We can assign meanings to statements like “my sensor sees red” by picking out subsets of experiences, just as before.
How do you assign meaning to statements like “my sensor will see red”? (In the OP you mention “my sensors will see the heads side of the coin” but I’m not sure what your proposed semantics of such statements are in general.)
Also, here’s an old puzzle of mine that I wonder if your line of thinking can help with: At time 1 you will be copied and the original will be shown “O” and the copy will be shown “C”, then at time 2 the copy will be copied again, and the three of you will be shown “OO” (original), “CO” (original of copy), “CC” (copy of copy) respectively. At time 0, what are your probabilities for “I will see X” for each of the five possible values of X?
That’s a very good question! It’s definitely more complicated once you start including other observers (including future selves), and I don’t feel that I understand this as well.
But I think it works like this: other reasoners are modeled (0P) as using this same framework. The 0P model can then make predictions about the 1P judgements of these other reasoners. For something like anticipation, I think it will have to use memories of experiences (which are also experiences) and identify observers for which this memory corresponds to the current experience. Understanding this better would require being more precise about the interplay between 0P and 1P, I think.
(I’ll examine your puzzle when I have some time to think about it properly)
Defining the semantics and probabilities of anticipation seems to be a hard problem. You can see some past discussions of the difficulties at The Anthropic Trilemma and its back-references (posts that link to it). (I didn’t link to this earlier in case you already found a fresh approach that solved the problem. You may also want to consider not reading the previous discussions to avoid possibly falling into the same ruts.)
I have a solution that is completely underwhelming, but I can see no flaws in it, besides the complete lack of definition of which part of the mental state should be preserved to still count as you and rejection of MWI (as well as I cannot see useful insights into why we have what looks like continuous subjective experience).
You can’t consistently assign probabilities for future observations in scenarios where you expect creation of multiple instances of your mental state. All instances exist and there’s no counterfactual worlds where you end up as a mental state in a different location/time (as opposed to the one you happened to actually observe). You are here because your observations tells you that you are here, not because something intangible had moved from previous “you”(1) to the current “you” located here.
Born rule works because MWI is wrong. The collapse is objective and there’s no alternative yous.
(1) I use “you” in scare quotes to designate something beyond all information available in the mental state that presumably is unique and moves continuously (or jumps) thru time.
Let’s iterate through questions of The Anthropic Trilemma.
The Boltzmann Brain problem: no probabilities, no updates. Observing either room doesn’t tell you anything about the value of the digit of pi. It tells you that you observe the room you observe.
Winning the lottery: there’s no alternative quantum branches, so your machinations don’t change anything.
Personal future: Britney Spears observes that she has memories of Britney Spears, you observe that you have your memories. There’s no alternative scenarios if you are defined just by the information in your mental state. If you jump off the cliff, you can expect that someone with a memory of deciding to jump off the cliff (as well as all other your memories) will hit the ground and there will be no continuation of this mental state in this time and place. And your memory tells you that it will be you who will experience consequences of your decisions (whatever the underlying causes for that).
Probabilistic calculations of your future experiences work as expected, if you add “conditional on me experiencing staying here and now”.
It’s not unlike operator “do(X=x)” in Graphical Models that cuts off all other causal influences on X.
Exhibit A: flip a fair coin and move a suspended robot into a green or red room using a second coin with probabilities (99%, 1%) for heads, and (1%, 99%) for tails.
Exhibit B: flip a fair coin and create 99 copies of the robot in green rooms and 1 copy in a red room for heads, and reverse colors otherwise.
What causes the robot to see red instead of green in exhibit A? Physical processes that brought about a world where the robot sees red.
What causes a robot to see red instead of green in exhibit B? The fact that it sees red, nothing more. The physical instance of the robot who sees red in one possible world, could be the instance who sees green in another possible world, of course (physical causality surely is intact). But a robot-who-sees-red (that is one of the instances who see red) cannot be made into a robot-who-sees-green by physical manipulations. That is subjective causality of seeing red is cut off from physical causes (in the case of multiple copies of an observer). And as such cannot be used as a basis for probabilistic judgements.
I guess that if I’ll not see a resolution of the Anthropic Trilemma in the framework of MWI in about 10 years, I’ll be almost sure that MWI is wrong.
