Knot science

How is it that phone cords, earbuds, and the string for my son's gyroscope so often end up a knotted mess? To find out, biophysicists and mathematicians are developing experiments to exploring how knots can spontaneously form so quickly. Their research may provide insight not only into the tangled web of power cords behind your desk but also natural knots, like those in proteins and DNA. From Science News:

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…

In topology, a knot is any curved line that closes up on itself, possibly after a circuitous path in three dimensions. A circle is regarded as the "trivial" knot. Two loops are considered to be the same knot if you can turn one into the other by topological manipulation, which in this case means anything that does not break the curve or force it to run through itself.

Topologically, a knotted string is not a real knot, as long as its ends are free. That's because either of the ends can always thread back through any entanglement and undo the knot. An open string, no matter how garbled, is the same as a straight segment. (Mathematicians usually think of strings as being stretchable and infinitesimally thin, so in topology there is no issue of a knot being tight.)

Strictly speaking, then, the string in Raymer and Smith's box was never knotted. But it was still a mess.