Critical Mass: How One Thing Leads to Another

Once upon a time, people used to believe if you studied the components of a system, you could explain everything about it. If you studied atoms, you could explain everything about complex molecules; if you studied complex molecules you could understand cells; if you studied cells you could understand organisms; if you studied how individual organisms behaved you could understand populations. Then quantum mechanics came along and started revealing cracks in such reductionist approaches, and complexity further opened the cracks into gaping holes. Large systems often behave in ways that are not predictable from their components; nothing about the shape of a water molecule predicts thunderclouds. Likewise, applications from statistical physics to social sciences have suggested that the study of large numbers can often model the behavior of markets and social systems better than the study of human nature. This is the primary topic of Critical Mass.

Philip Ball's background is in chemistry and physics, but he has always written about broader topics in prose that assumes his readers are intelligent, but may have different educational backgrounds. His book The Self-Made Tapestry: Pattern Formation in Nature is a must-read for anyone who thinks that title sounds remotely interesting. It is one of the best books on complexity out there, devoid of the beyond-the-data-set generalization that chaos evangelists sometimes indulge in. In Critical Mass he covers some of the same ground, to provide readers with a background on how the study of large systems has increased our understanding of the world in the last century. However, he avoids duplication, so if you have already read Self-Made Tapestry those sections will be more refresher than repetition.

Critical Mass starts off with a brief history of social theory, followed by a history of the philosophy of matter. Then the study of large numbers -- a.k.a. statistics -- is introduced, and complexity in natural systems. The stage thus set and tools provided, Ball sets forth into applying these lessons to systems involving large numbers of people. Rush hour traffic, pedestrian footpaths, shapes of cities, stock markets, multi-national alliances, political systems, the internet, and Six Degrees of Kevin Bacon are all discussed. Ball is always clear on the separation between mathematical models and reality; just because a computer program behaves in ways similar to a natural system does not ergo mean nature uses the same rules. However, we can often draw qualified inferences from such similarities. Similarities between critical points in phase transitions of matter at different densities (e.g., from liquid to gas) and critical points in transitions between patterns of pedestrian traffic at different densities can aid urban planners and architects.

One of the biggest inferences to be drawn in the application of mathematics to markets is that, like most complex systems, they just aren't predictable. Many people mistakenly believe the only reason meteorologists can't tell whether it will be raining in my backyard at noon on Saturday is that our weather models aren't good enough yet. Actually, they are. Or more specifically, they are good enough to tell us we will never be able to predict weather at that level of granularity; there are too many probable outcomes, and no way to tell in advance which way the system will go, except in broad terms. Financial markets also function in non-predictive fashion, despite the best efforts of millions of people to try to prove this wrong. We can come up with mathematical models that behave similarly to stock indexes, but these models are by their nature non-deterministic. Thus market crashes and bubble-bursts will always catch even the "experts" off guard. Ball mentions a model that seemed to have predicted a couple of crashes (after the fact, of course) and was predicting a burst in the UK housing market bubble in late 2003 (Ball finished writing in October 2003). The burst never came, so the success rate of market prediction models holds steady at 0%.

The application of complexity to social systems and economics is hardly a new phenomenon; folks like Brian Arthur at the Santa Fe Institute have been at it for over twenty years. However, the behavior of crowds seems to have recently become a hot subject. What Malcolm Gladwell calls "the Tipping Point" in his acclaimed book is what physicists and complexity folk call a critical point; a point at which a system quickly adopts a new configuration. I regretfully cannot recommend James Surowiecki's The Wisdom of Crowds. Surowiecki repeatedly conflates lucky guesses with knowledge, and seems to miss the point that markets are unpredictable in his desire to show ordinary folk do just as well in commodities trading as experts. As Ball much better demonstrates, the reason experts don't do better than anyone else is that knowing a lot about markets doesn't make you any better able to predict what they will do. Market players who have made a few lucky guesses and thus think they are experts are, as Nissim Taleb phrased it in the title of his intriguing book, "fooled by randomness." Critical Mass provides a solid overview of the behavior of large systems in general, with particular emphasis on human affairs. Folks who were intrigued by The Tipping Point and want to delve further into the subject of critical points and the behavior of large groups will find this a good starting place. Critical Mass just won Britain's 2005 Aventis Prize for popular science books, so the word is out.

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