Posts tagged ‘Time Triads’


The only difference between trading and investing is of time. A larger holding period is called investing and a smaller holding period is trading. Shorter holding period reduces the risk in terms of time, if a trader can get in and get out fast, it is assumed to be less risky than staying there. Since large moves take time, a trader uses derivatives to leverage and assume more risk, the same risk he wanted to reduce when he moved from becoming an investor to trader. So the idea is that what really matters is how long you are holding the asset, and what is the leverage you are working with.

There are more of such misconceptions we live with. Fundamentals is the most followed research and news is considered the driver for markets, but the underlying theory that is efficient market hypothesis (EMH) clearly believes that one cannot profit from markets consistently as market movements are random. In other words what the theory says is that trading systems cannot work.



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The philosophy of time starts from the Socratic debate questioning time.

Socrates often said his wisdom was limited to the awareness of his own ignorance. He believed the best way for people to live was to focus on self-development rather than the pursuit of material wealth. Socrates seems to have been notorious for asking questions but not answering, claiming to lack wisdom. Perhaps his most important contribution to western thought is his dialectic method of inquiry, known as the Socratic Method, which he largely applied to the examination of key moral concepts such as the good and justice.

To solve a problem, one would pose a series of questions and the answer will filter out. The influence of this approach is most strongly felt today in the use of the scientific method, in which hypothesis is the first stage. The development and practice of this method is one of Socrates’ most enduring contributions, and is a key factor in earning his mantle as the father of political philosophy, ethics or moral philosophy, and as a figurehead of all the central themes in Western philosophy. “I know you won’t believe me, but the highest form of human excellence is to question oneself and others”. He was put on trial and condemned to die by drinking hemlock, for the expression of his ideas against those of Athens. Jacques Louis David immortalized the event in his 1787 painting ‘The Death of Socrates’.

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Can we trade time as an asset class?

On one side we have comments like will the equilateral triangle lose symmetry as time triads move and on the other side is a clear idea of time triads being an empty philosophy. A controversy is a start, at least there is a debate, a thought. Volatility has been around since markets started trading, but it was not until 1993 that the idea started trading as a VIX index. Now we have hedge funds trading volatility, as an asset class. Will the market evolve to trade new asset classes? Can the market trade time as an asset class? Can we have something called time indexing?

As a start it looks counterintuitive. We are already trading time indirectly, but how can you trade time directly? And even if you could, how will you commoditize time as an asset class? Before we understand how time triads can itself become an asset class, one should realize that indexing techniques over the last centuries have moved from price weighting to free float to fundamental indexing. The idea of a benchmark is simple and investible.

So what’s time indexing?



The TIME Index

Can we trade time as an asset class?

On one side we have comments like will the equilateral triangle lose symmetry as time triads move and on the other side is a clear idea of time triads being an empty philosophy. A controversy is a start, at least there is a debate, a thought. Volatility has been around since markets started trading, but it was not until 1993 that the idea started trading as a VIX index. Now we have hedge funds trading volatility, as an asset class. Will the market evolve to trade new asset classes? Can the market trade time as an asset class? Can we have something called time indexing?

As a start it looks counterintuitive. We are already trading time indirectly, but how can you trade time directly? And even if you could, how will you commoditize time as an asset class? Before we understand how time triads can itself become an asset class, one should realize that indexing techniques over the last centuries have moved from price weighting to free float to fundamental indexing. The idea of a benchmark is simple and investible.

So what’s time indexing? The time index tracks the performance of a pair of assets, a quantifiable study of pair performance. Pairs can be between Nikkei- Bovespa, Dow Industrials - Dow Transports, Gold - Oil, Sensex - Dow, Sensex - Gold or between any two economic time series. Pairs can tell us a lot about markets and where we are headed tomorrow. But what do pairs have to do with time? When you are long on an asset class and short on the other, you are taking out the price and just trading on time. This is why long Dow Industrials and short Dow Transports (or vice versa) is a pair idea, which lets us trade time as an asset class. Now conventionalists may argue, what fun is it to trade two indices, which move up and down together?

