Edit : I am adding a better answer to your argument of equivalent classes. I do not deny that such equivalence classes exist for some phenomena, however, if everything else requires perfect precision… Then we have some margin for error in some unimportant parts and have absolutely zero margin for error in the other parts, which would mean those equivalent classes would not help making the probability of simulating you higher than 0. To illustrate, if P(A)=X, and P(B)=0, P(A and B)=0.
We are not our brain, though. Consciousness does not only come from the brain, as an example we have quite a lot of neurons in our stomach, and even worse, the intestinal flora is known to have an influence on behaviour and thinking. That means that in order to reproduce you exactly, you have to reproduce the whole body, not merely the brain, and even possibly the bacteria inside your stomach… Information about who you are is not only contained in the brain, it is contained in the whole body. It can be argued that the brain would be sufficient to recreate someone, but I have extreme doubts over such a hypothesis, someone who only had a brain and not a body would go insane from the complete absence of stimuli from their body, and any partial copy would not truly be you but only an inferior copy. Assuming such an inferior copy can be considered to be you, then every broken copy arising from randomness is also yourself, so there’s no escaping the statistical hell.
Secondly, you still don’t understand the problem of simulating one individual. We are the product of so many random events that it is not possible to find out exactly how one particular individual came into existence. Aliens would need to use a rational and deliberate computation process in order to reproduce a conscious being. If you think aliens could recreate you by using enough random coin tosses to get to you, then you’re only recreating a Boltzman brain but unlike the universe aliens do not have infinite ressources. The worst thing of them all, and the biggest dealbreaker, is the problem of chaos and the butterfly effect. Even an inaccuracy over a single cell of your body could lead to as an example a cancer killing you before making children and therefore completely changing the whole timeline of events by making people that would have existed in our universe disappear. If, say, your mother has a stray thought and decides to abort you, you simply won’t exist. Now, imagine this at every instant of the world you’re simulating. A single error can completely change the timeline.
If we look at proposition 1, the weakest form of my argument would be one where the universe has infinite time, but not infinite space nor infinite matter. In such a cyclical universe, I think your point about aliens being overwhelmingly more likely to simulate than random statistical noise is one I would entirely agree with. Because, in such a scecnario, we are not merely talking about one alien civilization, we are talking about potentially infinite alien simulations randomly recreating us over and over and over again.
If, however, the universe is “strongly infinite”, (Infinite time + infinite space + infinite matter), then no matter what aliens do, there is no way to surpass statistical hell. Every alien civilization would have finite ressources, whereas the universe has infinite ressources. No matter how efficient aliens would be with their technology, I don’t think it is possible to beat a “cubic infinity”. The aliens would have access to infinite time, with finite ressources in space and energy. Whereas, the universe has access to infinite time*infinite ressources*infinite space.
The reason disembodied individuals win, is because they can simulate one person perfectly without having to simulate their surroundings perfectly. Statistical noisy random processes do not need to retrieve ANY information about your past to remake you. Meanwhile, aliens have to somehow find your information again and reproduce it exactly, through a computation process. There is an asymetry. Aliens need to retrieve information that is impossible to get, whereas the universe doesn’t need to care about that.
Then we have some margin for error in some unimportant parts and have absolutely zero margin for error in the other parts
But all of the parts would have some margin for error because bounded physical processes can’t store infinite information(Bekenstein bound). Adding in your guts, microbiome etc. doesn’t fundamentally change the argument, they still have a far smaller number of degrees of freedom than your past light cone.
If you think aliens could recreate you by using enough random coin tosses to get to you, then you’re only recreating a Boltzman brain but unlike the universe aliens do not have infinite ressources
Flipping a quantum coin a bunch of times doesn’t actually require that many resources though, assuming you already have enough computational resources to store the brain. And aliens have a crucial advantage over vacuum fluctuations in that they can model dependencies that would be found in actual brains and only sample from brain states that would likely occur. Like if (made up numbers) there are 2^(10^15) possible brain states but only 2^(10^9) of them would be likely to occur in reality, the aliens can sample from that narrower space and thus get a relative factor of ~2^(10^15) more probability. (Yes aliens can’t perfectly sample from the actual state space but it doesn’t matter, any improvement over pure randomness will give a large increase in probability)
The first part of my answer will answer your point about Bekenstein’s limit. The second part of my answer will concede your point, and look at the logical consequences.
In our assumptions, the Bekenstein’s limit theorem is false. This theorem fundamentally assumes that the universe is pixelated, that it is possible to separate it into finite parts. But, in Proposition 5 bis, I assume that real numbers exist. It is basically a limited version of platonic realism. I consider the universe to merely be a mathematical structure. In the end, there is a fundamental chasm between reality itself, and the theories we can make about reality. My opinion is that physics is not the study of reality, but rather, the study of what we are able to measure and the informational patterns we are able to infer from those measurements. That would make the Bekeinstein’s limit a fundamental limit on physical epistemology rather than on ontology.
