Critical Mass: How One Thing Leads to Another
A review by Doug Brown
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.