Knots and Crosses
June 15, 2010 1:32 PM   Subscribe

Sure, knot theory is an interesting subject with a storied past, and self-avoiding walk theory takes it a bit further in describing real-world ropes, lines and wires, but can it be usefully applied to the knotty problem of spontaneously forming tangles? Robert Matthews of Aston University has suggested that there's a simple solution to avoiding tangles in all our computer cables, headphone cords and Vectran cored double braid halyard lines: make them into loops [pdf]. It's plausible, but not proven. Enter The Great British Knot Experiment which aims to provide "compelling empirical evidence to support the Loop Conjecture – and thus for its role in solving one of life's little irritations."

Self-forming knots are more than just an irritation when it comes to the DNA, sailing, climbing and expectant mothers.
posted by HE Amb. T. S. L. DuVal (36 comments total) 19 users marked this as a favorite
 
Btw, "flex" is the British term for insulated wires such as headphone cords.
posted by HE Amb. T. S. L. DuVal at 1:34 PM on June 15, 2010



What about my hair tangles?
posted by notreally at 1:38 PM on June 15, 2010


I'm about to spoil 95% of all knot theory jokes:

[joke setup]

Punchline: "I'm a frayed knot."
posted by kmz at 1:42 PM on June 15, 2010 [3 favorites]


And I'm going to spoil the other 5%:

[joke setup]

Punchline: "Sorry, he's tied up at the moment."
posted by The Winsome Parker Lewis at 1:50 PM on June 15, 2010 [1 favorite]


Notreally, just tie each hair back onto itself to make a loop. That should take care of any tangling problems.
posted by HE Amb. T. S. L. DuVal at 1:50 PM on June 15, 2010


Perhaps looping is an advantage of circular DNA? I'm am not a biologist, though.
posted by Philosopher Dirtbike at 1:51 PM on June 15, 2010


I don't think making a 'loop' out of your tangled thing will work.

if you have a closed loop of something, then stretch it out, you just have a doubled length of whatever you had before. so if you are coiling your tangleable thing, my gut reaction is to say that it would be just as likely to tangle as something that isn't a loop.

I will have to try it.
posted by ArgentCorvid at 1:56 PM on June 15, 2010


Eh. My guess is that in the not-so-distant future, wires will be obsolete anyway.
posted by Lutoslawski at 2:01 PM on June 15, 2010


if you have a closed loop of something, then stretch it out, you just have a doubled length of whatever you had before. have just gone open-loop.

FTFY.
posted by ZenMasterThis at 2:04 PM on June 15, 2010


AgentCorvid, what you've done is halve the length of the cord. From the simple remedy page of the Great British Knot Experiment site.
"One thing we all know about unwanted knots is that the longer a piece of rope is, the more likely it is to end up with a knot in it. In 1988, mathematicians De Witt Sumners and Stu Whittington actually managed to prove this. To do it, they used a branch of mathematics known as self-avoiding walk theory (which, unlike knot theory, is able to cope with knots forming in open-ended lengths of rope). Using this theory, they were even able to find the law governing the probability of a cord remaining knot-free falls as the length increases. Put simply, they found a so-called exponential decay law, according to which

Pr(no knots in cord of length L) exp(-a.L + b)

where a and b are positive constants. This formula highlights the importance of length in determining the risk of a cord acquiring knots. "

But, upon rereading your comment, I think you're talking about making loops out of already tangled lines. This loop conjecture is preventative, not remedial.
posted by HE Amb. T. S. L. DuVal at 2:11 PM on June 15, 2010


Sorry, that expression is supposed to read Pr(no knots in cord of length L) ∝ exp(-a.L + b). They used an image on the GBKE site for the proportionality symbol.
posted by HE Amb. T. S. L. DuVal at 2:15 PM on June 15, 2010


Huh. I had a long CAT5 cable I used for testing connections, and a little cross-over widget made up of two RJ-45 female sockets. I would often keep them together, joined as alarge loop, and then hang that up or throw it in a box.

Since most of the time I notice the free ends would fall through the loops randomly, causing knots, I figured this would lessen that chance.

Weird.
posted by clvrmnky at 2:27 PM on June 15, 2010


This is what happens when mathematicians figure out that they can triple their funding by spending a few days shaking a box full of wires.
posted by kaibutsu at 2:34 PM on June 15, 2010


This old AskMefi question of mine finally gets a scientific answer!
posted by elgilito at 2:46 PM on June 15, 2010 [1 favorite]


The self-avoiding walk thing is a piece of cake for me, but only because I've been stuck in the House of Leaves since 2006. Fuck you, Mr. Monster.