This is where we come in. Performance cyclicality was highlighted first time in the Kyoto University journal, Nistor, Pal. The paper illustrated performance cycles between Nikkei and the other BRIC countries. The research proved that performance between two economic zones illustrated through the countries composite equity index was not just cyclical, but even quantifiable. One of the conclusions of the paper was demonstrated through our feature here ‘Long India - Short China’. The pair delivered 50% over a quarter. Markets are quantifiable and they allow even regional indices to be pegged against each other profitably. What the paper demonstrated was that irrespective of the tight or lose correlation of an asset, performance cyclicality can be demonstrated at all time frames. The paper was indirectly demonstrating time fractals, triads.

There are some clear advantages of trading on time triads, time indexing, or say performance as an asset class. Being long and short two high correlated assets can reduce market risk i.e. offer market neutrality. This makes the strategy attractive. What is the investment world looking for? The first and foremost is a reduction in risk. For example shorting Nsebank and going long on Nifty reduces portfolio volatility and captures performance between the two sector indices creating relative alpha. Now this strategy may not perform better in a trended market, but it will surely outperform stagnation or declining market. The pace of wealth destruction and changing risk appetites also makes time indexing a viable option.

So what’s at the soul of the investment strategy? It is the ability to isolate the performance cycle. How do you do it? First, you accept that cyclicality of time exists and Kitchin, Juglar, Berry and Strauss were thinkers and not just illusionary pattern watchers. Second, one should understand that cycle regularity is not just about equality but power law proportionality. Third, one should start connecting or overlaying larger time fractals with smaller fractals. This again brings us to time triads, triangle in a triangle essence.

What kind of pairs? Large capitalization against Small capitalization indices, value vs. growth indices, mid economic vs. late economic etc. what if we go wrong? Well! If you can invest in a naked asset with a risk return history, you can invest in a market neutralizing, capital conserving simulated spot time index too. Above all if speculative volume can trade anything that moves, this is still an open source model. What about risk management? A diversified time index with many components could take care of emerging risk from the strategy.

We have been carrying pairs in this feature starting 2004. Frankly speaking it took us a lot of time to comprehend that what we were really trading, pairs or time. It took us more time to understand the fractal aspect in the subject. Long India, short China was one such pair we featured profitably. We have illustrated Oil - Sensex, CNXIT - Sensex, BSE500 -Sensex and many such pairs to highlight not only performance cyclicality but also market, economic perspectives and direction. We are not very far from the first Indian TIME index.

Another example of performance cyclicality can be built around the three pillars of global economy, Gold, Dow and Oil. So what does the Gold - Dow pair (ratio line) tell us? It says that Gold has hit an intermediate underperformance low against not only Dow, but also Sensex. This means that long Gold, Short Dow (Sensex) should be profitable pair for more than a few weeks. Even the larger primary performance cycle is also up in favor of Gold and against Dow. The respective performance cycle has been working from 1976 with an average 5 year cyclicality. The last cycle turned up in 2008 and should complete sometime in 2012. This means there is more for Gold ahead against American equity. This could mean that Dow should underperform and fall against Gold, Gold should rise or outperform Dow or Gold should fall but less compared to Dow. The very fact that Gold did not collapse against anything also suggests that the underlying larger cycle of Gold (2008-2012) outperformance against Dow continued to work.

If we need more confirming evidence we can look at Dow - Oil pair (ratio line). It might seem like a counterintuitive pair, but though Gold and Oil belong to the same commodity class, they can behave differently. Unlike Gold, Oil has pushed up to cycle highs against Dow. This could be owing to extreme oversold levels, reprieve in recession worries, or simply putting volatility cycles ruling OIL. There could be a thousand more reasons to explain why Oil shot up against both Gold and Dow. What really matters is where is the performance cycle (time oscillators) between Oil and Dow headed now? The respective pair has reached an extreme against Oil and is non confirming suggesting topping Oil performance against Dow. This means that the OIL intermediate topping could be near. Even if Dow pushes up above 8,800-9,000 levels in the ongoing leg, Oil needs magic to sustain and push to further highs against Dow. So if Oil is turning down against Dow, and Gold is turning up against Dow, what equity strength are we speaking about for the next few weeks? We have a history of contrarian calls from Oil at 100, when we said the oil rocket was not sustainable. The MAR low call on markets and Bsemetals compelling valuations where made at a time when $5 was thrown as another achievable figure for Oil. We are at $70 now.

