How do cords get so tangled

Knot theory is an area of mathematics that studies knots, as the name suggests, but not just the types of knots we are accustomed to — it has applications in biology , quantum computing , chemistry , and many other fields. In math, knots are always studied in closed loops and a knot is defined as a configuration that cannot be untangled into a simple loop. They are classified based on their number of crossings. Two knots are considered equivalent if one can be transformed into the other without detaching the ends.

Knots are classified by the number of crossings. The only way to make the hard part work is by testing one hypothesis after another. Every entrepreneur is a behavioural psychologist with the tools to pull it off. Lessons learned from two years as an analyst with Union Square Ventures. VC is about story recognition. Avoid companies where there are diminishing marginal returns to data.

It rests on a group of handpicked case studies that prove little or nothing. There are enormous gaps between what we want them to do, and what they can do. There is still an enormous gap between what many people do in jobs today, and what robots and AI can replace.

There will be for decades. They then used these data and computer simulations to explain how the knots are likely formed see figure below ; basically, when jostled, the strings tend to form coils, and then the loose end weaves through the other strands, much like braiding or weaving.

And voila! Tangled headphones to make your day just that much angrier. Spontaneous knotting of an agitated string. We performed experiments in which a string was tumbled inside a box and found that complex knots often form within seconds. We used mathematical knot theory to analyze the knots.

We analyzed the knots by calculating their Jones polynomials via computer analysis of digital photos of the string.

Remarkably, almost all were identified as prime knots: different types, having minimum crossing numbers up to 11, were observed in 3, trials. All prime knots with up to seven crossings were observed. Our model can qualitatively account for the observed distribution of knots and dependence on agitation time and string length.