To solve the mystery of headphone cord entanglement, scientists put the cord in a box and shook it more than 3,000 times

Review expert: Luo Huiqian, Associate Researcher, Institute of Physics, Chinese Academy of Sciences

On a beautiful day, when you suddenly want to take out your headphones from your pocket to listen to music, you will always find that the headphone wires have gotten tangled again!

The power cord and data cable are both wires, so they rarely get tangled when placed in a bag. Why is it that the headphone cable is so easy to get tangled? Is there a little goblin in your pocket, squatting in your pocket every day waiting to tangle the headphone cable?

What makes your headphone wires tangled? Learn about kink theory

A knot , as the name implies, is a knotted rope connected end to end, which may have twisted intersections. Knot theory is a branch of topology that studies the topological properties of knots. In knot theory, a prime knot is a non-trivial knot that cannot be decomposed.

All prime knots with 7 or fewer crossings.

Each prime knot is mainly marked by the crossing number, and prime knots with the same crossing number can be further distinguished by different subscripts.

Source: Wikipedia

Knot theory is a branch of mathematics that studies how to embed several circles into three-dimensional real Euclidean space. The object of its study must be a curve, and a curve in three-dimensional space, so we can attribute the problem of headphone cord knotting to knot theory. In knot theory, if a knot can be transformed into another knot without separating the two endpoints, the two knots before and after the transformation are considered equivalent.

As early as 2007, physicist Douglas E. Smith and undergraduate student Dorian Raymer had studied the feasibility of applying knot theory to rope knotting, and they also won the Ig Nobel Prize in Physics for this.

The experimenters placed ropes of different lengths and hardness in a transparent box and rotated the box at various speeds, conducting 3,415 experiments.

The experiment found that soft ropes are easier to tie into knots . From our daily life experience, we know that soft ropes, such as wool and needle thread, can be tied into a knot by just pinching them. In contrast, power cords and data cables are thick and hard, so it is difficult to form a complex knot like the headphone cable.

The experiment also found that a rope less than 46 cm long will hardly form a knot after being sealed in a rotating box for a period of time. But from 46 cm to 150 cm, the probability of knot formation will rise sharply. If the length of the rope exceeds this length, the probability of knot formation is basically stable at 50%.

Knot Probability-Rope Length (m)

Source: sciencealert

You might as well measure your headphone cord, and you will find that it is about 150 cm long . From the above figure, we can see that the vertical axis represents the probability of knotting, and the horizontal axis represents the length of the rope; 140 cm is 1.4 meters, and 1.4 on the horizontal axis corresponds to a number between 0.4 and 0.5 on the vertical axis, so we can see that it has a "minimum" probability of knotting of about 50%. Why is it "minimum"? Because the headphone cord can be regarded as a Y-shaped rope with three wires, and the weight of the headphones at both ends is heavier than the headphone cord, which makes it easy to drive the headphone cord, further increasing the probability of the headphone cords getting entangled with each other.

They also found that doubling the width of the cube box slightly increased the probability of knotting, but reducing the box width by 33% dramatically reduced the probability of knotting.

Finally, here's a diagram showing how a string begins to coil up in a spinning box. Research has shown that it only takes one end of the string crossing the other end twice to spontaneously form a knot:

Source: sciencealert

Now you can rest assured: these knots are formed for real physical reasons, not by some supernatural force.

How to avoid headphone cord entanglement?

From the experiment we can draw the following conclusions:

1. More flexible materials tend to tangle more easily. So if the headphone cable is stiffer, the chances of tangling will be reduced.

2. The more the headphone wires roll around, the more likely they are to get tangled and the more likely they are to get tangled. Chest pockets are usually smaller than trouser pockets, so it may be better to put your headphones in your chest pocket rather than in your trouser pockets.

3. The bigger the box, the more knots it will get. So if you put your earphones in a small pocket instead of a big bag, the earphone cord may have less chance of getting tangled.

Source: pixabay

So, if you want to keep the headphone cable from getting tangled, you can try the following three methods:

1. Bundling earphones: Manually wind up the earphone cord neatly so that it will not move around easily and will not easily get tangled.

2. Expose the headphone method: Expose both ends of the earphones outside your trouser pocket. As long as the earphone heads do not shuttle between the wires, the earphone wires will not form a knot by looping themselves.

3. Storage method: Place the headphone cable in a small box specifically for headphone cables.

Is it possible for a headphone cable knot to untie itself?

The answer is yes , but only if the earphones return along the path they are tangled in during vibration. However, this probability is very small. Generally speaking, objects tend to develop from order to disorder . But to return from disorder to order, it usually costs energy.

In other words, tying a knot is a more stable outcome than untying a knot, so headphone cables are naturally more likely to end up with a "knot".

Let's look at it from another angle - the outer skin of the headphone cable is usually made of TPE material (thermoplastic elastomer), which is elastic and has low hardness. The friction coefficient of TPE has nothing to do with the size of the contact area, but it is also related to hardness and is inversely proportional to its hardness, that is, when the hardness of TPE increases, the friction coefficient decreases. This means that when the headphone cables are tangled together, due to the existence of friction, these knots are more difficult to untie spontaneously.

Source: pixabay

Nowadays, wireless Bluetooth headsets have gradually become people's new favorite. Since there are no wires, there is no trouble about tangles.

But then again, if you find your headphone cords are tangled, why not take a moment to learn about these knots before you get too cranky?

Alexander the Great: What's the knot? Take my sword!

Source: Wikipedia