To me the simplest solution is that such people simply don’t exist. There are possible timelines in which they don’t exist, and timelines that have them seem likely to be unstable, so the actual timeline will be one of the stable ones in which they don’t exist.
There are other possible solutions of course, but “increasingly bizarre events occur in which their desires are thwarted” seems far more convoluted than “one of the other millions of sperm met the egg instead and that person never existed” or even a more general “this species’ brains develop in such a way that they don’t have such ideas”.
Of course, in general this leads to the much more stable state in which although (as per premise) every sentient being potentially has the capability to flip universes, in practice none of them know that it’s possible and even if they do then they don’t know how to actually do it.
There are other possible solutions of course, but “increasingly bizarre events occur in which their desires are thwarted” seems far more convoluted than “one of the other millions of sperm met the egg instead and that person never existed” or even a more general “this species’ brains develop in such a way that they don’t have such ideas”.
If we assume the universe is deterministic, that’s not really an option. Which sperm entered the egg is fixed and cannot be changed. Instead to find an equilibrium something about the future has to effect the past in such a way as to make itself consistent rather than inconsistent.
I suspect that I don’t know what you mean by “deterministic” here, since the meaning I have in mind can’t possibly apply to such a universe. That is, that future states are completely determined by prior states. That can’t possibly apply here since the universe has no global distinction between future and past. Even splitting our view into timelines within each semiverse doesn’t help, since determinism is violated by the sudden appearance of sentient beings and other materials that are not in any way determined by that semiverse’s prior states. So you must be using some other meaning for “deterministic”.
Perhaps you just mean that the universe timeline is single-valued? That is, only one set of events actually happens at each point in spacetime in each semiverse. That is also the model I’m using, but from a different point of view. Rather than taking that a contrary person exists as a fixed event that must be worked around, I am taking a wider view of what fraction (in some sense) of possible timelines that are otherwise very similar contain that contrary person vs those that don’t. Since the actual timeline has to be one of the possible timelines, this seems to be a useful consideration.
My conclusion is that contrary people drastically lower the measure of mostly-similar timelines that contain them, and so over trillions of sentient beings it seems likely that the proportion of contrary people is much more likely to be very, very small than that they are relatively frequent and cause lots of bizarre events.
My definition of deterministic is that taking one universe as fixed, there’s only one possible value for the other universe.
So if there’s nothing from the other universe that switches over and effects which sperm fertilizes which egg, then that is something which can’t change just because it will lead to a contradiction.
Thanks, that explains why I had no idea what you meant by deterministic. It’s not a meaning for the term that I would have guessed. I obviously wasn’t assuming that the universe is deterministic in that sense.
It does open up more questions, and so is interesting. Let us use the function notation D2(x) to refer to the deterministically single allowed timeline of semiverse 2 given that semiverse 1 has timeline x, and similarly for D1. Such a universe is only possible if D1 and D2 satisfy certain conditions, in particular that there exists at least one pair (x,y) such that D2(x) = y and D1(y) = x.
We can eliminate the case where D1 or D2 are constant, since those correspond to causally isolated or one-way semiverses and are therefore boring.
For almost all other function pairs, almost all timelines x in one semiverse have no corresponding timeline y since in general D1(D2(x)) != x. This places drastic limitations either on what single semiverse timelines are allowed in ways that are utterly foreign to conventional causality or even continuity, or on what sorts of functions D1 and D2 are allowed. Almost all ordinary deterministic laws of physics will fail this condition.
So for this notion of determinism to be sustained, we have to consider universes in which even within a single semiverse with no flipping, the laws of physics are utterly different from our own.
That’s a good way of framing it! There’s some discussion in acedemia on this topic under Novikov self-consistency principle (not quite the same, since it’s only in one universe, but pretty similiar, and I wouldn’t be surprised if results carry over).
Note that I do actually break this rule in my protocol which involves flipping a coin to decide whether to build a relationship. However this can be fixed by flipping an “equilibrium coin”. Effectively this is a device which has exactly two self consistent equilibria. For example you might have a device where either an item wont be switched at all, or it will be switched at exactly the right time to cause itself to switch in the first place. Flipping counts as heads, not flipping as tails.
