Some meaningful numbers and number systems in history

A mystical arrangement of numbers (author image)

According to a famous comic tale, there was once a very beautiful and intelligent young lady who was highly conceited about her profound spiritual knowledge.  She had rejected many suitors for her hand in marriage, mockingly telling them that their intellectual level was far below hers.   Some of these disgruntled suitors then plotted together to get their comeuppance.  To cut a long story short, they searched out the greatest fool they could find and promised him that they would marry him to this desirable woman as long as he would keep silent when he met her.

They then returned to tell the lady that they knew a young spiritual guru who was extremely intelligent, so much so in fact that he had risen above the level of speech and, like all the very wisest gurus, his only communication with mundane society was through silent communion.  She was immediately captivated by this, and begged them to introduce her to the guru nevertheless.  The rejected suitors then brought this fool before her, privately reminding him, no matter what happens, not to speak a word.

As the two of them sat together in silence, she had the idea to communicate with him symbolically.  The most profound idea she had was the unity of our reality as a single monad, Brahman, and she expressed this by holding up a single finger.  The fool, seeing this, thought she was saying she wanted to poke him in the eye.  He reacted by holding up two fingers, threatening to poke both her eyes out.

Seeing this, she understood his meaning to be that, although the world is one, nevertheless it seems to be a duality of multiplicitous reality (prakṛti) and witness consciousness (puruṣa).  In response, she held up her five fingers to indicate that it is only through the five senses that this appearance of duality comes about.  Now thinking she means to give him a slap with her open hand, the fool showed her his tightly closed fist, so enraged that he was struggling not to punch her in the face.

Looking at the fist, the lady understood that he was indicating the withdrawal of the five senses away from the external world, resulting in a spiritual realisation of the fundamental unity of reality, and she knew that he was truly the one for her.  The story continues, and, in fact, that fool was Kālidāsa, who later on became the greatest poet of India.

This story illustrates how we very often understand things according to our own preconceptions, rather than according to how things are in reality, but also, incidentally, how numbers were imbued with deep significance by ancient peoples.  Indeed, across the world, ancient peoples saw mathematics as the key to understanding reality, and this informed the ways in which they configured numeral systems and manipulated numbers within those.  In ancient Greece, for example, Plato connected his theory of Forms with a doctrine about numbers and identified particular numbers with specific abstract concepts.

In fact, Indian literature is replete with numbers that have special significance, much of which is no longer understood.  For example, 64 arts are listed in the Kāma Sūtra, which also suggests a few hypotheses about the precise significance of the number 64.  The number 16 is also of significance in this regard, being the number of adornments of a bride or newly-married woman (सोलह शृंगार), as well as the number of saṃskāras (sacraments) in Hindu tradition.

We may also note, for example, the significance of the number 18 in the Mahābhārata, where it appears as the number of days for which the battle lasted, the number of volumes that the work is divided into, and also the number of chapters within the section which is the Bhagavad Gītā.  Another numbers with the same prime factors as 18 is 108, a sacred number in Hinduism and the number of Upaniṣads held to be canonical.

Likewise, the development of number systems was doubtless carefully thought through in terms of the significance of how numbers would be manipulated within a particular number system.  The Babylonians, who developed the first positional number system, used a base of 60, a number notable for being highly divisible, and it was perhaps also suitable for their detailed calendrical calculations based on the movements of heavenly bodies.  We still use this Babylonian sexagesimal system when we divide a circle into 360 degrees and when we divide time into 60 minutes and 60 seconds.

The origins of the decimal system is lost in the sands of time, but would seem to be connected with the ten ‘digits’ on a normal pair of human hands.  Building on this, it was the Indian mathematicians who innovated by creating a positional or place-value system using a base 10 system.  This was a leap forward from the Babylonian base-60 system, as it introduced the zero symbol as a place-holder, so that for example 10 could be distinguished from 1.  As a result, the value of any integer was represented not only by the symbol but also by its relative position, thus making 12 different from ‘1 [and] 2’.

Traditional units of measurements were often based on relating ourselves to the world by connecting the scale of our bodies with the scale of things we found around us in the same way as the decimal system.  This is probably a natural and healthy human instinct, whereby we find ourselves at home in what would otherwise be an inhospitable world.  Thus the parts and movements of the human body are the basis for cubits, feet, [Roman] miles, inches and other similar units which seem to have naturally emerged in many parts of the world.  Human effort too is a basis for measurement, so for example, an acre was originally based on the amount of land that a farmer could plough in a day with one yoke of oxen.  Interestingly, too, we see a healthy number-pluralism in how these units were divisible, for example, in the English and Imperial systems, with division into fourteen parts, sixteen parts and so on.

This article has briefly touched on some aspects of the richness and diversity of numbering systems, and some ways in which particular numbers were thought to be of particular importance.    The thought processes behind many of these systems are no longer clear to us, and it is clear that further investigation is needed in order that we can properly cherish and sustain the various numbers and systems of units that we have inherited.

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