I don’t think you should give a large penalty to inverse square compared to other functions. It’s pretty natural once you understand that reality has three dimensions.
The conclusion seems pretty reasonable, assuming that the alternate hypotheses are simpler. This is not obvious to me—Eliezer claims the K complexity of the laws of physics is only ~500 bits. I’m not sure whether Newtonian physics is simpler than relativity once you include the information about electromagnetism contained in the apple.
If you have the apple’s spectrum, the problem seems much easier. Once you’ve located the hypothesis that the droplets are water and the apple contains water (I think not out of reach since water is such a simple molecule), you can probably confirm it.
I think astronomy and astrophysics might give intuitions for what superintelligences can do with limited data. We can do parallax, detect exoplanets through slight periodic dimming of stars or Doppler effect, estimate stellar composition through spectroscopy, guess at the climate and weather patterns of exoplanets using Hadley cells. But we don’t yet know the locations of particular islands on exoplanets (chaotic) or aesthetic tastes of aliens (extremely complicated to simulate, maybe also chaotic). The hypotheses are easy for humans to locate compared to physics, since we have better intuitions about configurations of objects than equations, and I do expect the superintelligence to have really good intuitions for equations.
I don’t think you should give a large penalty to inverse square compared to other functions. It’s pretty natural once you understand that reality has three dimensions.
This is a fair point. 1/r2 would definitely be in the “worth considering” category. However, where is the evidence that the gravitational force is varying with distance at all? This is certainly impossible to observe in three frames.
the information about electromagnetism contained in the apple
if you have the apple’s spectrum
What information? What spectrum? The color information received by the webcam is the total intensity of light when passed through a red filter, the total intensity when passed through a blue filter, and the total intensity when passed through a green filter, at each point. You do not know the frequency of these filters (or that frequency of light is even a thing). I’m sure you could deduce something by playing around with relative intensities and chromatic aberration, but ultimately you cannot build a spectrum with three points.
I think astronomy and astrophysics might give intuitions for what superintelligences can do with limited data. We can do parallax, detect exoplanets through slight periodic dimming of stars or Doppler effect, estimate stellar composition through spectroscopy, guess at the climate and weather patterns of exoplanets using Hadley cells.
It depends on what you mean by limited data. All of these observations rely on the extensive body of knowledge and extensive experimentation we have done on earth to figure out the laws of physics that is shared between earth and these outer worlds.
What information? What spectrum? The color information received by the webcam is the total intensity of light when passed through a red filter, the total intensity when passed through a blue filter, and the total intensity when passed through a green filter, at each point. You do not know the frequency of these filters (or that frequency of light is even a thing). I’m sure you could deduce something by playing around with relative intensities and chromatic aberration, but ultimately you cannot build a spectrum with three points.
I don’t think we disagree here. Getting a spectrum from an RGB image seems tough and so the problem of deriving physics from an RGB image alone seems substantially harder than if you’re provided an RGB image + spectrograph.
Indeed! Deriving physics requires a number of different experiments specialized to the discovery of each component. I could see how a spectrograph plus an analysis of the bending of light could get you a guess that light is quantised via the ultraviolet catastrophe, although i’m doubtful this is the only way to get the equation describing the black body curve. I think you’d need more information like the energy transitions of atoms or maxwells equations to get all the way to quantum mechanics proper though. I don’t think this would get you to gravity either, as quantum physics and general relativity are famously incompatible on a fundamental level.
Some thoughts:
I don’t think you should give a large penalty to inverse square compared to other functions. It’s pretty natural once you understand that reality has three dimensions.
The conclusion seems pretty reasonable, assuming that the alternate hypotheses are simpler. This is not obvious to me—Eliezer claims the K complexity of the laws of physics is only ~500 bits. I’m not sure whether Newtonian physics is simpler than relativity once you include the information about electromagnetism contained in the apple.
If you have the apple’s spectrum, the problem seems much easier. Once you’ve located the hypothesis that the droplets are water and the apple contains water (I think not out of reach since water is such a simple molecule), you can probably confirm it.
I think astronomy and astrophysics might give intuitions for what superintelligences can do with limited data. We can do parallax, detect exoplanets through slight periodic dimming of stars or Doppler effect, estimate stellar composition through spectroscopy, guess at the climate and weather patterns of exoplanets using Hadley cells. But we don’t yet know the locations of particular islands on exoplanets (chaotic) or aesthetic tastes of aliens (extremely complicated to simulate, maybe also chaotic). The hypotheses are easy for humans to locate compared to physics, since we have better intuitions about configurations of objects than equations, and I do expect the superintelligence to have really good intuitions for equations.
This is a fair point. 1/r2 would definitely be in the “worth considering” category. However, where is the evidence that the gravitational force is varying with distance at all? This is certainly impossible to observe in three frames.
What information? What spectrum? The color information received by the webcam is the total intensity of light when passed through a red filter, the total intensity when passed through a blue filter, and the total intensity when passed through a green filter, at each point. You do not know the frequency of these filters (or that frequency of light is even a thing). I’m sure you could deduce something by playing around with relative intensities and chromatic aberration, but ultimately you cannot build a spectrum with three points.
It depends on what you mean by limited data. All of these observations rely on the extensive body of knowledge and extensive experimentation we have done on earth to figure out the laws of physics that is shared between earth and these outer worlds.
I don’t think we disagree here. Getting a spectrum from an RGB image seems tough and so the problem of deriving physics from an RGB image alone seems substantially harder than if you’re provided an RGB image + spectrograph.
Indeed! Deriving physics requires a number of different experiments specialized to the discovery of each component. I could see how a spectrograph plus an analysis of the bending of light could get you a guess that light is quantised via the ultraviolet catastrophe, although i’m doubtful this is the only way to get the equation describing the black body curve. I think you’d need more information like the energy transitions of atoms or maxwells equations to get all the way to quantum mechanics proper though. I don’t think this would get you to gravity either, as quantum physics and general relativity are famously incompatible on a fundamental level.