The AEther

In early modern physics, the AEther (or Ether) was believed to be an invisible space-filling substance or field that was a transmission medium for electromagnetic or gravitational forces.

Tait's Tabulature of Knots

Peter Guthrie Tait (1837-1901) was a Scottish mathematical physicist, whose investigations in knot theory contributed to the field of topology as a mathematical discipline. while conducting experiments with a machine that blew smoke-rings. Tait observed that the rings had a regular donut-like form, which he hypothesised was the result of atoms within them bonding through the Ether.

1867
A note from Peter Guthrie Tait scribbled on an envelope asks an unknown recipient: "Can't you come on Monday the present at the performance? An elliptical hole gives the rings in a state of vibration!!!"

In a room, thick with smoke, Tait and William Thomson (Lord Kelvin) are conducting an experiment to test the German scientist Helmholtz's theory, that closed vortex lines in a fluid remain stable forever. Tait is using a box that emits smoke made from a pungent mixture of ammonia solution, salt and sulfuric acid. He taps the back of his makeshift vortex cannon, and thick rings waft from a hole drilled in its front. Tait describes them "like solid rings of India rubber". His theory is that each smoke ring is structured around knots in the ether, a space-filling substance that was believed to transmit matter. Tait begins to tabulate possible forms of mathematical knots, contributing to the mathematical field of knot theory.

Knots

A knot is an entanglement, an intentional complication in cordage.

Knot Theory

Knot theory is a field of mathematics that studies the topology of knots.

Unknot

The unknot, or torus, is the first type of mathematical knot listed in knot theory. Intuitively, the unknot is a closed loop of rope without a knot in it.

Mathematical knots

Mathematical knots, or knots which are studied in the field of knot theory, are based on the embedding of a circle within three-dimensional space. They are different from the usual idea of a knot, that is a string with free ends. Therefore, mathematical knots are (almost) always considered to be closed loops.

Knotworks

Knotworks are visualisations of network topologies which use mathematical knots to represent a collapsing of the distinction between node and link. Just as a knot is a complication in which the tangle can conceal parts contained (as in klein worm topologies), unravelling the knot reveals that it is homeomorphic to a continuous link. The link and the node are the same, unravelled.