I may have misunderstood, sorry. I thought you gave it near 100% certainty that there could be only 3 ways, not the more reasonable “my knowledge of this problem is so marginal, I can’t give it a good estimate of probability, since it would be drowned in error bars”.
would you agree that people trying to solve a problem over some time only to find that all the plausible approaches they could come up with seem quite difficult is useful evidence for that problem being intrinsically difficult?
Certainly it’s an indicator, especially if a group of smart people who have been able to successfully solve a number of related problems get stumped by something that appears to be in the same reference class. In my area it was the attempts to quantize gravity some time in the 50s and 60s, after successes with electromagnetism and weak interactions. After all, gravity is the weakest of them all. No one expected that there would be very little progress, half a century later, despite the signs being there.
I am not sure what “intrinsically difficult” means. My best guess is that it requires a Kuhnian paradigm change. Though sometimes it’s not enough, and there are also the issues of just having to grind through a lot of calculations, like with the Fermat’s last theorem, and the Poincaré conjecture. Special relativity, on the other hand, only required a “paradigm shift”, the underlying math is trivial.
It might be interesting to consider this argument from an outside view perspective. Can you give a sample of arguments that you think is comparable to this one so we can check how valid they tend to be in retrospect?
One off-hand example that springs to mind is the Landau pole, inevitable and unavoidable in gauge theories. That resulted in the whole approach having been rejected in the Soviet Union for years, yet the the development of the renormalization formalism made QED the most precise physical theory, while still being mathematically inconsistent to this day. I strongly suspect that similarly adequate progress in AI alignment, for example, can be made without resolving all the mathematical, philosophical or meta-philosophical difficulties. The scenario 5 hints at something like that.
I may have misunderstood, sorry. I thought you gave it near 100% certainty that there could be only 3 ways, not the more reasonable “my knowledge of this problem is so marginal, I can’t give it a good estimate of probability, since it would be drowned in error bars”.
Certainly it’s an indicator, especially if a group of smart people who have been able to successfully solve a number of related problems get stumped by something that appears to be in the same reference class. In my area it was the attempts to quantize gravity some time in the 50s and 60s, after successes with electromagnetism and weak interactions. After all, gravity is the weakest of them all. No one expected that there would be very little progress, half a century later, despite the signs being there.
I am not sure what “intrinsically difficult” means. My best guess is that it requires a Kuhnian paradigm change. Though sometimes it’s not enough, and there are also the issues of just having to grind through a lot of calculations, like with the Fermat’s last theorem, and the Poincaré conjecture. Special relativity, on the other hand, only required a “paradigm shift”, the underlying math is trivial.
One off-hand example that springs to mind is the Landau pole, inevitable and unavoidable in gauge theories. That resulted in the whole approach having been rejected in the Soviet Union for years, yet the the development of the renormalization formalism made QED the most precise physical theory, while still being mathematically inconsistent to this day. I strongly suspect that similarly adequate progress in AI alignment, for example, can be made without resolving all the mathematical, philosophical or meta-philosophical difficulties. The scenario 5 hints at something like that.