I think it goes without saying that if you can’t derive Newtonian gravity, deriving general relativity is a pipe dream.
The big deciding factor defending general relativity is that the precession of mercury … [and] observation that light that grazes the sun will be deflected by 1.75 arcseconds (about a thousandth of a degree).
This part seems off to me.
F = Gm₁m₂/r² is a prediction of Newtonian gravity, AND
F ≈ Gm₁m₂/r² is a prediction of GR.
In this section of the OP I believe we’re granting for the sake of argument that the superintelligence has observed that (probably) F ≈ Gm₁m₂/r². That observation is equally compatible with Newtonian gravity & GR. It doesn’t provide any evidence for Newtonian gravity over GR, and it likewise doesn’t provide any evidence for GR over Newtonian gravity. You seem to be assuming that Newtonian gravity is the “default”, and GR is not, and you need observational evidence (e.g. perihelion precession) to overcome that default ranking. But that assumption isn’t based on anything. I think that was Eliezer’s point.
From the perspective of a suprintelligence, it seems perfectly plausible to me that GR is simpler / more “natural” than Newtonian gravity, and therefore the “default” inference upon observing F ≈ Gm₁m₂/r² would be GR. Or at least that they’re comparably simple, and therefore both should be kept as viable options pending further observations that distinguish them.
We humans have some intuitive notion that Newtonian gravity is much much simpler than GR, but I think that’s an artifact of our intuitions, pedagogy, non-superintelligent grasp of math, etc. I’m not sure Newtonian gravity beats GR in “number of bits to specify it from first principles”, for example.
Also, I’m not sure if the superintelligence will have hypothesized QFT by this point, but if it has, then GR would a be far more natural hypothesis than Newtonian gravity. (QFT basically requires that weak gravity looks like GR—just assume a spin-2 particle and do a perturbative expansion, right?)
I find it very hard to believe that gen rel is a simpler explanation of “F=GmM/r2” than Newtonian physics is. This is a bolder claim that yudkowsky put forward, you can see from the passage that he thinks newton would win out on this front. I would be genuinely interested if you could find evidence in favour of this claim.
A Newtonian gravity just requires way, way fewer symbols to write out than the Einstein field equations. It’s way easier to compute and does not require assumptions like that spacetime curves.
If you were building a simulation of a falling apple in a room, would you rather implement general relativity or Newtonian physics? Which do you think would require fewer lines of code? Of course, what I’d do is just implement neither: just put in F=mg and call it a day. It’s literally indistinguishable from the other two and gets the job done faster and easier.
This is a bolder claim that yudkowsky put forward, you can see from the passage that he thinks newton would win out on this front.
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.)
If you were building a simulation of a falling apple in a room, would you rather implement general relativity or Newtonian physics?
I think you’re mixing up speed prior with simplicity (Solomonoff) prior. The question “what’s the best way to simulate X” involves speed-prior. The question “how does X actually work in the real world” involves simplicity prior.
For example, if I were building a simulation of a falling apple in a room, I would discretize position (by necessity—I don’t have infinite bits! The unit might be DBL_MIN, for example.). But would that imply “I actually believe that position in the real world is almost definitely discrete, not continuous”? No, obviously not, right? (I might believe that position is discrete for other unrelated reasons, but not “because it makes simulation possible rather than impossible”.)
Which do you think would require fewer lines of code?
“A differential equation that has a unique solution” is one thing, and “Code that numerically solves this differential equation” is a different thing. Lines of code is about the latter, whereas “How simple / elegant / natural are the laws of physics” is about the former.
I claim that this matches how fundamental physicists actually do fundamental physics. For example, people consider QCD to be a very elegant theory, because it is very simple and elegant when written as a differential equation. If you want to write code to numerically solve that differential equation, it’s not only much more complicated, it’s even worse than that: it’s currently unknown to science in the general case. (“Lattice QCD” works in many cases but not always.)
Likewise, writing down the differential equation of GR is much simpler than writing code that numerically solves it. In practice, if I were a superintelligence and I believed GR, I would find it perfectly obvious that Newton’s laws are a good way to simulate GR in the context of objects on earth—just as it’s perfectly obvious to you and me that using floats [which implicitly involves discretizing position] is a good way to simulate a situation where position is actually continuous.
A Newtonian gravity just requires way, way fewer symbols to write out than the Einstein field equations.
I thought the Einstein field equations were Rμν−12Rgμν+Λgμν=κTμν. That doesn’t seem like so many symbols, right?
Remember, we’re supposed to imagine that the superintelligence has spent many lifetimes playing around with the math of Riemannian manifolds (just like every other area of math), such that all of their “natural” constructions and properties would be as second-nature to the superintelligence as Euclidean geometry is to us.
