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.
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.