Page 228 - J. C. Turner "History and Science of Knots"

A History of Topological Knot Theory 219

a professor at the Darmstadt technical university, published a more rigorous
account, which also gives a detailed overview of the early history of topology
[301.
In 1897 Hermann Brunn observed that any knot has a projection with
a single multiple-point [20]. This proposition became attributed to James
Alexander, some 25 years later.
In this period Andre Hurwitz did some work on Riemann manifolds, which
were first steps leading towards theories of braids.
This completes our summary of German work in the field around that
time. We must cross the Channel to England to continue our story of the
history of knot theory.

5. The Work of Peter Tait

Further substantial progress in knot theory was not made until Sir William
Thompson (1824-1907; Baron Kelvin of Largs) announced his model of the
atom, his `vortex theory'. Thompson began writing about this concept in
the mid-1860s. He believed that all material matter was caused by motion
in the hypothetical ether medium, which he termed vortex motion [99]. How
did knots relate to these ideas? Scotsman Peter Tait (Dalkeith, 1831-1901)
was a close associate of Thompson. In 1867, having been greatly taken by
Helmholtz's papers on vortex motion, Tait devised an apparatus for studying
vortex smoke rings in which the rings underwent elastic collisions exhibiting
interesting modes of vibration. The experiment gave Thompson the idea of
a vortex atom. The imaginative picture painted by the theory he developed
subsequently was one of particles as tiny topological twists, or knots, in the
fabric of space-time. The stability of matter might be explained by the stabil-
ity of knots; their topological nature prevents them from untwisting. His aim
was to achieve a description of chemistry in terms of knots. More specifically,
Thompson wanted to produce a kinetic theory of gases, a theory which could
explain multiple lines in the emission spectrum of various elements. A swirling
vortex tube would absorb and emit energy at certain fundamental frequencies:
linked vortex tubes would explain multiple spectral lines. In short, he believed
that the variety of chemical elements could be accounted for by the variety
of different knots. The main advantage of Thompson's model was that its
indivisible bits would be held together by the `forces' of topology. This con-
struction would avoid the problems inherent in devising forces to hold together
an atom made up of little billiard balls.
The theory was taken seriously for quite some time, and even eminent
scientists like James Clark Maxwell stated that it satisfied more of the con-
ditions than any other hitherto considered. In fact, in retrospect one could
add transmutation to its merit-list. The ability of atoms to change into other