[HN Gopher] Alan Turing using math to repair his bike
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Alan Turing using math to repair his bike
Author : johndcook
Score : 110 points
Date : 2022-05-23 17:39 UTC (2 days ago)
(HTM) web link (mathmutation.blogspot.com)
(TXT) w3m dump (mathmutation.blogspot.com)
| janandonly wrote:
| I think I read about this incident in the book "Cryptonomicon" by
| Neal Stephenson. It's pure fiction, mind you...
| dredmorbius wrote:
| The book is fiction.
|
| The incidents mentioned in it ... _may_ not be.
| donquichotte wrote:
| 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.
| vcdimension wrote:
| You could make some of the money back from those tools, and
| help others in a similar situation, by renting them out on
| https://fatllama.com (or some other sharing website/app such as
| https://olioex.com/). Sharing & hiring saves money and
| environmental impact.
| dekhn wrote:
| 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.
| [deleted]
| Decabytes wrote:
| I'm always amazed at the genius of people like Turing and their
| ability to apply it in almost any situation they find themselves
| in
| BeniBoy wrote:
| 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.
| fyhn wrote:
| Isn't this only relevant for fixed gear bikes, where you can
| skid the rear wheel to brake, and you want maximize the number
| of possible "skid patches", or orientations of the rear wheel
| while the pedals are in a fixed position?
| analog31 wrote:
| It could also apply to the wear on the chainring and cog if
| their teeth are in a perfect proportion to one another, but
| without thinking too hard about it, I'm guessing that's
| actually rare. For instance a 2:1 ratio would be awkward for
| most cyclists riding on pavement (too low) and 3:1 too high,
| if they had to choose exactly one ratio.
|
| I ride 46:19, because those are the parts that were in my bin
| when I built the bike, and it's a pretty good all-round ratio
| for city riding unless you're a lot more athletic than I am.
|
| Also, those components wear out soon enough anyway -- a chain
| lasts 2 to 3 thousand miles, and a cog lasts a few chains.
| namdnay wrote:
| "I suppose this only applies to single sprocket bike."
| jstanley wrote:
| 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're a bicycle
| engineer trying to make things reliable and long-lasting,
| then there's no downside to making the number of links
| prime if you can arrange it.
|
| I don't know whether bike companies actually _do_ choose
| prime-numbered chains, maybe they have other constraints
| that are more important.
| dmurray wrote:
| > 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).
| 1-more wrote:
| > 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/
| et-al wrote:
| Just to add on:
|
| Track chainrings don't need a narrow-wide profile because
| there's very little slack in the system for the chain to
| come off. Saint Sheldon warns of the possibility of
| losing a finger also for this reason.
| et-al wrote:
| Yeah, chains and cassettes are considered wear items, so
| I doubt manufacturers put much thought into patterned
| wear. Avoiding chain drop and crisp shifting are higher
| priorities.
| jstanley wrote:
| 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
| factors with the number of teeth on either of the pulleys then
| you get the same effect: any given tooth on the belt only ever
| meshes with a small number of teeth on the pulley.
| dredmorbius wrote:
| You've just made me realise that several of the more popular
| freewheel / sprocket combinations are in fact prime: 11, 13,
| 17, 23.
|
| Usually contrasted against the decidedly non-prime 52 (2 * 2
| * 13) and 42 (2 * 3 * 7) chainrings. 38 if you're old-school
| triple (2 * 2 * 7).
|
| My chain lengths would vary and I never counted them
| specifically, though I'd typically remove a few links for
| fit.
| vcdimension wrote:
| 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.
| loeg wrote:
| (The web page hasn't been updated much for a while because
| Sheldon died several years ago.)
| vcdimension wrote:
| It's kept upto date by employees of the bike shop he worked
| for (Harris Cyclery), his widow, and his friend John Harris
| (a nationally recognized bicycle expert). The most recent
| post was about 3 weeks ago: https://sheldonbrown.com/blog/
| geocrasher wrote:
| I am absolutely delighted to see Sheldon Brown's website
| posted on HN! It is an incredible resource.
| loeg wrote:
| Yeah, that's why I qualified it with "much." Trying to
| provide some context for HN readers unfamiliar with
| Sheldon.
| spinaltap wrote:
| dav_Oz wrote:
| 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 the way some
| information was lost and something different added in that
| anectode.
|
| 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.
|
| [0]https://doi.org/10.1038/325386a0 (via paywall --> sci-hub)
| tokai wrote:
| 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.
| isaacfrond wrote:
| jacquesm wrote:
| I can't picture this in a way that it would work, can you
| explain please? How would it hold air?
| moistofreason wrote:
| It wouldn't
| chmod775 wrote:
| > GPT-3 continuation.
|
| It's AI-generated nonsense.
| jacquesm wrote:
| Oh... totally missed that link, wow, that's really bad. It
| pollutes HN with garbage.