I think the first question is the most important.
To me the simplest solution is that such people simply don’t exist. There are possible timelines in which they don’t exist, and timelines that have them seem likely to be unstable, so the actual timeline will be one of the stable ones in which they don’t exist.
There are other possible solutions of course, but “increasingly bizarre events occur in which their desires are thwarted” seems far more convoluted than “one of the other millions of sperm met the egg instead and that person never existed” or even a more general “this species’ brains develop in such a way that they don’t have such ideas”.
Of course, in general this leads to the much more stable state in which although (as per premise) every sentient being potentially has the capability to flip universes, in practice none of them know that it’s possible and even if they do then they don’t know how to actually do it.
If we assume the universe is deterministic, that’s not really an option. Which sperm entered the egg is fixed and cannot be changed. Instead to find an equilibrium something about the future has to effect the past in such a way as to make itself consistent rather than inconsistent.
I suspect that I don’t know what you mean by “deterministic” here, since the meaning I have in mind can’t possibly apply to such a universe. That is, that future states are completely determined by prior states. That can’t possibly apply here since the universe has no global distinction between future and past. Even splitting our view into timelines within each semiverse doesn’t help, since determinism is violated by the sudden appearance of sentient beings and other materials that are not in any way determined by that semiverse’s prior states. So you must be using some other meaning for “deterministic”.
Perhaps you just mean that the universe timeline is single-valued? That is, only one set of events actually happens at each point in spacetime in each semiverse. That is also the model I’m using, but from a different point of view. Rather than taking that a contrary person exists as a fixed event that must be worked around, I am taking a wider view of what fraction (in some sense) of possible timelines that are otherwise very similar contain that contrary person vs those that don’t. Since the actual timeline has to be one of the possible timelines, this seems to be a useful consideration.
My conclusion is that contrary people drastically lower the measure of mostly-similar timelines that contain them, and so over trillions of sentient beings it seems likely that the proportion of contrary people is much more likely to be very, very small than that they are relatively frequent and cause lots of bizarre events.
My definition of deterministic is that taking one universe as fixed, there’s only one possible value for the other universe.
So if there’s nothing from the other universe that switches over and effects which sperm fertilizes which egg, then that is something which can’t change just because it will lead to a contradiction.
Thanks, that explains why I had no idea what you meant by deterministic. It’s not a meaning for the term that I would have guessed. I obviously wasn’t assuming that the universe is deterministic in that sense.
It does open up more questions, and so is interesting. Let us use the function notation D2(x) to refer to the deterministically single allowed timeline of semiverse 2 given that semiverse 1 has timeline x, and similarly for D1. Such a universe is only possible if D1 and D2 satisfy certain conditions, in particular that there exists at least one pair (x,y) such that D2(x) = y and D1(y) = x.
We can eliminate the case where D1 or D2 are constant, since those correspond to causally isolated or one-way semiverses and are therefore boring.
For almost all other function pairs, almost all timelines x in one semiverse have no corresponding timeline y since in general D1(D2(x)) != x. This places drastic limitations either on what single semiverse timelines are allowed in ways that are utterly foreign to conventional causality or even continuity, or on what sorts of functions D1 and D2 are allowed. Almost all ordinary deterministic laws of physics will fail this condition.
So for this notion of determinism to be sustained, we have to consider universes in which even within a single semiverse with no flipping, the laws of physics are utterly different from our own.
That’s a good way of framing it! There’s some discussion in acedemia on this topic under Novikov self-consistency principle (not quite the same, since it’s only in one universe, but pretty similiar, and I wouldn’t be surprised if results carry over).
Note that I do actually break this rule in my protocol which involves flipping a coin to decide whether to build a relationship. However this can be fixed by flipping an “equilibrium coin”. Effectively this is a device which has exactly two self consistent equilibria. For example you might have a device where either an item wont be switched at all, or it will be switched at exactly the right time to cause itself to switch in the first place. Flipping counts as heads, not flipping as tails.