected and I’m more than happy to stick to that until our theories change.
They are approximately disconnected according to our current best theory. Like your clones in different rooms are approximately disconnected, but still gravitationally influence each other.
You can participate in a thousand fissure experiment in a row and accumulate a list of rooms and coin outcomes corresponding to your experience and I expect them to fit Lewis’s model. 75% of time you find yourself in room 1, 50% of time the coin is Heads.
Still don’t get how it’s consistent with your argument about statistical test. It’s not about multiple experiments starting from each copy, right? You still would object to simulating multiple Beauties started from each awakening as random? And would be ok with simulating multiple Fissures from one original as random?
Because coexistence in space happens separately to different people who are not causally connected, while coexistence in one timeline happen to the same person, whose past and future are causally connected. I really don’t understand why everyone seem to have so much trouble with such an obvious point.
I understand that there is a difference. The trouble is with justification for why this difference is relevant. Like, you based your modelling of Monday and Tuesday as both happening on how we usually treat events when we use probability theory. But the same justification is even more obvious, when both the awakening in Room 1 and the awakening in Room 2 happen simultaneously. Or you say that the Beauty knows that she will be awake both times so she can’t ignore this information. But both copies also know that they both will be awake, so why they can ignore it?
If you participate in a Fissure experiment you do not experience being at two rooms on Tails. You are in only one of the rooms in any case, and another version of you is in another room when it’s Tails.
Is this what it is all about? It depends on definition of “you”. Under some definitions the Beauty also doesn’t experience both days. Are you just saying that distinction is that no sane human would treat different moments as distinct identities?
They are approximately disconnected according to our current best theory. Like your clones in different rooms are approximately disconnected, but still gravitationally influence each other.
I think this level of accuracy is good enough for now.
Still don’t get how it’s consistent with your argument about statistical test. It’s not about multiple experiments starting from each copy, right?
It very much is. Every copy is its own person who can then participate in whatever experiments they chose to independently from the other copy.
You still would object to simulating multiple Beauties started from each awakening as random?
I don’t see how it is possible in principle. If the Beauty in the middle of experiment how can she starts participating in another experiment without breaking the setting of the current one? In what sense is she the same person anyway if you treat any waking moment as a different person?
Like, you based your modelling of Monday and Tuesday as both happening on how we usually treat events when we use probability theory. But the same justification is even more obvious, when both the awakening in Room 1 and the awakening in Room 2 happen simultaneously.
No, they are not. Events that happen to Beauty on Monday and Tuesday are not mutually exclusive because they are sequential. On Tails if an awakening happened to her on Monday it necessary means that an awakening will happen to her on Tuesday in the same experiment.
But the same argument isn’t applicable to fissure, where awakening in different Rooms are not sequential, and truly are mutually exclusive. If you are awaken in Room 1 you definetely are not awaken in Room 2 in this experiment and vice versa.
Or you say that the Beauty knows that she will be awake both times so she can’t ignore this information. But both copies also know that they both will be awake, so why they can ignore it?
Well if there was some probability theoretic reason why copies could not reason independently, then that would be the case. This is indeed an interesting situation and I’ll dedicate a separate post or even multiple of them to comprehensive analysis of it.
Is this what it is all about? It depends on definition of “you”. Under some definitions the Beauty also doesn’t experience both days.
Of course it depends on definitions. Everything does. But not all definitions are made equal. Some carve reality at its joints and some do not. Some allows to construct theories that adds up to normality and some—that lead to bizarre conclusions.
Are you just saying that distinction is that no sane human would treat different moments as distinct identities?
Well it’s a bit too late for that, because there definetely are otherwise sane people, who are eager to bite the bullet, no matter how ridiculous.
What I’m saying is that to carve reality at it’s joints we need to base our definitions on the causal graphs. And as an extra bonus it indeed seems to fit the naive intuition of personal identity and adds up to normality.
Somehow every time people talk about joints, it turns out being more about naive intuitions of personal identity, than reality^^.
