Slashdot Mirror
How and Why Knots Spontaneously Form
palegray.net writes "Scientists believe they have found the underlying reasons why knots are so common in the universe. This research helps us understand how knotty arrangements in various molecules lead to biological patterns, as in certain proteins. The article also provides a look at the field of topology, and how it relates to knots."
But can they explain why knots form in your hair after laying still for as little as an hour? My wife blames gnomes, and I'm inclined to agree with her.
End of lesson. You may press the button.
I thought this might be about the jungle under my desk.
and I thought it was just me...
TFA revealed some interesting physics.
MSBPodcast.com The opinions expressed here are my own. If you don't like 'em... Think up your own stuff.
http://www.sciencenews.org.nyud.net:8090/articles/20071222/bob11.asp
Tied Up in Knots
Anything that can tangle up, will, including DNA
Davide Castelvecchi
Knotted threads secure buttons to shirts. Knots in ropes attach boats to piers. You can find knots in shoestrings, ties, ribbons, and bows. But even without Boy Scouts or sailors, knots would be everywhere.
Call it Murphy's Law of knots: If something can get tangled up, it will. "Anything that's long and flexible seems to somehow end up knotted," says Andrew Belmonte, an applied mathematician at Pennsylvania State University in University Park. Belmonte has plenty of alarming anecdotal evidence. "It certainly happens in my house, with the cords of the venetian blind." But the knot scourge is a global one, as anyone who owns a desktop computer can confirm after peeking at the mess of connection cables and power cords behind the desk.
Now, scientists think they may have found out how and why things find their way into knotty arrangements. By tumbling a string of rope inside a box, biophysicists Dorian Raymer and Douglas Smith have discovered that knots--even complex knots--form surprisingly fast and often. The string first coils up, and then its free ends swivel around the other coils, tracing a random path among them. That essentially makes the coils into a braid, producing knots, the scientists say.
The results' relevance may go well beyond explaining the epidemic of tangled venetian blind cords. That's because spontaneous knots seem to be prevalent in nature, especially in biological molecules. For example, knottiness may be crucial to the workings of certain proteins (see "Knots in Proteins"). And knots can randomly form in DNA, hampering duplication or gene expression--so much so that living cells deploy special knot-chopping enzymes.
Raymer's interest in knots began as an answer waiting for a question. Two years ago, he was an undergraduate student working in Smith's lab at the University of California, San Diego (UCSD). Raymer fancied taking a class about the abstract theory of knots, offered by UCSD's math department. Smith told him that he should take it only if he could find a practical use for it--some kind of knot experiment.
Raymer never took the class, but he and Smith did come up with a simple idea for an experiment. They put a string in a cubic container the size of a box of tissue. By tumbling the box 10 times "like a laundry dryer," as Raymer puts it, the researchers hoped to observe knots forming spontaneously on occasion. They didn't have to wait for long: Knots formed right away. "The first couple of times, it was pretty amazing," Raymer says.
The researchers repeated the procedure more than 3,000 times, and knots formed about every other time. Longer strings, or more-flexible strings, tended to knot more often.
The researchers took pictures, planning to gather precise statistics of the types of knots that were forming. Raymer soon realized that, to make sense of the mess, he'd need to teach himself the mathematics of knots after all.
Ready-made tools
The theory of knots began in earnest in the 1860s, under the stimulus of the British physicist William Thomson, later known as Lord Kelvin. Kelvin suggested that atoms of different elements were really different kinds of knotted vortices in the ether. So to lay the foundations of chemistry, he believed, it was imperative to classify knots. Ultimately, physicists discovered that the ether didn't exist. But mathematicians took an interest in knots for knots' sake, as part of the young branch of mathematics called topology.
Topology studies shapes. Specifically, it studies shapes' properties that are not affected by stretching, moving, twisting, or pulling--anything that doesn't break up the object or fuse some of its parts. The proverbial example is that, to a topologist, a coffee mug is the same as a doughnut. In your imagination,
Any tip about packing christmas lights?