Punchline: "Sorry, he's tied up at the moment."

That's one of those statements that is so cliche that I cannot, for the life of me, imagine someone saying it when the person in question is not restrained in a chair/tangled up in christmas tree lights in a slapstick manner. Of course, as with all minor linguistic complaints, Dinosaur Comics has already covered it.
posted by Uppity Pigeon #2 at 3:09 PM on June 15, 2010


from the pdf:
"A single knot can reduce the breaking strength of climbing rope by up to 50 per cent [23], prompting mountaineers to take great care with the transport and storage of rope."

No. Mountaineers routinely use knots in the climbing rope and other cord. An unexpected knot in the rope can screw up your system, sometimes in a dangerous way but not typically due to the strength reduction.
posted by Manjusri at 3:23 PM on June 15, 2010


HE Amb. T. S. L. DuValPoster: "But, upon rereading your comment, I think you're talking about making loops out of already tangled lines. This loop conjecture is preventative, not remedial."

No, I was saying that if I join the ends of a long piece of string to make a loop, and then coil it, it seems like it would still get tangled up. I hadn't thought of the whole 'you are halving the length' thing.

And 'just as likely' might not have been the best choice of words. I didn't mean 'the probability of getting tangled without joined ends and the probability of getting tangled with joined ends are equal'. I meant something more along the lines of "if I join the ends of a cable, coil it up and put it away, it will still be a tangled mess when I need it again, with my luck".
posted by ArgentCorvid at 3:28 PM on June 15, 2010


"A single knot can reduce the breaking strength of climbing rope by up to 50 per cent [23], prompting mountaineers to take great care with the transport and storage of rope."

No. Mountaineers routinely use knots in the climbing rope and other cord. An unexpected knot in the rope can screw up your system, sometimes in a dangerous way but not typically due to the strength reduction.


Yes and No.

It is true that knots greatly reduce the tensile strength of a given rope. It is also true that modern ropes are many many times stronger than they need to be to support the weight of a climber, making it very unlikely that you will be killed because you tied a knot that compromised the strength of your rope.
posted by nathancaswell at 3:54 PM on June 15, 2010


But if you're rappelling down a rope and come to an unexpected knot, it causes minor or major difficulty, depending on whether you're prepared to change over to ascending the rope. Reaching an unexpected knot when rappelling is very much better than reaching an unexpected end of rope, which is why cavers (should) always tie a knot in the end of a rappel rope.
posted by Kirth Gerson at 4:09 PM on June 15, 2010


Figure of 8 Knot, Double Figure of 8 Knot, Bowline Knot, Fisherman's Knot, Butterfly Knot, Constrictor Knot...

And it used to drive my mother crazy, because she used to say, "Harlan Pepper, if you don't stop naming knots..."
posted by nathancaswell at 4:27 PM on June 15, 2010


Methodology. To investigate the effect of looping on knot formation, we randomly
agitated lengths of standard office parcel string manually for 10 seconds in both the
open-ended and looped states.


Ahh. Science.
posted by Avelwood at 4:40 PM on June 15, 2010


Oh man do I ever spend too much time thinking about this. I wish I could remember where, but I recall reading an article once that talked about how knots were largely an artifact of being embedded in 3-space, not so much that they were hard to construct in higher dimensions, but that they didn't seem to spontaneously form at anything approaching a similar frequency.
posted by Eideteker at 5:12 PM on June 15, 2010


I look forward to reading these. In addition to the examples cited above, knots and tangles are a real problem in the OR and ICU where a patient often has multiple cables for monitors, multiple vascular access lines, oxygen tubing, wires for things like pacemakers and elctrosurgery units and so on. And of course when moving a patient from one place to another they get incredibly tangled; it is easy to take a patient from the ICU to the OR and then spend 45 minutes untangling all of those things and sorting out what tube goes where; if you are not careful it is easy to pull out a line or catheter or interrupt the flow of something imprtant (like drugs or oxygen. The concept reminds me of the game Planarity, which also involves untangling things (link to wikipedia because the game is blocked here at work).

On the other hand, electicians solved this problem with extension cords long ago.
posted by TedW at 6:20 PM on June 15, 2010


The self-avoiding walk thing is a piece of cake for me, but only because I've been stuck in the House of Leaves since 2006. Fuck you, Mr. Monster.

