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Alan Turing using math to repair his bike

mathmutation.blogspot.com

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Re: Alan Turing using math to repair his bike

#31

Post by ravi-delia »

lelandfe wrote: post #26
matthewmcg wrote: post #3

This anecdote is memorably presented as an application of modular arithmetic (along with the behavior of Enigma machine rotors) in Neal Stephenson’s Cryptonomicon . See the discussion in this review of the book: https://www.ams.org/notices/199911/rev-kasman.pdf

I have a love/hate relationship with his writing – he adores going off on tangents, and action often gets put on pause while he savors them (REAMDE has several long paragraphs of a character pulling themselves onto a boat, admiring the hull, praising the usefulness of the tires lashed to it, etc). But it also introduces me to so many lovely things in the process. That moment in Cryptonomicon was quite cool.

It's funny, I almost feel the opposite. I love the little weird tangents, but something about the expository bits never squared with me. Not sure why

Re: Alan Turing using math to repair his bike

#32

Post by [deleted] »

avg_dev wrote: post #2

> 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. What? Is that for real? Edit: It is! > 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. Goo…

[deleted]

Re: Alan Turing using math to repair his bike

#33

Post by dmurray »

jstanley wrote: post #24
namdnay wrote: post #22

Earlier quoted context omitted.

"I suppose this only applies to single sprocket bike."

It applies to any bike. Ideally the number of links in the chain would be coprime to the number of teeth on every sprocket. The easiest way to achieve this is to make the number of links in the chain prime. It'll still work just fine if you ignore this idea, but it might wear out more quickly. If you're a hobbyist just trying to make something work, you can safely ignore it and do whatever is most convenient. If you'…

> It applies to any bike

On a bike with derailleur gears, every time you change gears the derailleur will add some slippage so you won't get this effect.

> The easiest way to achieve this is to make the number of links in the chain prime

The chainring is fixed, but you might need to add or remove a link in the chain. In practice it seems more common to make the chainring have a prime number of teeth (53 or 47).

Re: Alan Turing using math to repair his bike

#34

Post by donquichotte »

I guess if you have a hammer, everything looks like a nail, even if you are Alan Turing!

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.

Re: Alan Turing using math to repair his bike

#35

Post by tokai »

dav_Oz wrote: post #23

From occasionally repairing modern 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…

Bikes back then weren't much different. Some from that time are still around and are not technically anything special. I don't buy the story. It might be what he told himself, but what fixed it was just the maintenance in general. Probs moved the wheel and tightened the chain. In any case if the bump of a crocked wheel could throw his chain, it was waaaay to loose.

Re: Alan Turing using math to repair his bike

#36

Post by jacquesm »

chmod775 wrote: post #17
jacquesm wrote: post #12

Earlier quoted context omitted.

I can't picture this in a way that it would work, can you explain please? How would it hold air?

> GPT-3 continuation. It's AI-generated nonsense.

Oh... totally missed that link, wow, that's really bad. It pollutes HN with garbage.

Re: Alan Turing using math to repair his bike

#37

Post by dekhn »

donquichotte wrote: post #34

I guess if you have a hammer, everything looks like a nail, even if you are Alan Turing! 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 slight…

When I was a kid, I had a similar noise (and resistance to turning). I took apart my bike with whatever tools I had and at some point found the ball bearings. Took them out, wiped off "all the dirty grease" and put them back in and tightened it all up. Needless to say, it got worse. It was a good lesson, though- only take apart your spare bike, and bring the prod bike to a real mechanic until you know what you're doing.

Re: Alan Turing using math to repair his bike

#38

Post by bordercases »

This reminds me of when I unstuck a drawer using thermodynamics.

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 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.

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!

I shook the drawer vigorously.

It came unstuck.

Physics!

Re: Alan Turing using math to repair his bike

#39

Post by 1-more »

jstanley wrote: post #24
namdnay wrote: post #22

Earlier quoted context omitted.

"I suppose this only applies to single sprocket bike."

It applies to any bike. Ideally the number of links in the chain would be coprime to the number of teeth on every sprocket. The easiest way to achieve this is to make the number of links in the chain prime. It'll still work just fine if you ignore this idea, but it might wear out more quickly. If you're a hobbyist just trying to make something work, you can safely ignore it and do whatever is most convenient. If you'…

> then there's no downside to making the number of links prime if you can arrange it.

Bike chains always have to have an even number of links because they come in inner and outer pairs. But this has an effect on chainrings as well. When the tooth on a chainring or sprocket is in between two inner plates it's in a narrow gap. When the tooth is in between outer plates that's a wide gap. If you have a chainring with an even number of teeth then you can have the teeth match the narrow and wide profiles (called a narrow-wide chainring) which is supposed to make it less likely that you drop your chain off the chainrings. I'm not sure if it works, tbh. It seems to only be a thing in mountain or gravel bikes with a single chainring. I can't find any track chainrings that have the profile but I only looked for a second.

For chains themselves there's usually a pretty narrow number of links that work on a road drivetrain. I think I can live with one fewer or more pair of links on mine.

https://www.firstcomponents.com/narrow-wide-chainring/

Re: Alan Turing using math to repair his bike

#40

Post by onos »

sshlocalhost98 wrote: post #5

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.

I enjoyed the story too. I noticed in another on the blog a mention of a book of selections from the blog, and plan to buy a copy.

https://www.amazon.com/Math-Mutation-Classics-Interesting-Ma...

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