Alan Turing using math to repair his bike

Post by dredmorbius » Wed, May 25, 2022, 6:04 PM UTC

jstanley wrote: post #9

BeniBoy wrote: post #6

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.

This is called "hunting tooth". It applies to any system of gears or timing belts. In gears, if you make sure the number of teeth of mating gears is coprime then you wear the teeth of one gear evenly against the other gear. If there are low factors, then each tooth of one gear only engages with a small number of teeth on the other gear, exacerbating wear. With belts, if the number of teeth on the belt shares low fact…

Post by dTal » Wed, May 25, 2022, 6:34 PM UTC

ravi-delia wrote: post #29

dTal wrote: post #11

Earlier quoted context omitted.

I wonder which part of this (admittedly odd fashion statement) seemed surprising to you? Gas masks were of course ubiquitous during the war, so this was probably only about as eccentric as wearing an N95 mask would seem now. And the alarm clock seems like a fairly practical if whimsical hack in an age when chronometers would have been mechanical, and therefore quite expensive.

I feel like the average person absolutely was not wearing a gas mask at all times. Having myself used an N95 in my neverending war on pollen I totally understand though.

Post by burner556 » Wed, May 25, 2022, 9:13 PM UTC

phaedrus wrote: post #53

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

Your mention of modular arithmetic makes me draw a connection between this story and the way I think about ceiling fan pull chains. Suppose the fan is clearly starting on high and you want to turn it off, but you don't know if the order of settings is "high-low-off", or "high-medium-low-off" (three states or four). It's often difficult to tell if the fan is coasting off or just spinning down to low. If you get it wro…

Post by Anthony-G » Wed, May 25, 2022, 11:52 PM UTC

loeg wrote: post #45

vcdimension wrote: post #41

Interestingly the bike repair bible that most of the experts defer to, i.e. https://www.sheldonbrown.com/ 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.

(The web page hasn't been updated much for a while because Sheldon died several years ago.)

Post by jstanley » Fri, May 27, 2022, 9:54 PM UTC

1-more wrote: post #39

jstanley wrote: post #24

Earlier quoted context omitted.

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…