I appreciate the effort of this writeup! I think it helps clarify a bit of my thoughts on the subject.
I was trying to say “maybe it’s simpler, or maybe it’s comparably simple, I dunno, I haven’t thought about it very hard”. I think that’s what Yudkowsky was claiming as well. I believe that Yudkowsky would also endorse the stronger claim that GR is simpler—he talks about that in Einstein’s Arrogance. (It’s fine and normal for someone to make a weaker claim when they also happen to believe a stronger claim.)
So, on thinking about it again, I think it is defensible that GR could be called “simpler”, if you know everything that Einstein did about the laws of physics and experimental evidence at the time. I recall that general relativity is a natural extension of the spacetime curvature introduced with special relativity, which comes mostly from from maxwells equations and the experimental indications of speed of light constancy.
It’s certainly the “simplest explanation that explains the most available data”, following one definition of Ockham’s razor. Einstein was right to deduce that it was correct!
The difference here is that a 3 frame super-AI would not have access to all the laws of physics available to Einstein. It would have access to 3 pictures, consistent with an infinite number of possible laws of physics. Absent the need to unify things like maxwells equations and special relativity, I do find it hard to believe that the field equations would win out on simplicity. (The simplified form you posted gets ugly fast when you try and actually expand out the terms). For example, the Lorentz transformation is strictly more complicated than the Galilean transformation.
Yeah, I’m deliberately not defending the three-frame claim. Maybe that claim is an overstatement, or maybe not, I don’t really care, it doesn’t seem relevant for anything I care about, so I don’t want to spend my time thinking about it. ¯\_(ツ)_/¯
“Eliezer has sometimes made statements that are much stronger than necessary for his larger point, and those statements turn out to be false upon close examination” is something I already generically believe, e.g. see here.
Nitpick: special relativity says the universe is a flat (“pseudo-Euclidean”) Lorentzian manifold—no curvature. Then GR says “OK but what if there is nonzero curvature?”. I agree with your suggestion that GR is much more “natural” in a situation where you already happen to know that there’s strong evidence for SR, than in a situation where you don’t. Sorry if I previously said anything that contradicted that.
I appreciate the effort of this writeup! I think it helps clarify a bit of my thoughts on the subject.
So, on thinking about it again, I think it is defensible that GR could be called “simpler”, if you know everything that Einstein did about the laws of physics and experimental evidence at the time. I recall that general relativity is a natural extension of the spacetime curvature introduced with special relativity, which comes mostly from from maxwells equations and the experimental indications of speed of light constancy.
It’s certainly the “simplest explanation that explains the most available data”, following one definition of Ockham’s razor. Einstein was right to deduce that it was correct!
The difference here is that a 3 frame super-AI would not have access to all the laws of physics available to Einstein. It would have access to 3 pictures, consistent with an infinite number of possible laws of physics. Absent the need to unify things like maxwells equations and special relativity, I do find it hard to believe that the field equations would win out on simplicity. (The simplified form you posted gets ugly fast when you try and actually expand out the terms). For example, the Lorentz transformation is strictly more complicated than the Galilean transformation.
Yeah, I’m deliberately not defending the three-frame claim. Maybe that claim is an overstatement, or maybe not, I don’t really care, it doesn’t seem relevant for anything I care about, so I don’t want to spend my time thinking about it. ¯\_(ツ)_/¯
“Eliezer has sometimes made statements that are much stronger than necessary for his larger point, and those statements turn out to be false upon close examination” is something I already generically believe, e.g. see here.
Nitpick: special relativity says the universe is a flat (“pseudo-Euclidean”) Lorentzian manifold—no curvature. Then GR says “OK but what if there is nonzero curvature?”. I agree with your suggestion that GR is much more “natural” in a situation where you already happen to know that there’s strong evidence for SR, than in a situation where you don’t. Sorry if I previously said anything that contradicted that.