Disequilibrium: manmade or chaotic?

Unpredictability and determinism in human society

The butterfly-like Strange Attractor

by Kumar David-September 23, 2017, 12:00 pm 

Unfortunately chaos theory though mathematically well established, is near useless in problem solving since, usually, it is an after the event description of how some condition came about. It may explain how sea surface temperature and rotation of the planet led to a hurricane (‘typhoon’ or ‘cyclone’ in Asia), but you can do as much to stop a typhoon as to switch off a solar flare or fill up a galactic black-hole. Nevertheless it does provide deeper appreciation of the physics and mathematics of complex dynamic non-linear systems. Complex systems are interconnected phenomena where many factors influence each other; examples are the weather, smooth flowing rivers that if disturbed in excess break into turbulent eddies and gushing rapids, fusion reactors whose turbulence has thus far defeated the best engineering efforts to generate electricity from nuclear fusion, and the motion of the ten (including dwarf Pluto) planets and their moons around the sun.

A more complex dynamic phenomenon is human society; social-economic-political. It is difficult to model (write equations) with reliability, data acquisition (getting numbers to plug into equations) is another headache, and the crazy ways of people and leaders is near impenetrable; so how model? Analysts at best work with averages, trends, statistical indicators and cunning insight. But in human affairs, unlike natural or astronomical phenomena where the theory does not give us a lever for intervention, chaos and disequilibrium perceptions provide alarms to foil social catastrophes. I think one can credibly argue that the ethnic imbroglio cum civil war in Sri Lanka was, to a considerable degree, an avoidable calamity. Much is in the abstract domain and overlaps chaos theory; so a bit about that first.

A theoretical appetiser

Let me try to charm you with a few legends of chaos. In Greek mythology Chaos is not a chap, not a god, it is emptiness, nothingness, chasm, the first thing that was – "at first Chaos came to be" (Hesiod). And in Genesis I, 1&2, "In the beginning God created the heaven and the earth, and the earth was without form and void and darkness was upon the face of the deep". Likewise modern chaos theory inclines to things not tangible, odd, frightening, formless and catastrophic. The consequences of war and revolution are chaotic; before an aircraft breaks up in mid-air, airflow around it is chaotic and turbulent; a crime passionnel is a story of emotional chaos.

There are two aspects to chaos theory that, though purists may object, I think are separable. The first is the concept of a tipping-point, the last straw that breaks the camel’s back, the final provocation that is just too much and leads to war, revolution or divorce. The second concept says that in certain classes of complex non-linear dynamic systems, a tiny difference in the starting point, or injecting a tiny difference in the middle, can give rise to huge divergences later and lead to vastly different endings. It is the first concept, not second, that I think is important in social phenomena. But let me first say a little about the second concept.

The second concept gained traction in science in 1962 with the experiments of an American MIT and Harvard educated climatologist Edward Lorenz (1917-2000). Edward is not to be confused with the great Hendrik Lorentz (1853-1928) of Lorentz Transformation fame, which transformation was the bedrock of Einstein’s Special Relativity in 1905. Edward had set up a complex climatological mathematical model and was running it on his computer, then something bothered him so he restarted it and went for coffee. On his return in half-an-hour (computers were 100 times slower those days) he was amazed that it was going all over the place somewhere else. I have reproduced Edward’s famous first graph. He ran the program over and over again starting from what he thought were the same initial conditions. The crazy thing, after tracking the same path for a while, wandered off all over the place! Then it hit him. Although he thought he was starting from the same initial conditions each time, actually his inputs had tiny differences way down in the computer’s rounding off. Think of tiny differences far after the decimal point.

The conclusion was that in certain classes of non-linear dynamic systems, tiny differences in initial conditions may not show visible differences for a while, but later, differences grow. Edward justifiably reused the old word chaotic to describe the jig he had found. I don’t think this is significant in social, economic or political matters. One rupee more or less in the budget is not going to bring the economy crashing down. Though economics is non-linear complex and dynamic it does not have the same properties as Edward’s equations; remember I said "certain" classes of dynamic systems.

