Life itself lies in the ‘law’ of knots

According to the author of the study, which is awaiting publication, the following stands true of Murphy’s Law of Knots: if something can get knotted, it will.

The longer the piece of string, the greater the risk of it becoming knotted. Benoit Doppagne / AFP

It’s one of life’s small irritations, but also one of its most baffling: why do headphones get tangled up so easily? We unplug them from our gadgets, put them in our pocket, only to find they’ve become hopelessly knotted the next time we use them.

As a physicist, I’ve long been intrigued by this mysterious phenomenon of “spontaneous knotting”. Now I can reveal the science behind it – along with a simple but effective remedy.

I first started pondering the mystery in the 1990s, while looking for scientific evidence to support Murphy’s Law: “If something can go wrong, it will”.

First coined by United States air force engineers in the 1940s, Murphy’s Law is often dismissed as a rueful joke. That certainly wasn’t the view of Maj Edward Murphy himself. During his design work on some of the air force’s most advanced aircraft, he regarded it as a guiding principle in the design of safety-critical systems.

My research uncovered many manifestations of his law in everyday life, with perhaps the best-known being Murphy’s Law of Toast: that if toast can land butter-side down, it will.

After looking at the mathematics of tumbling toast, I found there was indeed some truth in the “law”.

Contrary to popular belief, it has nothing to do with either the weight of the butter or aerodynamics. It’s simply that when the toast slides off the edge of a plate, it teeters on the edge and then breaks into a spin. This dictates which way up the toast will land.

And the bad news is that for typical sizes of toast and height of fall, the spin rate simply isn’t fast enough to come butter-side up again by the time it hits the floor.

That, at least, is what the theory said. To confirm it, I set up a nationwide experiment in which school students across Britain let toast slide off plates, and noted the outcome.

The response was astounding: all told, the students completed more than 21,000 trials. And the results confirmed the theory: the chance of toast landing butter-side down is 62 per cent, far higher than the 50-50 split expected if mere fluke were the explanation. Murphy’s Law of Toast, it seems, is true.

My research into Murphy’s Law of Knots – “If something can get tangled up, it will” – has followed a similar path.

I soon learned that I was hardly the first to ponder the mystery of spontaneous knotting. In his classic 1889 comedy novel Three Men in a Boat, the Victorian author Jerome K Jerome noted how “there is something very strange and unaccountable about a tow-line. You roll it up … and five minutes afterwards, when you pick it up, it is one ghastly, soul-revolting tangle”.

By the 1960s, scientists had pointed out that the same thing happened with long, string-like molecules such as DNA.

Surprisingly, perhaps, it took some very esoteric theory to explain these “trivial” observations.

At its core are so-called self-avoiding random walks – random paths in three-dimensional space that aren’t allowed to pass through the same place twice.

These capture the essence of randomly-jumbled rope, flex or DNA, which can end up in a complete tangle, but whose thickness prevents them from passing through themselves.

Not until the 1980s did mathematicians succeed in proving what most people might regard as obvious: that the longer the string-like object being jumbled, the greater the chances of it becoming knotted.

The theory led to a formula for how the risk of knots depends on length. And the bad news is that this risk increases rapidly with length.

In other words, Murphy’s Law of Knots is also true: if something can get knotted, it will.

So what can we do? I realised the very same theory suggested a remedy: simply clip together the ends of the flex, rope or whatever, to form a loop.

This cuts the risk of knots in two ways. First, it effectively halves the length of the flex available to move around. Second, the creation of a loop also eliminates the two free ends, the prime movers in the formation of knots.

While this “Loop Conjecture” sounded plausible, it clearly needed confirmation. So again I enlisted the help of schools to carry out the necessary experiment. And once again, the response was impressive: one school alone contributed more than 12,000 data-points.

The results – to be published in a refereed journal this year – confirm the theory in mathematical detail.

First, they show that the risk of knots increases rapidly with length. But more importantly, they confirmed the Loop Conjecture. Simply clipping together ends of any string-like object greatly reduces the risk of tangling.

Pretty much any type of clip will work. With headphones, it’s vital to ensure that both earpiece buds are held together with the jackplug at the other end. Even a bit of leeway can be enough to allow Murphy’s Law of Knots to kick in.

Finding a remedy to a bane of everyday life is fun, but it can also seem a bit trivial. Shouldn’t scientists be focused on more important things, such as finding cures for diseases?

Oddly enough, the Loop Conjecture may have a role in precisely that.

The cells in our bodies each contain over a metre of DNA. Not surprisingly, it too gets tangled, which can lead to its genetic instructions being misread.

Amazingly, nature has evolved enzymes that can find these tangles, cut them out and stitch the DNA back together. But there’s also evidence that it uses loops to protect DNA from becoming tangled in the first place.

This suggests loops play a role in diseases and the ways of treating them. I’m hoping to work with biochemists to explore this possibility.

Whether it will lead to any major breakthroughs, I’ve no idea. But one thing I have learned is that even apparently mundane phenomena can have surprisingly deep roots.

Nature doesn’t seem to understand the meaning of “trivial”.

Robert Matthews is a visiting reader in science at Aston University, Birmingham.