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Birch Barks of Bakhshali

Way back around 800 CE, the Indic approach to computational insights was displayed on the birch barks with symbols representing arithmetical operations that foretells the algebraic equations of the modern times which prompted Indic scholar Frits Staal to quip that ‘the Indic approach to the exact sciences generally preferred computation to theory , and so assigns a role to language natural or aritifical, different to that in European science.’

The Indic lore of those birch barks of Bakhshali is a fascinating tale that gave to us what is known as the Bakhshali Manuscript inscribed with mathematical symbols and operations that gave rise to newer insights into the evolution of computational ideas in history that pre-dates European tales.

The Bakhshali Manuscript was founded in 1881 near the village Bakhshali of the Yuzufzai subdivision of the Peshawar District (now in Pakistan). A tenant residing in the house of Inspector of Police Mian An-Wan-Udin while digging a stone enclosure in a ruined place of the Bakhshali village stumbled upon the ancient leaves of the manuscript. Inpsector Mian An-Wan-Udin took the manuscript to the Assistant Commissioner of Police who was to forward it to the Lahore Museum. But the manuscript was sent to the Lieutenant Governor of Punjab – who under the advice of General Alexander Cunningham – directed it to be passed on to Dr Rudolf Hoernle of the Calcutta Madrasa for study and publication.

Dr Hoernle presented a description of the BM at the Asiatic Society of Bengal in 1882 and subsequently it was published in the Antiquary the next year. Its fuller account was presented by Dr Rudolf Hoernle at the Seventh Oriental Conference held at Vienna in 1886. In 1902, he presented the Bakshali Manuscript to the Bodleian Library, Oxford, where it remains in safety. As often with parchments and birch-bark leaves, only 70 leaves of birch bark of the BM survived at the time of discovery.

The origin of the Bakhshali Manuscript was literally drowned in a welter of claims. To begin with, Dr Rudolf  Hoernle placed it between the 3rd and 4th centuries AD. Many other historians of mathematics – Moritz Cantor, F Cajori, B Datta, S N Sen, A K Bag, and R C Gupta – agreed with this dating. In 1927-1933 the Bakhshali manuscript was edited by G R Kaye and published with a comprehensive introduction, an English translation, and a transliteration together with facsimiles of the text. Kaye claimed that the manuscript dated from the twelfth century AD and he even doubted that it was of Indian origin!

But, M N Channabasappa, writing on the square root formula in the Bakhshali Manuscript, observed that five specific mathematical terms which did not occur in the works of Aryabhata and that strongly supported a date for the Bakhshali manuscript earlier than the 5th century. Historian L V Gurjar put the date not later than 300 AD. Indic scholar T Hayashi, writing in The Bakshali Manuscript: An Ancient Indian Mathematical Treatise (1995), claims that the date of the original is probably from the 7th century, but also the manuscript itself is a later copy which was made between the 8th century and the 12th century AD.

G G Joseph in The Crest of the Peacock tells us what the BM consists of: “The Bakhshali manuscript is a handbook of rules and illustrative examples together with their solutions. It is devoted mainly to arithmetic and algebra, with just a few problems on geometry and mensuration. Only parts of it have been restored, so we cannot be certain about the balance between different topics.” Now the way that the manuscript is laid out is quite unusual for an Indian document (which obviously made Kaye to prefer the hypothesis that it is not Indian at all – an idea in which we cannot see any merit). The Bakhshali manuscript gives the statement of a rule. There then follows an example given first in words, then using mathematical notation. The solution to the example is then given and finally a proof is set out.

The notation used is not unlike that used by Aryabhata but it does have features not found in any other document. Fractions are not dissimilar in notation to that used today, written with one number below the other. No line appears between the numbers as we would write today, however. Another unusual feature is the sign + placed after a number to indicate a negative. It is very strange for us today to see our addition symbol being used for subtraction. Equations are given with a large dot representing the unknown. A confusing aspect of Indian mathematics is that this notation was also often used to denote zero, and sometimes this same notation for both zero and the unknown are used in the same document., explains Ian Pearce in his The Bakhshali Manuscript which is now in The MacTudor History of Mathematics archive.

There are more to the mathematical content in the Bakhshali Manuscript as interpreted by different scholars on the historical merits which I reckon would require a different set of blogpieces to write on them.




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