As he traced his path through the pages of the manuscript, rotating, spinning, tunneling through the page, searching for a way out, he thought he could discern a dim shape, monstrous and horned, like the outline of a bovine knot178

178I couldn't find any reference to a bovine knot in the standard treatment of the subject, Knot Enough -- Entanglement Through The Ages by PW Wintermute. Maybe he meant bowline?

Speaking of entanglement, I found myself thoroughly entangled with the limbs of the girl from the video store last night, lost in the labyrinth of her eyes. I hoped to find something, anything in our lust-crazed exertions on her pull-out sofa, but all I found was some loose change and an expired Target gift card. What could it all mean?
posted by empath at 6:31 PM on June 15, 2010 [1 favorite]


TedW: "On the other hand, electicians solved this problem with extension cords long ago."

Which is crocheting. My grandmother showed me what she was actually doing to make all those doilies, and it got kind of awkward when I made the comparison to some guy I saw doing it.
posted by ArgentCorvid at 6:32 PM on June 15, 2010


I think there's something to be said about the fact that we usually loosely coil up a cable, shove it in a box, and then grab one loose end and pull up. It's almost like we're trying to make knots. And when we feel a snag (which may or may not be a knot (especially if we're talking something that's not smooth, like a string of Christmas lights)), we try to "untie" it by backing a loose end up going the other way around some strand, potentially creating a new knot. I think that knot formation here has almost as much to do with how we retrieve the cord as it does with what happens to the cord in the box.

But this kind of research (both the theory and the experiments) is cool too.
posted by ErWenn at 7:06 PM on June 15, 2010


I finally solved my problem of tangled handphone cables in my bag with the help of an article I found online.

I coil them up by wrapping them in a figure eights around my index and pinkie (middle fingers curled down). Odd I never thought of doing that before.
posted by rmmcclay at 8:08 PM on June 15, 2010


The way to avoid tangles is to coil up your cables however you like and then put them in individual ziploc baggies. Then you can put them all in a milk crate or whatever and even after you root through them now and then for years, they don't turn into a terrible mess that makes you cry.

Next question for science: Is it possible to fold fitted sheets?
posted by aubilenon at 11:56 PM on June 15, 2010


TedW: On the other hand, electicians solved this problem with extension cords long ago.
You're right, they did. Step one, form a loop.

rmmcclay, I remember that article, too, which came out when iPods were all the rage. (Oh, the simpler days.) I think I saw it on Lifehacker, and I remember a commenter somewhere saying that there was a whole book dedicated to the proper stowage of ropes and lines. The book covered gigantic mooring lines for cargo ships down to small cords. This was before I really got into sailing, so I didn't pay too much attention. Now I can't seem to find it with all my (not inconsiderable) google-fu.
posted by HE Amb. T. S. L. DuVal at 12:16 AM on June 16, 2010


I couldn't find any reference to a bovine knot in the standard treatment of the subject, Knot Enough -- Entanglement Through The Ages by PW Wintermute. Maybe he meant bowline?

Maybe he meant Cow Hitch.
posted by Kirth Gerson at 4:38 AM on June 16, 2010


Next question for science: Is it possible to fold fitted sheets?

yes
posted by namewithoutwords at 7:03 AM on June 16, 2010


Maybe he meant Cow Hitch

I was just riffing on House of Leaves :)
posted by empath at 8:04 AM on June 16, 2010


TedW: "On the other hand, electicians solved this problem with extension cords long ago."

ArgentCorvid : Which is crocheting. My grandmother showed me what she was actually doing to make all those doilies, and it got kind of awkward when I made the comparison to some guy I saw doing it.

Too funny. I've always called this a "chain knot" and I learned it from my great-grandmother when I was just a little one. I mainly use it for ropes now, because by doubling and quadrupling the line before making the loops, you can store a lot of line in a short space, and deploy it really quickly with little risk of tangling.

It never occurred to me that she probably used it for crocheting and not for dynamic climbing rope storage.
posted by quin at 9:31 AM on June 16, 2010


I use it for static climbing ropes. It's the bee's knees.
posted by Kirth Gerson at 10:06 AM on June 16, 2010


quin: Isn't that a chain sinnet?

For fun I tie Turk's Heads to make bracelets & Scout neckerchief slides, and I tie other sinnets to make really strong dog leashes. Tying knots is an awesome hobby. (See Stormdrane's blog.) But keeping my extra cord organized is easier when it's in separate coils. *shrug* I'm no mathematician, I guess.
posted by wenestvedt at 10:19 AM on June 16, 2010


Sympletic geometry deals with a rather more substancial version of the folding fitted sheets problem aubilenon.
posted by jeffburdges at 9:47 AM on June 25, 2010


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