The hypothetical aliens wouldn’t need to merely flip a quantum coin a bunch of times. They’d need to do that across all the spacetime they are simulating. I think that, because quantum states involve uncountable infinities rather than countable infinities, that it would not be possible for a quantum computer to calculate “more” than a linear sum of infinities that depends on the volume of spacetime/energy that defines the computer’s upper limit of computation. By using a binary computer it is fundamentally impossible to simulate those things, because binary computers can only calculate “countable infinities”. However, my reasoning is shaky, because I do not have the mathematical prowesses necessary to, actually calculate all those things. Basically, aliens would be using some kind of analogical computers in order to force the universe to do the dirty work of calculations for them rather than trying to create an algorithm that does it.
In such a case, simulating a whole person… Could be possible. With a big enough quantum computer that would neutralize infinities using other infinities. In all honesty, you may have gotten me with this. There is no way for me to prove that broken simulations would vastly outnumber the “normal” ones. But, in that case, “waking up again” after your death is still inevitable from your own perspective. You’d have a random mix of both (infinite?) alien simulations (both broken and unbroken. But you’ll be at their complete mercy, if they want to torture you for fun they can) and infinite disembodied reincarnations of a few yottoseconds.
Now, I’ll look a the consequences if I concede your point. Here is the massive problem : as your simulation “ages”, in order to compute the older version of yourself accurately with all the memories it’ll take more and more computing power until it will eventually exceed what any civilization is capable to do. However, the universe is not bound by those limits, since it is infinite. Therefore, as you get reincarnated more and more, the odds that an alien civilization happens to reincarnate you become more and more impossible. Because everyone has eternal life (from the point of view of a deceased time does not pass), the more time passes, the worse the conditions for reincarnating get.
You’d have a random mix of both (infinite?) alien simulations (both broken and unbroken. But you’ll be at their complete mercy, if they want to torture you for fun they can) and infinite disembodied reincarnations of a few yottoseconds
I think the probabilities will be heavily tilted towards the aliens(or really, humanity/human-descended AIs in the future or an alternate timeline). But yes, I agree with the overall point that continuations of your stream of consciousness might become very weird and unpredictable past the point at which you would normally die on Earth(and probably even weirder as time goes on into the distant future)
It seems we are done for this particular debate. I would like to thank you for all your thoughts, which have been a precious help, and for giving a chance to my essay despite its negative karma.
If anyone has good counterarguments, on failures from my reasoning, I would gladly take the time to see if they are valid or if they can be refuted.
Edit : I am adding a better answer to your argument of equivalent classes. I do not deny that such equivalence classes exist for some phenomena, however, if everything else requires perfect precision… Then we have some margin for error in some unimportant parts and have absolutely zero margin for error in the other parts, which would mean those equivalent classes would not help making the probability of simulating you higher than 0. To illustrate, if P(A)=X, and P(B)=0, P(A and B)=0.
We are not our brain, though. Consciousness does not only come from the brain, as an example we have quite a lot of neurons in our stomach, and even worse, the intestinal flora is known to have an influence on behaviour and thinking. That means that in order to reproduce you exactly, you have to reproduce the whole body, not merely the brain, and even possibly the bacteria inside your stomach… Information about who you are is not only contained in the brain, it is contained in the whole body. It can be argued that the brain would be sufficient to recreate someone, but I have extreme doubts over such a hypothesis, someone who only had a brain and not a body would go insane from the complete absence of stimuli from their body, and any partial copy would not truly be you but only an inferior copy. Assuming such an inferior copy can be considered to be you, then every broken copy arising from randomness is also yourself, so there’s no escaping the statistical hell.
Secondly, you still don’t understand the problem of simulating one individual. We are the product of so many random events that it is not possible to find out exactly how one particular individual came into existence. Aliens would need to use a rational and deliberate computation process in order to reproduce a conscious being. If you think aliens could recreate you by using enough random coin tosses to get to you, then you’re only recreating a Boltzman brain but unlike the universe aliens do not have infinite ressources. The worst thing of them all, and the biggest dealbreaker, is the problem of chaos and the butterfly effect. Even an inaccuracy over a single cell of your body could lead to as an example a cancer killing you before making children and therefore completely changing the whole timeline of events by making people that would have existed in our universe disappear. If, say, your mother has a stray thought and decides to abort you, you simply won’t exist. Now, imagine this at every instant of the world you’re simulating. A single error can completely change the timeline.
If we look at proposition 1, the weakest form of my argument would be one where the universe has infinite time, but not infinite space nor infinite matter. In such a cyclical universe, I think your point about aliens being overwhelmingly more likely to simulate than random statistical noise is one I would entirely agree with. Because, in such a scecnario, we are not merely talking about one alien civilization, we are talking about potentially infinite alien simulations randomly recreating us over and over and over again.