Performance cycles (time oscillators) are easy to understand, but they become tougher to grasp when you start to explain them fundamentally. The real counterintuitive thinking is not how we can have long Dow and Short Oil and still call Gold as a performer, but how time indexing can revolutionize how we understand and trade time as an asset class.

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The TIME Translation

Extending time fractals to explain the transformation of the bell curve into the Pareto principle reconciles the 150 year efficient and inefficient market debate.

Robert Brown, a Scottish botanist observed the random Brownian motion nearly 250 years back. Nearly the same time Carl Gauss, also known as the Princeps mathematicorum (prince of mathematicians) created the bell curve. After 100 years Louis Bachelier connected these two great works by pioneering the study of financial mathematics and stochastic processes. Bachelier also referred to as the father of modern finance inspired the efficient school.

In a similar time frame Vilfred Pareto with his Pareto distribution started the work on fractional Brownian motion. One can easily generate a random sample from Pareto distribution. Bachelier and Pareto were on two sides of the Brownian randomness. What started from Robert Brown split into the efficient and inefficient school of thought.

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The TIME Translation

Extending time fractals to explain the transformation of the bell curve into the Pareto principle reconciles the 150 year efficient and inefficient market debate.

Robert Brown, a Scottish botanist observed the random Brownian motion nearly 250 years back. Nearly the same time Carl Gauss, also known as the Princeps mathematicorum (prince of mathematicians) created the bell curve. After 100 years Louis Bachelier connected these two great works by pioneering the study of financial mathematics and stochastic processes. Bachelier also referred to as the father of modern finance inspired the efficient school.

In a similar time frame Vilfred Pareto with his Pareto distribution started the work on fractional Brownian motion. One can easily generate a random sample from Pareto distribution. Bachelier and Pareto were on two sides of the Brownian randomness. What started from Robert Brown split into the efficient and inefficient school of thought.

Efficient school of thought was the bell curve believers who were more concentrated just like Mandelbrot’s clusters. Harry Markowitz, William Sharpe, Fischer Black, Myron Sholes, Eugene Fama etc. are a few of the efficient market theorists. The moment you start watching behavioral patterns, market patterns or fractals, start making S curve forecasts, talk about proportionality and the law of large numbers you are no more an efficient theorist focusing on mean, average, linearity and continuity. The Pareto rule drove the inefficient school of thought. It was widely distributed, de-clustered, characteristically proportional like the underlying law. Mandelbrot might feel uneasy in the way I respectfully group him with the other luminaries like Thomas Malthus, Pierre François Verhulst, Charles Dow, Kingsley Zipf, Ralph N. Elliott, Robert Prechter, Daniel Kahneman and Robert Shiller but the truth is that the father of fractals is a part of the pattern, fractal, anomaly, inefficiency watchers.

Did the inefficient school go too far in challenging the efficient model? A flapping butterfly causing a tornado in Texas seems like an exciting story, but how solid is the mathematics? Just because we see anomalies from normal, more volatility and extreme fluctuations, does the subject of value and calculus suddenly get trashed? Just because efficient theorists have failed to challenge the academic attacks, do all their work with CAPM model, beta, option pricing become worthless? Well if you look at it from Mandelbrot’s view, “pattern watchers are naive, bell curve is nonsense and conventional finance is based on unrealistic assumptions”.

Efficient theorists had a long running success. The inefficiency school can be given a benefit of doubt as they were not really noticed and were marginalized (compared to the efficient school) for a century. Now that the tide has turned and theories stand challenged, I would still think twice before calling conventional finance junk and Euclidean geometry as a redundant linear mathematics. Efficiency and inefficiency are thought to be two extremes that there could not be anything more sacrilegious in the academic world than trying to bridge the two disparate schools of thought.

Last time we talked about fluctuations, pulse and life in time rather than price or nature. We tried to make a case for a dynamic and proportional time that has a pattern. The movement of time we are talking about is called translation. This is different from the popular Google translate and should be one of the few reference of its kind on the world wide web, like some other of our ideas like time triads, time fractals, Econohistory etc..

