As we assume that coin tosses are quantum, and I will be killed if (I didn’t guess pi) or (coin toss is not heads) there is always a branch with 1⁄128 measure where all coins are heads, and they are more probable than surviving via some errors in the setup.
Not if we assume QI+path-based identity.
Under them the chance for you to find yourself in a branch where all coins are Heads is 1⁄128, but your over chance to survive is 100%. Therefore the low chance of failed execution doesn’t matter, quantum immortality will “increase” the probability to 1.
All hell breaks loose” refers here to a hypothetical ability to manipulate perceived probability—that is, magic. The idea is that I can manipulate such probability by changing my measure.
One way to do this is described in Yudkowsky’s ” The Anthropic Trilemma,” where an observer temporarily boosts their measure by increasing the number of their copies in an uploaded computer.
I described a similar idea in “Magic by forgetting,” where the observer boosts their measure by forgetting some information and thus becoming similar to a larger group of observers.
None of these tricks works with path-based identity. That’s why I consider it to be true—it seem to be totally adding up to normality. No matter how many clones of you exist in a different path—only yours path matters for your probability estimate.
Seems that, path-based identity is the only approach according to which all hell doesn’t break lose. So what counterargument you have against it?
Hidden variables also appear depending on the order in which I make copies: if each copy is made from subsequent copies, the original will have a 0.5 probability, the first copy 0.25, the next 0.125, and so on.
Why do you consider it a problem? What kind of counterintuitive consequences does it imply? It seems to be exactly how we reason about anything else.
Suppose there is the original ball, then an indistinguishable copy of it is created. Then one of these two balls is picked randomly and put into a bag 1, while the other ball is put into the bag 2 and then indistinguishable 999 copies of this ball is also put into bag 2.
Clearly we are supposed to expect that ball from bag 1 has 50% to be the original ball, while a random ball from bag 2 only 1/2000 chance to be the original ball. So what’s the problem?
“Anthropic shadow” appear only because the number of observers changes in different branches.
By the same logic “Ball shadow” appears because the number of balls is different in different bags.
Under them the chance for you to find yourself in a branch where all coins are Heads is 1⁄128, but your over chance to survive is 100%. Therefore the low chance of failed execution doesn’t matter, quantum immortality will “increase” the probability to 1
You are right, and it’s a serious counterargument to consider. Actually, I invented path-dependent identity as a counterargument to Miller’s thought experiment.
You are also right that the Anthropic Trilemma and Magic by Forgetting do not work with path-dependent identity.
However, we can almost recreate the magic machine from the Anthropic Trilemma using path-based identity:
Imagine that I want to guess in which room I will be if there are two copies of me in the future, red or green.
I go into a dream. A machine creates my copy and then one more copy of that copy, which will result in 1⁄4 and 1⁄4 chances each. The second copy then merges with the first one, so we end up with only two copies, but I have a 3⁄4 chance to be the first one and 1⁄4 to be the second. So we’ve basically recreated a machine that can manipulate probabilities and got magic back.
The main problem of path-dependent identity is that we assume the existence of a “global hidden variable” for any observer. It is hidden as it can’t be measured by an outside viewer and only represents the subjective chances of the observer to be one copy and not another. And it is global as it depends on the observer’s path, not their current state. It therefore contradicts the view that mind is equal to a Turing computer (functionalism) and requires the existence of some identity carrier which moves through paths (qualia, quantum continuity, or soul).
Also, path-dependent identity opens the door to back-causation and premonition, because if we normalize outputs of some black box where paths are mixed, similar to the magic machine discussed above, we get a shift in its input probability distribution in the past. This becomes similar to the ‘timeline selection principle’ (which I discussed in a longer version of this blog post but cut to fit format) in which not observer-moments are selected, but the whole timelines without updating on my position in the timeline. This idea formalizes the future anthropic shadow as I am more likely to be in the timeline that is fattest and longest in the future.
You are right, and it’s a serious counterargument to consider.
You are also right that the Anthropic Trilemma and Magic by Forgetting do not work with path-dependent identity.
Okay, glad we are on the same page here.
