Metaphysics of Mathematics

World Mythology 3 Comments

First Published in First City, New Delhi, August 2007

The number 18 keeps recurring in the Mahabharata. The epic has 18 sections and deals with a battle that is fought over 18 days and involves 18 armies. Krishna’s city, Mathura, is destroyed by Jarasandh after 18 attacks. Yudhishtir gambled away all his wealth in 18 games. And there are 18 chapters in the Bhagavata Gita. And two times 18, that is 36, is the duration of the glorious reign of the Pandavs after the war. What is the significance of the number 18?

Mathematically speaking, the sum of the numerals that make up 18, that is 1 and 8 is 9. And 9 is considered an indestructible number. Multiply 9 by any number and the sum of the digits that make up that number will stay 9. So 9×3=27 and 2+7=9. 9×7 =63 and 6+3=9. The number 9 stands between 8 and 0. Eight represents completeness or totality because it includes the 4 cardinal directions and the 4 ordinal directions. Geometrically, the number 8 is equal to a circle. Zero, by contrast, represents nothingness or emptiness. It is geometrically represented by a plain sheet with no marks on it. Thus 8 is everything and 0 is nothing. 9 is the threshold number between 8 and 0. The number 1 which follows 0 represents the beginning and is represented by a dot, the root of all geometrical patterns, while 8 is the number which represents fulfillment or end. So 18 indicates the beginning and the end. 108, which is also a sacred number for Hindus, is created by adding 0 or nothingness between the beginning 1 and the end 8. When digits of both numbers 18 and 108 are added we get the number 9, the eternal indestructible number. Mahabharata is thus the story of beginnings, endings and renewals, all indicated through the recurrent use of 18.

In modern times, in many societies, 18 is the believed to be the age of adulthood. The Hebrew word for life has a numeric value of 18. Thus the tradition has arisen in Jewish circles to give monetary gifts in multiples of 18 as an expression of blessings for long life. In the Chinese tradition, the sound of the number 18 resembles the sound of the word meaning prosperity. Consequently, building floors numbered 18 tend to be very expensive as they come with the promise of fortune.

Another number which has fascinated man is the number 40. Amongst Christians, there are forty days of Lent, the days of fasting before Easter Sunday. Forty is a recurring number in the Bible. The flood that forced Noah to build an arc lasted for 40 days and 40 nights. Moses and his people wandered in the desert for 40 years looking for the Promised Land. Jesus spent 40 days fasting in the desert after which he was tempted by the Devil.

At a very simplistic level, the word 40 means ‘a lot’ in Middle Eastern languages. Thus this was a very common way used by ancient poets to quantify a long duration. Later it is believed this was taken literally. At a more profound level, it has been observed that forty years is the duration taken by Venus across the sky to return to its original location. Venus is an ancient fertility symbol and this makes 40 a very important number of fertility, renewal and change.

Numbers have always fascinated man. They have been used to explain the universe. Take the number zero for example. Buddha in 500 BC introduced the concept of nirvana, which means the end of existence, the blowing out of flame. This was differentiated from the Hindu notion of moksha which means liberation of the soul. For Hindus, following liberation, the soul survives in its primal purity. But for Buddhists, nothing survives. This idea gave rise to the concept of Shunya or nothingness in Buddhist philosophy. The opposite of this Shunya was everything, infinity. Indian mathematicians converted these metaphysical concepts into mathematics. Shunya gave rise to zero and when any number was divided by 0 (nothingness) what emerged was infinity thus making nothingness and everything-ness, opposites of each other both metaphysically and mathematically. By 500 AD, these early concepts gave rise to the idea of decimal numbering. And was used extensively by Buddhist, Jain and Hindu scholars. This was taken by Persian scholars and Arab traders. They translated nothingness or shunya as ‘sipher’ which eventually became ‘ziphiro’ amongst Italian traders and finally the modern 0 which started appearing in Europe around 1100 AD. Visually, 0 was represented as a dot and later as a circle or sphere to represent the vast infinity of the horizon leading to the cosmos. All this information had led to the speculation that perhaps early mystics were actually mathematicians or vice versa. There was no divide between the scientist and the spiritualist in ancient times.

Hindu metaphysics say that in the beginning there was nothing (0). Then came the first sentient or conscious being (1). But this being was afraid. It did not know who it was. The only way, it concluded, it would know itself would be by distinguishing itself from all that it was not. So it split itself into the ‘self’ and the ‘other’. Thus came the great duality of 2: soul and substance, spirit and matter. Soul was not fettered by time and space. Matter was fettered to time and space.