The time triads we illustrated last time are made of hierarchy of Euclidean equilateral triangles. If time was static, all triangles (triads) in the set would be equilateral. Mathematically the time between two bases of a triangle is rarely equal. This is because the larger degree time (the higher amplitude triangle) pushes the underlying smaller time (triangle) causing it to translate, move or shift. This self feeding change creates an imbalance pushing time ahead. Real markets are full of such cases, when one period between two lows of a time triangle is not the same as the period in the other base (A<B>C). This is one reason why an average 3.3 business cycles vary from 3 to 5 years. Though the average periodicity holds, it’s irregular. This irregularity kept mathematicians away from time and this might be the reason Mandelbrot talks about contracting, expanding, flexible, speeding, slowing time. He might be simply talking about the moving and translating triads. Fractals are caused by time translation. There are other reasons linked with the human tendency of looking for average returns, looking for order etc. why time did not get the attention.

Mandelbrot’s asks a very similar question like Edward R Dewey asked 70 years back. Why do cycle repeat? Why do price and natural fractal exist everywhere? There are similar questions. Why do history, time, price, human mind, water claim to have memory? Is it not the memory associated with time?

The triads on one side demonstrate a clear power law behavior 9X, 3X, X, X/3, X/9, larger size lower frequency (if there is one cycle of 9X period), lower size-larger frequency (there are 81, X/9 cycles) and on the other side triads suggest why a bell curve might be the idealized form and the power law curve a translated form. Moving and translating caused more distortions from the idealized bell curve and created the power law curve. This means that all the inefficiency, anomalies, fluctuations were never a separate set but part of the universal time fractal set.

Time translation explains why nature is similar not equal (same)? Why there are more curves in nature than straight lines? Why we see order in randomness and randomness in order? Why chaos is not about disorder but about different time frequencies interacting through nature? Why moving time is CHANGE? Why risk perception is not about price but time polarity? Why time arbitrage will take over statistical arbitrage as the next investment strategy? Why dumping pattern watchers might be the biggest mistake in research? They just might be holding the truth.

In conclusion, it was never about rationality or irrationality. Time translation, time fractals may take time to be understood and be accepted, not because it is too complex, but because the idea is too simple. While working on some random operations Mandelbrot and James R Wallis produced some records which all appeared to display a long, slow up down cycle of three. Upon these long waves, smaller and more numerous cycles seemed to interpolate themselves. When they looked at small section of the record, they again saw three waves, each a third shorter than the section. Now these are some time triads Mandelbrot would find it tough to call static. The TIME was alive and TRANSLATING.




TIME Triads

Benoit Mandelbrot, the father of fractal geometry saw fractals everywhere. He might just have missed seeing them on TIME.


A fluctuation is a pulse, a change, amplitude. In a heartbeat a fluctuation signifies life. Researchers have spent decades researching fluctuations in an attempt to understand markets. Few like Mandelbrot have even gone ahead and defined nature by proving that the fluctuations are mathematical, fractalled. The father of fractal geometry illustrated the vastness of the idea, but he failed to extend the idea to time.

According to him though TIME does not run in a straight line, it changes according to price and stretches and shrinks like a balloon rubber. It speeds up and slows down. The 1993 Wolf Prize winner (most prestigious award after the Nobel Prize) focused all his mathematics on price and not on TIME. The seriousness of his work suggests that either TIME was not important enough to be featured in his lifelong work or he did not consider TIME to have a mathematical fluctuation or in words an organic life.


He was not the only one to ignore it, history of research starting Euclid never thought about TIME as a living pulsating system. Behaviorologists are far away from quantifying the subject and are more busy highlighting behavior errors rather than looking at something non-descript, as TIME. Barring a few, majority of behavioral finance researchers might consider fractal nature of emotions as ridiculous idea, leave aside fractal nature of time. Isn’t it strange, we have so many organic systems and entities built in and around time viz. the society, a market, nature, humans and the only thing, which we assume could not have life was TIME itself. The few, who thought, researched and wrote about time as a pulse, a cycle never made many decibels (fluctuation). Their ideas remain buried and unprinted, out of circulation, outside mainstream economics, more peripheral than the other struggling subject of pattern and fractal watchers, Technical Analysis.


How did Mandelbrot miss it? Mathematicians claim themselves to be purists working without assumptions. Mandelbrot cracks a joke on economists, as the ones who assume in his book, ‘The (Mis) behavior of markets’, missing a key and rather significant thought. The slip-up was monumental.

