Another book has caught my eye, *Complex Adaptive Systems: An Introduction to Computational Models of Social Life; *John H. Miller and Scott E. Page (2007). * *Oh, yes, another of those books that attempts to introduce people who remember a little math to what people who construct mathematical models are up to. This one seems pretty good.

The writing is readable and the attitude pleasantly modest. The authors write, for example,

Suppose we want to construct a model of a standing ovation. There is no set method or means by which to do so. To model such a phenomenon we could employ a variety of mathematical, computational, or even literary devices. The actual choice of modeling approach depends on our whims, needs, and even social pressure emanating from professional fields. (2007:11)

A standing ovation? Why a standing ovation? Turns out to be a good first example for introducing what modeling is about. First, everyone knows what we’re talking about. At the end of a performance, the applause begins. Some people rise to their feet. Others may join them. Then others may join as well….Or they may not. Sometimes only a few people stand. Sometimes everyone stands. Often there is a ripple effect, with wave after wave of people joining in. Seen from this perspective, a standing ovation is a good starter model for thinking about all sorts of things, social movements, political campaigns, lynch mobs, or epidemics, for instance. But how do you construct the model?

The authors lead us through a series of steps that show how rapidly complexities enter in.

Let N be the number of people in the audience and q the quality of the performance. Assume that each member of the audience responds to a signal defined as Si(q). The strength of the signal can vary, reflecting different personal estimates of q. To work that in, add a random variable e and define, Si(q) = q+e. Finally, assume that there is a threshold T, such that if Si (q)>T the individual rises. We now have a simple prediction. The number of people who join in is simply the number of people for whom Si(q)>T.

Notice, however, that this model fails to account for things like new waves of people joining in once the first people who stand have done so. Now we start thinking about things like the effects of people sitting in different places; those who sit in the front are seen by everybody but can’t see anyone behind them. Or the fact that people often come to concerts in couples or groups of friends or may know other people in the audience; if one member of a set stands up, will the others follow suit? What are the spatial distributions of individuals, groups and lines of sight that will make members of an audience more or less likely to join the standing ovation?

Practical applications? The authors suggest a number of possibilities:

Do performances that attract more groups lead to more ovations? How does changing the design of the theater by, say, adding balconies, influence ovations? If you want to start an ovation, where should you place your shills? If people are seated based on the preferences for the performance, say left or right of the aisle or more expensive seats up front, do you see different patterns of ovations?

Turns out to be difficult to write a simple formula like the one we started with. We need to look at simulations involve interacting agents, for which computer modeling works better than conventional assumption, theorem and proof mathematics. How does that work?

(To be continued)