TLDR: Because of quantum immortality, my consciousness will continuously pass through all possible minds, but first through the most similar, connected, nearest, and future ones. This is enabled by the extremely small chance that a mind can transform into any other mind. The theory solves the copy problem, as it can predict which of several fundamentally different copies I will become first.
Assuming that a mind can journey eternally through the functional space of all possible minds, we can create a numerical (though practically incomputable for now) measure of the distance between all possible minds. Such a measure can help us answer questions like: will my copy in another universe be me?
In short, any copy will be me, but after different periods of time, sometimes hyper-astronomically long. While exact computation of that time is difficult, the distances can be compared reliably and can predict which of the different types of copies I will be first. Solving the copy problem is practically needed to choose between different methods of life extension (more in "Immortality and Identity" ).
The idea that a mind can travel infinitely in the space of all possible minds follows from the idea of so-called quantum immortality (and also requires that the space of all possible minds be either finite – because of the finite Hubble volume – or have some metric that makes smaller minds more likely). Yampolsky wrote about space of minds. Even if not quantum immortality, a purely Nietzschean–Boltzmann eternal return may suffice.
In other words, the eternal travel of a mind through the functional space of minds assumes that real absolute death is impossible – there are no dead ends in the journey.
In the next two sections, I will discuss how the inherently local idea of quantum immortality transforms into a global property of "transitivity" of the space of all possible minds. There are two main competing theories of personal identity, both of which provide the needed result. One assumes that only the sameness of a mind's states is needed for identity, and the other requires continuity of consciousness for identity.
I – No Continuity Case
If continuity of consciousness is not needed for the preservation of identity, then the sameness of consciousness content is enough to ensure identity.
A simple practical example here would be a situation in which I become someone else in a dream. For any such dream, there is a real person somewhere in the space of minds, and such a person can have dreams about himself. So our dream content coincides, and I have a small chance of waking up as that other person (an idea of J. Miller). I discussed how it can happen in detail in "magic by forgetting". In that case, minds virtually merge often, and again the pointer of the now-moment passes through all possible minds in functional mind space.
II – Continuity Case
Let us assume that continuity of consciousness is needed for personal survival (if not, there is another approach explained below).
In MWI, for any mind there is a very small chance of becoming any other mind in the next moment of time. With extremely small probability, atoms can rearrange and I will become Britney Spears: at any moment a space particle can strike my brain and change the state of a single neuron. We can imagine a series of such strikes that completely rewrite my memories, etc. There can be simpler ways, like two brains merging during a car accident. An even simpler variant is if I regress to some simple blank state and after that "reincarnate" into another person.
While such probability is extremely small, it creates constant leakage of identity between minds. While we can safely ignore such a chance for any next-moment expectations, we cannot ignore it for the whole universe of mind spaces, especially where any mind has a chance of indefinite survival because of quantum immortality. This breaks borders between individual minds, and there are mind trajectories that tunnel between the minds.
The whole story is better described not as a story of real-world objects but as a pointer state of "now" circling through the functional space of possible minds. The idea here is that the pointer state will continuously pass through all possible mind states (similar to the Poincaré recurrence theorem).
III – Transformations becomes inevitable on long scale
One may ask how the now-moment can pass through minds that lived in the past, but here the idea of eternal return can help – the idea that our universe will eventually evolve into its own copy.
The transformation in other mind discussed here is low-probability and unobservable event. (Someone can try to build a theory that large enough shards of my self-determining information, which forget my age but not my main properties, can work as a soul and produce observations like more typical reincarnation.) If I believe in QI, I should expect that the bomb will not explode, not that I will become a toddler with vague memories about an explosion.
But taken over very long periods of time, small branches into transformation become dominant. I am more likely to transform into other mind than to survive for one million years defying aging by pure chance. Not sure? Think about a trillion.
If we take this to the limit, it just means that I will pass through all possible minds, but through more similar minds to me first of all. This may seem irrelevant – I will forget everything millions of times, and why care about events in trillions of years from now? But we can exclude all forgotten periods of time from consideration, so they will be instant jumps if counting starts from the moment where it was interrupted.
