The writhe of a knot is a mathematical measure of the net direction of crossing, summing clockwise against anticlockwise. The 2D writhe is the measure obtained from each of the crossings taken from a projection of the knot onto a two-dimensional surface. The 3D writhe, also called just 'writhe', is the average of 2D writhes across all possible projections.

It has recently been discovered that (3D) writhe is quantized. The quantum is 4/7.

This discovery was made by the Polish physicist Piotr Pieranski, using computer models of knotting techniques, taking into account how a loose knot can be shrunk to its ideal or minimal configuration. It was then confirmed by abstract mathematical methods by researchers Andrzej Stasiak and Corinne Cerf.

It is possible that this quantization may have implications for both the unfolding of DNA and the possible existence of knotted strings in string theory.

Source: this week's New Scientist (issue 2316). Cerf and Stasiak's work is in Proceedings of the National Academy of Sciences (vol. 97, p. 3795), Pieranski's is to appear in The European Physical Journal E.

Writhe (?), v. t. [imp. Writhed (?); p. p. Writhed, Obs. or Poetic Writhen (); p. pr. & vb. n. Writhing.] [OE. writhen, AS. wrian to twist; akin to OHG. ridan, Icel. ria, Sw. vrida, Dan. vride. Cf. Wreathe, Wrest, Wroth.]

1.

To twist; to turn; now, usually, to twist or turn so as to distort; to wring.

"With writhing [turning] of a pin."

Chaucer.

Then Satan first knew pain, And writhed him to and fro. Milton.

Her mouth she writhed, her forehead taught to frown. Dryden.

His battle-writhen arms, and mighty hands. Tennyson.

2.

To wrest; to distort; to pervert.

The reason which he yieldeth showeth the least part of his meaning to be that whereunto his words are writhed. Hooker.

3.

To extort; to wring; to wrest.

[R.]<-- ; extract -->

The nobility hesitated not to follow the example of their sovereign in writhing money from them by every species of oppression. Sir W. Scott.

 

© Webster 1913.


Writhe, v. i.

To twist or contort the body; to be distorted; as, to writhe with agony. Also used figuratively.

After every attempt, he felt that he had failed, and writhed with shame and vexation. Macaulay.

 

© Webster 1913.

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