A Five-Minute History of Knot Theory

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Hermann von Helmholtz worked out the interaction of two smoke rings traveling in the same direction: "If they have the same direction, the foremost widens and travels more slowly, the pursuer shrinks and travels faster, till, finally, if their velocities are not too different, it overtakes the first and penetrates it. Then the same goes on in the opposite order so that the rings pass through each other alternatively.” Kelvin incorporated Helmholtz's ideas into his theory of the vortex atom. According to this theory, chemical elements are small, knotted vortices of ether. Classify knots and links, and you classify the elements.

This is a representation of Helmholtz's theory in gif format produced by artists at American Scientist. Select the Download tab in the upper right to see the two-ring animation.

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