[not to be confused with thoughts about random networks]
Cosma Shalizi has a nice takedown of Stephen Wolfram's A New Kind of Science, somewhat late for a book that came out in 2002. Back then, I leafed through it casually and my impression was that it was a mixture of self-aggrandizement and old ideas. Now Cosma knows much more about this stuff then I and has actually read the book, and come to much the same conclusion, so two points for my intuition.
Since everything I think these days gets mapped to network theory, the major lesson I draw from this (not very original) is that science is a network of people and ideas, and if you operate outside of that network you are very likely a crank. Wolfram's egomania led him to pull out of the standard networks of scientific exchange and build his own little cult empire. By draining energy from real science, his book is an anti-contribution.
Speaking of science as a network, I recently stumbled upon an issue of PNAS devoted to Mapping Knowledge Domains. Cool stuff, but why isn't there a tool to do this as part of Google Scholar or something? Ok, here is something called HistCite, developed by Eugene Garfield who has been doing this sort of stuff for decades, but it is proprietary and looks kind of ugly to use. Good data though. Really, it's time for Google to take over and conquer this lucrative market. [[update here]]
Hm, Cosma also proposes applying social network analysis to the study of government cronyism, something I was vaguely thinking about myself. As he says, a difficult project to fund.
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