Shining a light on South India’s medieval measuring systems

What were the mathematical methods of measurement in ancient times in the region? How was land measured down to a fraction of the total extent; what parameters did ruling monarchies apply to determine which lands were to be taxed and which could be granted exemptions?

Addressing a two-day workshop on the ‘Social History of Vernacular Mathematical Practices in South India’ hosted by the French Institute of Pondicherry (IFP) and the Swiss National Science Foundation, ETH, Zurich, Y. Subbarayalu, the institute’s former Head of Indology and epigraphist detailed the medieval systems of measurement prevalent in South India from the study of inscriptions dating back to the 10th century. The ancient practices of land measurement in South India adhered to a mind-boggling and often puzzling range of values that were assigned to memorisation by rote and nomenclature, than a form of penned records or numerals, observed Prof. Subbarayulu.

The primary purpose of measuring land was to serve as metrics for taxation during the reign of a monarch, he said.

Though measuring methods may have existed before, it is from inscriptions dating from the 10th century onwards — especially from the Brihadeeswarar temple in Thanjavur built by Raja Raja Chola I around A.D. 1000 — that epigraphists have been able to gather insights into the minutiae of vernacular mathematical practices, Prof. Subbarayalu said.

These measurements, derived from the division and sub-division of land into primary, secondary and tertiary series of fractions, are beyond even modern-day computational methods.

The measurements ranged from the “veli”, the standard unit of land for the assessor, its primary fractions: the “ma” (1/20th), “kani” (1/80th) and the “muntiri” (1/320th). The second order fractions lesser than 1/320 were prefixed by the word “kil” and counted as the powers of muntiri multiplied by primary fractions. For example, the muntri multiplied by 1/2 was the “kil-arai”, and by 1/320 was the “kil-kil”.

Typically, a “veli” was the rough equivalent of today’s 2.5 hectares. While the approximative nature of the “veli” suited kings determining the devolution of land, levying tax or granting exemptions, at the level of the commoners the land units were measured in fractions.

However, the main challenge for the rulers was to convert what was a local computation practice into a standardised form of land measurement. Apart from being a system based on approximation, regional variations abounded even in the length of the wooden pole, ranging from 3.6 metres to 9 metres.

According to Prof. Subbarayalu, two of the most striking aspects of the system were that it was applied entirely with a wooden pole, about which there is no inscription but only anecdotal references, and that those assigned the crucial role from a revenue perspective were from non-Brahminical lineage.

S. S. Kamalavelan, from the Free Software Movement of India, explained the technological processes, and the challenges, involved in an ongoing exercise to upload the wealth of IFP research material on an open access digital platform.

With the open access of knowledge sharing now, the de facto standard set by the European Union, the expected outcome of the share-and-build digital effort at the IFP would be a rich aggregation of Wikipedia, Internet archive and contributions of scholars and students, he said.

In their introductory remarks, Senthil Babu and Roy Wagner from the IFP pointed out that the workshop was part of efforts to develop vernacular knowledge sources (inscriptions) as alternative to the canonised Sanskrit treatises on which the study of Indian mathematics has traditionally focused on.

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