Time had three dimensions (3): past, present and future. As did space: length, breath and width. Matter had three states: solid, liquid and gas. Thus three represented dynamism, a quest for harmony between the various dimensions and states.

Four directions (4) gave rise to the confined space of the settlement, the home, the household. Four anchored life on earth like the four legs of a horse or a cow or a dog or a sheep. Four pillars were needed to create a dwelling. Four elements were needed for survival – earth, water, fire and air.

But the dwelling needed a fifth element (5), the magical mysterious element called ether. The element of nothingness, the element of the void. Five thus came to represent the heavens, the aspirations of man, visualized as a pyramid. Five was also important because it was seen that the planet Venus traced the pentagram or the five pointed star across the starry sky. Venus was associated with femininity, intuition and emotion. Five was important because there were five sense organs (eye, ear, tongue, nose and skin) and five response organs (hands, feet, face, anus, genitals) according to Tantra.

Six (6) was created by two triangles. The upward pointing triangle represented male and the downward pointing triangle represented female. Thus the intersecting triangles represented creation and union (remember da Vinci code’s scalpel and chalice that came to represent Jesus and Mary Magdalene) while the separated triangles represented separation and destruction. Since six was associated with fertility, creation and destruction, in monastic orders where sex was frowned upon, six became an unlucky number.

In Christians mysticism, 6 became the number of the Devil since the bible refers to 666 as the mark of the beast. And since in Hebrew 6 is written as W, some people have concluded (quite wrongly) that WWW is the creation of the Devil! The same people have observed that if you take all the letters in Bill Gates III  and then convert it in ASCII code (American standard code for information interchange) and then add up all the numbers, you will get 666, which is the number of the beast!!! These conspiracy theorists have also found 666 in every barcode and hence concluded that the barcode behind every item in the supermarket, which forms the core of any market, is the creation of the Devil!

Seven was the holiest number. There were seven planets that were visible from the earth. Sacred constellations like the Sapta Rishi Mandala (Big Dipper) and the Kritika Mandala (Pleiades) had seven stars. Music had seven octaves or swaras (sa, re, ga, ma, pa, dha, ni). Seven colors were seen in the rainbow (violet, indigo, blue, green, yellow, orange, red). Seven was seen as the number of the heaven, the number of God. Thus in Chritianity, God created the world in six days and rested on the seventh, there were seven virtues in the world (Chastity, Moderation, Liberality, Charity, Meekness, Zeal, and Humility) and seven deadly sins (lust, gluttony, greed, pride, wrath, envy and sloth).  Almost all cultures in the world have tales of seven wise men, the seven virgins and the seven dwarves.

One can go on and on, but at the heart of this is man’s desire for meaning in this apparently random, meaningless, boundless world. Numbers have the magical ability to organize and define and confine the universe. Through numbers the infinite can be made finite, measurable hence manageable. From Pythogoras to Fibonacci, scholars in Europe have noticed that everything in nature could be reduced to a number or a formula. Truth lay in numbers. Beauty lay in numbers. God, they concluded, must have been a mathematician.

  • Maithili Shetty

    Hats off to you Sir.Thankyou for this informative article.Wish mathematics was taught in school in its purest form so that students wouldn’t dread numbers.

  • Devdutt Ji,

    9 is an indestructible number, but only if written in decimal notation. The other cultures of the world used numbers of base 16, 20 etc, so I don’t think they would be that serious about 9. The Greeks and Romans didn’t even have a positional notation, so they wouldn’t understand the concept.

    And 108 is a very curious number.

    108 = 1^1 * 2^2 * 3^3

    It embodies the very idea of recursion. This is why I think it has become popular. Similar to things like Fibonacci numbers, golden ratio etc. All of these are considered sacred in Hinduism.

    Then we have prime numbers that are generally considered transcendent and belonging to God, as they are not divisible by any other number.

  • . By 500 AD, these early concepts gave rise to the idea of decimal numbering.

    Actually, decimal numbering was existent in India for a much longer time. It is visible in how numbers were named (293 is said as three and ninety and two hundreds). Numbers were written also in decimal positional notation for a long time, with zero being marked with an empty space. What was invented in 500 AD was the symbol for zero.. A very curious symbol – a circle with a tiny dot inside it.

    In my blog, I have claimed that these ideas arose straight out of the Sāmkhya philosophical system of enumeration. This is the oldest philosophical system of India, may be of the world.

    The symbol for zero also raises my suspicion : the circle stands for nature (prakriti) and the dot (bindu) stands for the individual self (purusha). These symbols have such meaning in many religions today – Tantra, Buddhism etc.. all of which have been inspired by the Samkhya philosophy.