Thanks for the article, which clarified some stuff for me that I should have been able to put together on my own, but hadn’t!
I’d like to disagree with your conclusion, though, which seems to be that my utility function should necessarily be additive if interference is negligible. (If you’re just saying that this is what evolution is predicted to produce on most branches, I have no quibbles with that.)
Suppose that you wake up in a white room, and Omega appears to you and tells you that it’s simulating you, for one year, after which it will shut down the simulation. You have three options for how this time will be spent. In option (A), Omega will reveal to you the true physical Theory of Everything, and help you understand how it all really works. In option (B), Omega will explain to you in detail the workings of the human mind, and help you understand how subjective experience arises from it. In option (C), Omega will flip two fair quantum coins; if they land (heads,heads), it will run simulation (A), if they land (heads,tails), it will run (B), and if the first coin lands tails, Omega will shut down the simulation immediately.
If Omega also explains that Copenhagen is definitely true, picking (C) would make little sense, since with 50% probability you’d just die, which surely isn’t a reasonable price for not having to choose what simulation you’re going to be in. But if Omega explains that MWI is definitely true, option (C) would mean that you get to learn about both subjects, on distinct Everett branches. Sure, these two branches of you won’t ever get to compare notes, but does that really mean that on abstract grounds I’m not allowed to be willing to trade half of my amplitude for having the more diverse experience in the other half?
[ETA: By the way, the two simulations are deterministic—your further experiences will be exactly the same on all branches running a given simulation, except in the very small minority of branches where enough cosmic rays hit Omega’s circuits etc. that something goes seriously awry in its innards.]
Actually, after a little more thought, there’s a non-physically-impossible version of this that’s a bit more counterintuitive.
Suppose you’re about to decide what you’ll do with the rest of your life—you have a choice to study the true physical theory of everything, or you have a choice to study the workings of the human mind. You have similar confidence for both that you’ll find success. You calculate that you’ll have slightly higher utility if you do (pick your favorite).
So the question is, do you flip a qubit in order to choose what to do, on the premise that you’d rather “someone out there” study the other thing too?
Doing things this way fixes the fact that Omega is non-quantum-mechanical, so it gives you impossible certainty of the future and current wavefunctions. The fact that this is more counterintuitive suggests a few other approximations we might be making.
I’m pretty sure we agree that since this example is non-observable, evolution isn’t going to select for something like it :P
Yet here we are as a by-product of selecting for other things, apparently. So that’s a reasonable point. You appear to have come up with an intuitive “circularly polarized brain.”
Though that’s not to say I’d take (C) - getting shot half the time is a rather awful trade for someone out there like me knowing something cool.
Thanks for the article, which clarified some stuff for me that I should have been able to put together on my own, but hadn’t!
I’d like to disagree with your conclusion, though, which seems to be that my utility function should necessarily be additive if interference is negligible. (If you’re just saying that this is what evolution is predicted to produce on most branches, I have no quibbles with that.)
Suppose that you wake up in a white room, and Omega appears to you and tells you that it’s simulating you, for one year, after which it will shut down the simulation. You have three options for how this time will be spent. In option (A), Omega will reveal to you the true physical Theory of Everything, and help you understand how it all really works. In option (B), Omega will explain to you in detail the workings of the human mind, and help you understand how subjective experience arises from it. In option (C), Omega will flip two fair quantum coins; if they land (heads,heads), it will run simulation (A), if they land (heads,tails), it will run (B), and if the first coin lands tails, Omega will shut down the simulation immediately.
If Omega also explains that Copenhagen is definitely true, picking (C) would make little sense, since with 50% probability you’d just die, which surely isn’t a reasonable price for not having to choose what simulation you’re going to be in. But if Omega explains that MWI is definitely true, option (C) would mean that you get to learn about both subjects, on distinct Everett branches. Sure, these two branches of you won’t ever get to compare notes, but does that really mean that on abstract grounds I’m not allowed to be willing to trade half of my amplitude for having the more diverse experience in the other half?
[ETA: By the way, the two simulations are deterministic—your further experiences will be exactly the same on all branches running a given simulation, except in the very small minority of branches where enough cosmic rays hit Omega’s circuits etc. that something goes seriously awry in its innards.]
Actually, after a little more thought, there’s a non-physically-impossible version of this that’s a bit more counterintuitive.
Suppose you’re about to decide what you’ll do with the rest of your life—you have a choice to study the true physical theory of everything, or you have a choice to study the workings of the human mind. You have similar confidence for both that you’ll find success. You calculate that you’ll have slightly higher utility if you do (pick your favorite).
So the question is, do you flip a qubit in order to choose what to do, on the premise that you’d rather “someone out there” study the other thing too?
Doing things this way fixes the fact that Omega is non-quantum-mechanical, so it gives you impossible certainty of the future and current wavefunctions. The fact that this is more counterintuitive suggests a few other approximations we might be making.
I’m pretty sure we agree that since this example is non-observable, evolution isn’t going to select for something like it :P
Yet here we are as a by-product of selecting for other things, apparently. So that’s a reasonable point. You appear to have come up with an intuitive “circularly polarized brain.”
Though that’s not to say I’d take (C) - getting shot half the time is a rather awful trade for someone out there like me knowing something cool.
What if Omega is inside a simulation of a Copenhagen universe and was lied to by meta-Omega about it being a MWI metaverse?
Then Omega would have been wrong—and Omega is never wrong!
(Recall that this is a thought experiment...)