However, we can almost recreate the magic machine from the Anthropic Trilemma using path-based identity
I’m not sure I understand your example and how it recreates the magic. Let me try to describe to it with my own words, and then correct me if I got something wrong.
You are put to sleep. Then you are splitted into two people. Then, on random, one of them is put into red room and one into green room. Let’s say that person 1 is in red room and 2 in green room. Then the person 2 is splitted into two people: 21 and 22. Both of them are keept in green rooms. Then everyone is awaken. What should be your credence to awake in a red room?
Here there are three possibilities: 50% to be 1 in a red room and 25% chance to be either 21 or 22 in green rooms. No matter how much a person in a green room is split, the total probability for greenness stays the same. All is quite normal and there is no magic.
Now let’s add a twist.
Instead of putting both 21 and 22 in green rooms, one of them—let it be 21 - is put in a red room.
In this situation, total probability for red room is P(1) + P(21) = 75%. And if we split the 2 more and put more of its parts in red rooms we get highter and highter probability to be in red room. Therefore we get magical ability to manipulate probability.
Am I getting you correctly?
I do not see anything problematic with such “manipulation of probability”. We do not change our estimate just because more people with the same experience are created. We change the estemate because different fraction of people get different experience. This is no more magical than putting both 1 and 2 into red rooms and noticing that suddenly the probability for being in red room reached 100%, compared to the initial formulation where it was mere 50%. Of course it did! That’s completely lawful behaviour of probability theoretic reasoning.
Notice that we can’t actually recreate the anthropic trilemma and be certain to win lottery this way. Because we can’t move people between branches. Therefore everything adds up to normality.
Also, path-dependent identity opens the door to back-causation and premonition, because if we normalize outputs of some black box where paths are mixed, similar to the magic machine discussed above
We just need to restrict the mixing of the paths, which is the restriction of QM anyway. Or maybe I’m missing something? Could you give me an example with such backwards causality? Because as far as I see, everything is quite straightforward.
The main problem of path-dependent identity is that we assume the existence of a “global hidden variable” for any observer. It is hidden as it can’t be measured by an outside viewer and only represents the subjective chances of the observer to be one copy and not another. And it is global as it depends on the observer’s path, not their current state. It therefore contradicts the view that mind is equal to a Turing computer (functionalism) and requires the existence of some identity carrier which moves through paths (qualia, quantum continuity, or soul).
Seems like we are just confused about this “identity” thingy and therefore don’t know how to correctly reason about it. In such situations we are supposed to
Acknowledge that we are are confused
Stop speculating on top of our confusion and jumping to conclusions based on it
Outline the possible options to the best of our understanding and keep an open mind until we manage to resolve the confusion
It’s already clear that “mind” and “identity” are not the same thing. We can talk about identities of things that do not possess a mind, and identities are unique while, there can exist copies of the same mind.So minds can very well be Turing computers, but identities are something else, or even not a thing at all.
Our intuitive desire to drag in consciousness/qualia/soul also appears completely unhelpful after thinking about it for the first five minutes. Non-conscious minds can do the same probability theoretic reasonings as conscious ones. Nothing changes if 1, 21 and 22 from the problem above are not humans but programs executed on different computers.
Whatever extra variable we need it seems to be something that a Laplace’s demon would know. It’s a knowledge about whether a mind was split into n instances simultaneously or through multiple steps. It indeed means that something else except the immediate state of the mind is important for “indentity” considerations, but this something can very well be completely physical—just the past history of causes and effects that led to this state of the mind.
To achieve magic, we need the ability to merge minds, which can be easily done with programs and doesn’t require anything quantum. If we merge 21 and 1, both will be in the same red room after awakening. If awakening in the red room means getting 100 USD, and the green room means losing it, then the machine will be profitable from the subjective point of view of the mind which enters it. Or we can just turn off 21 without awakening, in which case we will get 1⁄3 and 2⁄3 chances for green and red.
The interesting question here is whether this can be replicated at the quantum level (we know there is a way to get quantum magic in MWI, and it is quantum suicide with money prizes, but I am interested in a more subtle probability shift where all variants remain). If yes, such ability may naturally evolve via quantum Darwinism because it would give an enormous fitness advantage – I will write a separate post about this.