IV – Application to counting copies
The first consequence of minds’ eternal journey is that all my copies will be me. We should not worry about preserving soul, continuity or any other identity token.
The second consequence is more subtle and claims that different copies will be achieved in the different moments of time. For example, me-tomorrow and me-day-after-tomorrow can be both regarded as my copies (assuming almost no changes had happened), but we know that me-tomorrow will be achieved first. It also means that me-day-after-tomorrow will be achieved only after I would be me-tomorrow, so I today can expect that I will wake up tomorrow and not in day after tomorrow. So, while both copies will be me, I will first "visit" me-tomorrow. However, if I will sleep all day tomorrow, my next copy will be me-day-after-tomorrow
The theory of predicts that if there are two imperfect copies of me, I will first become the one through which eternal journey would pass first.
It gives an instrument to solve different paradoxes related to copies. For example, in the Mars transporter, I will become my copy on Mars, and in the Broken Mars transporter in which both copy and original exist, I will remain the original (no 50-50 solution). Here is assumed that I will become Mars copy after trillions of trillions of years of the journey through all possible minds (and that there will be no closer copies.)
More generally speaking, if there is two my copies in the future – one is my next observer moment, and another is just appeared somewhere via some stochastic process – which one I will be in the next moment? To answer this question, we look at the whole functional space of minds and count the ordering of the moments then the pointer of now-moment is passing through minds which are informationally me. If two such copies exist, I will be both of them eventually, but first of them I will be the one which is located in the next moment of time. In that case I can ignore remote copy. However, if I die in the next moment of time, only remote copy will exist, and now my now-moment passing through it will be first my reappearance. In that case, this remote copy matters.
V – Does it make any sense?
One can argue that I count here completely unmeasurable things and thus this doesn’t matter. I want to point for three practical applications:
1. Excluding Boltzmann Brains as my next observer moments which refines our cosmological models.
2. Predicting the type of survival in quantum immortality.
TLDR: Because of quantum immortality, my consciousness will continuously pass through all possible minds, but first through the most similar, connected, nearest, and future ones. This is enabled by the extremely small chance that a mind can transform into any other mind. The theory solves the copy problem, as it can predict which of several fundamentally different copies I will become first.
Assuming that a mind can journey eternally through the functional space of all possible minds, we can create a numerical (though practically incomputable for now) measure of the distance between all possible minds. Such a measure can help us answer questions like: will my copy in another universe be me?
In short, any copy will be me, but after different periods of time, sometimes hyper-astronomically long. While exact computation of that time is difficult, the distances can be compared reliably and can predict which of the different types of copies I will be first. Solving the copy problem is practically needed to choose between different methods of life extension (more in "Immortality and Identity" ).
The idea that a mind can travel infinitely in the space of all possible minds follows from the idea of so-called quantum immortality (and also requires that the space of all possible minds be either finite – because of the finite Hubble volume – or have some metric that makes smaller minds more likely). Yampolsky wrote about space of minds. Even if not quantum immortality, a purely Nietzschean–Boltzmann eternal return may suffice.
In other words, the eternal travel of a mind through the functional space of minds assumes that real absolute death is impossible – there are no dead ends in the journey.
In the next two sections, I will discuss how the inherently local idea of quantum immortality transforms into a global property of "transitivity" of the space of all possible minds. There are two main competing theories of personal identity, both of which provide the needed result. One assumes that only the sameness of a mind's states is needed for identity, and the other requires continuity of consciousness for identity.
I – No Continuity Case
If continuity of consciousness is not needed for the preservation of identity, then the sameness of consciousness content is enough to ensure identity.
A simple practical example here would be a situation in which I become someone else in a dream. For any such dream, there is a real person somewhere in the space of minds, and such a person can have dreams about himself. So our dream content coincides, and I have a small chance of waking up as that other person (an idea of J. Miller). I discussed how it can happen in detail in "magic by forgetting". In that case, minds virtually merge often, and again the pointer of the now-moment passes through all possible minds in functional mind space.