If, however, the universe is “strongly infinite”, (Infinite time + infinite space + infinite matter), then no matter what aliens do, there is no way to surpass statistical hell. Every alien civilization would have finite ressources, whereas the universe has infinite ressources. No matter how efficient aliens would be with their technology, I don’t think it is possible to beat a “cubic infinity”. The aliens would have access to infinite time, with finite ressources in space and energy. Whereas, the universe has access to infinite time*infinite ressources*infinite space.
The reason disembodied individuals win, is because they can simulate one person perfectly without having to simulate their surroundings perfectly. Statistical noisy random processes do not need to retrieve ANY information about your past to remake you. Meanwhile, aliens have to somehow find your information again and reproduce it exactly, through a computation process. There is an asymetry. Aliens need to retrieve information that is impossible to get, whereas the universe doesn’t need to care about that.
But all of the parts would have some margin for error because bounded physical processes can’t store infinite information(Bekenstein bound). Adding in your guts, microbiome etc. doesn’t fundamentally change the argument, they still have a far smaller number of degrees of freedom than your past light cone.
Flipping a quantum coin a bunch of times doesn’t actually require that many resources though, assuming you already have enough computational resources to store the brain. And aliens have a crucial advantage over vacuum fluctuations in that they can model dependencies that would be found in actual brains and only sample from brain states that would likely occur. Like if (made up numbers) there are 2^(10^15) possible brain states but only 2^(10^9) of them would be likely to occur in reality, the aliens can sample from that narrower space and thus get a relative factor of ~2^(10^15) more probability. (Yes aliens can’t perfectly sample from the actual state space but it doesn’t matter, any improvement over pure randomness will give a large increase in probability)
The first part of my answer will answer your point about Bekenstein’s limit. The second part of my answer will concede your point, and look at the logical consequences.
In our assumptions, the Bekenstein’s limit theorem is false. This theorem fundamentally assumes that the universe is pixelated, that it is possible to separate it into finite parts. But, in Proposition 5 bis, I assume that real numbers exist. It is basically a limited version of platonic realism. I consider the universe to merely be a mathematical structure. In the end, there is a fundamental chasm between reality itself, and the theories we can make about reality. My opinion is that physics is not the study of reality, but rather, the study of what we are able to measure and the informational patterns we are able to infer from those measurements. That would make the Bekeinstein’s limit a fundamental limit on physical epistemology rather than on ontology.
The hypothetical aliens wouldn’t need to merely flip a quantum coin a bunch of times. They’d need to do that across all the spacetime they are simulating. I think that, because quantum states involve uncountable infinities rather than countable infinities, that it would not be possible for a quantum computer to calculate “more” than a linear sum of infinities that depends on the volume of spacetime/energy that defines the computer’s upper limit of computation. By using a binary computer it is fundamentally impossible to simulate those things, because binary computers can only calculate “countable infinities”. However, my reasoning is shaky, because I do not have the mathematical prowesses necessary to, actually calculate all those things. Basically, aliens would be using some kind of analogical computers in order to force the universe to do the dirty work of calculations for them rather than trying to create an algorithm that does it.
In such a case, simulating a whole person… Could be possible. With a big enough quantum computer that would neutralize infinities using other infinities. In all honesty, you may have gotten me with this. There is no way for me to prove that broken simulations would vastly outnumber the “normal” ones. But, in that case, “waking up again” after your death is still inevitable from your own perspective. You’d have a random mix of both (infinite?) alien simulations (both broken and unbroken. But you’ll be at their complete mercy, if they want to torture you for fun they can) and infinite disembodied reincarnations of a few yottoseconds.
Now, I’ll look a the consequences if I concede your point. Here is the massive problem : as your simulation “ages”, in order to compute the older version of yourself accurately with all the memories it’ll take more and more computing power until it will eventually exceed what any civilization is capable to do. However, the universe is not bound by those limits, since it is infinite. Therefore, as you get reincarnated more and more, the odds that an alien civilization happens to reincarnate you become more and more impossible. Because everyone has eternal life (from the point of view of a deceased time does not pass), the more time passes, the worse the conditions for reincarnating get.
I think the probabilities will be heavily tilted towards the aliens(or really, humanity/human-descended AIs in the future or an alternate timeline). But yes, I agree with the overall point that continuations of your stream of consciousness might become very weird and unpredictable past the point at which you would normally die on Earth(and probably even weirder as time goes on into the distant future)
It seems we are done for this particular debate. I would like to thank you for all your thoughts, which have been a precious help, and for giving a chance to my essay despite its negative karma.
If anyone has good counterarguments, on failures from my reasoning, I would gladly take the time to see if they are valid or if they can be refuted.