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."

Re:Hair

[captain_dope_pants]

I used to be a fisherman for a living. Miles and miles of nets, rope etc. When the "knot gnomes" had their way with that lot it was a nightmare!
There are also undersea variants of the "gnot knome". You go to haul your nets after a couple of days and they're gnotted all to hell.

Re:Yes, but what about shoe laces, huh?

[Tony Hoyle]

What gets me is how knots form when both ends of the cable are plugged into something. And they form in such a way that there's no way to untangle it without unplugging everything and painstakingly unpicking it from the mess.

Doesn't anybody know how to tie a knot?

[CaptScarlet22]

Spongebob: Doesn't anybody know how to tie a knot? (lightning appears as well as the Flying Dutchman)

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!!

Loose ends cause most of the trouble...

[jddj]

As a kayaker, I'm familiar with a rescue tool called a throw bag [riversafe.org.nz]. 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:

• Tie a rope through a hole in the bottom of a bag.
• Stuff the bag with the rope, leaving the tail end of the rope sticking out of the top.
• Grab the tail end of the rope and throw the bag towards the person who needs the rope.
• Watch as the rope magically pays out of the bag, completely free of knots or tangles.
• Don't get so awed by the rope coming out untangled that you let go of the end...

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!

Re:Hands-on knot theory

[poopdeville]

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.

You need to make the notion of counting ways to be tangled and untangled more precise. In any case, the problem with real cables is that most cable runs have a half turn in them. But where the turn happens varies. Moreover, the turn introduces distortion in the cable at the turn since it isn't under tension. Heating and cooling, and Type I and II Reidemeister moves [wikipedia.org] caused by the distortion moving do the rest.

But note that these kinds of knots are trivial to untangle if you keep the cables connected, and much harder if you don't, since Type I and II Reidemeister moves can't produce knots, just tangles.

Re:All knotted up for next year.

[hazem]

I worked for a summer with a flooring contractor before going to basic training in the army. They did a cool technique with their extension cords where they basically made a long loose crochet chain out of them. A 50 ft cord would end up about 10 feet long and then they'd toss them all in their big "contractor box".

For some reason, cords that were already looped up like this didn't tend to knot up with each other. Which makes me wonder if there is a maximum knotty potential... straight un-knotted cords have a higher probability of knotting while ones that are already knotted will be less likely to. It seems I read something recently, maybe out of the "Book of Ignorance" (http://www.amazon.com/Book-General-Ignorance-John-Mitchinson/dp/0307394913 [amazon.com]), said that straight hair tends to get knotted more then curly hair.

It's amazing to me that seemingly simple things end up yielding entire fields of math and science.