【Earphone Manufacture】about braided cable

I believe that children's shoes who have used wired earphones have all experienced this problem. When taking out earphones from their pockets or bags to use, the earphone cables always tangle up in a tangled mess, without exception. In fact, there is a lot of science behind this seemingly simple phenomenon that can be explained in detail.

In life, we can find that long and soft ropes spontaneously form many different configurations in their natural state: perhaps a neat straight line, or perhaps one end of the rope bends and crosses with the middle section. In reality, the latter situation accounts for the majority: the rope always tends to self entangle and eventually forms a ball. Among these random configurations, there are hardly any that do not form clumps, so these ropes will eventually turn into a tangled mess. Once a knot is tied, it is unlikely to automatically unravel from an energy perspective. Therefore, the knots of the rope will only increase.

We can explain the phenomenon of tying ropes and wrapping headphones using the branch of topology - knot theory. According to mathematical terminology, knot theory is a branch of mathematics that studies how to embed several rings into a three-dimensional real Euclidean space. The object it studies must be curves in three-dimensional space. In a two-dimensional space, due to insufficient dimensionality, we cannot make a curve entangle itself and form a knot; In four-dimensional or more spaces, due to the excessive dimensionality, any knot can be easily unraveled into a curve without any knots.

In 2007, physicist Douglas Smith and his undergraduate student Dorian Raymer decided to personally verify the feasibility of knot theory using real ropes. In the experiment, they put a rope into a box and flipped the box for 10 seconds. Subsequently, Rimer changed the length, hardness, box size, flipping speed and other parameters of the rope and conducted approximately 3000 repeated experiments.

The results show that with a probability of approximately 50%, the rope will tie a knot. One of the main factors affecting this result is the length of the rope: ropes less than 1.5 feet (about 46 centimeters) in length are less likely to tie knots; As the length increases, the probability of knotting also increases. However, there is also an upper limit to this. When the length of the rope reaches 5 feet (about 152 centimeters), it will fill the entire box and will not knot in more than 50% of cases.

Raymer and Smith also used the Jones polynomial invented by mathematicians to classify the knots they observed. After each flip, they will take a photo of the rope and input the image data into a computer algorithm to classify the knots. According to the knot theory, there are 14 basic knots, each containing no more than 7 intersections. Raymer and Smith observed all 14 types of knots during the experiment and also discovered more complex knots, some of which had up to 11 intersections.

The researchers ultimately established a model to explain their observations. Overall, in order to put the rope into the box, it must be coiled up. At this point, the end of the rope will be parallel to certain segments of the rope. When the box flips, the end of the rope may fall into the middle of the parallel segments, forming a cross. After multiple crossings, the end of the rope will basically wrap around a certain section of the rope, forming different knots.

Explaining the scientific basis for why so many headphone cables are tangled, what we really want to know is how to make the headphone cables not tangled? Researchers have observed in the experiment that using harder ropes reduces the likelihood of tying knots. When applied to headphone cables, it can be found that some headphones covered with nylon mesh material have better anti entanglement effect than ordinary headphones. Additionally, using shorter headphone cables to reduce the total amount of variation can also reduce knotting, such as neck mounted sports Bluetooth earphones or TWS wireless Bluetooth earphones. Or organize it in advance before putting it into your pocket.

Alternatively, it's better to tangle it up on your own, and from a probabilistic perspective, it's unlikely that it will become even more chaotic when taken out.