Knot Theory

                Knot Theory: A means of describing the internal structure of knots in mathematical terms.

In 1771/ the French musician Alexandre-Theophile Vandermonde (1735-96) recognized that pinpointing the possition of a one-diamentional, non intersecting line in space would deepen mathematical understanding. But the world had to wait untill 1833 for German Mathematician Carl Friedrich Gauss (1777-1855) to develop a mathematical model that discribed the universal nature of loops that cannot be undone.

                 Knots occupy three-dimensional space, but they also link a line within that space that is always in mathematical studies joined to itself. Describing the possition of this linked curve in numerical terms is a hugely complex problem: it requires a geometry of position, a notable to show how a looped and twisted three-dimensional object is located both relative to itself and in relation to the space surrounding it. For this, Gauss defined the linking integral, a whole number that describes how many loops or links a knot has.

                People have been braiding and tying knots using them to remember things and making patterns out of them, almost since the evolution of opposable thunbs. Developing a theory that described these twists and loops was a phenomenal challenge. Ultimately, knot theory is knowledge for this own sake, a kind of Zen appreciation of a koan (paradox) or problem numerically defined. Perhaps, more than any other idea, it shows that sometimes solving a puzzle requires no further justification than its inherent merit. However, since its development, the theory has proved usefull as a basis for understanding how DNA behaves and the arrangement and position of other polymers in space. It will also help in the development of quantum computers when our thirst for more powerful information processors outweighs the capacity of current silicon-based systems.