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:
 Articles 20071222 A9136 1490 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.

Previously on BB:
• Scientific study on why knots happen Link
• Many better ways to tie your shoes Link
• Ideal knots spun in 3D Link


  1. I was just thinking about know mathmatics yesterday, while trying to un-knot some Christmas tree lights. Apparently anything but a pefectly strait line is on its way to becoming a knot. Our super strings must have formed the knot from hell.
    And yet, folding (which is what protiens do) is a lot more complex than a knot. Nature is crazy for details.

  2. Is it wrong that the first thing that came to mind when I saw this post was Clive Barker’s short story, “The Inhuman Condition”? Beware what comes of untangling knots….

  3. Not exactly, Registrado. LQG says that spin networks have equivalence classes under diffeomorphisms on a 3-manifold that are isomorphic to knots, but all that means is that fermions aren’t allowed to occupy the same place and state, per the usual Pauli exclusion principle, and when you view interactions from a different frame of reference, it has the same connectivity.

    I loved knot theory as an undergrad, but I’m glad I didn’t go into it, like, it would be less valuable than a history degree.

  4. “Strictly speaking, then, the string in Raymer and Smith’s box was never knotted.”

    I can think of no clearer statement that mathematicians do not bother themselves with reality.

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