Messy Tangled Cables

April 10, 2012

The nuisance:

You stuff your headphone cables into your pocket, and mere seconds later, they form a knot of epic proportions you yourself could not have tied even if you tried. Does that sound familiar? How about this:

Tangled cables

Gordium called: They want their string back. (Photo credit: Wikipedia)

This seems to happen everywhere. The cables connected to your computer, bits of string in your household drawers, your hair, unless…

Telly Savalas

Who loves ya, baby? (Photo credit: Wikipedia)

The science:

There is apparently a mathematical discipline that specializes entirely on this: mathematical knot theory. Basically, it says that in long, flexible, thin objects above a certain critical length, there are more possible knotted states than untangled ones, and even only a little motion makes those states catastrophically accumulate.
They even proved that experimentally, which was probably preceded by the following exchange:
Scientist X: “Hey, look at my latest experiment!”
Scientist Y: “Not now, I’m writing a grant proposal!”
X: “But it explains knots!”
Y: *sighs* “Oh well…”
X: “Look, I’ve got this shoe box, and now I put this piece of string in it…”
Y: “Fascinating.”
X: “Yeah, and now I shake it! Look!”
Y: “Whoa!”
X: *beaming* “What do you say!”
Y: “Cool, let’s call it… let’s call it… Ah! Spontaneous knotting of an agitated string
X: “Ka-ching!”

They do. The theory also predicts that a 100% chance of knotting cannot be reached unless the string is very long and extremely flexible… like…

...like this. (image via wikimedia commons)

And here is the winner of the “applied mathematical knot theory”-contest:

Dreadfully long

Dreadfully long (Photo credit: the MaGe)

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