Now the next interesting thing: If I look at the experiment from outside, I will give all three variants 1⁄3, but from inside it will be 1⁄4, 1⁄4, and 1⁄2. The probability distribution is exactly the same as in Sleeping Beauty, and likely both experiments are isomorphic. In the SB experiment, there are two different ways of “copying”: first is the coin and second is awakenings with amnesia, which complicates things.
Identity is indeed confusing. Interestingly, in the art world, path-based identity is used to define identity, that is, the provenance of artworks = history of ownership. Blockchain is also an example of path-based identity. Also, in path-based identity, the Ship of Theseus remains the same.
To achieve magic, we need the ability to merge minds, which can be easily done with programs and doesn’t require anything quantum.
I don’t see how merging minds not across branches of the multiverse produces anything magical.
If we merge 21 and 1, both will be in the same red room after awakening.
Which is isomorphic to simply putting 21 to another red room, as I described in the previous comment. The probability shift to 3⁄4 in this case is completely normal and doesn’t lead to anything weird like winning the lottery with confidence.
Or we can just turn off 21 without awakening, in which case we will get 1⁄3 and 2⁄3 chances for green and red.
This actually shouldn’t work. Without QI, we simply have 1⁄2 for red, 1⁄4 for green and 1⁄4 for being turned off.
With QI, the last outcome simply becomes “failed to be turned off”, without changing the probabilities of other outcomes
The interesting question here is whether this can be replicated at the quantum leve
Exactly. Otherwise I don’t see how path based identity produces any magic. For now I think it doesn’t, which is why I expect it to be true.
Now the next interesting thing: If I look at the experiment from outside, I will give all three variants 1⁄3, but from inside it will be 1⁄4, 1⁄4, and 1⁄2.
Which events you are talking about, when looking from the outside? What statements have 1⁄3 credence? It’s definitely not “I will awake in red room”, because it’s not you who are too be awaken. For the observer it has 0 probability.
On the other hand, an event “At least one person is about to be awaken in red room” has probability 1, for both the participant and the observer. So what are you talking about? Try to be rigorous and formally define such events.
The probability distribution is exactly the same as in Sleeping Beauty, and likely both experiments are isomorphic.
Not at all! In Sleeping Beauty on Tails you will be awaken both on Monday and on Tuesday. While here if you are in a green room you are either 21 or 22, not both.
Suppose that 22 get their arm chopped off before awakening. Then you you have 25% chance to lose an arm while participating in such experiment. While in Sleeping Beauty, if your arm is chopped off on Tails before Tuesday awakening, you have 50% probability to lose it, while participating in such experiment.
Interestingly, in the art world, path-based identity is used to define identity
Yep. This is just how we reason about identities in general. That’s why SSSA appears so bizarre to me—it assumes we should be treating personal identity in a different way, for no particular reason.
For the outside view: Imagine that an outside observer uses a fair coin to observe one of two rooms (assuming merging in the red room has happened). They will observe either a red room or a green room, with a copy in each. However, the observer who was copied has different chances of observing the green and red rooms. Even if the outside observer has access to the entire current state of the world (but not the character of mixing of the paths in the past), they can’t determine the copied observer’s subjective chances. This implies that subjective unmeasurable probabilities are real.
Even without merging, an outside observer will observe three rooms with equal 1⁄3 probability for each, while an insider will observe room 1 with 1⁄2 probability. In cases of multiple sequential copying events, the subjective probability for the last copy becomes extremely small, making the difference between outside and inside perspectives significant.
When I spoke about the similarity with the Sleeping Beauty problem, I meant its typical interpretation. It’s an important contribution to recognize that Monday-tails and Tuesday-tails are not independent events.
However, I have an impression that this may result in a paradoxical two-thirder solution: In it, Sleeping Beauty updates only once – recognizing that there are two more chances to be in tails. But she doesn’t update again upon knowing it’s Monday, as Monday-tails and Tuesday-tails are the same event. In that case, despite knowing it’s Monday, she maintains a 2⁄3 credence that she’s in the tails world. This is technically equivalent to the ‘future anthropic shadow’ or anti-doomsday argument – the belief that one is now in the world with the longest possible survival.
