Mathematical Digest

Short Summaries of Articles about Mathematics
in the Popular Press

"Round the Twist," by Keith Devlin. New Scientist, 10 November 2001, pages 40-42.

Knot theory is a branch of mathematics that studies properties of idealized loops of knotted, twisted string. Recent computer experiments led a physicist to make a surprising conjecture about knots, and this conjecture has now been proved by two mathematicians. The conjecture concerns the "writhe" of a knot. Take a knot floating in 3-dimensions, shine a light on it from a particular angle, and then look at the 2-dimensional shadow of the knot. The "2-dimensional writhe" of the knot is obtained by assigning numbers to the crossing points in a particular way, and then adding up the numbers. The "3-dimensional writhe" is obtained by averaging the 2-dimensional writhe over all possible angles from which the light is shone. The surprising result is that the 3-dimensional writhe is "quantized"; for any knot, the 3-dimensional writhe is a multiple of 4/7. According to the article, this result could improve understanding of the knotting of loops of DNA. And because the tiny "strings" of string theory are thought to be knotted, "Quantum theory itself might even be a product of the quantum nature of knots," Devlin writes.

--- Allyn Jackson