II – Continuity Case
Let us assume that continuity of consciousness is needed for personal survival (if not, there is another approach explained below).
In MWI, for any mind there is a very small chance of becoming any other mind in the next moment of time. With extremely small probability, atoms can rearrange and I will become Britney Spears: at any moment a space particle can strike my brain and change the state of a single neuron. We can imagine a series of such strikes that completely rewrite my memories, etc. There can be simpler ways, like two brains merging during a car accident. An even simpler variant is if I regress to some simple blank state and after that "reincarnate" into another person.
While such probability is extremely small, it creates constant leakage of identity between minds. While we can safely ignore such a chance for any next-moment expectations, we cannot ignore it for the whole universe of mind spaces, especially where any mind has a chance of indefinite survival because of quantum immortality. This breaks borders between individual minds, and there are mind trajectories that tunnel between the minds.
The whole story is better described not as a story of real-world objects but as a pointer state of "now" circling through the functional space of possible minds. The idea here is that the pointer state will continuously pass through all possible mind states (similar to the Poincaré recurrence theorem).
III – Transformations becomes inevitable on long scale
One may ask how the now-moment can pass through minds that lived in the past, but here the idea of eternal return can help – the idea that our universe will eventually evolve into its own copy.
The transformation in other mind discussed here is low-probability and unobservable event. (Someone can try to build a theory that large enough shards of my self-determining information, which forget my age but not my main properties, can work as a soul and produce observations like more typical reincarnation.) If I believe in QI, I should expect that the bomb will not explode, not that I will become a toddler with vague memories about an explosion.
But taken over very long periods of time, small branches into transformation become dominant. I am more likely to transform into other mind than to survive for one million years defying aging by pure chance. Not sure? Think about a trillion.
If we take this to the limit, it just means that I will pass through all possible minds, but through more similar minds to me first of all. This may seem irrelevant – I will forget everything millions of times, and why care about events in trillions of years from now? But we can exclude all forgotten periods of time from consideration, so they will be instant jumps if counting starts from the moment where it was interrupted.
IV – Application to counting copies
The first consequence of minds’ eternal journey is that all my copies will be me. We should not worry about preserving soul, continuity or any other identity token.
The second consequence is more subtle and claims that different copies will be achieved in the different moments of time. For example, me-tomorrow and me-day-after-tomorrow can be both regarded as my copies (assuming almost no changes had happened), but we know that me-tomorrow will be achieved first. It also means that me-day-after-tomorrow will be achieved only after I would be me-tomorrow, so I today can expect that I will wake up tomorrow and not in day after tomorrow. So, while both copies will be me, I will first "visit" me-tomorrow. However, if I will sleep all day tomorrow, my next copy will be me-day-after-tomorrow
The theory of predicts that if there are two imperfect copies of me, I will first become the one through which eternal journey would pass first.
It gives an instrument to solve different paradoxes related to copies. For example, in the Mars transporter, I will become my copy on Mars, and in the Broken Mars transporter in which both copy and original exist, I will remain the original (no 50-50 solution). Here is assumed that I will become Mars copy after trillions of trillions of years of the journey through all possible minds (and that there will be no closer copies.)
More generally speaking, if there is two my copies in the future – one is my next observer moment, and another is just appeared somewhere via some stochastic process – which one I will be in the next moment? To answer this question, we look at the whole functional space of minds and count the ordering of the moments then the pointer of now-moment is passing through minds which are informationally me. If two such copies exist, I will be both of them eventually, but first of them I will be the one which is located in the next moment of time. In that case I can ignore remote copy. However, if I die in the next moment of time, only remote copy will exist, and now my now-moment passing through it will be first my reappearance. In that case, this remote copy matters.
V – Does it make any sense?
One can argue that I count here completely unmeasurable things and thus this doesn’t matter. I want to point for three practical applications:
1. Excluding Boltzmann Brains as my next observer moments which refines our cosmological models.
2. Predicting the type of survival in quantum immortality.
3. Solving Mars transporter-like paradoxes.