To make it slightly more concrete, we could say: one copy is put in a red room, and the other in a green room; but at first the lights are off, so both rooms are pitch black. I wake up in the darkness and ask myself: when I turn on the light, will I see red or green?
There’s something odd about this question. “Standard LessWrong Reductionism” must regard it as meaningless, because otherwise it would be a question about the scenario that remains unanswered even after all physical facts about it are known, thus refuting reductionism. But from the perspective of the test subject, it certainly seems like a real question.
Can we bite this bullet? I think so. The key is the word “I”—when the question is asked, the asker doesn’t know which physical entity “I” refers to, so it’s unsurprising that the question seems open even though all the physical facts are known. By analogy, if you were given detailed physical data of the two moons of Mars, and then you were asked “Which one is Phobos and which one is Deimos?”, you might not know the answer, but not because there’s some mysterious extra-physical fact about them.
So far so good, but now we face an even tougher bullet: If we accept quantum many-worlds and/or modal realism (as many LWers do), then we must accept that all probability questions are of this same kind, because there are versions of me elsewhere in the multiverse that experience all possible outcomes.
Unless we want to throw out the notion of probabilities altogether, we’ll need some way of understanding self-location problems besides dismissing them as meaningless. But I think the key is in recognizing that probability is ultimately in the map, not the territory, however real it may seem to us—i.e. it is a tool for a rational agent to achieve its goals, and nothing more.
First of all, strong upvote. The points you raised have made me thought hard as well.
I don’t think the probability about which room I am in is the same as the self-locating probability. Coincidentally I made my argument use color coding as well ( the probability of I am red or blue). The difference being which color I get labeled is determined by a particular process, the uncertainty is due to the randomness of that process or my lack of knowledge about it. Whereas for self-locating probability, there is nothing random/unknown about the experiment. The uncertainty, i.e. which physical person I am, is not determined by anything. If I ask myself why am I this particular human being? Why am I not Bill Gates? Then the only answer seems to be “Because the available subjective is connected to this person. Because I am experiencing the world from this person’s perspective, not of Bill Gates’.” It is not analyzable in terms of logic, only be regarded as a reasoning starting point. Something primitive.
Whether or not the questioner knows which person is being referred to by “I” is another interesting matter. Say the universe is infinite, and/or there are countless universes. So there could be many instances of human beings that are physically indistinguishable from me. But does that mean I don’t know which one I am? It can be said that I do not know because I cannot provide any discernable details to distinguish myself from all of them. But on the other hand, it can be said I inherently know which is me. I can point to myself and say “I am this person” and call it a day. The physical similarities and differences are not even in the concern. This identification is nothing physical, it is inherently understandable to me because of my perspective. It is because of this primitive nature people consider “the probability of I am the Orginal” as a valid question instead of asking who is this “I” before answering.
My way of rejecting the self-locating probability is incompatible with the Many-Words interpretation. Sean Carroll calls this idea the “simple-mined” objection for the source of probability in Many-Worlds. Yet he admits that’s a valid objection. I think treating perspectives as primitives would naturally lead to Copenhagen interpretation. It should also be noted that for Many-Worlds, “I” or “this branch” are still used as primitive notions when self-locating probabilities are derived.
Finally, the self-locating probability is not useful to decision-making. So even as tools, they are not justifiable. Goals such as maximizing the total or average benefit of a group can be determined by using probabilities of random samples from said group. e.g. probability of a randomly selected copy being Original. If the goal is strictly about the primitively identified “I” as in self-locating probability then there exists no valid strategy. As shown by the frequentist analysis in the post.
To make it slightly more concrete, we could say: one copy is put in a red room, and the other in a green room; but at first the lights are off, so both rooms are pitch black. I wake up in the darkness and ask myself: when I turn on the light, will I see red or green?
There’s something odd about this question. “Standard LessWrong Reductionism” must regard it as meaningless, because otherwise it would be a question about the scenario that remains unanswered even after all physical facts about it are known, thus refuting reductionism. But from the perspective of the test subject, it certainly seems like a real question.
Can we bite this bullet? I think so. The key is the word “I”—when the question is asked, the asker doesn’t know which physical entity “I” refers to, so it’s unsurprising that the question seems open even though all the physical facts are known. By analogy, if you were given detailed physical data of the two moons of Mars, and then you were asked “Which one is Phobos and which one is Deimos?”, you might not know the answer, but not because there’s some mysterious extra-physical fact about them.
So far so good, but now we face an even tougher bullet: If we accept quantum many-worlds and/or modal realism (as many LWers do), then we must accept that all probability questions are of this same kind, because there are versions of me elsewhere in the multiverse that experience all possible outcomes.
Unless we want to throw out the notion of probabilities altogether, we’ll need some way of understanding self-location problems besides dismissing them as meaningless. But I think the key is in recognizing that probability is ultimately in the map, not the territory, however real it may seem to us—i.e. it is a tool for a rational agent to achieve its goals, and nothing more.
First of all, strong upvote. The points you raised have made me thought hard as well.
I don’t think the probability about which room I am in is the same as the self-locating probability. Coincidentally I made my argument use color coding as well ( the probability of I am red or blue). The difference being which color I get labeled is determined by a particular process, the uncertainty is due to the randomness of that process or my lack of knowledge about it. Whereas for self-locating probability, there is nothing random/unknown about the experiment. The uncertainty, i.e. which physical person I am, is not determined by anything. If I ask myself why am I this particular human being? Why am I not Bill Gates? Then the only answer seems to be “Because the available subjective is connected to this person. Because I am experiencing the world from this person’s perspective, not of Bill Gates’.” It is not analyzable in terms of logic, only be regarded as a reasoning starting point. Something primitive.
Whether or not the questioner knows which person is being referred to by “I” is another interesting matter. Say the universe is infinite, and/or there are countless universes. So there could be many instances of human beings that are physically indistinguishable from me. But does that mean I don’t know which one I am? It can be said that I do not know because I cannot provide any discernable details to distinguish myself from all of them. But on the other hand, it can be said I inherently know which is me. I can point to myself and say “I am this person” and call it a day. The physical similarities and differences are not even in the concern. This identification is nothing physical, it is inherently understandable to me because of my perspective. It is because of this primitive nature people consider “the probability of I am the Orginal” as a valid question instead of asking who is this “I” before answering.
My way of rejecting the self-locating probability is incompatible with the Many-Words interpretation. Sean Carroll calls this idea the “simple-mined” objection for the source of probability in Many-Worlds. Yet he admits that’s a valid objection. I think treating perspectives as primitives would naturally lead to Copenhagen interpretation. It should also be noted that for Many-Worlds, “I” or “this branch” are still used as primitive notions when self-locating probabilities are derived.
Finally, the self-locating probability is not useful to decision-making. So even as tools, they are not justifiable. Goals such as maximizing the total or average benefit of a group can be determined by using probabilities of random samples from said group. e.g. probability of a randomly selected copy being Original. If the goal is strictly about the primitively identified “I” as in self-locating probability then there exists no valid strategy. As shown by the frequentist analysis in the post.
Yes, rejecting probability and refusing to make predictions about the future is just wrong here, no matter how many fancy primitives you put together.
I disagree that standard LW rejects that, though.