If there’s X Boltzmann brains, each of them takes log2(X) bits to specify, which carries a 1/X probability penalty, that is exactly cancelled by the large number of brains. So you just never get the overwhelming confidence in Boltzmann that presents a problem.
Conceptually, the simplest algorithm for predicting your experiences is not going to be “simulate a world of Boltzmann brains, and choose BB number 198573859385 …..” because then all of the ordered experiences you are having need to be encoded into that selection, and you lose the ordering simplicity.
On reflection, I get it. Boltzmann brains as a class probably do have longer description length conditional on our physics than non-Boltzmann brains. I can specify an Earth-brain cheaply just by naming its spacetime position, because earth is close to the low-entropy initial conditions of the universe and so my index can be small. A Boltzmann brain is extremely far away from the low-entropy initial conditions of the universe, so singling it out will require a very large index, with the bit count growing larger for every bit of coherent perception the Boltzmann brain experiences. And that is all we need for Boltzmann brains to be negligible in the SI posterior, no matter how many of them there are.
As you said, this same argument works to dismiss many other schemes that try to embed huge numbers of minds within our physics using high-complexity bridging rules, and then turn around and go “since there are so many of these weird minds, we ought to suppose we are likely one of them.” E.g. dust theory, or a lot of variants of the simulation hypothesis. The SI posterior assigns most of these lower probability than the ’naive’ explanation that we live in baseline physics, just because the bridging rules for living in a simulation within a physics or a random dust cloud interpreted as a mind within a physics are longer.
In the case of simulation hypotheses, you have to specify the bridging rule to find the simulation within baseline physics and then specify the bridging rule to find the mind within the simulation on top of that.[1]
In the case of dust theory, you have to specify the interpretation rule that makes a dust cloud count as a mind, and the dust cloud address, and the actual physics. This one gets beaten up especially badly, losing out in the SI posterior not just to normal minds living within baseline physics, but even to the dust-cloud-as-mind interpretation rule on its own without any actual dust cloud or physics for the rule to be embedded in.
This also makes me feel less confused about living early in the universe. It also defuses the doomsday argument.
Whole piles of sketchy anthropic reasoning dealt with.
This doesn’t necessarily work to dismiss simulation hypotheses that suppose the simulators live at a simpler address than ours within a simpler physics than ours.
Re footnote, if you have a simple simulator you still need to specify all of our physics, so it’s going to end up more complicated than other models unless the simulator theory actually explains complex parts of our observations simply. Even if it does you can probably get those same explanatory algorithms more simply without a simulation. E.g. if the simulation cares about observers, you can find a simpler algorithm that cares about observers directly without simulation overhead.
Agree that the simulator theory actually needs to compress our observed bits. I don’t think you can always get the same explanatory algorithms more simply without a simulation though. As an extreme case, if the simulators make contact and demonstrate control over the simulation to us, you’re probably not getting a shorter explanatory algorithm that doesn’t involve a simulation. There could also be more subtle signs, like our physics in particular proving to be the sort of thing you’d expect to be simulated at a particular short address in a particular physics that’s notably simpler than ours.
Well sure. If you get something that’s Bayesian evidence of a simulation, then Solomonoff as a formalization of Bayes should then upweight simulations.
I don’t see how our physics could be simpler to simulate in a way that isn’t just even simpler to compute directly, though.
If there’s X Boltzmann brains, each of them takes log2(X) bits to specify, which carries a 1/X probability penalty, that is exactly cancelled by the large number of brains. So you just never get the overwhelming confidence in Boltzmann that presents a problem.
Conceptually, the simplest algorithm for predicting your experiences is not going to be “simulate a world of Boltzmann brains, and choose BB number 198573859385 …..” because then all of the ordered experiences you are having need to be encoded into that selection, and you lose the ordering simplicity.
On reflection, I get it. Boltzmann brains as a class probably do have longer description length conditional on our physics than non-Boltzmann brains. I can specify an Earth-brain cheaply just by naming its spacetime position, because earth is close to the low-entropy initial conditions of the universe and so my index can be small. A Boltzmann brain is extremely far away from the low-entropy initial conditions of the universe, so singling it out will require a very large index, with the bit count growing larger for every bit of coherent perception the Boltzmann brain experiences. And that is all we need for Boltzmann brains to be negligible in the SI posterior, no matter how many of them there are.
As you said, this same argument works to dismiss many other schemes that try to embed huge numbers of minds within our physics using high-complexity bridging rules, and then turn around and go “since there are so many of these weird minds, we ought to suppose we are likely one of them.” E.g. dust theory, or a lot of variants of the simulation hypothesis. The SI posterior assigns most of these lower probability than the ’naive’ explanation that we live in baseline physics, just because the bridging rules for living in a simulation within a physics or a random dust cloud interpreted as a mind within a physics are longer.
In the case of simulation hypotheses, you have to specify the bridging rule to find the simulation within baseline physics and then specify the bridging rule to find the mind within the simulation on top of that.[1]
In the case of dust theory, you have to specify the interpretation rule that makes a dust cloud count as a mind, and the dust cloud address, and the actual physics. This one gets beaten up especially badly, losing out in the SI posterior not just to normal minds living within baseline physics, but even to the dust-cloud-as-mind interpretation rule on its own without any actual dust cloud or physics for the rule to be embedded in.
This also makes me feel less confused about living early in the universe. It also defuses the doomsday argument.
Whole piles of sketchy anthropic reasoning dealt with.
This doesn’t necessarily work to dismiss simulation hypotheses that suppose the simulators live at a simpler address than ours within a simpler physics than ours.
Re footnote, if you have a simple simulator you still need to specify all of our physics, so it’s going to end up more complicated than other models unless the simulator theory actually explains complex parts of our observations simply. Even if it does you can probably get those same explanatory algorithms more simply without a simulation. E.g. if the simulation cares about observers, you can find a simpler algorithm that cares about observers directly without simulation overhead.
Agree that the simulator theory actually needs to compress our observed bits. I don’t think you can always get the same explanatory algorithms more simply without a simulation though. As an extreme case, if the simulators make contact and demonstrate control over the simulation to us, you’re probably not getting a shorter explanatory algorithm that doesn’t involve a simulation. There could also be more subtle signs, like our physics in particular proving to be the sort of thing you’d expect to be simulated at a particular short address in a particular physics that’s notably simpler than ours.
Well sure. If you get something that’s Bayesian evidence of a simulation, then Solomonoff as a formalization of Bayes should then upweight simulations.
I don’t see how our physics could be simpler to simulate in a way that isn’t just even simpler to compute directly, though.