One sunny day last summer, Mathias Kolle, a professor at the Massachusetts Institute of Technology, took a couple of eminent colleagues out sailing. They talked about their research. They had some drinks. Then Kolle noticed something was off: A rowboat tied to his boat had come loose and was drifting toward the horizon. As he tacked across the water to retrieve the wayward vessel, he realized his mistake. In securing the rowboat, he must have tied the knot wrong.
Original story reprinted with permission from Quanta Magazine, an editorially independent publication of the Simons Foundation whose mission is to enhance public understanding of science by covering research develop­ments and trends in mathe­matics and the physical and life sciences.
I almost lost a boat because I got one knot wrong, said Kolle, a mechanical engineer. That was pretty embarrassing.
This slip-up aside, Kolle has become quite the knot wonk. In a recent paper in Science, he and his colleagues used a new way of visualizing the forces inside tangled fibers to revisit an ancient question: What makes some knots stronger than others?
Scientists have a long-standing fascination with knots. More than 150 years ago, Lord Kelvinworking with fellow Scottish scholar Peter Guthrie Taitproposed that the chemical elements could be represented by different knots. The theory didnt pan out, but the diagrams they drew of different knots, and their attempts to classify them, jump-started the development of modern knot theory.
In the 20th century, researchers built on this legacy by developing mathematical descriptions of knots that distinguish one from another. Often these descriptions employ topological properties: simple, countable characteristics that dont depend on size or shape, such as how often strings in a knot cross.
The mathematics of theoretical knots tied in theoretical strings inspired biologists to investigate how real DNA and proteins twist and tangle. Scientists have also developed theoretical models for knots at larger scales, like the hitches that bind ropes to poles. Some have put their models to the test, using titanium wire to determine how much force is needed to pull a knot tight, or using fishing line or strands of spaghetti to explore what parts of a knot tend to break.
Its a creative art in my mind, being able to develop an experiment that will capture these properties, said Ken Millett, a knot theory pioneer at the University of California, Santa Barbara.
But these experiments all tend to have the same limitationone that makes it difficult for researchers to truly understand how everyday knots operate, said Jörn Dunkel, a mathematician at MIT.
The problem is that you could not look inside the material, Dunkel said. A lot of things are hidden on the inside.
Researchers simulated which parts of a knot felt the most stress (top row), then compared the results to actual knots made from special fibers that changed color based on strain.
Illustration: Joseph Sandt (experiment); Vishal Patil (simulations)
Kolle and his wandering rowboat would agree. But a few years ago, he received inspiration from an unexpected source: a vivid blue seed mailed to a colleague, in a matchbox, by a reporter in Mexico. Plucked from the colorfully named bastard hogberry, the fruit gets its hue from the arrangement of cells in light-bending patterns.
Kolle adapted this optical trick to create plastic fibers that not only shine brightly in white light, but change color when stretched or bent. As their microscopic structures deform, the fibers turn yellow, green and other shades, revealing the stresses and strains within.