- Maynard Smith and Szathmary, The Major Transitions in Evolution
http://smg.media.mit.edu/papers.html
As for more traditional sociology research, see:
It is...perhaps...a thing that falls under the rubric of "socialogical phenomena", but that doesn't really regard the science as such. It's just it's self-declared field of study. The science itself could have never existed and people would have still made webpages of various types.
Again, I don't think I need to point out that mathematics are a necessary condition (10,000 times over) for "web 2.0" to even exist.
I think it's more helpful to consider whether mathematics is at the core of most web 2.0 services or whether it is somewhat removed (e.g., part of an encryption library used by the service, part of building a computer, etc.).
(Not quite there, yet. But trying.)
I found it interesting, because it's the first time I internalized that ambiguity prevents long chains of arguments, because fuzziness is multiplicative (so to say). As a corollary, if social behavior was not ambiguous, sociology would be potentially just as deep as physics.
The quote actually has very little to do with the rest of the book. It was merely a prelude to their discussion on the evolution of societies, which is one of the Major Transitions.
The last remark is cool too, "it may be that no operative theories are possible in the social sciences", because it applies to biology as well. We do have some operative theories on evolution, but there's absolutely no guarantee that every phenomena has a simple holistic explanation. As far as I'm concerned, we still don't have a proof that evolution (Darwin's axiom) could lead to complex structures. We just have a lot of very convincing hand-waving.
That aside, the nature of the "soft sciences" is that you can't very well conduct controlled experiments, because it is unethical, or it is hard to control all the variables. So current soft sciences plod about trying to gather some type of predictablity in their theories, but often falling back to trying to make causal statements of their experimental observations.
I think there's been attempts before, like cybernetics, that tries to model human behavior using signal processing techniques. To my understanding, it's since fallen out of favor. So while it's been tried before--and I don't know for sure, but my gut says that there probably is mathematics, other than statistics, to bring more analysis into the social sciences.
Otherwise, the math just hasn't been invented yet. Currently there are studies in nonlinear systems, complex systems, and math of intervation and manipulation. My shallowly informed guess is that one of these will help out.
Or else we just have to wait for a Physicist to help us out here.
i have no reservations, however, declaring that by and large undergraduate sociology education is bullshit.
The issue goes even deeper. You could argue that the above argument is a semantic trick, because modeling is outside the realm of maths as a science. But even the formal foundations are in doubt if you consider Goedels incompleteness theorems (http://en.wikipedia.org/wiki/GAXdel%27s_incompleteness_theor...)
Sorry, the link is broken. Apparently this forum doesn't support umlauts in URLs
Second, Godel's incompleteness theorem is about incompleteness, not ambiguity. The statement x = y + 10 is unambiguous in the sense that all mathematicians would always interpret it in exactly the same way. There is no question that x = 12, y = 2 is consistent with that statement, and x=y is not.
Also, I like to look at sociology as the study of complex systems - extremely complex systems. It is difficult to study systems over which you do not have complete experimental control, however it is possible to view history as a series of experiments.