Hm, let’s see if I understand you correctly. I don’t see the difference between our positions on Nadal and art, etc. What I mean by “productive”, in Nadal’s case, is that simply that many people wants to watch his games. Hence when he plays and his games are broadcast, lots of preferences are satisfied.
Your idea about science is interesting, though. What you’re saying is that one can’t just look at the number of discoveries that, for instance, von Neumman did, but also at what would have happened if he hadn’t made them. Say that von Neumann had tragically died when he was just a child prodigy; what would then have happened to science? Counterfactuals (“what would have happened if x never had happened?”) are important for causal explanations (“y happened because of x”).
This question is hard to answer, but given that von Neumann made so many discoveries in so many areas, it seems to me unlikely that science wouldn’t have proceeded slower in the possible world where he had died as a child.
Anyway, let’s assume for the sake of the argument that science really didn’t proceed slower in that possible world. Now the next question is: who does all the discoveries that von Neumann did in the actual world in this possible world? If it’s a guy as smart as von Neumann, then it seems your argument doesn’t defeat my thesis (that beyond a certain level of ability, productivity increases massively). If it’s a guy who’s not as smart as von Neumann then that would be a problem for my thesis—but it seems to me unlikely that that would have happened.
It might be that the phenomenon you’re pointing to means that productivity-as-a-function-of-ability curve is a bit less steep than it seems (though I’m not sure of it), but it seems to me unlikely that it could make it entirely linear.
Your last argument is interesting. Can you give me a link on the similar dynamics across fields?
Anyway, let’s assume for the sake of the argument that science really didn’t proceed slower in that possible world. Now the next question is: who does all the discoveries that von Neumann did in the actual world in this possible world? If it’s a guy as smart as von Neumann, then it seems your argument doesn’t defeat my thesis (that beyond a certain level of ability, productivity increases massively). If it’s a guy who’s not as smart as von Neumann then that would be a problem for my thesis—but it seems to me unlikely that that would have happened.
What if it’s several guys rather than “a guy”? Then it is possible that each one of them is not as smart as von Neumann and each one makes fewer discoveries than him, but all together they make all of his discoveries.
Hm, let’s see if I understand you correctly. I don’t see the difference between our positions on Nadal and art, etc. What I mean by “productive”, in Nadal’s case, is that simply that many people wants to watch his games. Hence when he plays and his games are broadcast, lots of preferences are satisfied.
Your idea about science is interesting, though. What you’re saying is that one can’t just look at the number of discoveries that, for instance, von Neumman did, but also at what would have happened if he hadn’t made them. Say that von Neumann had tragically died when he was just a child prodigy; what would then have happened to science? Counterfactuals (“what would have happened if x never had happened?”) are important for causal explanations (“y happened because of x”).
This question is hard to answer, but given that von Neumann made so many discoveries in so many areas, it seems to me unlikely that science wouldn’t have proceeded slower in the possible world where he had died as a child.
Anyway, let’s assume for the sake of the argument that science really didn’t proceed slower in that possible world. Now the next question is: who does all the discoveries that von Neumann did in the actual world in this possible world? If it’s a guy as smart as von Neumann, then it seems your argument doesn’t defeat my thesis (that beyond a certain level of ability, productivity increases massively). If it’s a guy who’s not as smart as von Neumann then that would be a problem for my thesis—but it seems to me unlikely that that would have happened.
It might be that the phenomenon you’re pointing to means that productivity-as-a-function-of-ability curve is a bit less steep than it seems (though I’m not sure of it), but it seems to me unlikely that it could make it entirely linear.
Your last argument is interesting. Can you give me a link on the similar dynamics across fields?
What if it’s several guys rather than “a guy”? Then it is possible that each one of them is not as smart as von Neumann and each one makes fewer discoveries than him, but all together they make all of his discoveries.