Chapter 12 Summary and Analysis

Chapter 12 is called "The Sense of Randomness (In a State of Sin)." Much of the chapter discusses the work of Gregory Chaitin, a mathematician who was fascinated with Gödel's proof that all formal logic systems must be incomplete, which Gleick explained in Chapter 6. Chaitin was also familiar with Shannon's work on information theory and his concept of entropy as uncertainty. He proposed that the concept was related to what mathematicians called randomness in numbers.

Random is a word that everyone seems to understand, Gleick writes, but he asks what it truly means. A number may appear to be random to one person, but another might recognize a pattern in it or devise a way that the number could be calculated. Certainly random numbers could not be based on the knowledge of the observer, Chaitin proposed. He defined random numbers as...