Equality, mean, price independence has been the corner stone of modern finance. Mandelbrot challenges the modern finance techniques and calls them as “foolhardy underestimation of risk of ruin”. The ‘Bell Curve’ has an equal portion of standard deviations on each side. Tests proved that in real situations the ‘Bell Curve’ fails miserably. Prices cluster and do not take a bell shape form. Mandelbrot also says that prices are not predictable or controllable, therefore seeing nature through probabilities theory is tough. “If the physical world is so uncertain, how much uncertain must be the world of money”. “Fractal geometries multifractals begin with the realization that mean is not golden”. It also goes ahead and challenges the work of Louis Bachelier, Harry Markowitz, William Sharpe and Eugene Fama. Till it was modern finance it was fine, but it seems Mandelbrot assumed a similar equality for TIME, which was static and perfect rather than proportional or fractalled as he saw it in price.


The power law was more about proportion than mean or equality. The law applies to negative and positive price movements, leaves room for big price changes far away from mean. If everything in nature was proportional (language, income, markets, nature, etc.), based on the Vilfredo Pareto 80-20 statistical distribution and the unchallenged ZIPF law, then why was TIME harshly judged on equality. Cyclical periodicity written and researched for more than 200 years did not exhibit perfect regularity but an average periodicity. Samuel Benner demonstrated the cyclicality of 16-18-20 and 8-9-10 repetitive year cycles. William Strauss and Neil Howe presented a strong case for an intergenerational, 85- to 99-year cycle. Brian Berry pointed to the presence of a generation-length, 25- to 35-year, cycle. Clement Juglar reported a medium term, seven- to 11-year, cycle. Joseph Kitchen reported a short-term, three- to five-year, business cycle. Business cycles were some observation, which according to Mandelbrot occurred and disappeared. And strangely all the above cycles had a mathematical proportion X, X/3, X/9, X/27. Despite such research Mandelbrot did not mention TIME. For him TIME was not alive, not proportional, and had nothing to do with fluctuations, which were just meant for price and nature.


There were further partial omissions. Mandelbrot gives a large weightage to pictures in identifying fluctuations. “Assault on normal with pictures not numbers”, “pictures are undervalued in science”, “Financial prices has memory and today influences tomorrow”, “Different kind of prices, different degrees of memory”. “Fractal geometry is about spotting repeating patterns”. “Pictures say more than words” His idea of “Price dependence” also gives credit to history”. However, this past to future linkage, cyclicality was just limited to identifying the fluctuation patterns.

This was partial acceptable of pattern recognition on one side and on the other he said there was no predictable pattern. Price had the memory of 1929, time had no memory. On one side he said, “The wigglies (fluctuations) looked the same in different times” and on the other he trashes all ‘Head and Shoulder’ watching. “My mathematical models can generate charts that purely by the operation of random process appear to trend and cycle”. A similar exercise of computer generated charts were put in Hersh Shefrin’s book ‘Greed and Fear’. The aim was to highlight that conventional chartists can’t differentiate original from fake. This was a very crude way to judge the pattern recognition skill. Mandelbrot says “pattern watching at times can be correct”, “everybody knows about support points”, “technical analysis is financial astrology”, and “pattern watching is for neophytes”.


Though pattern watchers are pulled down by both psychologist and mathematicians, it’s only the pattern watchers who are left to predict and claim that forecasting works. Despite all the mathematics and psychology understanding, both behavioral finance and fractal geometry schools say that predictability is an illusion. Mandelbrot even goes ahead and says that ‘Fluctuations’ are predictable not what is between them.

With all this behavioral and mathematics understanding, the only lesson fractal geometry teaches us is how to avoid losing money. But you can only avoid losing money if you invest first. Whom should the investor go to, if he needs an investing advice? Behavioral finance says advisors don’t know, just diversify, buy the losers, sell the winners and save. The majority will herd again and the bubbles will come again, as a repeating fluctuation and cyclical pattern unfolds. Both the pattern bashers never address ‘WHEN’? The sentiment indicators that are supposed to give some indication are also junked by psychologists. So we have these grand theories, which tell us how to avoid risk and losses, but they don’t tell us ‘WHEN’ to invest? The question of TIME is not their business.

If all this was not enough, Mandelbrot says that “markets are not chaotic unlike the chaos theory it espouses and one should not attempt to TIME”. Robert Shiller used larger market extremes (fluctuations) in 1980 to challenge efficient theorists and Robert Prechter rolled out Elliott fractal work (similar to Mandelbrot’s multi fractal) in a systematic way, applying it for predictive work since 1970. Both Mandelbrot and Shiller suggest predictability is tough and an illusion respectively.