I wonder if you’re implicitly stacking the deck by assuming that flat Euclidean space is self-evident and doesn’t need to be specified with symbols, whereas Riemannian manifolds are not self-evident and you need to spend a bunch of symbols specifying what they are and how they work.
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.
This part seems off to me.
F = Gm₁m₂/r² is a prediction of Newtonian gravity, AND
F ≈ Gm₁m₂/r² is a prediction of GR.
In this section of the OP I believe we’re granting for the sake of argument that the superintelligence has observed that (probably) F ≈ Gm₁m₂/r². That observation is equally compatible with Newtonian gravity & GR. It doesn’t provide any evidence for Newtonian gravity over GR, and it likewise doesn’t provide any evidence for GR over Newtonian gravity. You seem to be assuming that Newtonian gravity is the “default”, and GR is not, and you need observational evidence (e.g. perihelion precession) to overcome that default ranking. But that assumption isn’t based on anything. I think that was Eliezer’s point.
From the perspective of a suprintelligence, it seems perfectly plausible to me that GR is simpler / more “natural” than Newtonian gravity, and therefore the “default” inference upon observing F ≈ Gm₁m₂/r² would be GR. Or at least that they’re comparably simple, and therefore both should be kept as viable options pending further observations that distinguish them.
We humans have some intuitive notion that Newtonian gravity is much much simpler than GR, but I think that’s an artifact of our intuitions, pedagogy, non-superintelligent grasp of math, etc. I’m not sure Newtonian gravity beats GR in “number of bits to specify it from first principles”, for example.
Also, I’m not sure if the superintelligence will have hypothesized QFT by this point, but if it has, then GR would a be far more natural hypothesis than Newtonian gravity. (QFT basically requires that weak gravity looks like GR—just assume a spin-2 particle and do a perturbative expansion, right?)
I find it very hard to believe that gen rel is a simpler explanation of “F=GmM/r2” than Newtonian physics is. This is a bolder claim that yudkowsky put forward, you can see from the passage that he thinks newton would win out on this front. I would be genuinely interested if you could find evidence in favour of this claim.
A Newtonian gravity just requires way, way fewer symbols to write out than the Einstein field equations. It’s way easier to compute and does not require assumptions like that spacetime curves.
If you were building a simulation of a falling apple in a room, would you rather implement general relativity or Newtonian physics? Which do you think would require fewer lines of code? Of course, what I’d do is just implement neither: just put in F=mg and call it a day. It’s literally indistinguishable from the other two and gets the job done faster and easier.
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.)
I think you’re mixing up speed prior with simplicity (Solomonoff) prior. The question “what’s the best way to simulate X” involves speed-prior. The question “how does X actually work in the real world” involves simplicity prior.
For example, if I were building a simulation of a falling apple in a room, I would discretize position (by necessity—I don’t have infinite bits! The unit might be DBL_MIN, for example.). But would that imply “I actually believe that position in the real world is almost definitely discrete, not continuous”? No, obviously not, right? (I might believe that position is discrete for other unrelated reasons, but not “because it makes simulation possible rather than impossible”.)
“A differential equation that has a unique solution” is one thing, and “Code that numerically solves this differential equation” is a different thing. Lines of code is about the latter, whereas “How simple / elegant / natural are the laws of physics” is about the former.
I claim that this matches how fundamental physicists actually do fundamental physics. For example, people consider QCD to be a very elegant theory, because it is very simple and elegant when written as a differential equation. If you want to write code to numerically solve that differential equation, it’s not only much more complicated, it’s even worse than that: it’s currently unknown to science in the general case. (“Lattice QCD” works in many cases but not always.)
Likewise, writing down the differential equation of GR is much simpler than writing code that numerically solves it. In practice, if I were a superintelligence and I believed GR, I would find it perfectly obvious that Newton’s laws are a good way to simulate GR in the context of objects on earth—just as it’s perfectly obvious to you and me that using floats [which implicitly involves discretizing position] is a good way to simulate a situation where position is actually continuous.
I thought the Einstein field equations were Rμν−12Rgμν+Λgμν=κTμν. That doesn’t seem like so many symbols, right?
Remember, we’re supposed to imagine that the superintelligence has spent many lifetimes playing around with the math of Riemannian manifolds (just like every other area of math), such that all of their “natural” constructions and properties would be as second-nature to the superintelligence as Euclidean geometry is to us.
I wonder if you’re implicitly stacking the deck by assuming that flat Euclidean space is self-evident and doesn’t need to be specified with symbols, whereas Riemannian manifolds are not self-evident and you need to spend a bunch of symbols specifying what they are and how they work.
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.