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 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 stable polygon structure. 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. The 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 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 unite 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 the study of logic has its 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 the earth, the core- the mantle- the 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 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 produces 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 3 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. We have three hands in a watch; seconds, minutes, and hours. 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.

If all the above seems occult, you should read Li and Yorke's 1975 paper, "Period 3 Implies Chaos" in which the authors prove how period 3 allows chaotic systems to become periodic. Yorke was born on the 3rd August 1941.