Posted on Tuesday 13 February 2007 to unknown
Counting in groups of ten, a practice evidently suggested by the number of fingers on two hands has been practiced by many cultures for millennia . But the act of writing them down using a system of place notation system which can expand without limit is only comparatively recent innovation.
Here then is the story of 1 to 9 and of 0 and 10.
In the last few centuries before the Christian era, by our reckoning, India emerged from a dark age that had endured
since the fall of the Indus
valley civilization fifteen hundred years earlier. It was at this time
that the written word started to reappear, especially in the form of edicts
and inscriptions left by Ashok , the
great emperor of the Mauryan Empire.
These words were written in a script known as Brahmi and in amongst
its letters we find symbols to express numeric quantities which look like
this:
The Sand ReckonerIt has been argued that the reason why this innovation occurred in India rather than the West was largely because of a peculiarly Indian fascination with astronomically huge numbers .
Greek mathematical notation was not positional; it utilized many symbols and was cumbersome to work with.
The "M" is a myriad , and represents 10,000. The Greek work is murious (uncountable, pl. murioi ). The Romans converted to this to myriad .
The traditional Indian cosmology states that the universe undergoes cyclic periods of birth, development and decay, lasting 4.32×109 years, each of these periods is called a Kalpa or ``day of Brahma''. During each Kalpa the universe develops by natural means and processes, and by natural means and processes it decays; the destruction of the universe is as certain as the death of a mouse (and equally important). Each Kalpa is divided into 1000 ``great ages'', and each great age into 4 ages; during each age humankind deteriorates gradually (the present age will terminate in 426,902 years). These is no final purpose towards which the universe moves, there is no progress, only endless repetition. We do not know how the universe began, perhaps Brahma laid it as an egg and hatched it; perhaps it is but an error or a joke of the Maker.The Brahmi script went through a continuous evolution, spawning numerous variants, the most important of which was the Devanagari (or sometimes simply Nagari) script. With Devanagari numerals, the 1 was rotated by 90 degrees and had developed a serif-like loop at the top. The 2 and 3 took on their familiar shapes due to shortcuts taken by scribes, who chose to link the parallel bars rather than lifting their pens.
This description of the universe is remarkable for the enormous numbers it uses. The currently accepted age of the universe is about 1018 seconds and this corresponds to about 7 Kalpas+335 great ages. A unique feature of Indian cosmology is that no other ancient cosmology manipulates such time periods.
In the Surya Siddanta it is stated that the stars revolved around the cosmic mountain Meru at whose summit dwell the gods. The Earth is a sphere divided into four continents. the planets move by the action of a cosmic wind and, in fact, the Vedic conception of nature attributes all motion to such a wind. It was noted that the planets do not move in perfect circles and this was attributed to ``weather forms'' whose hands were tied to the planets by ``cords of wind''
I will omit all discussion of the science of the Indians, ... , of their subtle discoveries in astronomy, discoveries that are more ingenious than those of the Greeks and the Babylonians, and of their valuable methods of calculation which surpass description. I wish only to say that this computation is done by means of nine signs. If those who believe, because they speak Greek, that they have arrived at the limits of science, would read the Indian texts, they would be convinced, even if a little late in the day, that there are others who know something of value.However, it had to wait until the Arab conquests before the Indian numerals began to be adopted widely and even then only very gradually. In the 11th century, the Muslim mathematician and astronomer al-Biruni referring to Indian numerals wrote:
Whilst we use letters for calculation according to their numerical value, the Indians do not use letters at all for arithmetic. And just as the shape of the letters that they use for writing is different in different regions of their country, so the numerical symbols vary.