I wonder if this will explain why the cord on my phone, mouse and headphones always gets tangled up ...
This research helps us understand how knotty arrangements in various molecules lead to biological patterns, as in certain proteins.
Because He reached out his noodly appendage and put the spark of life in our universe.
"And the earth was without form, and void; and straightness was upon the face of the pan. And His Noodly Appendage moved upon the face of the sauce.
And FSM said, Let there be knots: and there were knots.
And FSM saw the knots, that they were good: and FSM divided the knots from the straightness as happens when you boil short and long pasta at the same time.
And FSM called the knots Spaghetti, and the straightness he called Ziti. And the strands and tubes were the first course."
Duh?
Get a long sheet (about 50 cm x 2-5 meters, depending on the number of lights.) Starting at one end, wrap it around the short end of the rectangle, then fold it over about 10 cm. Repeat until all your lights are in a big cigar tube.
Have you been touched by his noodly appendage?
That explains why knots spontaneously form in wires and cables when you stick them in a box, but what about the way knots spontaneously come undone in your shoe laces? Perhaps in an alternate universe, shoe laces spontaneously knot themselves, and wires and cables untangle in storage. Of course, with that sort of altered physics, Homer Simpson would probably be the President of the United States.
Oh, wait.
"My country, right or wrong; if right, to be kept right; and if wrong, to be set right." --Senator Carl Schurz (1872)
!knotcometonaught = notknotcometonaught?
Fishing line is epic.
It can be straight, but the moment it comes into contact with anything, or disappears outside of the line of view, or for no apparent reason at all, it's a virtual loom of spontaneous knots.
GAAH! MY PRINTER IS ON FIRE!!! PUT IT OUT! PUT IT OUT!
In this case it began with the same question:
Why knot?
Subatomic particles are actually microscopic Boy Scouts.
Despite being pretty much a Macfan boy I have one MAJOR irk with Apple -- the stuff they make all their cable out of. It has to be the most knottable substance known to mankind.
Every single time I pick up the earphones from my iPod they are knotted. I am very careful to wrap them in a way I think they will stay unknotted, but every time, every time, they are knotted again.
Drives me nuts.
I heard he spits in your mouth as you sleep too.
What if Tetris was invented by Nazis?
Flying Dutchman: Did somebody say knot?
Spongebob: (eyes grow large) I did.
Flying Dutchman: So, you wanna tie knots, do ya? Well, do ya?
Spongebob: Yes, please, Mr Flying Dutchman, sir.
Flying Dutchman: Then you've come to the right flying ghost, kid. You're looking at the first place winner in the fancy knottin' contest for the last 3,000 years!
Spongebob: Hooray! (floats up into the air and into a heart)
Flying Dutchman: (grabs Spongebob) You're gonna have to not do that. And stop staring at me with them big old eyes! (Spongebob's eyes shrink) Now, stand back and watch me be knotty. (laughs and pulls out a rope) Haha! Behold! (rope is in pretzel shape) The pretzel knot!
Spongebob: Ohh. (Flying Dutchman makes the rope into 2 diamonds)
Flying Dutchman: The double-diamond knot! (holds the rope, now in the shape of a square, in front of Spongebob) The square knot! (rope slithers over and squeezes Spongebob) The constrictor. (Grabs Spongebob and pulls him apart revealing a knot that looks like intestines) The gut knot! (Flying Dutchman makes a knot in the shape of a pillow) The pillow knot. (turns the knot over where Spongebob is sleeping. Then he makes the knot into a butterfly) The butterfly knot.
Spongebob: Ohh...
Flying Dutchman: Wait! There's more. (Spongebob takes out a pen and paper and his glasses) The monkey chain! (shows the rope as a chain) The monkey's fist! (shows the rope into a ball) The monkey! (shows the rope as a monkey)
Monkey: Ohh, ohh!
