The critical mass and the catastrophe theory

In the field of sociology is called critical mass the amount of people from which a particular phenomenon occurs and acquires an own dynamic that allows it to hold itself and continue existing, even grow. This concept has its equivalent in physics, which considers the critical mass as the minimum amount of material needed to produce and maintain a nuclear chain reaction.

When a person stands on the street and looks skyward, usually nothing outstanding happens and the rest of the people continues its path, ignoring her. When three people stop and look at the sky, maybe some others look curiously for a moment before continuing with their own. But there is a certain number of people —in this case would depend on several factors such as culture where the scene takes place, weather or width of the street— which can make others stop and look skyward also.

If a specific number of people look at the sky at the same time, they can get others to do the same —Image Unknown Author

Long time that disciplines such as biology, history, sociology or mathematics have been interested in the phenomenon, mainly because of its enormous capacity to generate lasting or permanent changes, as specified by the catastrophe theory, which shares field with the critical mass and was launched in the late 60s by the French mathematician René Thom and widespread later by the Christopher Zeeman studies, which applied it to the human sciences.

The catastrophe theory is especially useful for the study of dynamic systems that represent natural phenomena —whose characteristics can not be accurately described by the differential calculus— and represents the propensity of structurally stable systems to manifest discontinuity, divergence and hysteresis.

Discontinuity implies that in any system may occur sudden changes in behavior or outcome and then, at a certain point, is no longer possible to maintain the same state and undergoes an abrupt change.

Divergence is the tendency of small changes to produce big changes. If a plane can accommodate 100 passengers, a demand of 101 will motivate the need for a larger plane, and perhaps having to land at a different airport. In other words, very small variations in the starting point can derive to results totally divorced.

Hysteresis is the phenomenon by which the state of a material depends on its previous history. The tendency of a material is to preserve their properties even in the absence of the stimulus that generated them, although it is true that if the behaviors vary can lead to not return to starting position. A very simple example of a process of this type is the length of a metal rod depending on the temperature: if certain degrees are exceeded the metal rod will melt, a piece come off and it will be impossible to return to the initial state.

Slavery dates back to Antiquity —Aristotle even claimed that it was a natural phenomenon— and was common practice until the late XVIII century —Image Unknown Artist

Although these terms are very technical and relatively recent, in practice for centuries the most intrepid parts of the social mass have been starred acts that have marked the political and social future of the world, affecting the system and in some cases modifying paradigms: from the struggle of the plebeians against the patricians for their rights as citizens of Rome to the French Revolution, passing through the rebellion of African slaves across all America, to name just a few. After that, the world was never already the same.