In general, chaos theory is not about disorder, it is about very complicated systems of order. In social sciences, chaos theory is the study of complex non linear dynamic systems of social complexity. This field of theory was born in the 1970s and has grown by leaps and bounds since then in all of the sciences.
There is the study of the way that things and people interact. The very connection, contact, or connections between people in society creates conditions where even the smallest point of interaction can have non linear or seemingly chaotic and even very large results.
Chaos theory does not assume that there is exquisite and exact, but complicated order to everything, or that all systems will eventually be made predictable with complete accuracy. This theory aims for finding the general order of systems and of systems that are similar to each other. In other words, the assumption is that the unpredictability in a system can be represented as overall behavior or in representations of behavior, which in turn gives some amount of predictability, even where the system is unstable.
In that sense, there is the idea that systems can be modeled through mathematics and other methods.
Linear mathematics describes the predictable things that flow along a straight line. Linear regression mathematics attempt to make the crooked lines straighter. The non linear aspect describes a world that does not operate on straight line principles.
The natural world also has recursive aspects and that requires complicated mathematical algorithms and differential equations to create models of that activity. In chaos theory there are issues of insanely small changes that can have huge results that come back to create more change until the original behavior is gone, replaced by entirely new behavior.
There are inconsistent activities that do not have established periodic aspects, but the overall behavior of the attractor is pretty much the same.
And the issues are complex. The more complex the system, the more the model is required to look like the real system in order to predict results. Hence, the beauty of weather models and fractal art. Crop circles are said to actually have corresponding mathematical calculations.
The terms used in chaos theory are the butterfly effect, fractals, sensitive dependence on initial conditions, strange attractors, similar attractors and systems of dynamic equations. The butterfly effect is the famous thought of the effect of the moving butterfly wings on the weather: a very small movement that may have huge implications.
Sensitivity to initial conditions applies to the understanding that even the slightest change in the starting point can lead to greatly different results or outcomes.
Truly random systems are not chaotic systems as chaotic systems have some kind of order, with an equation that determines overall behavior.
Chaos theory is not exactly widely available as a tool that has easily calculated or that has direct applications in the social sciences these days. It is a background theory that helps to look at he natural world and complex societal systems in new and exciting ways. The mathematics involved are highly complex and require some advanced study in maths.
There are, however, an increasing number of real world applications in modeling population growth, epidemics, market and economic behavior and arrhythmic heart palpitations. Chaos mathematics are highly adaptable to painting and art, film FX, and other areas where complex and recurring natural structures must be convincingly shown in virtual representations.
