Imagine a scenario in which the people running the simulation decided to simulate every human on Earth as an actual observer.
In this case, Pr(I’m distinct | I’m not in a simulation) = Pr(I’m distinct | I’m in a simulation) because no special treatment has been shown to you. If you think it is very unlikely that you just happened to be distinct in a real world, then in this scenario, you ought to think that it is very unlikely that you just happened to be distinct in a simulated world.
I think what you are actually thinking about is a scenario where only you are an actual observer, whereas everyone else is a p-zombie (or an NPC if you wish).
But this scenario also raises a few questions. Why would the simulators make you a real observer and everyone else a p-zombie? Apparently, p-zombies are able to carry on any tasks that are useful for observation just as well as actual observers.
But even leaving that aside, it is unclear why is your Pr(I’m distinct | I’m in a simulation) so high? Computer-game-style simulations where you are “the main character” are plausible, but so are other types of simulations. For example, imagine a civilization wanting to learn about its past and running a simulation of its history. Or imagine a group of people who want to run an althistory simulation. Perhaps they want to see what could’ve happened had Nazi Germany won WW2 (specifics are irrelevant here). Clearly, in the althistory simulation, there would be no “main characters,” so it would be plausible that everyone would be an actual observer (as opposed to there being only one actual observer). And let’s also imagine for a second that althistory simulation has one hundred billion (10¹¹) observers in total. The chances of you being the only real observer in this world vs. being one of a trillion real observers in althistory world are 1:10¹¹.
And from here, we can generalize. If it is plausible that simulators would ever run a simulation with 10¹¹ observers (or any other large number), then it would require 10¹¹ (or any other large number) simulations with only one observer to match the odds of you being in a “one observer” simulation.
Other people here have responded in similar ways to you; but the problem with your argument is that my original argument could also just consider only simulations in which I am the only observer. In which case Pr(I’m distinct | I’m in a simulation)=1, not 0.5. And since there’s obviously some prior probability of this simulation being true, my argument still follows.
I now think my actual error is saying Pr(I’m distinct | I’m not in a simulation)=0.0001, when in reality this probability should be 1, since I am not a random sample of all humans (i.e., SSA is wrong), I am me. Is that clear?
Lastly, your final paragraph is akin to the SSA + SIA response to the doomsday paradox, which I don’t think is widely accepted since both those assumptions lead to a bunch of paradoxes.
but the problem with your argument is that my original argument could also just consider only simulations in which I am the only observer. In which case Pr(I’m distinct | I’m in a simulation)=1, not 0.5. And since there’s obviously some prior probability of this simulation being true, my argument still follows.
But then this turns Pr(I’m in a simulation) into Pr(I’m in a simulation) + Pr(only simulations with one observer exist | simulations exist). It’s not enough that a simulation exists with only one observer. It needs to be so that simulations with multiple observers also don’t exist. For example, if there is just one simulation with a billion observers, it heavily skews the odds in favor of you not being in a simulation with just one observer.
And I am very much willing to say Pr(I’m in a simulation) + Pr(only simulations with one observer exist | simulations exist) is going to be lower than Pr(I’m distinct | I’m not in a simulation).
I now think my actual error is saying Pr(I’m distinct | I’m not in a simulation)=0.0001, when in reality this probability should be 1, since I am not a random sample of all humans (i.e., SSA is wrong), I am me. Is that clear?
That answer seems reasonable to me. However, I think that there is value in my answer as well: it works even if SSA (the “least favorable” assumption) is true.
Can you please explain why my explaination requires SIA? From a quick Google search: “The Self Sampling Assumption (SSA) states that we should reason as if we’re a random sample from the set of actual existent observers”
My last paragraph in my original answer was talking about a scenario where simulators have actually simulated a) a world with 1 observers AND b) a world with 10¹¹ observer. So a set of “actual existent observers” includes 1 + 10¹¹ observers. You are randomly selected from that, giving you 1:10¹¹ odds of being in the world where you are the only observer. I don’t see where SIA is coming in play here.
