The Cutting Edge in Topology Research: Strings in a Box

A simple box turned by a motor shows the complexity of knot formation.

By Josie Glausiusz|Monday, February 04, 2008

Extension cords and computer cables have an irritating tendency to tie themselves into knots without obvious outside influence. Yet despite more than a century of abstract mathematical knot theories, few have experimentally tested how these convoluted coils form. That’s why physicist Doug Smith of the University of California at San Diego and Dorian Raymer, a student, decided to unravel the mystery of knot formation—by tossing bits of string around and around in a box 3,415 times.

The researchers took a clear box, attached a motor, and dropped in bits of string between 1½ feet and 20 feet long. After tumbling each piece individually for 10 revolutions, they found that a complex knot could form in a string as short as 2 feet. A 10-foot-long string would get knots more than 50 percent of the time. The longer the string, though, the more complex the knots. When they fed photos of the tangles into a knot-classifying computer program, they found 120 different types with up to 11 crossings each.

Smith says his research could be used to study tangles in umbilical cords or DNA. “If two pieces of DNA are knotted, the cell can’t divide, and that’s a serious problem,” Smith says. “The techniques that we developed for analyzing the knots in our string could also be used for analyzing knots in DNA. I’d like to investigate that.”

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