In his 1999 article, “A multifractal walk down wall street”, Mandelbrot used a 3 wave pattern, the first and last being in the direction of the general trend, the middle against the general trend to illustrate how market fractalled by subdividing in similar forms. A picture of his example from the article is illustrated (left hand side).

He focused on the price and not the TIME. This is the reason why price fractals and TIME fractals seem disconnected. We redrew Mandelbrot’s multifractals from a TIME cycle (up leg and down leg) rather than from a price trend (up leg - down leg - up leg) perspective (right hand side). TIME fractals break down into X, X/3, X/9, X/27 and further on just like the documented economic cycles. A triangle breaking down into three smaller triangles and so on.

X- AXIS AND Y AXISSo now either TIME is fractalled or price and nature is. It’s a simple mathematical idea that both X and Y axis cannot have a fractalled pattern at the same time. The Y axis contains all of Mandelbrot’s nature symmetry and beauty while the X axis just has TIME. One of the ideas is wrong, either TIME is not fractalled or only TIME is fractalled giving everything a beauty and a form. Just to prove our case we starting looking for TIME TRIADS (time fractals) on a ratio line (remember long India, short china). We were not surprised. The triads were there too. TIME was indeed a THREE, working independent of the Y axis. Draw a rate of change on a price or a price ratio or on any time series, you will see them.

Tony Plummer in his book ‘Forecasting financial markets’ does give reference to time cycles as a triad of patterns, but does not extend the work to fractals.


TIME fractals change the way we look at nature. It brings order in the disorder of the Chaos Theory. Butterfly effect suddenly starts to lose its mystery.  The sensitivity dependence the Chaos theory talks about is owing to the genetic code of time, which is always different as there is an infinite TIME above and below us. We may have some TIME till we find the next theory of everything, but till then start watching the fluctuation.

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The THREE systems

The omnipresent three systems is not a coincidence, it might be the pulse of everything.

Three is often the largest number written with as many lines as the number represents. To this day 3 is written as three lines in Roman and Chinese numerals. This was the way the Indians wrote it, and it was all the way after the Guptas, the Nagaris and the Western Ghubar Arabs that we created our modern 3.

The triad (3) comes after one (1) and two (2). Its geometric expression is an equilateral triangle. In comparison with the circle, which encloses the greatest area within the smallest perimeter, the triangle encloses the smallest area within the greatest parameter. Three is unique. It’s the only number to equal the sum of all terms below it (3=2+1) and the only number whose sum with those below equals their product (1+2+3=1*2*3). The triangle is the only polygon structure that is stable. Triad symbolizes efficiency, balance and symmetry. A triangle is a perfect figure which if all endpoints have hinges will never change its shape unless the sides themselves are bent. Study of Pascal’s triangle and Sierpinski’s gasket helps us appreciate the triangular symmetry.

Mathematics is replete with numerous three systems like the triad. The study of vectors combines three of the fundamental areas of mathematics viz. quantity, structure, and space. Every odd integer greater than 5 can be written as a sum of three primes. There could be three ways to represent an equation ><= (greater than, less than or equal to). Vulgar fractions with 3 in the denominator have a single digit repeating sequences in their decimal expansions, (.000…, .333…, .666…). Because of this, the reverse of any number that is divisible by three (or indeed, any permutation of its digits) is also divisible by three. For instance, 1368 and its reverse 8631 are both divisible by three (and so are 1386, 3168, 3186, 3618, etc..). Also, every sufficiently large number is the sum of three powerful numbers.

Three is not just limited to mathematics. Ancient mathematical philosophers referred to the triad as prudence, wisdom, piety, friendship, peace and harmony. Priya Hemenway quotes is her book, ‘The Secret code’ about the triad and its relationship between opposites that unites them. No enduring resolution of any kind is possible without three aspects, two opposites and a neutral balancing, arbitrating, or transforming factor. Knowing how to choose the third element means the difference between a conflict’s resolution and its perpetuation. The word trinity derives from “Tri-Unity” or “Three as one” and the triangle is the world’s preeminent symbol of divinity. The ancient gods of the Hindu religion are called Trimurti (Sanskrit for “One whole having three forms” Brahma, Vishnu, and Shiva) in Hindu mythology. We have the Father, Son, and Holy Spirit in Christianity. Fu Lu Shou is the concept of Good Fortune (Fu), Prosperity (Lu), and Longevity (Shou). The term is commonly used in Chinese culture to denote the three attributes of a good life.

