Applications 2

Even the great practical knot tyers have been fascinated by the form of knots as much as by their use. In his foreword to "The Book of Knots", Clifford W Ashley wrote:

To me the simple act of tying a knot is an adventure in unlimited space. A bit of string affords the dimensional latitude that is unique among the entites. For an uncomplicated strand is a palpable object that, for all practical purposes, possesses one dimension only. If we move a single strand out of the plane, interlacing at will, actual objects of beauty result in what is practically two dimensions; and if we choose to direct our strand out of this plane, another dimension is added which provides an opportunity that is limited only by the scope of our own imagery and the length of a ropemakers coil.

It is this same spirit of discovery that inspires mathematicians.

Fluid Flows

New studies of equations which determine flows like those in the atmosphere around our planet, show how particles can move in complicated knotted paths. Knotted patterns can be seen in the smallest particles of life and in the motion of storms around a planet.

String Theory

The origins of mathematical knot theory go back to attempts to interpret the properties of atoms in terms of knots in the aether . That attempt failed as new knowledge about both knots and atoms showed that there was no clear link between them. Since 1984 a new link between knots and theoretical physics has begun to take form. The discovery of some new invariants in knot theory took place. These invariants were discovered by Vaughan Jones who was working in an area of mathematics closely related to physics. Combining them with aspects of "string theory", a branch of theoretical physics, has produced a very rich theory that may one day give a unified description of the four fundamental forces of nature, gravity, electro-magnetism, and strong and weak interactions between particles.

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© Mathematics and Knots, U.C.N.W.,Bangor, 1996 - 2002
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