A passage that I found especially intriguing in Neal Stephenson’s Cryptonomicon, is when Waterhouse and Turning are on a bike ride in the English countryside. In these few complex mathematical pages, we are taught about modular arithmetic, which helps us understand how the Germans used the Enigma machine during the war. The part of this passage that I grasped, is when they are describing modular arithmetic through the cycles of Turning’s bike, which has one bent spoke on the back wheel. Turning knows that when the link and the spoke come in contact with each other, the chain will break and the bike will be useless. However, he figures out a way around this malfunction as it only occurs when the wheel and the chain happen to coincide.
Stephenson incorporates math when he proceeds to introduce variables. He lets l stand for the number of links in the chain, n for the number of spokes, and C for the position of the chain. In order to calculate the value of C, you must do modular arithmetic. Stephenson explains the steps by saying “if the chain has a hundred links (l=100) and the total number of links that have moved by is 135, then the value of C is not 135, but 35” (166). The values of C, each time the wheel spins one full rotation, is n mod l, 2n mod l, etc. Ultimately this tells us that the chain will fall off his bike, when some multiple of n happens to match up with a multiple of l as well. This passage is a clever way to describe modular arithmetic, which we have covered in class.