This anecdote is memorably presented as an application of modular arithmetic (along with the behavior of Enigma machine rotors) in Neal Stephenson’s <i>Cryptonomicon</i>. See the discussion in this review of the book: <a href="https://www.ams.org/notices/199911/rev-kasman.pdf" rel="nofollow">https://www.ams.org/notices/199911/rev-kasman.pdf</a>
Interestingly the bike repair bible that most of the experts defer to, i.e. <a href="https://www.sheldonbrown.com/" rel="nofollow">https://www.sheldonbrown.com/</a> is written by a man who claims he was strongly influenced by the writings of Bertrand Russell, and he is married to a mathematician and has two children who are both mathematicians.
The webpage contains several simple maths formulas for calculating things such as gear ratios.
From occasionally repairing <i>modern</i> bicycles the way the chain is falling off "regularly" doesn't click with me: If one spoke is bent so much (more like a serious wheel wobble) that - at some point - it touches a "damaged" chain link; this is quite a spectacular failure.
I have to assume back then those bicycles were built quite differently that something like that could happen in such a predicatble fashion. Or along the way some information was lost and something different added in that anectode.<p>Curious to see other versions I have quickly traced back the ancetode to a Nature article "Are mathematician logical" (1987) by Ian Stewart[0]; the version/wording unfortunately here is quite the same.<p>[0]<a href="https://doi.org/10.1038/325386a0" rel="nofollow">https://doi.org/10.1038/325386a0</a> (via paywall --> sci-hub)
That's a charming story. It reminds me of skid-patch calculations on fixed gear bikes.<p>If you have ride a brakeless track bike and "stop" or slowdown the bike by skidding, there's certain gear ratios that you'll want to avoid. Basically, in skidding, you unweight the rear wheel by moving your body forward and lock the position of your cranks. The rear wheel will then skid and you can end up with a flat spot of wear on your tire (assuming your don't face-plant yourself when you do it wrong). The fewer the number of skid patches for your gear-ratio, the more rapid the wear-down on the tire will be.<p>There's even a calculator for this... <a href="https://www.bikecalc.com/skid_patch_calculator" rel="nofollow">https://www.bikecalc.com/skid_patch_calculator</a><p>If you're over 35, please, just use brakes and keep the track bike on the track! (stupid dangerous examples of skidding <a href="https://www.youtube.com/watch?v=W9xQcMniV84" rel="nofollow">https://www.youtube.com/watch?v=W9xQcMniV84</a>, don't do it).
> 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.<p>What? Is that for real?<p>Edit: It is!<p>> He loved to ride his bicycle through the countryside. To time himself, he would simply tie an alarm clock around his waist. During the war, according to I.J. Good, a Cambridge mathematician, Turing suffered horribly from hay fever during the first week of June every year. So to keep the pollen off while riding, he wore a military gas mask.<p>- <a href="https://www.washingtonpost.com/archive/1999/06/09/alan-turing/3640bb61-b23d-41df-9f39-d00a6b2e30cc/" rel="nofollow">https://www.washingtonpost.com/archive/1999/06/09/alan-turin...</a>
I guess if you have a hammer, everything looks like a nail, even if you are Alan Turing!<p>Tangentially related, I have recently become aware of a sound similar to a bag of potato chips being crushed coming from the rear wheel of my mountain bike. Closer inspection showed that the rear wheel hub exhibited an unwanted additional degree of freedom with respect to the rest of the wheel. The hub was able to be moved slightly back and forth radially. "An excuse to get my hands dirty, and an easy fix", I thought foolishly -- it is only mechanics, after all, nothing that will not surrender immediately to the agile mind and nimble hands of a computer programmer! Fast forward 300$ in tools of and 4 weeks of attempts to fix this, which typically resulted in the purchase of a new specialized tool, and the bike runs again. I learned more than I had hoped about the vast number of very small metal balls that reside in a modern freewheel hub, and it was a good lecture in humility.
Kind of reminded me of the traditional wisdom that you should select chains and sprocket to avoid patterned wear. I don't know if there is an effect (especially with bikes and their low torque),but I always think about it when changing my chain. I suppose this only applies to single sprocket bike.
Thanks for the fun story. I began appreciating mathematics and sincerely loving it due to the biographies of mathematicians like Sir Isaac Newton in Veritasium channel.
This reminds me of when I unstuck a drawer using thermodynamics.<p>The drawer was getting locked after I pulled it out X or so inches, where Y is the full length the drawer can come out and X < Y.<p>I thought, "this is an implicit restriction on the degrees of freedom the drawer should have". Then I thought, well, if this system has fewer degrees of freedom than it should have, then I need to add degrees of freedom to it so that it may come unstuck.<p>How to add degrees of freedom? Well, I could attempt to add entropy to the system, so that becoming unstuck could asymptotically become a part of its configuration space, and it may come free!<p>I shook the drawer vigorously.<p>It came unstuck.<p>Physics!