[Without having looked at the link in your response to my other comment, and I also stopped reading cubefox’s comment once it seemed that it was going in a similar direction. ETA: I realized after posting that I have seen that article before, but not recently.]
I’ll assume that the robot has a special “memory” sensor which stores the exact experience at the time of the previous tick. It will recognize future versions of itself by looking for agents in its (timeless) 0P model which has a memory of its current experience.
For p(“I will see O”), the robot will look in its 0P model for observers which have the t=0 experience in their immediate memory, and selecting from those, how many have judged “I see O” as Here. There will be two such robots, the original and the copy at time 1, and only one of those sees O. So using a uniform prior (not forced by this framework), it would give a 0P probability of 1⁄2. Similarly for p(“I will see C”).
Then it would repeat the same process for t=1 and the copy. Conditioned on “I will see C” at t=1, it will conclude “I will see CO” with probability 1⁄2 by the same reasoning as above. So overall, it will assign:
p(“I will see OO”) = 1⁄2,
p(“I will see CO”) = 1⁄4,
p(“I will see CC”) = 1⁄4
The semantics for these kinds of things is a bit confusing. I think that it starts from an experience (the experience at t=0) which I’ll call E. Then REALIZATION(E) casts E into a 0P sentence which gets taken as an axiom in the robot’s 0P theory.
A different robot could carry out the same reasoning, and reach the same conclusion since this is happening on the 0P side. But the semantics are not quite the same, since the REALIZATION(E) axiom is arbitrary to a different robot, and thus the reasoning doesn’t mean “I will see X” but instead means something more like “They will see X”. This suggests that there’s a more complex semantics that allows worlds and experiences to be combined—I need to think more about this to be sure what’s going on. Thus far, I still feel confident that the 0P/1P distinction is more fundamental than whatever the more complex semantics is.
(I call the 0P → 1P conversion SENSATIONS, and the 1P → 0P conversion REALIZATION, and think of them as being adjoints though I haven’t formalized this part well enough to feel confident that this is a good way to describe it: there’s a toy example here if you are interested in seeing how this might work.)
Then it would repeat the same process for t=1 and the copy. Conditioned on “I will see C” at t=1, it will conclude “I will see CO” with probability 1⁄2 by the same reasoning as above. So overall, it will assign:p(“I will see OO”) = 1⁄2,p(“I will see CO”) = 1⁄4,p(“I will see CC”) = 1⁄4
If we look at the situation in 0P, the three versions of you at time 2 all seem equally real and equally you, yet in 1P you weigh the experiences of the future original twice as much as each of the copies.
Suppose we change the setup slightly so that copying of the copy is done at time 1 instead of time 2. And at time 1 we show O to the original and C to the two copies, then at time 2 we show them OO, CO, CC like before. With this modified setup, your logic would conclude P(“I will see O”)=P(“I will see OO”)=P(“I will see CO”)=P(“I will see CC”)=1/3 and P(“I will see C”)=2/3. Right?
Similarly, if we change the setup from the original so that no observation is made at time 1, the probabilities also become P(“I will see OO”)=P(“I will see CO”)=P(“I will see CC”)=1/3.
Suppose we change the setup from the original so that at time 1, we make 999 copies of you instead of just 1 and show them all C before deleting all but 1 of the copies. Then your logic would imply P(“I will see C”)=.999 and therefore P(“I will see CO”)=P(“I will see CC”)=0.4995, and P(“I will see O”)=P(“I will see OO”)=.001.
This all make me think there’s something wrong with the 1⁄2,1/4,1/4 answer and with the way you define probabilities of future experiences. More specifically, suppose OO wasn’t just two letters but an unpleasant experience, and CO and CC are both pleasant experiences, so you prefer “I will experience CO/CC” to “I will experience OO”. Then at time 0 you would be willing to pay to switch from the original setup to (2) or (3), and pay even more to switch to (4). But that seems pretty counterintuitive, i.e., why are you paying to avoid making observations in (3), or paying to make and delete copies of yourself in (4). Both of these seem at best pointless in 0P.
But every other approach I’ve seen or thought of also has problems, so maybe we shouldn’t dismiss this one too easily based on these issues. I would be interested to see you work out everything more formally and address the above objections (to the extent possible).
Is the puzzle supposed to be agnostic to the specifics of copying?