I don’t see how it is possible in principle. If the Beauty in the middle of experiment how can she starts participating in another experiment without breaking the setting of the current one?
If you insist on Monday and Tuesday being on the same week, then by backing up her memory: after each awakening we save memory and schedule memory loading and new experiment to a later free week. Or we can start new experiment after each awakening and schedule Tuesdays for later. Does either of these allow you to change your model?
In what sense is she the same person anyway if you treat any waking moment as a different person?
You can treat every memory sequence as a different person.
No, they are not. Events that happen to Beauty on Monday and Tuesday are not mutually exclusive because they are sequential. On Tails if an awakening happened to her on Monday it necessary means that an awakening will happen to her on Tuesday in the same experiment.
But the same argument isn’t applicable to fissure, where awakening in different Rooms are not sequential, and truly are mutually exclusive. If you are awaken in Room 1 you definetely are not awaken in Room 2 in this experiment and vice versa.
I’m not saying the arguments are literally identical.
Your argument is:
The awakening on Tuesday happens always and only after the awakening on Monday.
I mean that different branches are casually connected—there is some level of interference between them. In practice you would be approximating it differently—coin toss causing all branches as opposed to Monday causing Tuesday, yes. But it’s basically the same causal graph as if we copy Beauty instead of reawakening, so I don’t get why such causality matters. You said in another comment, that copying changes things, but I assume (from the OP) that you still would say that Elga’s model is not allowed, because both rooms exist simultaneously? Well, branches also exist simultaneously.
It doesn’t—if all branches exist, then P of everything is 1. Even if you believe in Born probabilities, they are probably indexical too.
...or do you accept Elga’s model for copies and it is really all about awakenings being sequential? Why the same arguments about changing probability of questions wouldn’t apply here? Or “if two models are claiming that you get different amount of knowledge while observing the same data one is definitely wrong”?
Can’t we model interference as separate branches? My QM is a bit rusty, what kind of casual behaviour is implied? It’s not that we can actually jump from one branch to the other.
Simultaneous of existence has nothing to do with it. Elga’s model is wrong here because unlike the Sleeping Beauty, learning that you are in Room 1 is evidence for Heads, as you could not be sure to find yourself in Room 1 no matter what. Here Lewis’ model seems a better fit.
I think some cloning arrangement can work according to Elga’s model, it fully depends on the specific of the cloning procedure. Whether the process that led to your existence can be correctly approximated as random sampling or not. Though, I need to think more about it as these cases still feel a bit confusing to me. There definitely are settings where SIA-like reasoning is valid, like when there is a limited set of souls that a randomly picked to be instantiated in bodies, it just doesn’t really seem to be the way our universe works.
Don’t know specifics, as usual, but as far as I know, amplitudes of the branch would be slightly different from what you get by evolving this branch in isolation, because other branch would also spread everywhere. The point is just that they all exist, so, as you say, why use imperfect approximation?
I meant the experiment where you don’t know which room it is, but anyway—wouldn’t Lewis’ model fail statistical test, because it doesn’t generate both rooms on Tails? I don’t get why modeling coexistence in one timeline is necessary, but coexistence in space is not.
What do you mean by “can be correctly approximated as random sampling”? If all souls are instantiated, then Elga’s model still wouldn’t pass statistical test.
I’m afraid I won’t be able to address your concerns without the specifics. Currently I’m not even sure that they are true. According to Wei Dai in one of a previous comments our current best theory claims that Everett branches are causally disconnected and I’m more than happy to stick to that until our theories change.
If you participate in a Fissure experiment you do not experience being at two rooms on Tails. You are in only one of the rooms in any case, and another version of you is in another room when it’s Tails. You can participate in a thousand fissure experiment in a row and accumulate a list of rooms and coin outcomes corresponding to your experience and I expect them to fit Lewis’s model. 75% of time you find yourself in room 1, 50% of time the coin is Heads.
Because coexistence in space happens separately to different people who are not causally connected, while coexistence in one timeline happen to the same person, whose past and future are causally connected. I really don’t understand why everyone seem to have so much trouble with such an obvious point.
