… and yet, Newton and Leibniz are among the most famous, highest-status mathematicians in history. In Leibniz’ case, he’s known almost exclusively for the invention of calculus. So even though Leibniz’ work was very clearly “just leading the parade”, our society has still assigned him very high status for leading that parade.
If I am to live in a society that assigns status at all, I would like it to assign status to people who try to solve the hard and important problems that aren’t obviously going to be solved otherwise. I want people to, on the margin, do the things that seems like it wouldn’t get done otherwise. But it seems plausible that sometimes, when someone tries to do this—and I do mean really tries to do this, and actually put a heroic effort toward solving something new and important, and actually succeeds...
… someone else solves it too, because you weren’t working on something that hard to identify, even if it was very hard to identify in any other sense of the word. Reality doesn’t seem that chaotic and humans that diverse for this to not have been the case a few times (though I don’t have any examples here).
I wouldn’t want those people to not have high status in this world where we’re trying at all to assign high status to things for the right reasons. I think they probably chose the right things to work on, and the fact that there were other people who did as well through no way they could have easily known shouldn’t count against them. Would Shannon’s methodology have been any less meaningful if there were more highly intelligent people with the right mindset in the 20th century? What I want to reward is the approach, the mindset, the actually best reasonable effort to identify counterfactual impact, not the noisier signal. The opposite side of this incentive mechanism is people optimizing too hard for novelty where impact was more obvious. I don’t know if Newton and Leibniz are in this category or not, but I sure feel uncertain about it.
I agree with everything else in this post very strongly, thank you for writing it.
The obvious but mediocre way to assign credit in the Newton-Leibniz case would be to give them each half credit.
The better but complicated version of that would be to estimate how many people would have counterfactually figured out calculus (within some timeframe) and then divide credit by that number. Which would still potentially give a fair bit of credit to Newton and Leibniz, since calculus was very impactful.
That sounds sensible, though admittedly complicated.
This is obviously the correct way to interpret what’s happening.
At some point the per person Shapley value becomes small but I’d guess that the shapely impact of Newton & Leibniz is substantial for quite a long time.
If I am to live in a society that assigns status at all, I would like it to assign status to people who try to solve the hard and important problems that aren’t obviously going to be solved otherwise. I want people to, on the margin, do the things that seems like it wouldn’t get done otherwise. But it seems plausible that sometimes, when someone tries to do this—and I do mean really tries to do this, and actually put a heroic effort toward solving something new and important, and actually succeeds...
… someone else solves it too, because you weren’t working on something that hard to identify, even if it was very hard to identify in any other sense of the word. Reality doesn’t seem that chaotic and humans that diverse for this to not have been the case a few times (though I don’t have any examples here).
I wouldn’t want those people to not have high status in this world where we’re trying at all to assign high status to things for the right reasons. I think they probably chose the right things to work on, and the fact that there were other people who did as well through no way they could have easily known shouldn’t count against them. Would Shannon’s methodology have been any less meaningful if there were more highly intelligent people with the right mindset in the 20th century? What I want to reward is the approach, the mindset, the actually best reasonable effort to identify counterfactual impact, not the noisier signal. The opposite side of this incentive mechanism is people optimizing too hard for novelty where impact was more obvious. I don’t know if Newton and Leibniz are in this category or not, but I sure feel uncertain about it.
I agree with everything else in this post very strongly, thank you for writing it.
The obvious but mediocre way to assign credit in the Newton-Leibniz case would be to give them each half credit.
The better but complicated version of that would be to estimate how many people would have counterfactually figured out calculus (within some timeframe) and then divide credit by that number. Which would still potentially give a fair bit of credit to Newton and Leibniz, since calculus was very impactful.
That sounds sensible, though admittedly complicated.
This is obviously the correct way to interpret what’s happening. At some point the per person Shapley value becomes small but I’d guess that the shapely impact of Newton & Leibniz is substantial for quite a long time.