Education…In medieval universities, the trivium comprised the three subjects taught first;  grammar, logic, and rhetoric. Triad is a Latin term meaning “the three ways” or “the three roads” forming the foundation of education. Even study of logic has it’s THREE’s. Traditionally, there are three “modes” or “moods” or “modalities” represented by modal logic, namely, possibility, probability, and necessity. History classifies prehistory in the Stone, Bronze and Iron Ages. Astronomy has three types of galaxies, ellipticals, spirals and irregulars. The constellation Orion’s belt is made up of 3 stars in a row. Earth is the third planet in its local Solar System.

The systems continue in anatomy. Humans are referred to as “third chimpanzee”. Both RNA and DNA have a triplet codon system. Chemistry subdivides atomic level into three constituents viz. protons, neutrons, and electrons. There are three basic chemical reactions, acids, bases and salts. There are three states e.g. water can also take the form of ice, steam.

Geology suggests three basic divisions in earth, the core- mantle- crust. There are three basic rock formations, Igneous- Metamorphic- Sedimentary. We perceive our universe to have three spatial dimensions. Science is full of three variable laws, E=MC2, Speed=distance*time, Acceleration=Velocity*Time, Voltage=Resistance*current.

Psychology has three systems. Freud proposed that the psyche was divided into three parts; Ego, super-ego, and id. Freud discussed this structural model of the mind in the 1920 essay ‘Beyond the Pleasure Principle’, and fully elaborated it in ‘The Ego and The Id’, 1923, where he developed it as an alternative to his previous topographic schema (conscious, unconscious, preconscious).

Social Expression and Science fiction have their THREE’s. We have tri colored flags. We write and shoot trilogies. Klimt Gustav, painted the famous ‘The Three Ages of Woman’ in 1905. Addidas brands its shoes and produce by three stripes. Indian music has mainly three forms of classical music, Hindustani, Carnatic, and Dhrupad styles. Musicology is the study of the subject of music. The earliest definitions defined three sub-disciplines; systematic musicology, historical musicology, and ethnomusicology. Third Time lucky, 3 P’s of marketing, Isaac Asimov’s Three Laws of Robotics, warm-cold-neutral colors, the three dots in an ellipsis…



Technical Analysis is part of the three systems. John Murphy called it ‘The Magic of 3′, open-high-low-close makes three cycles, head and shoulder, triple top, three stages of the DOW theory, three tests of a trendline, Samuel T Benner’s three period periodicity of 16-18-20 and years. Fractals can also be classified according to their self-similarity. There are three types of self-similarity found in fractals, exact self-similarity, quasi-self-similarity and statistical self-similarity.

It’s not strange that the THREE SYSTEMS are omnipresent. What is strange is that nothing has been written about them. It’s a taken for granted aspect of our life. Just like everything even Time is a three, a triad, a low-high-low, a pulse. Time is subdivided into three parts, past, present and future, ever thought why? We have three hands in a watch; seconds, minutes and hour. The father of modern cycles talked about time dividing into 2 and 4, while Tony Plummer said Time was a 3, way back in 1989. Tony was right, what he might have missed was the aspect that a TIME TRIAD could be at the soul of all three systems, the pulse of everything.

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The TIME Fractal


Do you think understanding TIME will help us understand economics better?

My friend from Reuters Thompson always says that my presentations are more interesting than his, a polite way of saying that I am more animated than him. At the same time he wonders why I have so many pictures in my slides rather than text. I also keep wondering the same. Pictures just let me express more. It was a similar graphic exercise I did while speaking at the Academy of Economic Studies, Bucharest a few weeks back. I put the picture of a few historical research gurus (who are also known as creators or father of a certain subject) and started querying my shy audience.

The first slide was a famous painting, ‘The School of Athens’, or ‘Scuola di Atene’ in Italian, by the Italian Renaissance artist Raphael. It was painted between 1510 and 1511 as a part of Raphael’s commission to decorate with frescoes the rooms now known as the Stanze di Raffaello, in the Apostolic Palace in the Vatican. 500 years back technology was poor, so one of the Fathers from the ten thinkers on my slides was portrayed there. Raphael considered as one of the trinity with Michelangelo and Leonardo da Vinci is believed to have portrayed Euclid, the father of geometry in his heavenly fresco.

