I’ve also been thinking about these issues for a while, and I’m glad you’ve taken the plunge and posted up some thoughts. I think one model that might be worth thinking of is that physics (and other fields) have a ‘tournament game’ dynamic, such that one gets significant positional rewards.
So the best physicists have much higher measures of productivity than average physicists not because they are so much smarter, nor because physics happens to be extraordinarily sensitive to differences in physics ability, but because things like publications, patents, fame etc. are strongly positional, and so the very best can get outsize rewards of these things. On this model, if there was never an Einstein (or a Neumann), their discoveries would have been made by others not long after they were actually discovered.
This ‘tournament’ model seems to do very well at things like sport and the arts. The reason Nadal et al. get so much more money and prestige than an average pro is that you might as well watch the very best (instead of the almost-best) play tennis against each other, and all the reward structures in pro tennis are positional rather than objective. You might want to use the same story in the arts, especially (if you buy Taleb) given how modern technology allows the best performers to leverage their output: why listen to a very good pianist in concert when you can have the world best on CD? Etc. Etc.
Ruling against this model for physics and science would be there is some objective measure of achievement in terms of theory, discovery, etc. But I think on the tournament model still makes a good fit: we should think things like discovery and theory generation have significant positional component (all the kudos goes to the first person there, and so the fractionally better physicists can capture outsize rewards by getting to the answer a couple of weeks before their not-quite-so-good fellows).
Perhaps the best evidence I can think of in support of the tournament model would be that you see very similar ‘power law’ dynamics in terms of fame or citation count across many fields across a large span of time: this fits a positional model (and, to be fair, a ‘big difference in human ability’ model), but seems harder to fit on an ‘high sensitivity of productivity to ability’ model, as it would seem odd that across so many different fields, across so much of their development, the ‘sensitivity’ area should remain constantly centered on the right-tail of human ability.
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.
I’ve also been thinking about these issues for a while, and I’m glad you’ve taken the plunge and posted up some thoughts. I think one model that might be worth thinking of is that physics (and other fields) have a ‘tournament game’ dynamic, such that one gets significant positional rewards.
So the best physicists have much higher measures of productivity than average physicists not because they are so much smarter, nor because physics happens to be extraordinarily sensitive to differences in physics ability, but because things like publications, patents, fame etc. are strongly positional, and so the very best can get outsize rewards of these things. On this model, if there was never an Einstein (or a Neumann), their discoveries would have been made by others not long after they were actually discovered.
This ‘tournament’ model seems to do very well at things like sport and the arts. The reason Nadal et al. get so much more money and prestige than an average pro is that you might as well watch the very best (instead of the almost-best) play tennis against each other, and all the reward structures in pro tennis are positional rather than objective. You might want to use the same story in the arts, especially (if you buy Taleb) given how modern technology allows the best performers to leverage their output: why listen to a very good pianist in concert when you can have the world best on CD? Etc. Etc.
Ruling against this model for physics and science would be there is some objective measure of achievement in terms of theory, discovery, etc. But I think on the tournament model still makes a good fit: we should think things like discovery and theory generation have significant positional component (all the kudos goes to the first person there, and so the fractionally better physicists can capture outsize rewards by getting to the answer a couple of weeks before their not-quite-so-good fellows).
Perhaps the best evidence I can think of in support of the tournament model would be that you see very similar ‘power law’ dynamics in terms of fame or citation count across many fields across a large span of time: this fits a positional model (and, to be fair, a ‘big difference in human ability’ model), but seems harder to fit on an ‘high sensitivity of productivity to ability’ model, as it would seem odd that across so many different fields, across so much of their development, the ‘sensitivity’ area should remain constantly centered on the right-tail of human ability.
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.