Edward’s butterflies

Let us take Edward’s system of many variables connected by dynamic equations. Let the computer run, then plot one of the variables on the X-axis and another on the Y-axis. The graphic would cycle on and on, never exactly repeating itself but always keeping the same rough pattern.

The plot which looks like a butterfly is called a Strange Attractor because it never repeats itself exactly, but always retains fractal symmetry. A doe in season runs away but makes sure never to get too far away from the stag. Strange Attractors have an analogy in politics; for seventy years the UNP and SLFP have been attractors for the voting masses; though exposed as corrupt and discredited as vile, the voter still spins around them, never repeating exactly the same pattern but never entirely deserting them. In personal life we are familiar with unhappy loved ones who can’t summon the willpower to break from a callous partner or a family despot; a strange attractor indeed.

There is another butterfly associated with Edward Lorenz’s name which is palpably false. It claims that a tiny action at one place at one time may unleash catastrophic events elsewhere at another time. This Butterfly Effect (not to be confused butterfly shape of the previous para) is false. Certain closed systems of non-linear differential equations may "secretly" build up great differences that become evident much later. A butterfly flapping its wings in Brazil creates a tornado in China years later. This is false because butterflies in Brazil and storms in China do not form a closed system. Millions upon millions of factors, large and small, not included in the equations, intervene in the real world and smooth things out rendering the flapping butterfly an immaterial pest.

The tipping-point

The breaking point, or going beyond the limit when a safe situation tips over into disorder, is a concept people have been familiar with from the beginning of history. A case on our doorstep was when the gritty hand of power-greedy Rajapaksa reached for the Eighteenth Amendment. This was a critical boundary which if not crossed may have allowed the despot to retain power.

A much quoted example is that fabled assassination in Sarajevo on 28 June 1914. Could one argue that if Serbian terrorist Gavrilo Princip and his five associates had restrained themselves the world would have been spared the ‘Great War’ and 20 million dead? Tipping-point hypotheses are advanced for revolutions, the Great Depression, Richard III’s defeat on Bosworth Field and July 1983 in Lanka.

The hypotheses go like this; if the heir to the Austro-Hungarian throne had not been cut down the Empire would not have invaded Serbia; Germany and Russia would not have mobilised, etc. If the Fed had cut interest rates and boosted the money supply (what Treasury Secretary Andrew Mellon and President Hoover did not do) there would have been no Great Depression. Shakespeare’s Richard III bellowed "A horse a horse my kingdom for a horse" and if only a blasted mare had been found the outcome at Bosworth Field would have been reversed. And there are those who believe that if the LTTE had not blown up 13 soldiers on 23 July the worst communal carnage in our history would not have occurred. All this I argue is utter rubbish.

The truth to the tipping-point thesis is that the truck was already overloaded, it was hanging over the cliff, the last push simply made the inevitable happen. If it was not tipped on this occasion the next gust of wind would have done it. These were catastrophes waiting to happen. The cause of WW1 was the scramble of European Imperial powers to divide the colonial world, Richard’s defeat was unavoidable in the face of Tudor power, the Great Depression was structured into the architecture of interwar capitalism, and 1983 was a sore in a bigger pathology of communal eczema oozing from our national psyche. The tipping-point is only a tipping point; the reality is the big load that tipped.

The crisis version of chaos theory that describes, after the event, what happened at a volatile tipping-point is interesting as history. It’s not much use in problem solving which is concerned with the dirt-truck which should have been emptied before it tipped.

If a brick fell in September 1917 and conked Lenin, there would still have been revolution in Russia because of hunger, the horrors of war and a poverty stricken landless peasantry. The outcome, I grant, may have been a little less certain. Hmm, now that’s a thought to ponder!