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The geometry of turbulence

Mukul Pal 

Before he died, physicist and Nobel laureate Werner Heisenberg had two questions for God. These were "Why relativity? Why turbulence?". Heisenberg also felt that God knew the answer just for the first question. Turbulence was beyond God. It’s strange the conviction Heisenberg had regarding turbulence also known as fluctuation, noise, divergence, extremity, fat tail, chaos, black swan, etc.

Mathematics is full of conjectures based on turbulence on probability framework. Like the famous birthday paradox, which suggests that we need 57 people to have a 99 per cent probabilistic certainty to meet a birthday twin? In real life, even smaller groups see this repeated rarity. The new discoveries in science suggest that what was thought to be rare isn't. Life, which was thought to be a rare fluctuation (turbulence), is now proved to be more common around the universe.

So much this question of turbulence has bothered thinkers that some of the greatest discoveries have come from understanding turbulence, whether it was the noise leading to expanding universe, Mandelbrot’s fractals or even Pareto’s curve. Nobel laureate Richard Feynman described turbulence as “the most important unsolved problem of classical physics”.

We at Orpheus started with a blindfold called capital but reached the same turbulence. Technical analyst and author Martin Pring called it mega overbought, mega oversold momentum levels. Market analyst John Murphy called it intermarket failures. We called it divergence and the study of outliers. Turbulence is the interconnectedness that drives all of us. Turbulence is the natural connect which explains at a basic level why stock are like earthquakes.

What Heisenberg could be suggesting on the deathbed, apart from referring to God's incomprehension of turbulence, was that if one could comprehend turbulence we have answered a priceless quest of society. There are more questions that are connected to Heisenberg’s observation. Why does nature exhibit exponentially? Why does Pareto 80 - 20 patterns exist? What drives fat tails? What makes a stock deliver extreme gains and another stock lose all of its gains? All these questions are connected to turbulence. And all of these point us to one question, what is the geometry of turbulence?

Before we answer that we have to accept that cause and effect dilutes our understanding of turbulence. It's the human need to see patterns that somewhere drives cause and effect. Stretch the band of history and you can see cause and effect patterns all over the place, in conventionally related or unrelated areas. Correlations are omnipresent and connect butter production in Bangladesh to US GDP, etc. So, if cause and effect is a weak science, understanding turbulence needs more focus on the study of outliers. There is a need for change in mind set from experiencing outliers to studying them.

This is what we highlighted in our paper on ‘The divergence cyclicality’ that outliers were not only periodic but even polarized. They were not rare but regular. They changed phase from positive to negative, transformed from solid to liquid, from black to white. And this geometry of turbulence is a part of everything organic or animated. Turbulence interacts at different levels and creates chaos which is also ordered and patterned.

German mathematician and philosopher Gottfried Leibniz imagined that a drop of water contained a whole teeming universe, containing, in turn, water drops and a new universe within. To see the world in a grain of sand summarises the interconnectedness of everything from stock to life. Without a focus on studying turbulence and just wishing it away, turbulence would remain like the popular animation comedy ‘Horton Hears a Who!’. We can laugh about it without understanding we are part of the geometry.



The author is CMT, and founder of Orpheus CAPITALS, a global alternative research firm

First Published: Fri, December 21 2012. 00:02 IST