Imagine that an outside observer uses a fair coin to observe one of two rooms (assuming merging in the red room has happened). They will observe either a red room or a green room, with a copy in each. However, the observer who was copied has different chances of observing the green and red rooms.
Well obviously. The observer and the person being copied participate in non-isomorphic experiments with different sampling. There is nothing surprising about it. On the other hand, if we make the experiments isomorphic:
Two coins are tossed and the observer is brought into the green room if both are Heads, and is brought to the red room, otherwise
Then both the observer and the person being copied will have the same probabilities.
Even without merging, an outside observer will observe three rooms with equal 1⁄3 probability for each, while an insider will observe room 1 with 1⁄2 probability.
Likewise, nothing is preventing you from designing an experimental setting where an observer have 1⁄2 probability for room 1 just as the person who is being copied.
When I spoke about the similarity with the Sleeping Beauty problem, I meant its typical interpretation.
I’m not sure what use is investigating a wrong interpretation. It’s a common confusion that one has to reason about problems involving amnesia the same way as about problems involving copying. Everyone just seem to assume it for no particular reason and therefore got stuck.
However, I have an impression that this may result in a paradoxical two-thirder solution: In it, Sleeping Beauty updates only once – recognizing that there are two more chances to be in tails. But she doesn’t update again upon knowing it’s Monday, as Monday-tails and Tuesday-tails are the same event. In that case, despite knowing it’s Monday, she maintains a 2⁄3 credence that she’s in the tails world.
This seems to be the worst of both worlds. Not only you update on a completely expected event, you then keep this estimate, expecting to be able to guess a future coin toss better than chance. An obvious way to lose all your money via betting.
Not if we assume QI+path-based identity.
Under them the chance for you to find yourself in a branch where all coins are Heads is 1⁄128, but your over chance to survive is 100%. Therefore the low chance of failed execution doesn’t matter, quantum immortality will “increase” the probability to 1.
None of these tricks works with path-based identity. That’s why I consider it to be true—it seem to be totally adding up to normality. No matter how many clones of you exist in a different path—only yours path matters for your probability estimate.
Seems that, path-based identity is the only approach according to which all hell doesn’t break lose. So what counterargument you have against it?
Why do you consider it a problem? What kind of counterintuitive consequences does it imply? It seems to be exactly how we reason about anything else.
Suppose there is the original ball, then an indistinguishable copy of it is created. Then one of these two balls is picked randomly and put into a bag 1, while the other ball is put into the bag 2 and then indistinguishable 999 copies of this ball is also put into bag 2.
Clearly we are supposed to expect that ball from bag 1 has 50% to be the original ball, while a random ball from bag 2 only 1/2000 chance to be the original ball. So what’s the problem?
By the same logic “Ball shadow” appears because the number of balls is different in different bags.
You are right, and it’s a serious counterargument to consider. Actually, I invented path-dependent identity as a counterargument to Miller’s thought experiment.
You are also right that the Anthropic Trilemma and Magic by Forgetting do not work with path-dependent identity.
However, we can almost recreate the magic machine from the Anthropic Trilemma using path-based identity:
Imagine that I want to guess in which room I will be if there are two copies of me in the future, red or green.
I go into a dream. A machine creates my copy and then one more copy of that copy, which will result in 1⁄4 and 1⁄4 chances each. The second copy then merges with the first one, so we end up with only two copies, but I have a 3⁄4 chance to be the first one and 1⁄4 to be the second. So we’ve basically recreated a machine that can manipulate probabilities and got magic back.
The main problem of path-dependent identity is that we assume the existence of a “global hidden variable” for any observer. It is hidden as it can’t be measured by an outside viewer and only represents the subjective chances of the observer to be one copy and not another. And it is global as it depends on the observer’s path, not their current state. It therefore contradicts the view that mind is equal to a Turing computer (functionalism) and requires the existence of some identity carrier which moves through paths (qualia, quantum continuity, or soul).
