# Conga Line Mathematics

Recently I was situated on a mezzanine floor overlooking a heaving dance party, and had the opportunity to witness the spontaneous formation, growth, and eventual breakdown of a conga-line. It was a fascinating structure to observe, and when I searched for research on the mathematical and sociological aspects of this behaviour, I drew a blank.

So I have a duty to science to record my observations, for the benefit of humanity.

Before embarking on this study we must discuss the nature and definition of a conga line, with a little brushing up on the history books.

According to some sources, the Conga line is a novel carnival dance from Cuba that rose to popularity in the 1930s, but other sources point out that trilobytes have been fossilized mid-conga as many as 480 million years ago. So the truth is probably somewhere in between.

Strictly speaking a conga line involves people lined up, one behind the other, with each person's hands on the hips (or shoulder) of the person in front, marching in a 1-2-3-kick shuffle in time to music.

Now that we've described the basic system, we could hopefully recognize one if we encountered it in the wild, and armed with this background knowledge we can discuss the pertinent aspects I wish to share.

# Phase 1: Formation

A dance floor, at any moment in time, has a certain energy. The energy varies as people leave or join the dance floor, as songs change from one to the next, as alcohol or other substance enters the blood stream of the revelers, and so on. For a conga line to form, the energy level, ε, must be above a certain threshold which we will call:

Τc

A simplistic simulation of the conga equation would simply say, when ε > Τc there is a probability ρc that a conga line will form, and leave it at that.

But the granularity here is insufficient for any useful predictions to be enjoyed. We need to attack the problem at a deeper level.

## Simulation

I wanted to find a way to simulate conga dynamics. I started to write a logo program, and got as far as a dance floor filled with random dancers:

But I didn't know how to use the type system to create an array of dancers.

I considered modelling them in a C# program, and releasing it as a game through the Itch.io platform for indie gamers.

But a different option that I found particularly intriguing would be to create a text adventure game, from the point of view of a person on a dance floor, confronted with the choice of starting, or joining, or not joining, or breaking into, or leaving, a conga line.