Abstract
Chaos theory results from natural scientists’ findings in the area of non-linear dynamics. The importance of related models has increased in the last decades, by studying the temporal evolution of non-linear systems. In consequence, chaos is one of the concepts that most rapidly have been expanded in what research topics respects. Considering that relationships in non-linear systems are unstable, chaos theory aims to understand and to explain this kind of unpredictable aspects of nature, social life, the uncertainties, the nonlinearities, the disorders and confusion, scientifically it represents a disarray connection, but basically it involves much more than that. The existing close relationship between change and time seems essential to understand what happens in the basics of chaos theory. In fact, this theory got a crucial role in the explanation of many phenomena. The relevance of this kind of theories has been well recognized to explain social phenomena and has permitted new advances in the study of social systems. Chaos theory has also been applied, particularly in the context of politics, in this area. The goal of this chapter is to make a reflection on chaos theory – and dynamical systems such as the theories of complexity – in terms of the interpretation of political issues, considering some kind of events in the political context and also considering the macro-strategic ideas of states positioning in the international stage.
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Notes
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- 2.
Examples are the occurrence of earthquakes, rainstorms or volcanic eruptions.
- 3.
Examples are air temperature and humidity or the flow of water in perennial rivers.
- 4.
For example, we may measure air temperature only once per hour, over many days or years.
- 5.
For some authors (see [3]), a flow is a system of differential equations. For others (see [45]), a flow is the solution of differential equations. Note that for the Navier–Stokes equations, that describe the motion of fluid substances, surprisingly, given their wide range of practical uses, mathematicians have not yet proven that in three dimensions solutions always exist, or that if they do exist, then they do not contain any singularity.
- 6.
Nonlinear means that output is not directly proportional to input, or that a change in one variable does not produce a proportional change or reaction in the related variable(s).
- 7.
The spontaneous and mass revolution in Iran is considered a massive rupture of chaotic uncertainties and bifurcations into unpredictable dynamical changes in a political system.
- 8.
The scenarios for the future could be based on chaotic uncertainties and bifurcations resulting into unpredictable dynamic changes in the political system.
- 9.
A single man was considered the “butterfly wing” that could cause the German system to bifurcate from democracy to totalitarianism.
- 10.
The tragic event of 11st September in New York brought a chaotic uncertainty to the international political and military arena.
- 11.
The Macedonian Alexander, endowed with great political vision, has created one of the largest empires of the ancient world, unifying the Greek state-cities and mastering the whole Eastern Antique World, with huge consequences for Humanity.
- 12.
A military victory of the Chinese dynasty Han around the year 100 over a Mongolian tribe of the North (Xiongnu tribe) can be considered as the beating of the “butterfly wings” for the tragedies that would occur in medieval Europe. Indeed, the arrival of Attila and his Hunnish Army to the north of the Black Sea in the fourth century may well have been the consequence of that victory in China. This arrival would promote events with long lasting destructive effects in Europe in the middle ages. The Alliance between German and Asian tribes led to invasions and destruction throughout Europe and North Africa. It was the “butterfly effect” working.
- 13.
The discovery of gunpowder in China may have been the initial condition for Europe leaving of the tragic situation in which it was emerged, particularly through its military expansion to the Americas, with the known consequences.
- 14.
On a warm afternoon, on the second floor of a splendid palace that overlooked the market place of the city, sat a king and his minister. While the king was eating some puffed rice on honey, he looked over his land with satisfaction. What a prosperous city he ruled. What a magnificent city.
As he was daydreaming, a little drop of honey dripped from his puffed rice onto the window ledge.
The minister was about to call a servant to wipe up the honey, when the king waved a hand to stop him. “Don’t bother, it’s only a little drop of honey, it’s not our problem.”
The minister watched the drop of honey slowly trickle down the window ledge and land on the street below.
Soon, a buzzing fly landed on the sweet drop of honey.
A nearby lizard shot out its long tongue and caught the fly.
The lizard was taken by surprise when a cat leapt on it.
The cat was pounced on by its worst enemy the dog that had broken free from its chain.
Meeowing and barking erupted from the street below the King and his minister. The minister was about to call a servant to go and deal with the brawling cat and dog when the king said, “Relax, the cat and dog belong to the market people. We shouldn’t interfere. It’s not our problem.”
The cat’s owner was horrified to see her cat being attacked by the big bully of a dog and started whacking the dog with her broom. The dog’s owner was horrified to see her dog being attacked by the big bully of a cat and started whacking the cat with her broom.
Soon, people started coming out from their stalls and houses to see what all the screaming and shouting was about. Seeing their friend’s cat being attacked, they joined in berating the dog and its owner. Others, seeing their friend’s dog being attacked by the cat, also joined in. Very quickly, the shouting became violent and a fight broke out in the street.
The worried minister turned to the King but his only comment was, “Not our problem. Here, have some more puffed rice and honey.” The king and his adviser ate as they watched the fray below.
Soon the police were called in to break up the fight, but the people were so angry, each side convinced that they were right, (right about what, they couldn’t remember). They started attacking the policemen. The fight rapidly broke out into a full-scale riot.
The king eyed the minister and said, “I know what you are thinking, but the army will handle it. Besides, this is not our problem.”
The riot swiftly escalated into a civil war with looting and destruction all over the city. Buildings were set alight and by nightfall, the magnificent city was reduced to a pile of smoking ashes. The king and his minister stood spellbound rooted to the spot where they had been watching all day. Their mouths were hanging open in horror.
“Oh…” said the king quietly, “maybe the little drop of honey WAS our problem.” (freely adapted from the tale of Hovanés Tumanian).
- 15.
And also, evidently, in the area of other reproducing and harvesting natural resources, see [17–24]. Other interesting literature on chaos in biological systems are [29], [32–36] and [38, 39]. In the fisheries field see [5, 6] and [9]. Finally, see [46] for a very interesting connection between ecology and the social sciences.
- 16.
Evidently, this is the compound interest capitalization formula, at interest rate b used for financial purposes.
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Ferreira, M.A.M., Filipe, J.A.C.B., Coelho, M.F.P., Pedro, I.C. (2014). Chaos in World Politics: A Reflection. In: Banerjee, S., Erçetin, Ş., Tekin, A. (eds) Chaos Theory in Politics. Understanding Complex Systems. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-8691-1_6
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