Flying Dutchman: This one here's a loop knot, otherwise known as the 'poop loop'. (pulls the rope)
Rope: Poooop!
Spongebob: (laughs) Those are great, Mr Flying Dutchman, sir! Now can you show me how to tie my shoes?
Flying Dutchman: (laughs) I don't know how to tie me shoes. I haven't worn shoes for over 5,000 years! (holds a sock with two blue stripes up) But sometimes I like to wear this little sock over me ghostly tail. (laughs as he flies off. Scene cuts to Spongebob crawling into his pineapple) No need to RTFA, I bet the Flying Duchman would know...we should ask him!!
It's left blank because I have nothing to say to you punks!
As a kayaker, I'm familiar with a rescue tool called a throw bag. Apparently, throw bags were developed for the maritime industry, then downsized for kayakers.
The theory is quite simple, but it's amazing to watch how well it works:
I've watched these bags work time and time again, amazed that with the rope just stuffed into the bag, they work reliably. I've used store-bought bags and ones I've made myself and have never seen the rope tangle.
I realize that without loose ends proper knots can't form, but with a throw bag, you don't even get close to tangles!
The photo of the DNA in the article does not appear knotted to me. Does anyone have a link to a DNA image that is truly knotted?
Surely the fundamental reason why knots form (or rather why they persist/accumulate)is because of the inherent assymmetry of them formign/unforming.
A loose end in a jumble of coils, if jiggled around, is almost bound at some point to pass though a coil and form a potential knot, but a knot once formed is by no means destined to become unknotted, especially once additional knots form on the loose end thereby securing earlier knots.
If the chance of becoming knotted is less than the chance of becoming unknotted, then there's going to be a trend towards becoming increasingly knotted (to some limit where the accumulated knots limit mobility of the mass).
It seems there may also be a ratcheting effect once a loose knot forms - the knot/loop being bulky will more likely catch on the surrounding mass then the single stands leading into it, so that if the loose ends get tugged by the jiggling of the surrounding mass then the knot will tighten.
But there again I'm just a dude who uses string rather than a high powered topologist getting paid to research string, so what do I know?!
How hard is this? The Universe is a box full of string. Knots form. Some make pretty big knots.
Eventually, when the chimps write a decent but unpopular novel, balls of string form. Many balls. In time, these seem to have gathered and caused all sorts of interesting phenomenae, like stars, Western clothing, and Jessica Alba.
Unfortunately, this can only end one of two ways...
1- The string gets untangled. All devolves into a box of string again. Knots form again.
2- All this gets emptied into another box. Sold at a yard sale. Who knows what happens with the new owner... Actually, even if the string gets untangled, it ends up in a yard sale.
Physics. It's really all about yard sales.
deleting the extra space after periods so i can stay relevant, yeah.
As a sysadmin who has spent days untangling hundreds of tangled cables from the backs of too-crowded racks - hundreds of A/V lines criss-crossed by dozens of network lines criss-crossed by power cords - I've had some time to think about practical knot theory. I've established two primary hypotheses:
1. Placing cables is difficult because you are not just defining the position of that cable, you are also defining the position of every other cable in relation to that cable. As the number of cables rises, the complexity increases combinatorially. (Or exponentially. Or something. I faked my way through those math classes.)
2. There are many more ways for cables to be tangled than to be untangled, so statistically, tangling is overwhelmingly likely. It's like entropy that way: There are many more ways for particles to move in different directions than there are ways for particles to move in the same direction, so it takes special effort or special circumstances to get them all to line up.
When I parsed the mentioned comment, it stated "undeclared-your" hair was the subject of the knotting. The Wife's spurious attribution of the cause to small semi-sentient beings does not change the knots in your hair.
Meanwhile, when is the last time you swapped your hair strands around with the purpose of installing new hardware?