Also, path-dependent identity opens the door to back-causation and premonition, because if we normalize outputs of some black box where paths are mixed, similar to the magic machine discussed above, we get a shift in its input probability distribution in the past. This becomes similar to the ‘timeline selection principle’ (which I discussed in a longer version of this blog post but cut to fit format) in which not observer-moments are selected, but the whole timelines without updating on my position in the timeline. This idea formalizes the future anthropic shadow as I am more likely to be in the timeline that is fattest and longest in the future.
Okay, glad we are on the same page here.
I’m not sure I understand your example and how it recreates the magic. Let me try to describe to it with my own words, and then correct me if I got something wrong.
You are put to sleep. Then you are splitted into two people. Then, on random, one of them is put into red room and one into green room. Let’s say that person 1 is in red room and 2 in green room. Then the person 2 is splitted into two people: 21 and 22. Both of them are keept in green rooms. Then everyone is awaken. What should be your credence to awake in a red room?
Here there are three possibilities: 50% to be 1 in a red room and 25% chance to be either 21 or 22 in green rooms. No matter how much a person in a green room is split, the total probability for greenness stays the same. All is quite normal and there is no magic.
Now let’s add a twist.
Instead of putting both 21 and 22 in green rooms, one of them—let it be 21 - is put in a red room.
In this situation, total probability for red room is P(1) + P(21) = 75%. And if we split the 2 more and put more of its parts in red rooms we get highter and highter probability to be in red room. Therefore we get magical ability to manipulate probability.
Am I getting you correctly?
I do not see anything problematic with such “manipulation of probability”. We do not change our estimate just because more people with the same experience are created. We change the estemate because different fraction of people get different experience. This is no more magical than putting both 1 and 2 into red rooms and noticing that suddenly the probability for being in red room reached 100%, compared to the initial formulation where it was mere 50%. Of course it did! That’s completely lawful behaviour of probability theoretic reasoning.
Notice that we can’t actually recreate the anthropic trilemma and be certain to win lottery this way. Because we can’t move people between branches. Therefore everything adds up to normality.
We just need to restrict the mixing of the paths, which is the restriction of QM anyway. Or maybe I’m missing something? Could you give me an example with such backwards causality? Because as far as I see, everything is quite straightforward.
Seems like we are just confused about this “identity” thingy and therefore don’t know how to correctly reason about it. In such situations we are supposed to
Acknowledge that we are are confused
Stop speculating on top of our confusion and jumping to conclusions based on it
Outline the possible options to the best of our understanding and keep an open mind until we manage to resolve the confusion
It’s already clear that “mind” and “identity” are not the same thing. We can talk about identities of things that do not possess a mind, and identities are unique while, there can exist copies of the same mind.So minds can very well be Turing computers, but identities are something else, or even not a thing at all.
Our intuitive desire to drag in consciousness/qualia/soul also appears completely unhelpful after thinking about it for the first five minutes. Non-conscious minds can do the same probability theoretic reasonings as conscious ones. Nothing changes if 1, 21 and 22 from the problem above are not humans but programs executed on different computers.
Whatever extra variable we need it seems to be something that a Laplace’s demon would know. It’s a knowledge about whether a mind was split into n instances simultaneously or through multiple steps. It indeed means that something else except the immediate state of the mind is important for “indentity” considerations, but this something can very well be completely physical—just the past history of causes and effects that led to this state of the mind.
Thanks for your thoughtful answer.
To achieve magic, we need the ability to merge minds, which can be easily done with programs and doesn’t require anything quantum. If we merge 21 and 1, both will be in the same red room after awakening. If awakening in the red room means getting 100 USD, and the green room means losing it, then the machine will be profitable from the subjective point of view of the mind which enters it. Or we can just turn off 21 without awakening, in which case we will get 1⁄3 and 2⁄3 chances for green and red.
The interesting question here is whether this can be replicated at the quantum level (we know there is a way to get quantum magic in MWI, and it is quantum suicide with money prizes, but I am interested in a more subtle probability shift where all variants remain). If yes, such ability may naturally evolve via quantum Darwinism because it would give an enormous fitness advantage – I will write a separate post about this.
Now the next interesting thing: If I look at the experiment from outside, I will give all three variants 1⁄3, but from inside it will be 1⁄4, 1⁄4, and 1⁄2. The probability distribution is exactly the same as in Sleeping Beauty, and likely both experiments are isomorphic. In the SB experiment, there are two different ways of “copying”: first is the coin and second is awakenings with amnesia, which complicates things.
