Right, the point is to throw away certain deals. I am suggesting another approach from the OP.
The OP says: ignore deals involving small numbers. I say: ignore deals that violate physical intuitions (as they are). Where my heuristic differs from the OP is my heuristic is willing to listen to someone trying to sell me the Brooklyn bridge if I think the story fundamentally makes sense to me, given how I think physics ought to work. I am worried about long shot cases not forbidden by physics explicitly (which the OP will ignore if the shot is long enough). My heuristic will fail if humans are missing something important about physics, but I am willing to bet we are not at this point.
In your example, the OP and I will both reject, for different reasons. I because it will violate my intuition and the OP because there is a small number involved.
Relativity seems totally, insanely physically impossible to me. That doesn’t mean that taking a trillion to one bet on the Michelson Morley experiment wouldn’t have been a good idea.
May I recommend Feynman’s lectures then? I am not sure what the point is. Aristotle was a smart guy, but his physics intuition was pretty awful. I think we are in a good enough state now that I am comfortable using physical principles to rule things out.
Arguably quantum mechanics is a better example here than relativity. But I think a lot of what makes QM weird isn’t about physics but about the underlying probability theory being non-standard (similarly to how complex numbers are kinda weird). So, e.g. Bell violations say there is no hidden variable DAG model underlying QM—but hidden variable DAG models are defined on classical probabilities, and amplitudes aren’t classical probabilities. Our intuitive notion of “hidden variable” is somehow tied to classical probability.
It all has to bottom out somewhere—what criteria do you use to rule out solutions? I think physics is in better shape today than basically any other empirical discipline.
Do you know, offhand, if Baysian networks have been extended with complex numbers as probabilities, or (reaching here) if you can do belief propagation by passing around qubits instead of bits? I’m not sure what I mean by either of these thing but I’m throwing keywords out there to see if anything sticks.
I don’t think the consensus of physicists is good enough for you to place that much faith in it. As I understand modern day cosmology, the consensus view holds that universe once grew by a factor of 10^78 for no reason. Would you pass up a 1 penny to $10,000,000,000 bet that cosmologists of the future will believe creating 10^100 happy humans is physically possible?
what criteria do you use to rule out solutions?
I don’t know :-(. Certainly I like physics as a darn good heuristic, but I don’t think I should reject bets with super-exponentially good odd based on my understanding of physics. A few bits of information from an expert would be enough to convince me that I’m wrong about physics, and I don’t think I should reject a bet with a payout better than 1 / the odds I will see those bits.
Right, the point is to throw away certain deals. I am suggesting another approach from the OP.
The OP says: ignore deals involving small numbers. I say: ignore deals that violate physical intuitions (as they are). Where my heuristic differs from the OP is my heuristic is willing to listen to someone trying to sell me the Brooklyn bridge if I think the story fundamentally makes sense to me, given how I think physics ought to work. I am worried about long shot cases not forbidden by physics explicitly (which the OP will ignore if the shot is long enough). My heuristic will fail if humans are missing something important about physics, but I am willing to bet we are not at this point.
In your example, the OP and I will both reject, for different reasons. I because it will violate my intuition and the OP because there is a small number involved.
Relativity seems totally, insanely physically impossible to me. That doesn’t mean that taking a trillion to one bet on the Michelson Morley experiment wouldn’t have been a good idea.
May I recommend Feynman’s lectures then? I am not sure what the point is. Aristotle was a smart guy, but his physics intuition was pretty awful. I think we are in a good enough state now that I am comfortable using physical principles to rule things out.
Arguably quantum mechanics is a better example here than relativity. But I think a lot of what makes QM weird isn’t about physics but about the underlying probability theory being non-standard (similarly to how complex numbers are kinda weird). So, e.g. Bell violations say there is no hidden variable DAG model underlying QM—but hidden variable DAG models are defined on classical probabilities, and amplitudes aren’t classical probabilities. Our intuitive notion of “hidden variable” is somehow tied to classical probability.
It all has to bottom out somewhere—what criteria do you use to rule out solutions? I think physics is in better shape today than basically any other empirical discipline.
Do you know, offhand, if Baysian networks have been extended with complex numbers as probabilities, or (reaching here) if you can do belief propagation by passing around qubits instead of bits? I’m not sure what I mean by either of these thing but I’m throwing keywords out there to see if anything sticks.
Yes they have, but there is no single generalization. I am not even sure what conditioning should mean.
Scott A is a better guy to ask.
I don’t think the consensus of physicists is good enough for you to place that much faith in it. As I understand modern day cosmology, the consensus view holds that universe once grew by a factor of 10^78 for no reason. Would you pass up a 1 penny to $10,000,000,000 bet that cosmologists of the future will believe creating 10^100 happy humans is physically possible?
I don’t know :-(. Certainly I like physics as a darn good heuristic, but I don’t think I should reject bets with super-exponentially good odd based on my understanding of physics. A few bits of information from an expert would be enough to convince me that I’m wrong about physics, and I don’t think I should reject a bet with a payout better than 1 / the odds I will see those bits.