A Christmas tree isn't a Christmas tree without those pretty colored lights, right? OK, no problem. You stored them in a box marked "Xmas lights" 11 months ago. You know where the box is. Now you just have to open the box, grab the lights, and—

That's where it gets tricky. Unless you're very lucky, or extremely well organized, the lights are likely all tangled up; soon you're down on your hands and knees, struggling to untangle a spaghetti-like jumble. (And it's not just you: A couple of years ago, the British grocery chain Tesco hired temporary "Christmas light untanglers" for the holiday season.) But why are Christmas lights so prone to tangling in the first place—and can anything be done about it?

## Why do Christmas lights get tangled in the first place?

There are really two separate problems, explains Colin Adams, a mathematician at Williams College in Williamstown, Massachusetts, and the author of The Knot Book, an introduction to the mathematical theory of knots. First, the cord on which the lights are attached is prone to tangling—just as headphone and earbud cords are (or, in the past, telephone handset cords).

Several years ago, physicists Dorian Raymer and Douglas Smith, then at the University of California, San Diego, did a study to see just how easily cords can get tangled. 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, repeating the experiment more than 3400 times. The first knots appeared within seconds. More than 120 different types of knots spontaneously formed during the experiment. They also found—perhaps not surprisingly—that the longer the string, the more likely it was to become knotted (few knots formed in strings shorter than 18 inches, they noted). As the length of the string increased, the probability of a knot forming approached 100 percent.

The material that the string (or cord) is made of is important too; a more flexible cord is more likely to tangle than a less flexible one. And while the length of the cord matters, so does its diameter: In general, long cords get tangled more easily than short ones, but a cord with a large diameter will be less flexible, which reduces the risk of knotting. In other words, it's the ratio of length to diameter that really matters. That's why a garden hose can get tangled—it's relatively stiff, but it's also very long compared to its diameter.

But that's not the end of the story. If a cord has a metal wire inside it—as traditional Christmas lights do—then it can acquire a sort of "natural curvature," Jay Miller, a senior research scientist at the Connecticut-based United Technologies Research Center, tells Mental Floss. That means that a wire that's been wrapped around a cylindrical spool, for example, will tend to retain that shape.

"Christmas lights are typically spooled for shipping or packing, which bends metal wire past its 'plastic limit,' giving it natural curvature approximately the size of the spool it was wound around," Miller says. Christmas lights can be even harder to straighten than other wound materials because they often contain a pair of intertwined wires, giving them an intrinsic twist.

And then there's the additional problem of the lights. "Christmas lights are doubly difficult, once things get tangled, because there are all of these little projections—the lights—sticking out of them," Adams says. "The lights get in the way of each other, and it makes it very difficult to pull one strand through another. That means once you're tangled, it's much harder to disentangle."

## How do you fix tangled Christmas lights?

What, then, can be done? One option would be for manufacturers to make the cord out of a stiff yet elastic material—something that would more readily "bounce back" from the curvature that was imparted to it while in storage. A nickel-titanium alloy known as Nitinol might be a candidate, says Miller—but it's too expensive to be a practical choice. And anyway, the choice of material probably makes little difference as long as the lights still protrude from the cord. Perhaps the biggest breakthrough in recent years has been the proliferation of LED "rope lights" that don't employ traditional bulbs at all; rather, they use LEDs embedded within the rope-like cord itself. Of course, these can still get tangled up in the manner of a garden hose, but without those pesky protrusions, they're easier to untangle.

A simpler solution, says Adams, is to coil the lights very carefully when putting them away, ideally using something like twist-ties to keep them in place. (Martha Stewart has proposed something similar, using sheets of cardboard instead of twist-ties.)

Meanwhile, the mathematicians have some advice if you find yourself confronted with a hopelessly tangled, jumbled cord: Find one of the "free" ends, and work from there.

"Eventually," Adams assures us, "you will succeed."