The second slide was easy. The hands raised were confident. It was Adam Smith, the father of economics. The third slide saw silence, there were no hands raised this time. It was Pareto. Vilfred Pareto was the father of micro economics and one behind the Pareto principle. “His legacy as an economist was profound. Partly because of him, economics evolved from a branch of social philosophy as practiced by Adam Smith into a data intensive field of scientific research and mathematical equations. His books look more like modern economics than most other texts of that day. The Pareto principle (also known as the 80-20 rule), the law of the vital few and the principle of factor sparsity states that, for many events, roughly 80% of the effects come from 20% of the causes. He observed that 80% of the land in Italy was owned by 20% of the population or 80% of a business sales will come from 20% of the clients etc.


Though Pareto gave a mathematical impetus to economics as early as 1848, he is faintly remembered compared to Adam Smith. Pareto’s own principle worked against him, as the father of economics Smith took most of the 80% available attention, leaving 20% limelight for the rest great economic minds to share. The 80-20 attention span works for everything else, the attention span is skewed. It works for news, for aspects in our life, in psychology and everything else.

Even though CHARLES DOW, Father of Technical Analysis or Father of modern finance contributed sizably to modern finance by constructing the DOW INDEX, Elliott redefined DOW’s work. It is a text book saying that for the 10 who know The DOW Theory, only 1 high priest knows Elliott. Though Elliott improved and extended DOW’s work, he did not get the deserved attention. Charles Dow was there on the slide as a revered Father, while Elliott did not make it. Elliott introduced market fractals in 1938, but it was scientific evidence that got the Father of Fractals title to Benoit Mandelbrot, who coined the term in 1970 and proved that nature and markets were fractalled. A fractal is generally “a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole, a property called self-similarity.


In the slide that followed I had illustrated the father of efficient market hypothesis, Eugene Fama; founding father of Econophysics, Eugene Stanley; the father of Socionomics, Robert Prechter and the Father of Behavioral Finance, Daniel Kahneman.


1. Adam Smith 2. Vilfredo Pareto 3. Charles Dow 4. Benot Mandelbrot 5. Daniel Kahneman 6. Eugene Stanley 7. Eugene Fama 8. Robert Prechter

Apart from the fun with the 80-20 attention our mind plays with our memory, I was making another significant observation in the session. History of research is replete with examples how Mathematicians, Scientists, Economists, Linguists, Historians, Cyclists, Market Technicians, Behaviorologists have witnessed overlaps in research thought and work. Across the centuries, mathematicians like Euclid (350 B.C) said similar aspects of divine ratio like Georg Ohm (1789). We had economists like Thomas Malthus (1766) seeing their work extended first by mathematicians like Pierre Verhulst (1804) and in current times by scientists like Theodore Modis. Even Pareto principle is quoted simultaneously with a famous linguist Kingsley Zipf (1902) of (Zipf law and power law fame). We even saw historians like Karl Lamprecht (1915) and J M Draper (1811) talking about mathematical nature of History. This same idea has been widely written by well quoted cyclists like William Strauss and Neil Howe. The overlap of ideas is everywhere. Mathematicians talked about patterns, Scientists talked about proportions and Economists have created statistical curves. There is a thin line between Historians and Cyclists. Historians talked about cyclicality, while cyclists talked about repeating history. Market Technicians talked about fractals and psychologists talked about human irrationality.

In essence the history of research boils down to three aspects psychology, fractals and time. If one could connect TIME AND FRACTALS, we can challenge the psychologists as mathematical time is something psychologists can’t contest. The TIME FRACTAL is a subject that can not only explain the connection between overlapping research of a few thousand years, but also answer a question bothering Edward R Dewey, when he started the Foundation of CYCLES in 1940. Why do cycles seem to work in different phenomenon with uncanny precision all the time? The repetitive activity, which our mind registers 20% of the time happens 80% of the time around us.  It happens because time is non linear, it pulses, breaks, multiplies in the same fractal form, again and again. How true is this? How scientific? What is the pattern of time? Will the clock work?

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