INTRODUCTION

Eratosthenes used geometry to solve a physical problem, measuring the circumference of the Earth. This chapter will deal with a different branch of mathematics, probability theory, and some very different problems, measuring the extent to which a social network is connected and measuring properties of conscious and unconscious memory. These two problems are different from each other, and very different from the geographic problem that Eratosthenes tackled. All three problems apply mathematics in the same way.

Probability theory deals with the likelihood that an event might happen. The notion of a probabilistic event is familiar to all of us, though perhaps not in those terms. For example, each autumn the Centers for Disease Control (CDC) urges Americans to receive an influenza vaccination. There is no claim that the vaccine will prevent you from getting the flu, nor is there any claim that you will, for sure, get the flu if you don't get the shot. The argument is that the probability that you will get influenza will be reduced if you receive the vaccine, compared to what it would be if you don't become vaccinated.

Examples like this are so familiar that they seem trite. Indeed, probabilistic reasoning is so common in our world that elementary courses in probability are part of the middle school mathematics curriculum. The first part of almost every introductory course in statistics contains a brief discussion of probability.