Mathematics of Christmas

Post-Christmas, actually. The backside of the holiday, when all that glitters, sparkles, blinks, and sings or dances at the flip of a switch, must be packed away until next year. I always aim to repack things exactly as I found them, but inevitably I fail miserably. Luckily though, in my house we have a system that has been in place for as long as I can remember for many of the ornaments, including some original 1970's Bloomingdale's packaging! You can't beat that.

You know what else you can't beat? The tendency of Christmas lights to tie themselves in knots no matter how hard you try to outsmart them.


Each year, you open the box to find a tangled mess, right? And after each Christmas, possessed with renewed determination, you scheme to store them more carefully this year, convinced you have finally come up with a fool proof system. So maybe you roll each strand in a loop around your elbow and then lay it carefully in a box, or you return each rolled strand to it's original box, or perhaps you wrap each one in tissue paper, secure them with a rubber band, twist tie, or god forbid, even a scrunchy. Once all the holiday accoutrements have been put away, you relax, rest assured that this time you have bested the Christmas lights and their confounding ways. But then next Christmas rolls around, and you retrieve the box full of lights only to open them and discover a twisted, tangled mess, taunting you.

Good news!...sort of. You can stop blaming yourself for this frustrating phenomenon as researchers at the University of San Diego have recently concluded that it's a mathematical and physical certainty. Blame the universe instead!

There are a couple reasons for this argument. The first being the Second Law of Thermodynamics (Code name: Entropy). Order tends to disorder, and your carefully packed strands obey by doing their part. The second more complicated reason is explained in great detail by UCSD physicists, Douglas Smith and Dorian Raymer, in their October 16th paper: "Spontaneous Knotting of an Agitated String."

Basically, mathematicians have studied knots forever and developed all sorts of theories and classifications of their variations, but physicists have only recently began to explore what equations govern their formation. To look into this, Smith and Raymer built a very simple experimental apparatus consisting of a clear plastic box and a motor. They put one piece of string in the box at a time and spun it around and around, then took it out and documented its final state - knotted or not. They did this 3,415 times varying: length of string, rotation speed, number of rotations, and size of the box.

Why 3,415 times, you may ask? I quote: "The scientific answer is that 3,415 was around the point where we had statistically compelling results," Smith said. "The human answer is that 3,415 times was about as much as we could stand." ('A string theory just in time for Christmas', Scott LaFee, Bend Weekly)

They concluded that with a minimum length of string (18.124 inches) and sufficient space for the string to shift around in it's container, knots formed fairly quickly, often within the first few seconds. Inputting these results into a computer model, they even managed to create a program which could identify the 'Jones polynomial' for each resulting knot, a mathematical property based on parameters such as the number of string crossings.

So think about the length of your Christmas tree lights (undoubtedly more than 18.124 inches), how much space they have to move around in their storage boxes (a fair amount I would presume), and how often they might be jostled when moved to and from their yearly resting place (not exactly a smooth ride up those attic stairs). In all likelihood, a knot has formed while the box is till in your hands. I guess you can still blame yourself! 

Another and better, in-depth write-up of this labyrinthine marvel can be found here.

Thrill-a-minute, edge-of-your-seat video lets you see the fun first hand!


Think you are immune to knots? They go deeper into your life than Christmas. Think about all the electrical cords in your house and the iPod headphones in your bag. Deeper still, knots are required for the DNA molecules in your cells to fit into the tiny spaces they are allotted. And even more fundamental than that, knots in the fabric of space-time could explain the distribution of matter we see today. ESA is even launching a satellite next year to look for them.

And...we're back to blaming the universe.

(photo credit: Eduardo Contreras, Union-Tribune)