With the arrival of summer weather in many parts of the U.S., it’s time to think again about various outdoor activities. Watching a few bicycles pass by my house the other day brought to mind a famous anecdote about pioneering mathematician and computer scientist Alan Turing. As you may recall, Turing was the famous British thinker who not only founded theoretical computer science, but also was the primarily visionary in the project to crack the German Enigma code, a key contribution to the Allied victory in World War II. As often happens with such geniuses, his personal life was very odd, though he usually had reasons for whatever he did. For example, he was mocked as ridiculously paranoid for chaining his favorite coffee mug to a radiator. But there are rumors that years later, a pile of smashed coffee mugs was found near his old office, apparently thrown away by a disgruntled co-worker. Another crazy story involves Turing’s efforts to repair his bicycle.
As the story goes, Turing noticed that every once in a while, the chain on his bike would come loose, and he would have to stop and kick it a certain way to get it back on its track again. After a while, he noticed that the intervals at which this was happening seemed kind of regular, so decided to check that theory rigorously. He attached a mechanical counter, and started measuring the exact interval at which this problem was occurring. It turned out he was right— the intervals were regular. The number of clicks between failures was proportional to the product of the number of spokes in his wheel, the number of links in the chain, and the cogs in the bicycle gears. Once he discovered that, he took a close look at the components, and soon discovered the root cause: there was a particular spoke that was slightly bent, and when this got too close to a particular link in the chain that was also damaged, the chain would be pulled off. Armed with this knowledge, he was able to correctly fix the bent spoke and resolve the problem. It’s been said that any competent bike repairman would have spotted the issue in a few minutes without bothering with counters and intervals, but the mathematics of that would be pretty boring.
Naturally, as with any anecdote about someone famous, there are some alternate versions of this story. My favorite is the one that changes the ending slightly: once Turing figured out the formula for when the chain would jump off, he started carefully calculating the intervals as he rode the bike, and stopping to kick it at the exact right times he calculated. That’s a fun one, and certainly fits into the stereotypes of Turing’s eccentricity. But I do find it a bit hard to believe. When riding a bike outdoors, there are lots of variables involved to interrupt your concentration: road obstacles, changing inclines, approaching cars, etc. Could someone safely riding a bicycle successfully keep a running count of the wheel and chain rotations, over a continuous ride of several miles? And in Turing’s case, it was further complicated by the fact that he always wore a gas mask as he rode, to prevent triggering his allergies. But the alarm clock he was known to wear around his waist might have helped.
In honor of this story, there was actually a proposal back in 2015 to name a bicycle bridge in Cambridge, England after Turing. I didn’t see any further references to this online, so it looks like it didn’t pass. But there’s plenty of non-bicycle-related stuff named after him in the computer science world. If you want someone to propose a bicycle bridge in your name, next time your bike breaks down, think about the clever mathematical tricks you might use to diagnose the issue. Also, remember to found a branch of mathematics and win a world war. Or forget about the bridge, and just take your bike to a competent repair shop.
And this has been your math mutation for today.