Posted on: 3 August 2012

All for Nought
By accident, it records the oldest "0" in India for which one can assign a definite date..
By Bill Casselman
University of British Columbia, Vancouver, Canada

What the Gwalior tablet shows is that by 876 A. D. our current place-value system with a base of 10 had become part of popular culture in at least one region of India.

We know almost nothing of how this decimal place-value notation came about, although there are many suggestive facts. One feature of Hindu culture in the middle centuries of the first millennium was that its texts were largely in verse, and preserved through oral tradition. It is hard to fit a useful numerical notation into such a scheme, and in fact what we see is a large literature, written down only much later than it originated, with numbers - often very, very large numbers - written in a kind of decimal place-value notation, but in words instead of symbols. Furthermore, the demands of the metric of the verses required that the exact words chosen to represent a given digit might vary from one point to another, so as to scan correctly. Whether this usage overlay more convenient calculation with symbols is not known to us, although it is almost inconceivable that it did not.

Another problem is that the climate of India is harsh. Paper was introduced to India late, and until then the materials on which things were written were birch bark in the north and palm leaves in the south. These are both extremely fragile. There are many extant manuscripts written on these, but nearly all of relatively recent date.

One of the more intriguing questions about the origin of decimal place-value notation is what connection it had to a much older tradition from a nearby region. The Babylonians began writing in about 3000 B.C., and had the good fortune to write on clay tablets, which can last for a very long time. We have extensive records from several thousand years of their development. They used an extremely sophisticated place-value system, remarkably much the one we use today, from very roughly 2000 B.C. on, but with a base of 60 instead of 10, and without "0". All the evidence that I am aware of suggests that this was technology acquired only by an elite group through rigorous training. This somewhat ambiguous notation persisted to about 300 B.C. when Babylonian astronomical tables started to incorporate a symbol that to some extent performed as zero, that is to say as a sign to indicate a space between two "digits". This was adopted in modified form by Greek astronomers after the conquests of Alexander, and this science in turn was transmitted (along with astrology!) to India sometime in the first few centuries of the current era. Exactly how these transmissions occurred is lost to us.

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This article is courtesy of Devashish Deb.


Interesting article

What about the Bakhshali manuscript, discovered near taxila ? Thats dated earlier than 876 AD by most, & it records the zero, represented by a dot ( see - ) ...

The ' 0 ' has temple

Ratnesh Mathur: Yes...the book on Bakhshali manuscript has been scheduled to be posted later.

some resolution? anyone?

vERY old but great and very beautiful temple.........

The article is by and large good, but this has unnecessary part in the end: >> nd this science in turn was transmitted (along with astrology!) to India sometime in the first few centuries of the current era. Exactly how these transmissions occurred is lost to us. There is zero proof of such statement, in that light why make such absurd hypothesis? Swarswati-Sindhu Civilization had deep and broad trade and other links with Babylon since the first recorded material from any site. In such a case why would both parties which wre advanced mathematically have to wait for 3000 years to know about their individual mathematical systems. Absurd and meaningless assertion, spoiling an otherwise decent write up.