If simulations exist, we are choosing between two potentially existing scenarios, either I’m the only real person in my simulation, or there are other real people in my simulation. Your argument prioritizes the latter scenario because it contains more observers, but these are potentially existing observers, not actual observers. SIA is for potentially existing observers.
I have a kind of intuition that something like my argument above is right, but tell me if that is unclear.
And note: one potential problem with your reasoning is that if we take it to it’s logical extreme, it would be 100% certain that we are living in a simulation with infinite invisible observers. Because infinity dominates all the finite possibilities.
But the thing is that, there is a matter of fact of whether there are other observers in our world if it is simulated. Either you are the only observer or there are other observers, but one of them is true. Not just potentially true, but actually true.
The same is true of my last paragraph in the original answer (although perhaps, I could’ve used a clearer wording). If, as a matter of fact there actually exist 10¹¹ + 1 observers, then you are more likely to be in 10¹¹ group as per SSA. We don’t know if there are actually 10¹¹ + 1 observers, but that is merely an epistemic gap.
The way I understand it, the main difference between SIA and SSA is the fact that in SIA “I” may fail to exist. To illustrate what I mean, I will have to refer to “souls” just because it’s the easiest thing I can come up with.
SSA: There are 10¹¹ + 1 observers and 10¹¹ + 1 souls. Each soul gets randomly assigned to an observer. One of the souls is you. The probability of you existing is 1. You cannot fail to exist.
SIA: There are 10¹¹ + 1 observers and a very large (much larger than 10¹¹ + 1) amount of souls. Let’s call this amount N. Each soul gets assigned to an observer. One of the souls is you. However, in this scenario, you may fail to exist. The probability of you existing is (10¹¹ + 1)/N
This is an interesting observation which may well be true, I’m not sure, but the more intuitive difference is that SSA is about actually existing observers, while SIA is about potentially existing observers. In other words, if you are reasoning about possible realities in the so-called “multiverse of possibilities,” than you are using SIA. Whereas if you are only considering a single reality (e.g., the non-simulated world), you select a reference class from that reality (e.g., humans), you may choose to use use SSA to say that you are a random observer from that class (e.g., a random human in human history).
I guess the word “reality” is kind of ambiguous, and maybe that’s why we’ve been disagreeing for so long.
For example, imagine a scenario where we have 1) a non-simulated base world (let’s say 10¹² observers in it) AND 2) a simulated world with 10¹¹ observers AND 3) a simulated world with 1 observer. All three worlds actually concretely exist. People from world #1 just decided to run two simulations (#2 and #3). Surely, in this scenario, as per SSA, I can say that I am a randomly selected observer from the set of all observers. As far as I see, this “set of all observers” would include 10¹² + 10¹¹ + 1 observer because all of these observers actually exist, and I could’ve been born as any one of them.
Edit 1: I noticed that you edited one of your replies to include this:
And note: one potential problem with your reasoning is that if we take it to it’s logical extreme, it would be 100% certain that we are living in a simulation with infinite invisible observers. Because infinity dominates all the finite possibilities.
I don’t actually think this is true. My reasoning only really says that we are most likely to exist in the world with the most observers as compared to other actual worlds, not other possible worlds.
The most you can get out of this is the fact that conditional on a simulation with infinite observers existing, we are most likely in that simulation. However, because of the weirdness of actual infinity, because of the abysmal computational costs (it’s one thing to simulate billions of observers and another thing to simulate an infinity of observers), and because of the fact that it is probably physically impossible, I put an incredibly low prior on the fact that a simulation with infinite observers actually exists. And if it doesn’t exist, then we are not in it.
