Introduction

Abstract

To infinity, and beyond!

Buzz Lightyear

Let’s begin with a story. Once upon a time, a king was challenged to a game of chess by a poor scholar. If he lost, the king would have to pay the scholar a chessboard’s worth of grain, defined as one kernel of grain on the first square, two grains on the second square, four grains on the third square, and so on, with each subsequent square receiving double what was on the previous square. The king accepted the wager but lost the game. A chessboard has eight rows and eight columns, so the king had to pay 2⁶⁴–1 grains. (See Section 1.4 for an explanation of the math behind this formula.) Rice is 7,000 grains per pound (~ 65 mg each), so the king owed the scholar 1.199 x 10¹⁵ kg of rice, which is more than 150 tons of rice for every person currently on planet Earth (worth about $40,000 per person). For reference, people eat about 35 tons of food in a lifetime, so this is 4.4 lifetimes’ supply of food for every person on the planet. Clearly, the scholar’s winnings won’t all fit on an ordinary chessboard!