*Another old piece I wrote in **December 28, 2008**. This was half a decade before I questioned Richard Thaler in **"End of Behavioral Finance"**, (Pal, 2013). **I was still figuring out the connection between statistics and psychology, and was experimenting with various predictive tools. Amazing history of mathematics when Poincare referred to Cantor's idea as a grave disease.*

The October low we talked about held against all odds. A strange time cycle held against all conventional knowledge, which failed. And now that 2008 comes to end, we can sum up a few gaps in generational thinking which concerns us as a society and as economic beings. On one hand, the experience is overwhelming because the ideas overlap most areas of study viz. economics, finance, history, psychology, mathematics, sciences, time cycles and art. But on the other, it's no short of a revolution in research to be able to comprehend, interpret and derive applied predictive tools from such a vast scale of research areas. It may take another generation for us to look for convergence in ideas. And there are things we may never understand. But then it’s the quest that leads to solutions and differentiates one society from the other.

Though Adam Smith's capitalistic model stands challenged, we have had no alternate system that has stood so long. Even some long-standing socialistic systems have taken elements of capitalism and witnessed enhanced prosperity. Karl Marx’s idea of capitalism as a system prone to a cyclical crisis was true. But still, the system has survived and lived, more than any mortal soul today. We are sure, the human race will move beyond this model, but this is too farsighted a thought for us as a myopic society.

Charles Dow started modern finance discovering a fractal, without knowing it was one. Elliott an accountant by profession rediscovered that markets were fractalled. He redefined the Dow Theory with his principle. But even Ralph Elliott despite his fractal observation only later started connecting it with Fibonacci mathematics. Both Dow and Elliott mentioned about social behavior aspects along with their theories but did not quantify behavioral finance like Daniel Kahneman did with the prospect theory.

Father of fractal geometry Mandelbrot may have coined the term fractal, and proved them mathematically, but he only extended the work of Dow, Elliott and Gaston Julia. And if all these connections seem strange coincidences, the fact that Eugene Fama, the father of Efficient Market Hypothesis was a doctoral student under Mandelbrot should surprise fractal practitioners and fundamentalists who might consider themselves from different school of thoughts.

But this is where the gap lies. Mandelbrot’s M set has become popular outside mathematics both for its aesthetic appeal and for being a complicated structure arising from a simple definition, but this has not really pushed Elliott structures forward to a similar popularity. It’s this lack of convergence of market fractals with the M-set that has also pushed the fractal work done by Thomas Malthus and Verhulst as peripheral despite being part of the same extended thought.

This is not the only disconnect. Fractals are growth, decay structures, whether we take the M-set, Elliott’s Fractals or Verhulst’s ‘S’ curve, they all convey the natural process of growth and decay, which is cyclical. Not many attempts have been made to connect cycles with fractals. Tony Plummer makes an attempt at explaining Elliott fractals through cycles. But this is such a nascent area that even experienced cyclists admit they have never thought about Elliott being a footnote in the larger subject of cycles. In crux market fractals being a subset of market cyclicality.

The discontinuity extends, when you read the work of physicists like Eugene Stanley from Boston, who has written many papers on power law in markets extending the thought of Kingsley Zipf, the linguist who first proved the power law relationship in popular words spoken in the language, 150 years back. Though we have proofs of power law governing us in nature and markets, we never as academicians, practitioners and scientists thought of power law in cycles. Plummer despite his comprehensive attempt on Cycles fails to talk about it. We at Orpheus link Cycles with Fractals with Mathematics suggesting Cycles as the finality above fractals. Cycles also reinforce the thought we mentioned regarding history being modelable as a science.

Robert Prechter might disagree with the fact that we place cycles over fractals. Prechter also calls Elliott a science and not art. We disagree, as cycles are about two things periodicities and patterns. Watching and understanding a pattern will always be an art and not a science. This is where we come to the other aspect of mathematics.

George Cantor theorem implies the existence of an infinity of infinities. Cantor's theory of transinfinite numbers was regarded as so counterintuitive - even shocking that it encountered resistance from mathematical contemporaries such as Henri Poincare. A few saw Cantor's work as a challenge to the uniqueness of absolute infinity in the nature of God. Poincare referred to Cantor's ideas as a grave disease infecting the discipline of mathematics. Some even went ahead and called him a "Scientific Charlatan", "renegade" and "corruptor of youth”, "utter nonsense", "laughable and wrong". The debate Cantor opened is also a cyclicality linked with the subject of Mathematics, which illustrates order and chaos. We humans are scared of the uncertain and it’s only when we overcome the fear that we understand how little we know.

This is where behavioral finance comes in. The subject illustrates the errors in our thinking. We mentioned about aversion to ambiguity (uncertainty aversion), which describes an attitude or preference for known risk over unknown risks. It is demonstrated in the Ellsberg paradox i.e. people prefer to bet on a box with 50 red and 50 blue balls than one with 100 total balls but where the number of red or blue balls is unknown. The probability of winning on a bet remains unchanged in both cases. But still, we prefer betting on familiar scenarios over unfamiliar territory.

Behavioral finance researchers have also found that we as humans process uncertainty of risk and time similarly. This means that we don't think rationally when future is uncertain and when time aspects (return to certainty) are unclear. This bias has proven to be expensive in markets both in terms of actual losses and opportunity loss. The aversion to uncertainty also explains why we as masses need more information. More information is generally considered as removing future uncertainty or ambiguity as it creates a familiar ground. But still, this does not change the underlying risk and return. The news efficiency also has been challenged. It has been proven statistically that more information is necessarily not efficient.

Behavioral finance has junked 200 years of economic thought just because the psychologist were not scared of challenging economists at an unfamiliar territory. And still, this does not mean that Behavioral gurus will not be challenged. Hersh Shefrin mentions about predictability being an illusion. He also talks about the limitation of behavioral finance to predict and forecast and time markets. This is not true. Fractal watching can give unprecedented accuracy. This is why Behavioral finance is incomplete without connecting fractals with the subject. Stand alone sentiment surveys also have predictive elements. Comprehending and connecting the idea of patterns and psychology might be unfamiliar to the current generation of behavior finance experts.

Challenging a thought is not easy. We will always challenge the new, as we love certainty. But there is never a certainty, it’s a bias. The research revolution is ongoing and it will keep changing the way we think. Prechter’s thoughts about Economics being different from Finance might just be a research paper now, but this is the economics our children will read. Conventional research may not die, but it will become marginal, as the thought process of the society will migrate ahead. Predictability is much ahead of stories, even if we like stories. And even predictability is not fool proof, as we will always have a chaos, which will tell us that we know nothing about the world we live in