2 Even religious view of the world was deterministic. In the Middle Ageâs religious dogma there were four types of causes: Material, Formal, Final and Efficient. Scientists just inherited this view and accepted it because their results of experiments showed correctness with the behavior of nature. In the past (and even today), Determinism could not explain all events as people notice that there are things that happen randomly. By random events, we speak about events that happen by chance or, compared with Determinism, there is maybe a particular cause for this event to happen, but the outcome (consequence) cannot be predicted. The random event can be explained by throwing a dice. If the dice is well balanced, all six sides of a dice can show up equally and we cannot predict which one will happen with accuracy. Scientifically, I can say that, the probability of each of them to happen is equal and that is the reason why I cannot predict which one of them will show up after tossing.
In general, the random events are events of guessing and the cause of happening as these cannot say anything that will predict the future events by knowing the past and the present events. If I throw a coin and I get a âtailâ, throwing a coin one more time will produce a result I can only guess. Simply, the âtailâ from the previous throw will not contribute to my understanding of the process, it will not help me predict whether I get a âheadâ or a âtailâ in the next throw.
Approximately around 1960s, the world was deterministic and random, but in the second half of the last century, slowly, another âview of the worldâ was discovered: The Chaos!
At the beginning, the Chaos was discovered only in complex systems. Complex systems, in the general meaning of the word,3 are systems that consist of many parts. The system functioning depends on the functioning of the parts, individually and in combination, with other parts, in the scope of the system. Actually, the system does not necessarily need to be complex (made by many parts). It could be also very simple, but it is enough if the interactions between the parts are complex. Most of the complex systems have interactions between the parts inside which are nonlinear, and as such, it is not easy to (scientifically) find the solutions of the equations that describe the system. In general, the Chaos can show up if the description of the functioning of the system can be described by three or more variables. If there are only two variables, the Chaos cannot happen.
The evident example of the complex system, where the Chaos can be registered, is the weather. Other examples are the turbulence in the air, the flowing of liquid through the pipes, the predator-prey model in nature, etc.
Usually, the complexity of the systems is connected by uncertainty of the prediction of how the system will behave: More nonlinearity â more uncertainty. And more uncertainty â more unpredictability.
The Chaos was noticed by the humans around 1960s as a purely mathematical concept and, as such, it was not accepted immediately by the physicists. Although there was some research dedicated to the nonlinear dynamics of the complex systems, during those times, the physicists mostly dealt with the theory of relativity and the quantum mechanics. But thanks to some of the âstubbornâ scientists, the Chaos found its âplace under the sunâ. At the beginning, it was not so revolutionary due to its abstract nature, but having in mind that it was dealing with nonlinear systemâs behavior, it developed very fast.
3 There are also complex systems in regard to the equipment (Âmachinery!), which may differ from this general meaning. Later researches showed that the Chaos can be noticed even in simple systems with nonlinear structure. Of course, if the structure of the systems is more complex, the Chaos will bring more unpredictability. Today, there are Chaos researches in the fields of meteorology, physics, biology, chemistry, cardiology, economy, etc.