Identity is indeed confusing. Interestingly, in the art world, path-based identity is used to define identity, that is, the provenance of artworks = history of ownership. Blockchain is also an example of path-based identity. Also, in path-based identity, the Ship of Theseus remains the same.
I don’t see how merging minds not across branches of the multiverse produces anything magical.
Which is isomorphic to simply putting 21 to another red room, as I described in the previous comment. The probability shift to 3⁄4 in this case is completely normal and doesn’t lead to anything weird like winning the lottery with confidence.
This actually shouldn’t work. Without QI, we simply have 1⁄2 for red, 1⁄4 for green and 1⁄4 for being turned off.
With QI, the last outcome simply becomes “failed to be turned off”, without changing the probabilities of other outcomes
Exactly. Otherwise I don’t see how path based identity produces any magic. For now I think it doesn’t, which is why I expect it to be true.
Which events you are talking about, when looking from the outside? What statements have 1⁄3 credence? It’s definitely not “I will awake in red room”, because it’s not you who are too be awaken. For the observer it has 0 probability.
On the other hand, an event “At least one person is about to be awaken in red room” has probability 1, for both the participant and the observer. So what are you talking about? Try to be rigorous and formally define such events.
Not at all! In Sleeping Beauty on Tails you will be awaken both on Monday and on Tuesday. While here if you are in a green room you are either 21 or 22, not both.
Suppose that 22 get their arm chopped off before awakening. Then you you have 25% chance to lose an arm while participating in such experiment. While in Sleeping Beauty, if your arm is chopped off on Tails before Tuesday awakening, you have 50% probability to lose it, while participating in such experiment.
Yep. This is just how we reason about identities in general. That’s why SSSA appears so bizarre to me—it assumes we should be treating personal identity in a different way, for no particular reason.
For the outside view: Imagine that an outside observer uses a fair coin to observe one of two rooms (assuming merging in the red room has happened). They will observe either a red room or a green room, with a copy in each. However, the observer who was copied has different chances of observing the green and red rooms. Even if the outside observer has access to the entire current state of the world (but not the character of mixing of the paths in the past), they can’t determine the copied observer’s subjective chances. This implies that subjective unmeasurable probabilities are real.
Even without merging, an outside observer will observe three rooms with equal 1⁄3 probability for each, while an insider will observe room 1 with 1⁄2 probability. In cases of multiple sequential copying events, the subjective probability for the last copy becomes extremely small, making the difference between outside and inside perspectives significant.
When I spoke about the similarity with the Sleeping Beauty problem, I meant its typical interpretation. It’s an important contribution to recognize that Monday-tails and Tuesday-tails are not independent events.
However, I have an impression that this may result in a paradoxical two-thirder solution: In it, Sleeping Beauty updates only once – recognizing that there are two more chances to be in tails. But she doesn’t update again upon knowing it’s Monday, as Monday-tails and Tuesday-tails are the same event. In that case, despite knowing it’s Monday, she maintains a 2⁄3 credence that she’s in the tails world. This is technically equivalent to the ‘future anthropic shadow’ or anti-doomsday argument – the belief that one is now in the world with the longest possible survival.
Well obviously. The observer and the person being copied participate in non-isomorphic experiments with different sampling. There is nothing surprising about it. On the other hand, if we make the experiments isomorphic:
Two coins are tossed and the observer is brought into the green room if both are Heads, and is brought to the red room, otherwise
Then both the observer and the person being copied will have the same probabilities.
Likewise, nothing is preventing you from designing an experimental setting where an observer have 1⁄2 probability for room 1 just as the person who is being copied.
I’m not sure what use is investigating a wrong interpretation. It’s a common confusion that one has to reason about problems involving amnesia the same way as about problems involving copying. Everyone just seem to assume it for no particular reason and therefore got stuck.
This seems to be the worst of both worlds. Not only you update on a completely expected event, you then keep this estimate, expecting to be able to guess a future coin toss better than chance. An obvious way to lose all your money via betting.