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."

Comments

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.

Loose ends cause most of the trouble...

[jddj]

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:

• 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 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.