Edit 2: You don’t even need to posit a 10¹¹ simulation for it to be unlikely that you are in an “only one observer” simulation. It is enough that the non-simulated world has multiple observers. To illustrate what I mean, imagine that a society in a non-simulated world with 10¹² observers decides to make a simulation with only 1 observer. The odds are overwhelming that you’d be among 10¹² mundane, non-distinct observers in the non-simulated world.
No, I don’t think it is.
Imagine a scenario in which the people running the simulation decided to simulate every human on Earth as an actual observer.
In this case, Pr(I’m distinct | I’m not in a simulation) = Pr(I’m distinct | I’m in a simulation) because no special treatment has been shown to you. If you think it is very unlikely that you just happened to be distinct in a real world, then in this scenario, you ought to think that it is very unlikely that you just happened to be distinct in a simulated world.
I think what you are actually thinking about is a scenario where only you are an actual observer, whereas everyone else is a p-zombie (or an NPC if you wish).
But this scenario also raises a few questions. Why would the simulators make you a real observer and everyone else a p-zombie? Apparently, p-zombies are able to carry on any tasks that are useful for observation just as well as actual observers.
But even leaving that aside, it is unclear why is your Pr(I’m distinct | I’m in a simulation) so high? Computer-game-style simulations where you are “the main character” are plausible, but so are other types of simulations. For example, imagine a civilization wanting to learn about its past and running a simulation of its history. Or imagine a group of people who want to run an althistory simulation. Perhaps they want to see what could’ve happened had Nazi Germany won WW2 (specifics are irrelevant here). Clearly, in the althistory simulation, there would be no “main characters,” so it would be plausible that everyone would be an actual observer (as opposed to there being only one actual observer). And let’s also imagine for a second that althistory simulation has one hundred billion (10¹¹) observers in total. The chances of you being the only real observer in this world vs. being one of a trillion real observers in althistory world are 1:10¹¹.
And from here, we can generalize. If it is plausible that simulators would ever run a simulation with 10¹¹ observers (or any other large number), then it would require 10¹¹ (or any other large number) simulations with only one observer to match the odds of you being in a “one observer” simulation.
Other people here have responded in similar ways to you; but the problem with your argument is that my original argument could also just consider only simulations in which I am the only observer. In which case Pr(I’m distinct | I’m in a simulation)=1, not 0.5. And since there’s obviously some prior probability of this simulation being true, my argument still follows.
I now think my actual error is saying Pr(I’m distinct | I’m not in a simulation)=0.0001, when in reality this probability should be 1, since I am not a random sample of all humans (i.e., SSA is wrong), I am me. Is that clear?
Lastly, your final paragraph is akin to the SSA + SIA response to the doomsday paradox, which I don’t think is widely accepted since both those assumptions lead to a bunch of paradoxes.
But then this turns Pr(I’m in a simulation) into Pr(I’m in a simulation) + Pr(only simulations with one observer exist | simulations exist). It’s not enough that a simulation exists with only one observer. It needs to be so that simulations with multiple observers also don’t exist. For example, if there is just one simulation with a billion observers, it heavily skews the odds in favor of you not being in a simulation with just one observer.
And I am very much willing to say Pr(I’m in a simulation) + Pr(only simulations with one observer exist | simulations exist) is going to be lower than Pr(I’m distinct | I’m not in a simulation).
That answer seems reasonable to me. However, I think that there is value in my answer as well: it works even if SSA (the “least favorable” assumption) is true.
I think you are overlooking that your explanation requires BOTH SSA and SIA, but yes, I understand where you are coming from.
Can you please explain why my explaination requires SIA? From a quick Google search: “The Self Sampling Assumption (SSA) states that we should reason as if we’re a random sample from the set of actual existent observers”
My last paragraph in my original answer was talking about a scenario where simulators have actually simulated a) a world with 1 observers AND b) a world with 10¹¹ observer. So a set of “actual existent observers” includes 1 + 10¹¹ observers. You are randomly selected from that, giving you 1:10¹¹ odds of being in the world where you are the only observer. I don’t see where SIA is coming in play here.
