I came here with this exact question, and still don’t have a good answer. I feel confident that Eliezer is well aware that lucky guesses exist, and that Eliezer is attempting to communicate something in this chapter, but I remain baffled as to what.
Is the idea that, given our current knowledge that the theory was, in fact, correct, the most plausible explanation is that Einstein already had lots of evidence that this theory was true?
I understand that theory-space is massive, but I can locate all kinds of theories just by rolling dice or flipping coins to generate random bits. I can see how this ‘random thesis generation method’ still requires X number of bits to reach arbitrary theories, but the information required to reach a theory seems orthogonal to the truth. It feels like a stretch to call coin flips “evidence.” I’m guessing that’s what Robin_Hanson2 means by “lucky draw from the same process”; perhaps there were a few bits selected from observation, and a few others that came from lucky coin flips.
Perhaps a better question would be, given a large array of similar scenarios (someone traveling to look at evidence that will possibly refute a theory), how can I use the insight presented in this chapter to constrain anticipation and attempt to perform better than random in guessing which travelers are likely to see the theory violated, and which travelers are not? Or am i thinking of this the wrong way? I remain genuinely confused here, which i hope is a good sign as far as the search for truth :)
My original reading was ‘there was less arrogance in Einstein’s answer than you might think’. After rereading Eliezer’s text and the other comments again today, I cannot tell how much arrogance (regarding rationality) we should assume. I think it is worthwhile to compare Einstein not only to a strong Bayesian:
On the one hand, I agree that a impressive-but-still-human Bayesian would probably have accumulated sufficient evidence at the point of having the worked-out theory that a single experimental result against the theory is not enough to outweigh the evidence. In this case there is little arrogance (if I assume the absolute confidence in “Then I would feel sorry for the good Lord. The theory is correct.” to be rhetoric and not meant literally.)
On the other hand, a random person saying ‘here is my theory that fundamentally alters the way we have to think of our world’ and dismissing a contradicting experiment would be a prime example of arrogance.
Assuming these two cases to be the endpoints of a spectrum, the question becomes where Einstein was located. With special relativity and other significant contributions to physics already at that point in time, I think it is safe to put Einstein into the top tier of physicists. I assume that he did find a strong theory corresponding to his search criteria. But as biases are hard to handle, especially if they concern one’s own assumptions about fundamental principles about our world, there remains the possibility that Einstein did not optimize for correspondence-to-reality for finding general relativity but a heuristic that diverged along the way of finding the theory.
As Einstein had already come up with special relativity (which is related and turned out correct), I tend towards assuming that his assumptions about fundamental principles were on an impressive level, too.
With all this i think it is warranted to take his theory of general relativity very seriously even before the experiment. But Einstein’s confidence is much stronger than that: it seems that he neglects the possibility that some of his fundamental assumptions might be wrong (his confidence in deriving general relativity from these assumptions seems warranted). This means that either he was (to a degree) mistaken in his confidence or that he was on a hard-to-believe level of rationality regarding the question of general relativity. Einstein actually was right, so it is problematic to claim that he was mistaken in his confidence.
After writing this, my conclusion is that i) evidence-gathering for humans might imply that when detecting a signal (finding the theory of general relativity), it’s likely that we have actually accumulated a large pile of evidence, ii) Einstein does seem surprisingly confident, but (i) implies that this could be warranted and it is problematic to criticise correct predictions
I came here with this exact question, and still don’t have a good answer. I feel confident that Eliezer is well aware that lucky guesses exist, and that Eliezer is attempting to communicate something in this chapter, but I remain baffled as to what.
Is the idea that, given our current knowledge that the theory was, in fact, correct, the most plausible explanation is that Einstein already had lots of evidence that this theory was true?
I understand that theory-space is massive, but I can locate all kinds of theories just by rolling dice or flipping coins to generate random bits. I can see how this ‘random thesis generation method’ still requires X number of bits to reach arbitrary theories, but the information required to reach a theory seems orthogonal to the truth. It feels like a stretch to call coin flips “evidence.” I’m guessing that’s what Robin_Hanson2 means by “lucky draw from the same process”; perhaps there were a few bits selected from observation, and a few others that came from lucky coin flips.
Perhaps a better question would be, given a large array of similar scenarios (someone traveling to look at evidence that will possibly refute a theory), how can I use the insight presented in this chapter to constrain anticipation and attempt to perform better than random in guessing which travelers are likely to see the theory violated, and which travelers are not? Or am i thinking of this the wrong way? I remain genuinely confused here, which i hope is a good sign as far as the search for truth :)
My original reading was ‘there was less arrogance in Einstein’s answer than you might think’. After rereading Eliezer’s text and the other comments again today, I cannot tell how much arrogance (regarding rationality) we should assume. I think it is worthwhile to compare Einstein not only to a strong Bayesian:
On the one hand, I agree that a impressive-but-still-human Bayesian would probably have accumulated sufficient evidence at the point of having the worked-out theory that a single experimental result against the theory is not enough to outweigh the evidence. In this case there is little arrogance (if I assume the absolute confidence in “Then I would feel sorry for the good Lord. The theory is correct.” to be rhetoric and not meant literally.)
On the other hand, a random person saying ‘here is my theory that fundamentally alters the way we have to think of our world’ and dismissing a contradicting experiment would be a prime example of arrogance.
Assuming these two cases to be the endpoints of a spectrum, the question becomes where Einstein was located. With special relativity and other significant contributions to physics already at that point in time, I think it is safe to put Einstein into the top tier of physicists. I assume that he did find a strong theory corresponding to his search criteria. But as biases are hard to handle, especially if they concern one’s own assumptions about fundamental principles about our world, there remains the possibility that Einstein did not optimize for correspondence-to-reality for finding general relativity but a heuristic that diverged along the way of finding the theory.
As Einstein had already come up with special relativity (which is related and turned out correct), I tend towards assuming that his assumptions about fundamental principles were on an impressive level, too.
With all this i think it is warranted to take his theory of general relativity very seriously even before the experiment. But Einstein’s confidence is much stronger than that: it seems that he neglects the possibility that some of his fundamental assumptions might be wrong (his confidence in deriving general relativity from these assumptions seems warranted). This means that either he was (to a degree) mistaken in his confidence or that he was on a hard-to-believe level of rationality regarding the question of general relativity. Einstein actually was right, so it is problematic to claim that he was mistaken in his confidence.
After writing this, my conclusion is that i) evidence-gathering for humans might imply that when detecting a signal (finding the theory of general relativity), it’s likely that we have actually accumulated a large pile of evidence, ii) Einstein does seem surprisingly confident, but (i) implies that this could be warranted and it is problematic to criticise correct predictions