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Component-I (A) – Personal Details Component-I (A) – Personal details: Prof. P. Bhaskar Reddy Sri Venkateswara University, Tirupati. Prof. P. Bhaskar Reddy & Dr. K. Muniratnam Director i/c, Epigraphy, ASI, Mysore Dr. Subrata Kumar Acharya Ravenshaw University, Cuttack. Prof. P. Bhaskar Reddy Sri Venkateswara University, Tirupati. Component-I (B) – Description of module: Subject Name Indian Culture Paper Name Indian Epigraphy Module Name/Title Ancient Indian Numerals Module Id IC / IEP / 14 The vast inscriptional literature of India preserves the traces of the early notational systems and how they progressed in the direction of forming new Pre requisites symbols. The symbols in the Brahmi and Brahmi- derived scripts have been discussed in the module The main objective of this module is to get familiar with the numerous systems of notations known to the people living in the past. It is also important to focus how and when the decimal place value Objectives notation that people across the world use today was invented in India and the knowledge flowed out of it and transmitted to other countries in course of time. Numerals, Brahmi, Numerical System, Decimal Keywords System, Inscriptions, Symbols. E-text (Quadrant-I) : 1. Introduction In this module we shall discuss on the ancient Indian numerals. How the people were counting the numbers and putting them into written forms are the major issues to be addressed. We all know that two different scripts were in use in India during the time of Asoka. Some of the Asokan inscriptions located in the north-western part of India were written in Kharosthi script, while most of his edicts written in other parts of his empire were written in Brahmi. In both the scripts we find the numerals were used in the forms of different symbols. The Kharosthi script was short lived and was mostly confined to the north-western part of early India. The numerical system used in the script was believed to have been borrowed from the Aramic system with slight modification. But the Brahmi script was widely popularized and it is considered as the parent of almost all the subsequent regional scripts of India. Like the alphabets, the numerical symbols in the Brahmi had a long process of evolution. In the following paragraphs we shall chiefly focus on the system of numeration in Brahmi and the other systems that developed afterwards. 2. The Brahmi numerical notational system The numerical system of notation was in general use in a large part of India in early times and persisted at least up to the tenth century CE, until it was finally displaced by the decimal place value system. It has been also termed as Sanskrit, Ancient Nagari or Old Indian Notation. In this system the first three numerals are expressed by one, two and three horizontal strokes, from four to nine there are special symbols and there is a distinct figure for each of the orders of numbers such as ten and its multiples up to ninety while it has also separate signs for a hundred and a thousand. Thus, there are twenty basic signs. The intermediate units are expressed by simply adding their signs. To cite an example, if 77 is to be written then at first the symbol for 70 and then the figure for 7 is written. But the figures for 100 and 100 are treated multiplicatively. The multiples of 2 and 3 are indicated by the addition of one or two horizontal strokes respectively, at the right side of the sign for 100 and 1000. However, when the number 777 is to be expressed then the symbol for 100 is written with the figure for 7, then the figure of 70 and finally the figure for 7. Similarly the number 7777 is denoted at first by the symbol for 1000 followed by 7, then 100 followed by 7, then the symbol for 70 and finally the figure for 7. Thus, the system is essentially an additive and multiplicative system where the numbers are either added or multiplied to express the desired numbers. As in the Brahmi script so also in the Brahmi numerals, the symbols are written from left to right beginning with the symbols of higher values. It is a non-place value notational system and there is no trace of the employment of the zero. The twenty symbols by which the numbers were expressed are given below. 3. Theories on the origin of the Brahmi numerical notational system The origin of the Brahmi numerals is a subject of wide controversy among scholars and remains to be solved scientifically and satisfactorily. The subject has long been engaged attention of scholars ever since the discovery of the existence of the old Brahmi numerical symbols by James Prinsep in 1838. Since then a large number of theories have been advanced to explain the origin of the Brahmi numerals. Prinsep was the first to believe that the numerical symbols derived from the characters for the initial letter of the Sanskrit word for each number. The theory is obviously unsatisfactory. In 1877, Bhagwanlal Indraji advanced another theory that rests on the assumption that all the numerical symbols excepting the first three were denoted by letters or groups of letters. In his postscript to Bhagwanlal’s article, Buhler accepted the theory, though he admitted that the actual origin of these numerals remained obscure, since no rationale could be discerned for the particular phonetic values attributed to the numerical signs. For this reason the idea that he numerical symbols are essentially derived from Brahmi letter-forms could not be accepted. Some scholars like A. Cunningham inclined to believe that the Brahmi symbols from 5 to 9 resemble the Ariano-Pali (Kharosthi) letters for initial syllables of the words for each number. But this superficial resemblance has long back rejected. E. C. Bayley opined that the Brahmi numerical system was derived from various sources like Phoenician, Egyptian, Bactrian and possibly from Cuneiform. Bayley’s assumptions are also not convincing to many scholars. Recently, Falk has proposed a possible influence from the early Chinese system of numerical notation. But that too is unconvincing and therefore, cannot be accepted. Thus, there is no consensus of opinion regarding the origin of the Brahmi numerals. The foreign origin theory has no basis at all. The system was essentially originated indigenously and was possibly older than the Brahmi script. 4. Early phase of development in Indian Inscriptions The inscriptions of Asoka furnish the earliest examples of the use of the Brahmi numerals followed by those found in the Nanaghat, Nasik and Karle caves. The inscriptions found from Mathura, Kousambi and the Western Ksatrapa coins and inscriptions are also of immense value for understanding the ancient Brahmi numerals. A complete set of figures is found in the series of dated coins of the Western Ksatrapas issued between second and fourth century CE. The subsequent development of the Brahmi numerals exhibited considerable variability leading to different forms in time and space. The ramification of the numerical symbols in the Brahmi-derived scripts of India is evident from the huge corpus of inscriptional literature. Fortunately, in many inscriptions, the numbers are written both in words and numerals, making the process of decipherment of the Brahmi numerals more easy and sure. 5. The Brahmi Numerical symbols The first three numerals such as one, two and three are indicated by one, two and three horizontal strokes respectively. The symbol for four is a simple cross. Five is represented by a vertical with a stroke or curve attached to its right medially. The symbol for six has two curves opening to the right and placed one above the other with or without having a loop in the middle. Seven is seen as a down facing curve with its right arm elongated. Eight ism again a curve opened to the top with the right arm gently curves down. Nine is a semi-circle opened to the left with a stroke added to its bottom. Ten and its multiples up to ninety have also separate signs for each of them. The symbol for ten is a circle with two horizontal lines joined to it on the right. The symbol of twenty is simple circle. The symbol for thirty is represented by a curve and a vertical joined together by a firm base-line. One of the early varieties of the symbol for forty is denoted by a small curve attached to a slanting stroke in the right and another small curve goes down from the middle of the stroke. The symbol for fifty is a broad curve either facing to the left or right. The symbol for sixty resembles to the English letter V or Y. The symbol for seventy is indicated by a vertical with a small bar attached to it on the either side. Eighty and ninety are represented respectively by a circle with a vertical and a circle with a cross in the middle. The symbol for one hundred is indicated by a cursive left half and angular right half joined together by a mid-line. The symbols for the multiples of one hundred is indicate such as two and three hundred are formed by adding one or two horizontal bars on the top right respectively. From four hundred onwards, the symbols for each of the numerals such as four, five, six etc., are joined to the symbol for one hundred on its right by an additional bar in order to denote the multiples of one hundred. The symbol of one thousand resembles the English letter T. As in the case of hundreds, so also in the case of the multiples of one thousand, the symbols are placed to the right of the symbol for one thousand.
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