This means that there exist an infinite number of Earths like ours that are in a simulation, and an infinite number of Earths like ours that are not in a simulation. Thus it becomes meaningless to ask whether or not we exist in a simulation. We exist in every possible world containing us that is a simulation, and exist in every possible world containing us that is not a simulation.
Just because a set is infinite doesn’t mean it’s meaningless to speak of measures on it.
Just because a set is infinite doesn’t mean it’s meaningless to speak of measures on it.
The infinite cardinality of the set doesn’t preclude the bulk of the measure being attached to a single point of that set. For Solomonof-like reasons, it certainly makes sense to me to attach the bulk of the measure to the “basement reality”
(FWIW I endorse this line of reasoning, and still think 99.5% is reasonable. Bwa ha ha.)
(That is, I also think it makes sense to attach the bulk of the measure to basement reality, but sense happens to be wrong here, and insanity happens to be right. The universe is weird. I continue to frustratingly refuse to provide arguments for this, though.)
(Also, though I and I think most others agree that measure should be assigned via some kind of complexity prior (universal or speed priors are commonly suggested), others like Tegmark are drawn towards a uniform prior. I forget why.)
… others like Tegmark are drawn towards a uniform prior.
I wouldn’t have thought that a uniform prior would even make sense unless the underlying space has a metric (a bounded metric, in fact). Certainly, a Haar measure on a recursively nested space (simulations within simulations) would have to assign the bulk of its measure to the basement. Well, live and learn.
Just because a set is infinite doesn’t mean it’s meaningless to speak of measures on it.
The infinite cardinality of the set doesn’t preclude the bulk of the measure being attached to a single point of that set. For Solomonof-like reasons, it certainly makes sense to me to attach the bulk of the measure to the “basement reality”
(FWIW I endorse this line of reasoning, and still think 99.5% is reasonable. Bwa ha ha.)
(That is, I also think it makes sense to attach the bulk of the measure to basement reality, but sense happens to be wrong here, and insanity happens to be right. The universe is weird. I continue to frustratingly refuse to provide arguments for this, though.)
(Also, though I and I think most others agree that measure should be assigned via some kind of complexity prior (universal or speed priors are commonly suggested), others like Tegmark are drawn towards a uniform prior. I forget why.)
I wouldn’t have thought that a uniform prior would even make sense unless the underlying space has a metric (a bounded metric, in fact). Certainly, a Haar measure on a recursively nested space (simulations within simulations) would have to assign the bulk of its measure to the basement. Well, live and learn.
Yeah, I also don’t understand Tegmark’s reasoning (which might have changed anyway).