## 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:

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

**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…

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