My first Journal Entry ever, in 8 years! http://slashdot.org/journal/365947/aphelion-scifi-fantasy-horror-poetry-webzine
I've never personally purchased a weave, but I hear many women do.
Oh, dear. I've said too much.
I tie my shoes with wires and cables. The only problem is when I want to take them off...
Does this also explain why shoelaces tie themselves into knots while I'm sleeping? I have long suspected my cat, but I guess science has a better explanation...
I read along time ago baton a whatknot. It's supposed to be what flat "ropes" like seatbelts become. Anybody know what I am talking about?
Why don't you guys have friends or journals?
A foundation for proof of the String Theory!
Am no fek Buddhist, but this is enlightenment.
There is no parallel to this miracle even as mysterious as transubstantiation itself! It is He that keep the pasta flowing! He that make it slide!
*bells ringing in the streets* we have proof! *bells ringing in the streets*
CS majors know the time/space tradeoff, but they never get taught the 3rd, crucial, tradeoff of the set: comprehension!
If you go clockwise from the top the thread goes over a thread, then under, over, under, over and under to get back to its starting point.
Once you agree with that, I think the string can't be twisted to become an simple loop.
There is an interesting feat of DNA more or less counter to the example given: how a chromosome manages to unfold into a string with length of the order of centimeters during cell division without getting completely entangled.
Shouldn't the title be something like "How often do knots spontaneously form"? The experiment doesn't give any new information on why knots form. On the other hand it may give some information of how fast the knots form and the probability of knots at equilibrium.
A string walks into a bar.
He asks for a shot of tequila. The bartender replies "Sorry we don't serve strings". So the string leaves.
The next day, the same string walks back into the bar. He asks for a shot of tequila. The bartender replies "Sorry we do not serve strings, please go away."
The following day the string stands outside the bar debating about whether to go in or not. He ties himself up and messes the top of end so that it's loose and uneven.
He goes in and asks for a shot of tequila. The bartender replys "Hey aren't you that string that's been coming in here all the time."
The string replies "No I'm a freyed knot".
-no broken link
Most slashdotters can relate to the story about the computer cables, but how many are in a position to hear a woman complain about her hair? Especially one that's been in the same place for an hour.
Persistent length is a characteristic of a linear object (polymer molecule, for example) which characterizes bendability of this object.
I have thick USB cable to my Belkin wireless adapter and thin one to the mobile mouse. The first one never tangles, the second one tangles all the time. Belkin cable is twice longer than mobile mouse one. The difference is a persistent length.
I do not believe in karma. "Funny"=-6. Do good and forbid evil. Yours, Oft-Offtopic Flamebaiting Troll.
I have been fascinated for many years about knots.
From graph theory there is the Utility Pole problem. You have three houses A,B and C. You have three utility service points Water, Gas and Electric. The problem is: Can you connect all three utilities to all three houses with no wire crossing? The answer is no. Computer cabling can also be drawn as a planar graph. At some time some connection appears to require a crossing of a wire.
The idea I got out of the graph theory was: Hold the ends when working with cables. Coiling things tends to create twists. If you coil or fold the paired wires (not letting go of the ends) the structure you create does not form knots, and usually makes at worst easy to resolve tangles. Holding on to the ends forces folding and coiling to continuously have a kind of symmetry. Knots need the asymmetry of a loose end.
Here is Lee's super duper no tangle cable folding technique:
Hold the ends. Fold the cable, half, quarter etc. Wrap the folded cable with a scrap paper belly band. Tape the band. It is an easy to handle bundle: ends together tells type, easy to guess or calculate length.
Topology is a really interesting subject to study. My most recent enjoyable book:
Formal Knot Theory by Louis H. Kauffman, published by Dover, $14.95 paperback.
This one even caught Paul Kedrosky's attention. listen_to_slashdot
Singularity: a belief in the "God" idea with the "demiurge" relation inverted.
I'm trying to turn this piece of string into jessica alba, i'm not having much luck!