It seems to me that if by copying we mean fissure, when a person is separated into two, we have 1⁄2 for OO, 1⁄4 for CO and 1⁄4 for CC, while if by copying we mean “a clone of you is created” then the probability to observe OO a time 0 is 1, because there is no causal mechanism due to which you would swap bodies with a clone.
How do you assign meaning to statements like “my sensor will see red”? (In the OP you mention “my sensors will see the heads side of the coin” but I’m not sure what your proposed semantics of such statements are in general.)
Also, here’s an old puzzle of mine that I wonder if your line of thinking can help with: At time 1 you will be copied and the original will be shown “O” and the copy will be shown “C”, then at time 2 the copy will be copied again, and the three of you will be shown “OO” (original), “CO” (original of copy), “CC” (copy of copy) respectively. At time 0, what are your probabilities for “I will see X” for each of the five possible values of X?
That’s a very good question! It’s definitely more complicated once you start including other observers (including future selves), and I don’t feel that I understand this as well.
But I think it works like this: other reasoners are modeled (0P) as using this same framework. The 0P model can then make predictions about the 1P judgements of these other reasoners. For something like anticipation, I think it will have to use memories of experiences (which are also experiences) and identify observers for which this memory corresponds to the current experience. Understanding this better would require being more precise about the interplay between 0P and 1P, I think.
(I’ll examine your puzzle when I have some time to think about it properly)
Defining the semantics and probabilities of anticipation seems to be a hard problem. You can see some past discussions of the difficulties at The Anthropic Trilemma and its back-references (posts that link to it). (I didn’t link to this earlier in case you already found a fresh approach that solved the problem. You may also want to consider not reading the previous discussions to avoid possibly falling into the same ruts.)
I have a solution that is completely underwhelming, but I can see no flaws in it, besides the complete lack of definition of which part of the mental state should be preserved to still count as you and rejection of MWI (as well as I cannot see useful insights into why we have what looks like continuous subjective experience).
You can’t consistently assign probabilities for future observations in scenarios where you expect creation of multiple instances of your mental state. All instances exist and there’s no counterfactual worlds where you end up as a mental state in a different location/time (as opposed to the one you happened to actually observe). You are here because your observations tells you that you are here, not because something intangible had moved from previous “you”(1) to the current “you” located here.
Born rule works because MWI is wrong. The collapse is objective and there’s no alternative yous.
(1) I use “you” in scare quotes to designate something beyond all information available in the mental state that presumably is unique and moves continuously (or jumps) thru time.
Let’s iterate through questions of The Anthropic Trilemma.
The Boltzmann Brain problem: no probabilities, no updates. Observing either room doesn’t tell you anything about the value of the digit of pi. It tells you that you observe the room you observe.
Winning the lottery: there’s no alternative quantum branches, so your machinations don’t change anything.
Personal future: Britney Spears observes that she has memories of Britney Spears, you observe that you have your memories. There’s no alternative scenarios if you are defined just by the information in your mental state. If you jump off the cliff, you can expect that someone with a memory of deciding to jump off the cliff (as well as all other your memories) will hit the ground and there will be no continuation of this mental state in this time and place. And your memory tells you that it will be you who will experience consequences of your decisions (whatever the underlying causes for that).
Probabilistic calculations of your future experiences work as expected, if you add “conditional on me experiencing staying here and now”.
It’s not unlike operator “do(X=x)” in Graphical Models that cuts off all other causal influences on X.
Expanding a bit on the topic.
Exhibit A: flip a fair coin and move a suspended robot into a green or red room using a second coin with probabilities (99%, 1%) for heads, and (1%, 99%) for tails.
Exhibit B: flip a fair coin and create 99 copies of the robot in green rooms and 1 copy in a red room for heads, and reverse colors otherwise.
What causes the robot to see red instead of green in exhibit A? Physical processes that brought about a world where the robot sees red.
What causes a robot to see red instead of green in exhibit B? The fact that it sees red, nothing more. The physical instance of the robot who sees red in one possible world, could be the instance who sees green in another possible world, of course (physical causality surely is intact). But a robot-who-sees-red (that is one of the instances who see red) cannot be made into a robot-who-sees-green by physical manipulations. That is subjective causality of seeing red is cut off from physical causes (in the case of multiple copies of an observer). And as such cannot be used as a basis for probabilistic judgements.
I guess that if I’ll not see a resolution of the Anthropic Trilemma in the framework of MWI in about 10 years, I’ll be almost sure that MWI is wrong.
