This book looks at first sight like a new member of the genre in which a physicist or mathematician turns their gaze on the comparatively simple world of history, biology, human behaviour or economics, solves all its problems with some simple sums and is home in time for tea. Fred Hoyle on evolution or, more recently, Stephen Wolfram on more or less everything ( THES , June 7) are prime examples.
But Mark Buchanan's work is more interesting than it might appear. Its theme, interconnectedness, is a powerful one with wide ramifications. Buchanan explains via "Six degrees of Kevin Bacon", a game in which the Kevin Bacon Numbers of actors are calculated. Meryl Streep acted with Bacon in The River Wild and so has a Bacon Number of one, as do 1,471 others. An actor who had been in a film with her but not with Bacon would have a number of two, and so on. But hundreds of thousands of actors have a Bacon Number of three or fewer and none in the massive database of movie actors is more than ten degrees of separation from him.
Buchanan explains that this is a powerful observation about the world. With six degrees of separation - people knowing people - you are probably linked to Bacon and to Nelson Mandela or the emperor of Japan.
This insight is replicated in many other types of network, and they all share the curious feature that weak links are more important than strong ones. Your circle of close friends probably does not link to Bacon, but someone in the group probably has a slight acquaintance who is the route into another circle, and so on to Bacon.
Both natural and artificial systems seem to have similar structures, Buchanan argues, and they come in two forms. Some, such as the brain, have an egalitarian system in which all cells link to some others nearby. Others, such as the worldwide web, have a few super-connectors with many, sometimes far-reaching, links. In line with September 11-related US angst, he points out that this means that a tiny number of web nodes are worth protecting heavily, while the system will not suffer if many lesser ones are disabled. The same applies to sexually transmitted disease, where a few overactive types are disproportionately responsible for their propagation. It even works in academic life. Being an active research collaborator leads to more collaboration, he shows, while shrinking violets carry on shrinking.
These are useful insights but, as Buchanan admits, they are a work in progress. Some of the possible applications are vague. There is little genuine insight in his look at fractals, and river-basin formation and its lessons for the study of history. He seems simply to be saying that some things are too complex to predict. His example of trying to predict last year's Bradford riots makes it clear that such events depend on a few key actors, but also invokes a predetermined rioting threshold, from zero for someone who riots for no reason to 100 for an extreme pacifist. This is the sort of reductionism that gives scientists a bad name, and suggests that the model underlying it has no predictive power.
Despite these reservations, Small World is a quick and easy way of reaching into some powerful research, and Buchanan is a capable and pacy writer. It is a pity that the book is carelessly produced. If the same diagram is to be recycled cynically as both figures 6 and 20, it would be better if the caption did not contain the same mistake twice, too.
Martin Ince is deputy editor, The THES .
Small World: Uncovering Nature's Hidden Networks
Author - Mark Buchanan
ISBN - 0 297 60742 1
Publisher - Weidenfeld and Nicolson
Price - £18.99
Pages - 235