If I may presume...some paragraphs from the book I am currently writing. Most of this will be known to RBSI members, but even so, let me try and resolve some of the questions above: The discovery of zero cannot be attributed to any one person, nor can its first use be exactly pinned down. The idea of zero would have grown slowly through centuries of mathematical evolution, guided not necessarily by logic or conscious thought, but by chance discoveries and practical needs. It would have been the output of a collective mathematical consciousness, not of a single astronomer or mathematician. Slowly the idea would have gained currency as its obvious value and usefulness became evident, and would ultimately have taken firm root to become an established and essential part of mathematical practice. Many European scholars of the history of mathematics have attributed the discovery of zero to the Greeks. The ancient Greeks had two systems of numeral notation: one was the mathematical equivalent of the Roman system, and the other was an alphabetical system. Neither of the two systems used zero or place value. Though place-value was invented independently by four civilizations – the Chinese, the Babylonian, the Mayan and the Indian - it has now been established beyond a doubt that the discovery of zero took place in ancient India. The Sanskrit word for zero is ‘shunya’, the literal meaning of which is ‘void’ or ‘empty’. This word was in use long before the discovery of zero or the place value system. As we saw in the previous chapter, shunya or shunyata was the central concept of an ancient philosophy which is still very much a part of Indian philosophical and religious thought today. The idea that all of existence is a void does not mean that it does not exist, but that all things are illusion or maya, that they are impermanent and insubstantial, and absolute truth exists independent of existence or non-existence. From this philosophical construct developed the concepts of emptiness, absence, non-existence, nullity, non-being, and so on, so that when the place-value system finally came into existence, shunya came to represent the absence of units in a given order. .... on oral enumeration: The method of expressing numbers by stating only the names of the digits is called the ‘oral’ method of enumeration. In this method, there is no mention of the names which indicate the base and its powers – ten, hundred, thousand and so on. So the number ‘five, nine tens, five hundreds and seven thousands’ would have been expressed as five-nine-five-seven. Of course, this method would work only if the mathematicians using it were throughly and completely familiar with the place-value system. This method of expressing numbers made it absolutely essential that there be a special term to signify the absence of units in a certain order. For example, take any two digits, say 5 and 3. In the ancient Indian system, written next to each other as 53, they represent the number ‘five units and three tens’. Written with a space between them 5 3 they represent the number ‘five units, no tens and three hundreds’. To make sure that the there was no misunderstanding about the empty space, it was necessary to have a way of clearly indicating that space. Given the deeply-rooted ideas around shunya in the Indian mind, it was natural that ‘shunya’ represented by a dot or a small circle, was chosen to indicate that empty space. Thus the two numbers in our example could now be clearly distinguished from each other: ‘five units and three tens’ could now be expressed as five-three or written as 53, while ‘five units, no tens and three hundreds’could be expressed as five-shunya-three or written as 5·3 or 503, where the dot or circle represented shunya. Another interesting aspect of oral enumeration was the use of word-symbols for number names. Sanskrit is a language rich in words and imagery, and lent itself naturally to the association of ideas that led to the use of words that evoked a numerical value (in the same way that words such as couple, trio, and quartet in English evoke the numbers two, three and four). So instead of eka, which was the ordinary name for 1, the Indian astronomers would use words that expressed the idea of one – words such as adi (the beginning), or indu (the moon) or rupa (the body, form); instead of using ‘dvi’, the ordinary name for 2, they would use words that expressed the idea of two, such as netra (eyes), and bahu (arms). In the same way, ‘tri’ or three could be expressed by the word loka (the three worlds), and chatur or four by yuga (the four cosmic ages), or veda(the four vedas). ...... The origin of the circle or dot (which is nothing but the circle in elemental form, the dot representing its centre) to represent zero can be traced to the word-symbols used by ancient Indian mathematicians. As we have seen, words that meant sky and space came to mean ‘shunya’ or ‘nothing’. Since time immemorial, the sky ha

From my chapter on the Bakhshaki Manuscript (again, with apologies to all those who this already): Probably written during the 3rd or 4th century AD, it is a manual on the mathematics of ancient India and contains mathematical rules, example problems and their solutions. Only a small part of the original manuscript survives; this deals mainly with algebra and arithmetic, with some problems on geometry and mensuration. We do not know what the missing portions of the Manuscript contained. Since the beginning and end of the Manuscript are missing, we also do not know what the work was called or who wrote it. Nevertheless it is a critical find, and provides a bridge between the mathematics of the ancient and the Classical era. It is also unique in that this is the first time we see mathematics in ancient India free from religious associations or philosophical considerations. The Bakhshali Manuscript deals with mathematics, and mathematics alone. It is written in the Sharada script, and zero is represented by a dot. There has been intense debate amongst historians and scholars regarding the date of this manuscript. After a detailed analysis of the contents of the manuscript – including the language in which it is written, the currency mentioned in several of the problems, the terminology used, and the absence of certain mathematical techniques which were known to have been in use by the 5th century AD – scholars and historians have concluded that while the physical manuscript dates back to the 8th century AD, it is a copy of a much older work which was probably composed sometime during the 3rd or 4th centuries AD. These dates place the contents of the Bakhshali Manuscript before the classical period which begins approximately around 500 AD with the work of the great mathematician Aryabhata. The precise dating of the manuscript is important from the point of view of discussing the developments in ancient Indian mathematics. If the above dates are accepted, they make the Bakhshali Manuscript roughly contemporary to the Lokavibhaga .....This makes sense, especially from the point of view of the invention of the place-value system which is used throughout the manuscript. Some scholars suggest that given the period in which it was probably first written, the Bakhshali Manuscript could have been the work of Jain monks, but there is no evidence to support this view.

I hope this sheds some light on zero...not much but some perhaps? This book of mine is very much work in progress. So please may I request that no one share this, or pass around what I have written here? Copyright matters to us writers. :)

Absolutely wonderful write up on the issue of zero. Very thoughtful and covers numerous points. Many thanks for sharing the valuable portions of your book even before its published.

Thank you Rohini .....wish you all the luck for the book.

Thanks for sharing with us Rohini! Absorbing, informative and delightfully eloquent as ever! Looking forward for your next book...

Thanks all. :)

Thank you Rohini Chowdhury for such wonderful detailed explanation

Hindi movies have a song for any occasion - even for explaining the significance of zero ("cipher" original arabic "sifr" meaning "empty") :

Precioso templo, Rohini. Estás muy " indianizada". Siempre me pregunto por qué no escribes. Sabiendo, hay muchos que lo hacen aunque no publiquen.

Fantastically articulate, intelligently interpreted and passionately written.. Ms. Rohini. Was about to hit share button, before I saw the request. Friends not on rbsi, missed something, but surely will wait for the book. Please keep updated.. Thanks