Suddenly it has become a fad to read or write a science best seller that are essentially about quantitative modeling, although they cross many disciplines such as marketing research, economics, finance, sociology, and political sciences. Blink, The Tipping Point,Freaknomics, Wisdom of Crowds…they have been churned out one after another and are catching fire among readers. Scientists have been using statistics, probability modeling and data mining techniques in a wide range of applications for decades (if not for centuries). Why does it only appeal to a broader readership until now? Since American education is especially poor in developing mathematics skill for its students, the current trend may help reignite some interest among a maths-fearing general public, especially when real problems that seemingly have nothing to do with mathematics can eventually solved by maths.
Critical Mass, a new book by acclaimed British science writer Philip Ball, went further than his American peels and presented actual maths models instead of sheer anecdotes. Ball has a doctor degree in Physics and this inevitably lured him to write in more rigor and abstraction. Ball’s essential interest lies in the human society modeled as a self-regulating system that consists of “a statistical melée of many individuals doing their own idiosyncratic thing”. Starting from here he quoted freely from statistics physics, chaos, evolutionary game theory, network, and stochastic models in economics and finance, while real examples are manifested through models used to explain traffic jams, flocking birds, bacterial colonies, urban growth, market crash, and, in one of the most fascinating chapters, the six degree of separations in social network. Underlying the large spectrum of these unrelated phenomena, there is one common thread: The mass of smaller individuals are to interact and evolve and change the collective nature of the system under the influence of both internal and external forces. This is exactly what the applied mathematics is about, the ability to model and predict the system behavior. Applied mathematics has become both a broader and narrower field as more branches get developed and grown out. My own field, operations research, is essentially one small branch, but nowadays more or less stands at its own.
It is easy to deviate to too many other topics as Ball undertook such an ambitious subject. Nevertheless he primarily focused on the human society and various topics in political science or political philosophy since he recognized that as the most significant. After all, peace and war and social engineering have the most impact on all of us. If any of the maths can be used to prevent war and positively construct a more civil society, that would be the most important science of all. But as the God is still rolling the dice, maths does not seem to lead to one final utopian solution. The system will continue to oscillate, just as the invisible hand of capitalism that may help regulate the market but can't stop the economic downturns or polarization, and nobody can predict where the human society will end up with. That is one of the most important reason why life is worth living -- the unknown destinations!
