Six Degrees: The Science of a Connected Age.

Callingham, Rosemary

Six Degrees: The Science of a Connected Age Duncan J. Watts Published by Vintage (2004) ISBN 0-09-944496-8

Six degrees, as the title implies, addresses that slightly corny idea that everyone on this planet is separated by no more than six people from any other given person. This book, however, does far more than that. It describes, in very readable language, where this idea came from and the development into the science of networks that can be applied to many different situations.

Duncan Watts is an ex-pat Australian now teaching sociology at Colombia University in New York. In the early 1990s he went to Cornell University to undertake postgraduate study and this book, in part, describes the series of events that led to the development of new and exciting applications of mathematics. As with so much research a lucky confluence of people and ideas sparked off thinking that is having a considerable influence on fields as diverse as physics, economics, biology and sociology.

So what is the science of a connected age? Background is provided in the shape of Milgram's 1967 experiment of randomly selected people sending letters to a particular target person that they did not know. The only rule was that each person could only send the letter on to someone that they knew on a first-name basis. Regardless of whether the letter chain originated in the same city as the target or somewhere remote from it, the average number of steps in the letter chain was six: hence 'six degrees of freedom'. The next chapter of the book has a brief description of random graph theory, clearly explained with a minimum of technical language and making good use of appropriate diagrams. From this background, Watts begins to link the ideas to explain what is obviously fiendishly difficult mathematics in a simple, but not simplistic, description of 'small world networks'.

Despite the fact that much of the theory developed from physics, Watts uses social examples. In this way the reader can connect with the mathematics through personal experiences--how many times have you said, 'It's a small world'? Popular phenomena, such as Harry Potter (or the same ideas could be applied more recently to the Da Vinci Code) and the massive failure of the electricity grid in America in 1998 are used to exemplify various points. He explains why Toyota survived an apparently fatal critical failure of parts supply and why New York continued to function more or less normally after the events of 11 September.

Watts is a talented communicator. He has a breezy style and a way of presenting complex ideas that make them very understandable. For those who are interested a detailed bibliography, annotated as beginner, intermediate, advanced and expert, provides the opportunity for follow up. This book would be accessible to good Year 9 and 10 students but is also a good read for those with more advanced mathematical understanding.

Throughout the book Watts makes the point that the ideas he presents need input from experts in many different fields--mathematics is a necessary but not sufficient condition for solving many of the still untouched problems. Maybe we should make books like this required reading for potential mathematics students as a demonstration that mathematics is a living, breathing subject and not the province of dead white males.

Rosemary Callingham