It is well known that when the Sun is at zenith precisely over Buenos
Aires on odd numbered years (muslim calendar), the ray through the SW lower
corner of the third tallest stone and the NE upper corner of the tallest
stone in Stonehenge (Salisbury Plain, Wiltshire, S. England) points straight
at Neptune's moon Naiad (discovered 1989, Voyager 2). This fact is so stunning
it cannot possibly be due to chance alone; it must be a sign that the Gods
want us to study astrological lineups.
We therefore pick a knot, given as a specific embedding of S1 in R3,
and count the number of "Stonehenge-inspired chopstick towers" that can
be built upon it; namely, the number of delicate arrangements of chopsticks
whose ends are lying on the knot or are supporting each other in trivalent
corners joining three chopsticks each, so that each chopstick is pointing
at a different pre chosen point in heaven that has a high mythical meaning.
Quite amazingly, when these stellar webs are counted correctly, the
result is a knot invariant valued in some space of diagrams, deeply related
to certain aspects of Lie theory. This allows for a rich interplay between
the two seemingly unrelated topics of knots and Lie algebras.
While all of this could have been discovered some 4,000 years ago by
any visitor to Stonehenge, the history of the subject is somewhat briefer,
involving the names Witten, Vassiliev, Bott, Taubes, and D. Thurston, and
mostly involving dates later than 1988.