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paper-machine comments on Hack Away at the Edges - Less Wrong
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Comments (54)
While I agree with this statement, the preceding example doesn't support it. I participated in the polymath project, and while it is true that there were anonymous or pseudonymous contributors, the project was mostly sustained by the fame and communal pull of Gowers and Tao. The retelling of the story you chose made it seem like Tao appeared out of the blue, but in fact Tao and Gowers work in the same field and certainly knew each other beforehand.
Therefore I feel it's not impossible to read the polymath project through the lens of Few Great Men.
Most of the probability of victory flowed through Tao and Gowers, but I don't think that most of the math discovery was done by them?
Like, they caused a bunch of people to hack away at the edges, but I don't think that makes it less supporting of the original point.
I don't know how to quantify how much "math discovery" they did relative to the other participants. You can still read through the comments, so if you have some particular metric you're interested in, that will help clarify the issue. The roughest possible estimate would be in terms of numbered items (the de facto unit of polymath development), and it's clear that Gowers has more of these than any one else.
Thanks for that link.
There's another story that compromises between the "Genius" story (which is almost certainly false in general; I can't say whether it's true in this case) and the Bazaar / "everyone and nobody did it" story, which neglects the crucial importantances of people like Tao and Gowers.
How do trade hubs arise? There's a network effect, where if NYSE or Jita is a deep, liquid market, then NYSE or Jita becomes more desirable trade location, and therefore becomes even more liquid. How do we standardize on currencies? There's a network effect, where a dollar or a cowrie is valuable because it is widely accepted in trade, and so becomes more valuable.
However, if there is an initially symmetric situation, then there's a coordination problem of "where will the hub be?". The geometric centrality of Jita or New York (where "geometry" includes things like velocity of travel and political risks) is crucial for them to win the initial struggle with other candidate hubs. The value-density (lightness, ease of transport) fungibility, and difficulty of forging paper money, and perhaps the association with national identity and taxation was crucial for paper money winning out as the standard for trade.
Gowers and Tao's prestige might have acted more as a symmetry-breaker, identifying THIS as the hub that is likely going to eventually be the place to be.
I should clarify that I'm not saying the "Genius" story completely applies here. I disagree with the quote's presentation of the project (particularly the cherry-picking of Jason Dyer; most of the non-anonymous/pseudonymous contributors had some advanced training, as far as I can tell). While I agree with lukeprog's conclusion, I definitely think there are better illustrations of this process in action.
Certainly, but they also substantially contributed to the project as well.
Agree with atucker on the importance of the question. Responding to parent so that paper-machine is alerted.
I think that the thesis of the post relies on Gowers and Tao not bringing most of the mathematical brainpower to the project. paper-machine, since you were involved, can you shed some light on this?
For comparison, subsequent polymath projects have had a hard time coming to completion without the presence of a particularly strong and/or famous central mathematician. (The mini-polymaths were advertised by Tao, IIRC.)
Do you think that Tao or Gowers' mathematical talent was critical for the polymath project that you personally participated in? (Focusing on it because you probably know more about it than other ones.)
Yes.