In humanity's rise to global dominance, the invention of the knot doesn't get the same adulation as fire or the wheel, but its importance shouldn't be underestimated. Remarkably, after all these years, our understanding of why some knots are so much stronger than others is surprisingly patchy. Fibers that change colors when placed under stress are helping fill the gaps.
Sailors and mountain climbers, both of whose lives often depended on a knot holding, have spent centuries experimenting with different sorts of knots. E. Annie Proulx even got a Pulitzer-winning novel out of the staggering diversity of maritime knots. Knotting is a central feature of topology, an entire field of mathematics, yet a comprehensive theory predicting which sorts of knot will hold, and under which conditions, has eluded humanity.
MIT PhD student Vishal Patil has taken advantage of the production of color-changing fibers to develop rules about bend knots, publishing his study in the journal Science. These are knots where two lines are bound together to function as a single longer piece of material. In an example of how apparently unrelated fields of science enrich each other, the answers came through analogy with atomic spins in ferromagnetic materials.
Using a combination of mathematical theory and the colorful fibers Patil settled an old strength debate between the so-called Zeppelin and Alpine butterfly knots in favor of the former. He also demonstrated the merits of the well-known reef knot, showing that knots that consist of half knots tied in opposite directions are stronger than those tied in the same direction. More generally, knots are stronger if they have more crossings and changes in direction of rotation between strand segments.
“With this model, you should be able to look at two knots that are almost identical, and be able to say which is the better one.” said co-author Dr Jörn Dunkel in a statement.
Patil used fibers made by wrapping multiple transparent layers with different refractive indices (that is they slow light to different extents) around an elastic core. When bent, stretched or placed under strain the layers change thickness, altering the passage of light to produce colors that reveal their changes.
Knots are not just a human phenomenon – as with fire, we tamed and adapted an existing force of nature. Indeed, knots are literally in our DNA, or perhaps it should be said our DNA is sometimes in knots. We use them to make our clothes and to bind up surgery, and they don't always have to be solid. Patil and colleagues give turbulent plasmas, such as those we are trying to force to yield us the power of the Sun in the form of nuclear fusion, as an example of knots in action.