Christmas lights are one of the most recognizable signs of the holiday season. But unless you’re particularly well organised, they’re notorious for becoming tangled during the 11 months you have them shoved in that box marked ‘Xmas lights’. And boy are they ever a pain to untangle…

So how do they get tangled in the first place? Several years ago, physicists Dorian Raymer and Douglas Smith, then at the University of California, San Diego, actually studied how easily cords get tangled!

A short clip of the numerous experiments conducted in ‘Spontaneous knotting of an agitated string’

They put bits of string of various lengths in a cube-shaped box, and then mechanically rotated the box so that the strings tumbled around, like socks in a dryer. They repeated the experiment more than 3,400 times and observed the first knots appeared within seconds. Over 120 different types of knots spontaneously formed during the experiment. The longer the string, the more likely it was to become knotted. Indeed, as the length of the string increased, the probability of a knot forming approached 100 percent.

Material plays a role — a more flexible cord is more likely to tangle than a less flexible one — but diameter is also key. Yes, in general, long cords tangle more easily than short ones, but a cord with a large diameter is less flexible, reducing the risk of knotting. In other words, the ratio of length to diameter really matters. That's why a garden hose can get tangled — it's relatively stiff, but it's usually very long compared to its diameter.

Artist Liz Climo understands the struggle!

But wait, there’s more! Cords with metal wire inside — like traditional Christmas lights or headphones — can acquire a sort of natural curvature. That is, a wire that’s been wrapped around a cylindrical spool, for example, will tend to retain that shape. Since Christmas lights are typically spooled for shipping or packing, the metal wire bends past its ‘plastic limit’, giving it a natural curvature approximately the size of the spool it was wound around. They become even harder to straighten than other wound materials because they often contain a pair of intertwined wires, especially in parallel circuits, giving them an intrinsic twist.

And just for an added challenge, let’s talk about the light bulbs. All those little projections on the wire get in the way of each other, making it very difficult to pull one strand through another and ultimately disentangle your spaghetti jumble.

So what’s the solution? One option might be for manufacturers to make the cord out of a stiff yet elastic material — something that bounces back from the curvature imparted to it in storage. A nickel-titanium alloy known as Nitinol might be a candidate, but it’s too expensive to be a practical choice. Besides, the cord material may make little difference if there are still bulbs sticking out! Perhaps the biggest breakthrough comes in the proliferation of LED ‘rope lights’.

LEDs don’t use traditional bulbs. Instead, semiconductors embedded within the rope-like cord turn electricity into a single colour of light. Yes, they can still get tangled, but without protruding bulbs, they’re significantly easier to untangle. Bonus: they are more environmentally conscious, using less energy and being a bit safer than traditional incandescent bulbs.

The simpler solution, of course, is to coil your lights carefully when putting them away, using something like twist-ties to keep them in place or wrapping them around sheets of cardboard. But if you find yourself confronted with a hopelessly tangled jumbled mess of cord this year, mathematicians recommend finding one of the free ends and working from there. With a bit of patience, you’ll get there eventually…