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.
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.