Suppose in a Sleeping Beauty it’s Tails and the participant eats a big meal on Monday. On Tuesday they will likely need to visit the toilet as a result. But in Fissure on Tails if a person in one room eats a big meal it doesn’t affect in any way the person in the other room.
Probability is in the map. And this map may or may not correspond to the territory. When someone throws a coin it can usually be treated as a random sample from two outcomes. But it’s not some inherent law of the universe about coin tossing. Its possible to make a robot arm that throws coins in such a way to always produce Tails.
They are approximately disconnected according to our current best theory. Like your clones in different rooms are approximately disconnected, but still gravitationally influence each other.
Still don’t get how it’s consistent with your argument about statistical test. It’s not about multiple experiments starting from each copy, right? You still would object to simulating multiple Beauties started from each awakening as random? And would be ok with simulating multiple Fissures from one original as random?
I understand that there is a difference. The trouble is with justification for why this difference is relevant. Like, you based your modelling of Monday and Tuesday as both happening on how we usually treat events when we use probability theory. But the same justification is even more obvious, when both the awakening in Room 1 and the awakening in Room 2 happen simultaneously. Or you say that the Beauty knows that she will be awake both times so she can’t ignore this information. But both copies also know that they both will be awake, so why they can ignore it?
Is this what it is all about? It depends on definition of “you”. Under some definitions the Beauty also doesn’t experience both days. Are you just saying that distinction is that no sane human would treat different moments as distinct identities?
I think this level of accuracy is good enough for now.
It very much is. Every copy is its own person who can then participate in whatever experiments they chose to independently from the other copy.
I don’t see how it is possible in principle. If the Beauty in the middle of experiment how can she starts participating in another experiment without breaking the setting of the current one? In what sense is she the same person anyway if you treat any waking moment as a different person?
No, they are not. Events that happen to Beauty on Monday and Tuesday are not mutually exclusive because they are sequential. On Tails if an awakening happened to her on Monday it necessary means that an awakening will happen to her on Tuesday in the same experiment.
But the same argument isn’t applicable to fissure, where awakening in different Rooms are not sequential, and truly are mutually exclusive. If you are awaken in Room 1 you definetely are not awaken in Room 2 in this experiment and vice versa.
Well if there was some probability theoretic reason why copies could not reason independently, then that would be the case. This is indeed an interesting situation and I’ll dedicate a separate post or even multiple of them to comprehensive analysis of it.
Of course it depends on definitions. Everything does. But not all definitions are made equal. Some carve reality at its joints and some do not. Some allows to construct theories that adds up to normality and some—that lead to bizarre conclusions.
Well it’s a bit too late for that, because there definetely are otherwise sane people, who are eager to bite the bullet, no matter how ridiculous.
What I’m saying is that to carve reality at it’s joints we need to base our definitions on the causal graphs. And as an extra bonus it indeed seems to fit the naive intuition of personal identity and adds up to normality.
Somehow every time people talk about joints, it turns out being more about naive intuitions of personal identity, than reality^^.
If you insist on Monday and Tuesday being on the same week, then by backing up her memory: after each awakening we save memory and schedule memory loading and new experiment to a later free week. Or we can start new experiment after each awakening and schedule Tuesdays for later. Does either of these allow you to change your model?
You can treat every memory sequence as a different person.
I’m not saying the arguments are literally identical.
Your argument is:
The awakening on Tuesday happens always and only after the awakening on Monday.
Therefore !(P(Monday) = 0 & P(Tuesday) = 1) & !(P(Monday) > 0 & P(Tuesday) < 1).
Therefore they are not exclusive.
The argument about copies is:
The awakening in Room 1 always happens and the awakening in Room 2 always happens.
Therefore !(P(Room 1) < 1) & !(P(Room 2) < 1).
Therefore they are not exclusive.
Why the second one doesn’t work?
I agree, some are more preferable. Therefore probabilities depend on preferences.