| avg_dev wrote:
| > 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. 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.
|
| - https://www.washingtonpost.com/archive/1999/06/09/alan-turin...
| natly wrote:
| Wasn't he a long distance runner. I wonder if he wore it then
| too.
| donthellbanme wrote:
| For years before Covid, I would wear a N95 mask while doing
| yard work, construction, biking, and even night walks.
|
| I got some stares.
|
| For awhile, I felt some of my neighbors thought I was trying to
| conceal my identity; but it was just for allergies.
|
| The last thing I wore it for was germs.
| CrazyStat wrote:
| I've tried wearing an N95 for allergies, but my eyes still
| itch like mad so it's only moderately helpful.
| ravi-delia wrote:
| I thought about commenting you could wear goggles, but
| that's just reinventing the gas mask. Turing was a genius!
| dTal wrote:
| 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.
| ravi-delia wrote:
| 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.
| dTal wrote:
| No, of course people didn't routinely wear them. But every
| citizen was issued one. Children took them to school every
| day, and were drilled in their use.
|
| It's still an eccentric thing to do, of course. But, like
| the alarm clock tied around his waist, it was an instance
| of solving a problem by grabbing something close to hand.
| avg_dev wrote:
| I didn't know about the gas masks being ubiquitous during the
| war; that makes that part a little less surprising. History
| can be sad.
| ihaveajob wrote:
| I bought one at a swap meet in Amsterdam a few years ago.
| They were piled up high and cheap. It made a fun gift for a
| friend back home, but we got really odd looks on the train
| when wearing it :).
| thenthenthen wrote:
| Try Wear a N96 or FFP or surgical mask now in the train
| in NL and people will look at you in the same fashion
| haha
| gmac wrote:
| Ah, careful:
| https://www.nationalasbestos.co.uk/news/wwii-gas-masks-a-
| lif...
| switchbak wrote:
| They were common, but you wouldn't have seen folks wearing
| them around the countryside, certainly not on a bike!
| [deleted]
| matthewmcg wrote:
| 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
| phaedrus wrote:
| 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 wrong and pull one time too
| many, it goes back to high and you have to start over.
|
| Therefore I always pull fan chains eleven (11) times to turn
| them off, so that I don't have to know if it's a three or four
| state fan. (Also works for on-off pull chains.) Pulling the
| chain 59 times would extend this technique to cover five-state
| fans, but I've never encountered one.
| burner556 wrote:
| I just smash my hand in the blades after each pull of the
| chain and eyeball the acceleration when it starts moving
| again. Who's with me?!
| Arrath wrote:
| ...huh. Well, I am going to try this.
| lelandfe wrote:
| 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.
| ravi-delia wrote:
| 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
| idontwantthis wrote:
| Reamde is the only book of his I couldn't get through.
| filoeleven wrote:
| I had just assumed that this was Neal working more necessary
| maths into the book with an amusing anecdote attributed to
| Turing.
|
| Given that this blog post is from this year, I'm going to
| continue to assume as much.
| [deleted]
| bbno4 wrote:
| He used maths*, Alan was British.
| [deleted]
| helloworld11 wrote:
| Cue inevitable Cryptonomicon mentions.... What an amazing book
| though. Stephenson's best.
| rtkwe wrote:
| Huh I always assumed that story was made up when it appeared in
| Cryptonomicon by Neal Stephenson.
| [deleted]
| bordercases wrote:
| crispyambulance wrote:
| That's a charming story. It reminds me of skid-patch calculations
| on fixed gear bikes.
|
| 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.
|
| There's even a calculator for this...
| https://www.bikecalc.com/skid_patch_calculator
|
| If you're over 35, please, just use brakes and keep the track
| bike on the track! (stupid dangerous examples of skidding
| https://www.youtube.com/watch?v=W9xQcMniV84, don't do it).
| zh3 wrote:
| Even if you don't do skiddy tricks (but do a lot of miles)
| knowing the arithmetic leads into all sorts of interesting
| thinking about prime numbers - and, indeed, figuring out
| optimum gears ratios for (personal perference for) particular
| gear inches. Added to which, to minimise chain wear how big can
| we go at the front without hitting the chainstays/still making
| kerb jumps plus we want the number of links in the chain to be
| relatively prime as well.
|
| Agreed re brakes, on a bike having a decent front brake is all
| that matters (irrespective of age)- if stopping quickly, the
| back wheel is generally waving about in the air anyway so
| whether its leg-braked or other makes no difference (except
| fixed riders will still be pedalling, force of habit and all
| that).
| phiiiillll wrote:
| That's funny, I'm 41 and planning on setting up my brakeless
| track bike for the road again this afternoon (changing the
| gearing to 42-17 and switching from drops to a wide riser bar).
| If it goes badly I'll think of your warning.
| sshlocalhost98 wrote:
| 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.
| onos wrote:
| 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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