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The application of three systems

By Mukul Pal
May 18, 2009 15:07 IST
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Three is often the largest number written with as many lines as the number represents. To this day it is written as three vertical lines in Roman and Chinese numerals. This was the way the Indians wrote it, and as did the Guptas, the Nagaris and the Western Ghubar Arabs before we created our modern 3.

The triad

The triad (3) comes after one (1) and two (2). Its geometric ex-pression 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 that equals 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.

Quantity, structure, space

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 >, <, and = (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, 1,368 and its reverse 8,631 are both divisible by three (and so are 1,386, 3,168, 3,186, 3618). Also, every sufficiently large number is the sum of three powerful numbers.

Social impact

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.

Three in 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 threes. 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 three 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, core, mantle, and 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 ex-pression and science fiction have their threes. We have tricoloured flags. We write and shoot trilogies. Klimt Gustav, painted the famous 'The Three Ages of Woman' in 1905. Adidas brands its shoes and produce by three stripes. Indian classical music has mainly three forms---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...

The Magic of 3

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-similarityexact, quasi and statistical. Its not strange that the three systems are omnipresent. What is strange is that nothing has been written about them. Its 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.

The author is CEO, Orpheus Capitals, a global alternative research company.

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Mukul Pal
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