Undergraduate’s Research Makes New York Times’
Top Science Stories of 2007

A   Southern Californian at heart, Dorian Raymer surfs, skateboards and fishes for yellowtail. But he also enjoys dabbling in different academic disciplines. He brought together three of his academic pursuits—mathematics, physics and computer programming—in a study he initiated while an undergraduate physics major at UC San Diego that was named one of the top science stories of the year.

The New York Times Magazine recently named the study on knot formation by Raymer and Douglas Smith, an assistant professor of physics at UCSD, one of the Top Science Stories of 2007 in its annual “Year in Ideas” issue. The editors of the Sunday New York Times Magazine chose the stories from a pool of nominees submitted by New York Times reporters.

Since their paper was published in the Proceedings of the National Academy of Sciences in October, the two physicists’ work has captured headlines in daily newspapers and magazines around the world, as well as more technical publications such as Popular Science, Science News, New Scientist and Physics Today. A feature on their research will appear in the February issue of Discover Magazine.

“It was fun to talk to the reporters from many publications, as far away as Sweden, who contacted us about the story,” said Raymer. “But we were most happy about the response of the mathematicians. We were using mathematical concepts that can take years to fully understand, so we weren’t sure how our research would be received. However, Andrew Belmonte, a math professor at Penn State University, published a favorable commentary on our paper in the following issue of PNAS. He concluded that the study of physical knots has now come into its own as an experimental science and that the mathematical model we proposed is likely to have interesting implications.”

“Many undergraduate students have worked in my lab over the years, but this is the first time one of my students initiated a project that has generated so much interest from the press,” said Smith. “It is a great lesson for students that the most important thing in science is to be curious and creative.”

Digital photos of knots with computer-generated drawings
based on mathematical calculations.

Image credit: Dorian Raymer, UCSD

In recognition of the importance of providing undergraduate students with research experience, this year UCSD launched the Regents Scholars Research Initiative. The program guarantees experience in a research laboratory for top entering freshmen.

“In the Division of Physical Sciences, we have a high faculty to student ratio that makes it possible for many of our undergraduate students to get involved in research,” said Mark Thiemens, dean of UCSD’s Division of Physical Sciences. “Many of our alumni, whether they have gone into industry or academia, tell us that gaining research experience as undergraduates was the single most important part of their education.”

“In the Division of Physical Sciences, we have a high faculty to student ratio that makes it possible for many of our undergraduate students to get involved in research,” said Mark Thiemens, dean of UCSD’s Division of Physical Sciences. “Many of our alumni, whether they have gone into industry or academia, tell us that gaining research experience as undergraduates was the single most important part of their education.”

Raymer and Smith’s study investigated the likelihood of knot formation and the types of knots formed in a tumbled string.

“We began the study because I was curious about knot theory in mathematics, and we wondered whether it might be applicable in a physics experiment,” said Raymer.

“When we started looking into this, it soon became clear that very little experimental work had been done to apply knot theory to the analysis and classification of real, physical knots and there was little understanding of how knots form,” said Smith. “But knot formation is important in many fields. For example, knots often form in DNA, which is a long string-like molecule. Certain anti-cancer drugs stop tumor cells from dividing by blocking the unknotting of DNA.”

Raymer and Smith designed a simple experimental set up consisting of a plastic box spun by a computer-controlled motor. A piece of string was dropped into the box and tumbled around like clothes in a dryer. Knots formed very quickly, within 10 seconds. The researchers repeated the experiment more than 3,000 times varying the length and stiffness of string, box size and speed of rotation. The result was a lot of tangles to be classified.

“It is virtually impossible to distinguish different knots just by looking at them,” said Raymer. “So I developed a computer program to do it.”



Dorian Raymer

The program translated the crossings of the string into a mathematical fingerprint for each knot. It used the Jones polynomial—a famous math formula developed by Vaughn Jones, a mathematics professor at UC Berkeley—which automatically simplifies knots that are identical, but look different.

Raymer and Smith developed a basic model for knot formation. String forms concentric coils, like a looped garden hose, due to its stiffness and the confinement of the box. The free end of the string weaves through the coils, with a 50 percent probability of going under or over any coil. The computer simulation that they developed based on this model mimicked the experimental results.

Raymer is currently a research assistant working with Smith and is thinking about graduate school. He is still deciding between his love of physics, mathematics, neuroscience and computer programming, and keeping his eye out for a new project that will bring them all together.

Press Clips

String Theory
San Diego Union-Tribune- December 19, 2007 -- nyone who has ever put up Christmas lights knows the problem: Holiday strands so carefully packed away last year are now more knotty than nice. In fact, they have become an inextricable, inexplicable, seemingly inevitable mess. It happens every year, like some sort of universal law of physics. More >>

Knot Physics
New York Times Magazine - December 9, 2007 --When Doug Smith pulls the power cord for his laptop out of his bag, he inevitably finds that — whoops! — it has somehow tangled itself into a dense knot. This is, of course, a common complaint of the high-tech age (and before, with other types of cord). Most of us simply shrug. But Smith is a physics professor at the University of California, San Diego, and he wanted to know precisely why the knots form in the first place. More >>

UC San Diego Physicists Tackle Knotty Puzzle
UC San Diego News Center - October 1, 2007 -- Electrical cables, garden hoses and strands of holiday lights seem to get themselves hopelessly tangled with no help at all. Now research initiated by an undergraduate student at the University of California, San Diego has resulted in the first model of how knots form. More >>

Knot a Problem
San Diego Union-Tribune, October 11, 2007-- The subject may not rank up there with, say, dark matter or the origins of life, but scientists remain puzzled by knots. Science, it seems, can't yet explain why garden hoses and Christmas lights invariably seem to get tangled. But if the why remains a mystery, some new research at UCSD offers clues to the how. More >>

A Tangled Tale
Science News, October 13, 2007-- You put the headphones in your bag in a tidy coil, but when you pull them out, they're a snarled mess every time. It may seem like a personal curse, but a new study shows that it's just physics in action. Dorian M. Raymer and Douglas E. Smith of the University of California, San Diego worked out the physics of random knotting by putting lengths of string into a contraption resembling a miniature clothes dryer that spun the loose string around. A mere ten turns, they found, had a fifty-fifty chance of putting a knot in a piece of string. The longer it tumbled, the greater the chance of a knot forming. More >>