This is what I was thinking:
If simulations exist, we are choosing between two potentially existing scenarios, either I’m the only real person in my simulation, or there are other real people in my simulation. Your argument prioritizes the latter scenario because it contains more observers, but these are potentially existing observers, not actual observers. SIA is for potentially existing observers.
I have a kind of intuition that something like my argument above is right, but tell me if that is unclear.
And note: one potential problem with your reasoning is that if we take it to it’s logical extreme, it would be 100% certain that we are living in a simulation with infinite invisible observers. Because infinity dominates all the finite possibilities.
But the thing is that, there is a matter of fact of whether there are other observers in our world if it is simulated. Either you are the only observer or there are other observers, but one of them is true. Not just potentially true, but actually true.
The same is true of my last paragraph in the original answer (although perhaps, I could’ve used a clearer wording). If, as a matter of fact there actually exist 10¹¹ + 1 observers, then you are more likely to be in 10¹¹ group as per SSA. We don’t know if there are actually 10¹¹ + 1 observers, but that is merely an epistemic gap.
You are describing the SIA assumption to a T.
The way I understand it, the main difference between SIA and SSA is the fact that in SIA “I” may fail to exist. To illustrate what I mean, I will have to refer to “souls” just because it’s the easiest thing I can come up with.
SSA: There are 10¹¹ + 1 observers and 10¹¹ + 1 souls. Each soul gets randomly assigned to an observer. One of the souls is you. The probability of you existing is 1. You cannot fail to exist.
SIA: There are 10¹¹ + 1 observers and a very large (much larger than 10¹¹ + 1) amount of souls. Let’s call this amount N. Each soul gets assigned to an observer. One of the souls is you. However, in this scenario, you may fail to exist. The probability of you existing is (10¹¹ + 1)/N
This is an interesting observation which may well be true, I’m not sure, but the more intuitive difference is that SSA is about actually existing observers, while SIA is about potentially existing observers. In other words, if you are reasoning about possible realities in the so-called “multiverse of possibilities,” than you are using SIA. Whereas if you are only considering a single reality (e.g., the non-simulated world), you select a reference class from that reality (e.g., humans), you may choose to use use SSA to say that you are a random observer from that class (e.g., a random human in human history).
I guess the word “reality” is kind of ambiguous, and maybe that’s why we’ve been disagreeing for so long.
For example, imagine a scenario where we have 1) a non-simulated base world (let’s say 10¹² observers in it) AND 2) a simulated world with 10¹¹ observers AND 3) a simulated world with 1 observer. All three worlds actually concretely exist. People from world #1 just decided to run two simulations (#2 and #3). Surely, in this scenario, as per SSA, I can say that I am a randomly selected observer from the set of all observers. As far as I see, this “set of all observers” would include 10¹² + 10¹¹ + 1 observer because all of these observers actually exist, and I could’ve been born as any one of them.
Edit 1: I noticed that you edited one of your replies to include this:
I don’t actually think this is true. My reasoning only really says that we are most likely to exist in the world with the most observers as compared to other actual worlds, not other possible worlds.
The most you can get out of this is the fact that conditional on a simulation with infinite observers existing, we are most likely in that simulation. However, because of the weirdness of actual infinity, because of the abysmal computational costs (it’s one thing to simulate billions of observers and another thing to simulate an infinity of observers), and because of the fact that it is probably physically impossible, I put an incredibly low prior on the fact that a simulation with infinite observers actually exists. And if it doesn’t exist, then we are not in it.
Edit 2: You don’t even need to posit a 10¹¹ simulation for it to be unlikely that you are in an “only one observer” simulation. It is enough that the non-simulated world has multiple observers. To illustrate what I mean, imagine that a society in a non-simulated world with 10¹² observers decides to make a simulation with only 1 observer. The odds are overwhelming that you’d be among 10¹² mundane, non-distinct observers in the non-simulated world.