The black spots on the bottom of the swimming pool are signatures of topological defects dynamically induced in the surface (of fluid density discontinuity) that separates the water and the air. The topological defects are called Falaco Solitions and, in the words of I. Prigogine, they are states of matter far from (thermodynamic) equilibrium Yet, in a still pool of water these topological defects have a surprisingly long lifetime -- they will last for many minutes.
A remarkable feature of Falaco solitons is that they are easy to create and are
so ubiquitous. Similar topological phenomena are to be expected in
discontinuities at all scales -- from the micro physics of nucleii to the
galactic defects in cosmology.
Just after WW II, one of my first contacts at MIT was a Brazilian young man
named Jose Haraldo Hiberu FALCAO.
Now MIT is not known for its athletic achievements, and when one weekend Haraldo scored two goals - giving MIT one of its few wins (ever) - the sports section of one of the Boston papers, misspelled his name with the headline ~
"FALACO SCORES TWO GOALS - MIT WINS"
Frankly I do not remember the exact headline from > 55 years ago, but one thing
is sure: Haraldo was known as FALACO ever since.
Haraldo moved back to Brazil and our ways parted.
I became interested in many things, the most pertinent to this story included topological defects and topological evolution in physical systems.
In 1986 I thought it would be great fun to go to Rio to see my old college friend, and then go to Machu Pichu to watch Haley's comet go by. My son was an AA pilot, so as parents we got a free Airline Ticket ticket to Brazil
Haraldo had married into a very wealthy family and had constructed a superb
house, that his wife had designed, hanging onto a cliff-side above Sao Coronado
beach south of Rio. He had a white marble swimming pool next to the house fed
by a pristine stream of clear water.
The morning after my wife and I arrived in Rio (Haraldo's chauffeur met us at
the airport in a big limo) I got up, after sleeping a bit late, and went to the
pool for a morning dip. Haraldo and his family had gone to work, and no one was
about. I sat in the pool. wondering about the fortunes of life, and how
Haraldo - who I had help tutor to get through MIT - was now so very wealthy, and
here I was - just a poor university professor.
I climbed out of the pool, and was met by two servants who had been waiting in
the wings. One handed me a towel and a terry cloth robe, and the other poured
coffee and set out some breakfast fruit, croissants, etc.
I put a lot of sugar into the strong Brazilian coffee, as Haraldo had taught me
to do long ago, and was stirring the coffee when I turned toward the pool (about
5-10 minutes after climbing out of the pool). In the otherwise brilliant
sunshine, two black disks (about 15 cm in diameter ) with bright halo rings were
slowing translating along the pool floor.
I went over to the pool, jumped in to investigate what was going on, and
Voila!!!, the black discs disappeared. I thought: Here was my first encounter
of the third kind and I blew it.
I climbed out of the pool, again, and then noticed that a pair of Rankine vortices was formed as my hips left the water, and that these rotational surfaces of positive Gauss curvature, within a few seconds, decayed into a pair of rotational surfaces of negative Gauss curvature. Each of the ultimate rotational surfaces were as if someone had depressed slightly a rubber sheet with a pencil point forming a dimple. As the negative Gauss curvature surfaces stabilized, the optical black disks were formed on the bottom of the pool. The extraordinary thing was that the surface deformations, and the black spots, lasted for some 15 minutes !!!. They were obviously rotational solitons.
The rest is history, and is described on my website and articles in some detail.
Snell's law projects the solar rays in the manner observed, but what was not at
first apparent was that there is a circular "string" -- a 1D topological defect
-- that connects the two 2D topological defects of negative Gauss curvature.
The string extends from one dimple to the other, and is evident if you add a few
drops of dye to the water. Moreover, experimentation indicated that the long
term soliton stability was due to the Global effect of the "string" connecting
the two dimpled rotational surfaces. Dye injection later on demonstrated the 1D
arc connecting the dimples. If the arc is sharply severed, the dimples do not
"ooze" away, as you would expect from a diffusive process; instead they
disappear quite abruptly.
Upon returning to the US, I gave a talk at the 1986-87 Dynamics Days meeting in
Austin, Texas, describing the observations.
I knew that finally I had found a visual, easily reproduced, experiment that
could be used to show people the importance and utility of Topological defects
in the physical sciences.
Most of these ideas are available on Cartan's Corner.