Tango Physics

Here is something Michele emailed me recently which I think is very clever indeed. It is by a chap called Mike Barrow and appears on yahoo tango chat room:

http://groups.yahoo.com/group/tango-uk/message/4543

I think we would all have a better knowledge of tango if we understood the fundamental physics underlying it. I have been researching the academic journals and for your education and enjoyment I have summarised the current state of knowledge. It answers such unresolved questions such as:

Why is tango so difficult?
Why do you never see three people dancing tango together?
Why collisions occur on the dance floor.
Why tango exists.

Some knowledge of quantum physics is desirable but by no means essential. Now read on...

Tango Physics

The laws of physics apply to tango just as they do to other phenomena. Here is a summary of current knowledge, obtained from leading text books and recent research papers. Some of the more advanced theories must remain speculative, pending further research.

Basics

Tango consists of the interaction of electrically charged particles operating within a musical energy field.

There exist just two types of elementary particle: the tanguera particle and the complementary tanguero particle. The tanguera particle (or simply tanguera) is electrically charged by the addition of high heeled shoes and a glamorous dress. The quantity of charge is directly proportional to the height of the heels and inversely to the quantity of material in the dress.

In contrast to the tanguera, the tanguero particle is more easily and economically charged. The very appearance of a suitably charged tanguera isusually sufficient to charge the tanguero. Some tangueros find themselves already charged on waking up in the morning, for no apparent reason. The quantity of charge appears totally unrelated to the tanguero's shoes or apparel. Indeed, it also seems to be based on the tanguera's shoe height and dress material.

Having complementary charges, the tanguera and tanguero are naturally attracted to each other. The force of attraction is proportional to theproduct of their individual charges and inversely proportional to the square of the distance between them (the inverse square law). As this distance approaches zero (the so-called close embrace) the attraction increases without limit, leading to important and potentially unstable quantum effects (see below).

The charges of two such particles in a close embrace cancel each other (being of opposite polarity) and the couple become electrically neutral, thus attracting no further particles. This is why you hardly ever see three particles dancing together. (The Tango Lesson was trick photography. ) It also explains why couples (which are electrically neutral) can collide with each other.

Two tanguera particles have charges of the same polarity and are therefore likely to repel each other, especially if wearing similar shoes or dress.

Two tanguero particles are able to happily co-exist in spite of the similarity of their charges. The exception to this occurs in the presence of a single tanguera particle, when one of the tangueros attaches to the tanguera and the other is ejected.

Interactions of particles

Tango particles interact within a chamber known as a milonga under the influence of musical energy supplied by an orquestra or, more cheaply, a portable CD player.

The particles resonate with the application of the musical energy. Ideally the particles resonate in proportion to the energy supplied (the basic energy of Argentine tango, or 'beat' for short). However, not all particles resonate at the appropriate frequency.
Those which do are said to possess the property of musicality. Tanguera particles are particularly strongly attracted to tangueros possessing this property.

A tanguero at the extreme of the distribution, usually resonating at an excessively high frequency relative to the beat is known as the null tanguero particle. Continued contact with the null tanguero will usually cause the tanguera particle to become completely
electrically discharged and to leave the dance floor.

Newton's laws of tango

1. A tanguera particle will remain at rest or continue in constant motion unless acted upon by a force, usually applied by the tanguero particle.
2. A tanguera of mass m, acted upon by a force f exerted by the tanguero will move with an acceleration a according to a = f/m. Beyond this, it is generally unwise to refer to the mass of the tanguera particle.
3. For every tango teacher there is an equal and opposite tango teacher. E.g. if a teacher says one should never lead with the left hand, then there exists somewhere a teacher who says this is permitted or even encouraged. If one teacher says the cross should be led, there is another who says it isn't. This is why one should never change teacher, except in extremis.

Tango and chaos theory

The discovery of the mathematical theory of chaos in the 1980s shed new light on some unresolved mysteries in tango. Just as a butterfly flapping its wings in South America can cause a cyclone in Europe, so a misplaced step in one part of the dance floor can cause, through a consequential series of collisions, avoidances and sudden changes of direction, several particles to trip over each other some time later in another part of the milonga.

This is particularly likely if a new (i.e. inexperienced) tanguero particle enters the dance floor, holding an excessive charge due to the close proximity of so many charged tangueras. Attempting to restore its equilibrium and shed excess energy, it moves at high velocity with many sudden and unanticipated changes of direction. This initiates a
series ofcollisions which turns an initially orderly dance floor (low entropy) into one of disorder (high entropy).

Chaos also reveals itself at the level of individual particles, for example when executing a giro. The giro normally progresses according to the well-known Salas-Naveira equations of motion. However, a tiny perturbation to the initial step can become magnified in subsequent steps such that the two particles complete the giro in totally the wrong positions or, in the worst scenario, fly apart completely. This solves the mystery of why the tango is so difficult.

Why tango particles exist

Very occasionally two particles resonate together with perfect symmetry and harmony, in time with the beat. The force of attraction between them increases as the distance between them decreases until they effectively become, for a short time, a single particle (a singularity in mathematical terms). These are the quantum effects referred
to above and they lead to a tear in the very fabric of space-time itself and the particles disappear from view, into a state known as nirvana (in the popular imagination this is often located in the Buenos Aires area of Latin America). No communication with the particles is possible during this time. The particles only reappear when the energy supplied by the musical field is turned off. We can only speculate where the tango particles go. The particles themselves are quite unable to explain since, for them, time has slowed to a standstill (in accordance with Einstein's theory of relativity). Indeed, some of them are incapable of speech for several minutes on their return. However, there is general agreement that this state of nirvana is the very reason for the tango particles' existence.