Book Review: Small Worlds, Volume 47, Number 8

The phenomenon that any person is only six handshakes, or “six degrees of separation”, away from any other person on the planet is the essential feature of the “small worlds” referred to in the title of this book. The term “small worlds” also provides an apt self-referential metaphor for this book, which shows the way many diverse areas of research— from graph theory to epidemiology to coupled oscillators—have some surprising connections. Almost everyone has had the experience of finding that he or she shares a mutual acquaintance with a total stranger. This casual observation was put to the test by Stanley Milgram in the late 1960s at Harvard University [7]. He conducted an experiment in which he asked a random group of people in Kansas and Nebraska to send letters to a particular individual whom they did not know in Boston, Massachusetts. Each person was instructed to send the letters to a person whom they knew on a first name basis and who they felt might have a greater chance of knowing the intended recipient. The new letterholder was then asked to continue the chain. Amazingly enough, some letters actually reached the person in Boston, and the median chain length was six. Milgram coined the term “six degrees of separation”, and the concept has permeated the popular consciousness ever since. Six Degrees of Separation is the title of a play by John Guare and a subsequent film adaptation. In the parlor game “Six Degrees of Kevin Bacon” participants are given the name of a movie actor and must link that actor to Kevin Bacon through mutual appearances in films. In the lounges of academia, how many mathematicians have not made some attempt to compute their “Erdős number”, the number of connections through coauthorship to Paul Erdős? As of January 2000, 507 privileged people have an Erdős number of one [4].