[Without having looked at the link in your response to my other comment, and I also stopped reading cubefox’s comment once it seemed that it was going in a similar direction. ETA: I realized after posting that I have seen that article before, but not recently.]
I’ll assume that the robot has a special “memory” sensor which stores the exact experience at the time of the previous tick. It will recognize future versions of itself by looking for agents in its (timeless) 0P model which has a memory of its current experience.
For p(“I will see O”), the robot will look in its 0P model for observers which have the t=0 experience in their immediate memory, and selecting from those, how many have judged “I see O” as Here. There will be two such robots, the original and the copy at time 1, and only one of those sees O. So using a uniform prior (not forced by this framework), it would give a 0P probability of 1⁄2. Similarly for p(“I will see C”).
Then it would repeat the same process for t=1 and the copy. Conditioned on “I will see C” at t=1, it will conclude “I will see CO” with probability 1⁄2 by the same reasoning as above. So overall, it will assign: p(“I will see OO”) = 1⁄2, p(“I will see CO”) = 1⁄4, p(“I will see CC”) = 1⁄4
The semantics for these kinds of things is a bit confusing. I think that it starts from an experience (the experience at t=0) which I’ll call E. Then REALIZATION(E) casts E into a 0P sentence which gets taken as an axiom in the robot’s 0P theory.
A different robot could carry out the same reasoning, and reach the same conclusion since this is happening on the 0P side. But the semantics are not quite the same, since the REALIZATION(E) axiom is arbitrary to a different robot, and thus the reasoning doesn’t mean “I will see X” but instead means something more like “They will see X”. This suggests that there’s a more complex semantics that allows worlds and experiences to be combined—I need to think more about this to be sure what’s going on. Thus far, I still feel confident that the 0P/1P distinction is more fundamental than whatever the more complex semantics is.
(I call the 0P → 1P conversion SENSATIONS, and the 1P → 0P conversion REALIZATION, and think of them as being adjoints though I haven’t formalized this part well enough to feel confident that this is a good way to describe it: there’s a toy example here if you are interested in seeing how this might work.)
If we look at the situation in 0P, the three versions of you at time 2 all seem equally real and equally you, yet in 1P you weigh the experiences of the future original twice as much as each of the copies.
Suppose we change the setup slightly so that copying of the copy is done at time 1 instead of time 2. And at time 1 we show O to the original and C to the two copies, then at time 2 we show them OO, CO, CC like before. With this modified setup, your logic would conclude P(“I will see O”)=P(“I will see OO”)=P(“I will see CO”)=P(“I will see CC”)=1/3 and P(“I will see C”)=2/3. Right?
Similarly, if we change the setup from the original so that no observation is made at time 1, the probabilities also become P(“I will see OO”)=P(“I will see CO”)=P(“I will see CC”)=1/3.
Suppose we change the setup from the original so that at time 1, we make 999 copies of you instead of just 1 and show them all C before deleting all but 1 of the copies. Then your logic would imply P(“I will see C”)=.999 and therefore P(“I will see CO”)=P(“I will see CC”)=0.4995, and P(“I will see O”)=P(“I will see OO”)=.001.
This all make me think there’s something wrong with the 1⁄2,1/4,1/4 answer and with the way you define probabilities of future experiences. More specifically, suppose OO wasn’t just two letters but an unpleasant experience, and CO and CC are both pleasant experiences, so you prefer “I will experience CO/CC” to “I will experience OO”. Then at time 0 you would be willing to pay to switch from the original setup to (2) or (3), and pay even more to switch to (4). But that seems pretty counterintuitive, i.e., why are you paying to avoid making observations in (3), or paying to make and delete copies of yourself in (4). Both of these seem at best pointless in 0P.
But every other approach I’ve seen or thought of also has problems, so maybe we shouldn’t dismiss this one too easily based on these issues. I would be interested to see you work out everything more formally and address the above objections (to the extent possible).
Is the puzzle supposed to be agnostic to the specifics of copying?
It seems to me that if by copying we mean fissure, when a person is separated into two, we have 1⁄2 for OO, 1⁄4 for CO and 1⁄4 for CC, while if by copying we mean “a clone of you is created” then the probability to observe OO a time 0 is 1, because there is no causal mechanism due to which you would swap bodies with a clone.