(3) I think it is possible to do better in the real world. In the extreme case, a Bayesian superintelligence could use enormously less sensory information than a human scientist to come to correct conclusions. First time you ever see an apple fall down, you observe the position goes as the square of time, invent calculus, generalize Newton’s Laws… and see that Newton’s Laws involve action at a distance, look for alternative explanations with increased locality, invent relativistic covariance around a hypothetical speed limit, and consider that General Relativity might be worth testing.
Hmm, “real world” and “superintelligence” in the same breath...
The real problem here is more serious- even if one grants such a superintelligence, hypothesis space is extremely large. And it isn’t clear why a superintelligence would immediately want to look for hypotheses that involved increased locality. Moreover, unless one has a lot more data (like say planetary orbits) one can’t even get easy evidence for the idea of an inverse square law for gravitational strength, and that requires very careful observations (to a close approximation all the orbits of major planets are circles. It is only when one has a lot of good data over time that one sees that they are ellipses.) The paragraph and much of the rest of the essay is a combination of failure to appreciate how much information is necessary and a failure to appreciate the incredible size of hypothesis space in a way that seems similar to hindsight bias/ illusion of transparency.
It is only when one has a lot of good data over time that one sees that they are ellipses.
The case of Gauss computing the orbit of Ceres (which I am now surprised to find was not just a case of plug in the data and run least squares over a class of simple orbital models) suggests that intelligence coupled with the determination/capability to work through long chains of computation can substantially reduce the amount of data required for inference.
Gauss made that computation after he already had Newton’s laws and Kepler’s work behind him. He knew that the result had to be very close to an ellipse and that any deviation was going to be from nearby planets, and he knew the rough order of magnitude from that. If he had just had the small amount of data he had, and had no idea what the orbit should look like he wouldn’t have been able to do so.
Hmm, “real world” and “superintelligence” in the same breath...
The real problem here is more serious- even if one grants such a superintelligence, hypothesis space is extremely large. And it isn’t clear why a superintelligence would immediately want to look for hypotheses that involved increased locality. Moreover, unless one has a lot more data (like say planetary orbits) one can’t even get easy evidence for the idea of an inverse square law for gravitational strength, and that requires very careful observations (to a close approximation all the orbits of major planets are circles. It is only when one has a lot of good data over time that one sees that they are ellipses.) The paragraph and much of the rest of the essay is a combination of failure to appreciate how much information is necessary and a failure to appreciate the incredible size of hypothesis space in a way that seems similar to hindsight bias/ illusion of transparency.
The case of Gauss computing the orbit of Ceres (which I am now surprised to find was not just a case of plug in the data and run least squares over a class of simple orbital models) suggests that intelligence coupled with the determination/capability to work through long chains of computation can substantially reduce the amount of data required for inference.
Gauss made that computation after he already had Newton’s laws and Kepler’s work behind him. He knew that the result had to be very close to an ellipse and that any deviation was going to be from nearby planets, and he knew the rough order of magnitude from that. If he had just had the small amount of data he had, and had no idea what the orbit should look like he wouldn’t have been able to do so.