Newsflash: I have an odd fixation on ’s Cryptonomicon. I already tested one of its theories here:

And now I’m back at it. This time, I targeted a passage in the book, that most of the readers glided over. It includes a bunch of pages of modular arithmetic about a bicycle chain. Yes, I know how it sounds—physics degree and all, I gave up on it too, on my first pass of the book—but it kept pecking on my brain, so I went back, all in.

The premise is simple: Turing (as the dude in Turing test, and who was breaking Nazi codes during WW2 left and right) is riding his bike which, turns out, has one spoke bent and one chain link crooked in just the way that makes the chain fall off now and then when the two culprits align just so with each other.

Trivial enough, yet when you stop to consider what exactly “now and then” means, the realization hits you how much algebra it involves, and even more so when you start pondering its relation to the wartime codebreaking.

So, I went and built an interactive simulation of Turing’s bike:

» Open the demo

The coolest part is how the Turing’s bike analogy (which is a true story by the way) fits into the principles of some of the actual cyphers that were in use by Germans in WW2.

There were no computers back then, so the encryption involved shifting alphabet by a awkward mechanical contraptions.

The famous Enigma worked differently, but there was a machine was actually built like Turing’s bicycle—Lorenz, the teleprinter cipher that carried German High Command traffic. Unlike the bike, it had twelve wheels (!), which made it virtually impossible for the combination to repeat itself, and thus were thought unbreakable.

Funny thing, Bletchley Park cracked it anyway.

Going back to Cryptonomicon, I still wouldn’t call those pages a fun read, but they’re definitely not a filler either.

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Turing’s Bicycle