B.V.Subbarayappa - Number Mysticism

Reference --Article in vedic on line ---

http://www.archaeologyonline.net/artifacts/vedic%20journalonline.pdf

Iravatham Mahadevan

Aryan, Dravidian, or Neither?

A Study of Recent Attempts to Decipher the Indus Script  (1995-2000)

‘Number Mysticism’

                     Dr. B.V. Subbarayappa is the honorary Director of the Centre for History and Philosophy of Science at the Indian Institute of World Culture, Bangalore. He has published several books on the history of science in India. His book Indus Script: it’s Nature and Structure was published in 1996.

                        Subbarayappa examines the reasons why the proposed decipherments based on language have failed. According to him, it is unlikely that there was a single language spoken over the vast area covered by the Harappan civilisation. In any case, he doubts whether the Harappan vocabulary could be so limited as to possess only about 450 words represented by the signs of the Indus script. He also points out that early societies with oral tradition like the Vedic had highly developed number systems; the Harappan society could have been one such. This is the basis for Subbarayappa’s radically different solution that the Indus signs are all numbers ‘expressed in an ingenious manner’ and that the Indus texts are a ‘ciphered system involving additive-multiplicative approach to arrive at and express the desired numbers’.

                         The proposed numeral system is decimal with base 10. There are different symbols for the numbers 1 to 9, for 10, 100 and 1000, and for their multiples. Subbarayappa identifies two types of numerical representation in the texts. The symbols with the orderly sequence of one to twelve strokes represent the numbers 1 to 12. The number 10 is represented by a circle. The other type is much more complex in which pictorial symbols or geometric forms represent various numbers.

                            For example, any sign with four lines, whether it is a square, or oblong or diamond or a cross, represents the number 4. Higher numbers are represented by additional strokes attached to the basic signs. Many of the numbers are identified from their supposed resemblance to numbers in various other numerical systems including Babylonian, Chinese, Attic Greek, Kharoshthi and Asokan Brahmi. There are also many imaginative derivations; for example, U stands for 20 because it looks like a ‘nail’ and we have twenty nails. The complexity of the system is increased further as many of the numeral signs are ‘condensed in an artistic way’ or ‘embellished’ to look like pictorial depictions.

                             The Indus texts are all strings of numbers. They are generally written from right to left. Subbarayappa cites the ancient Indian practice of writing the numeral digits from right to left. The ‘mechanism’ proposed by him to derive higher numbers comprises (1) repetition, (2) addition of strokes, (3) ligaturing of signs and (4) use of some special additive devices. Subbarayappa claims that the advantage of this numerical system lies in the ‘ease with which a purposeful and realistic recording can be accomplished’. One may however dispute his claim as he himself describes the system as a cipher, which by definition, has to be deciphered before it can be understood.

                             The Indus texts are regarded as ‘exclusively quantitative records with no words or ideograms interposed in between’. Subbarayappa has an interesting answer to the question as to what the quantitative records represent, as they are not mentioned in the texts. He believes that the animal motifs depicted on the seals represent various agricultural commodities, the quantities of which are specified in the numbers indicated in the texts which accompany them. For example, the ‘unicorn’ represents symbolically the three important field crops of barley, wheat and cotton, each crop being specified by the variations in the standard like object placed in front of the animal. Some of the other important identifications include

short-horned bull : six-rowed barley;

ox-antelope : two-rowed barley;

elephant : wheat;

rhinoceros : peas;

buffalo : sesamum;

gharial : rape-seed,

tiger : date fruit;

humped bull : cotton threads;

hare : boll of cotton.

                          The purpose of the inscriptions is to maintain an account of the grains and cotton made available to the people under a centralised dispensation. Duplicates of the inscriptions like those on the sealings indicated that so many bundles or packages were sent from one place to another. What about the texts without any animal or other pictorial motifs? Subbarayappa points to the perforations, a feature present on most of the seals, and explains that the text-seals were tied to other seals having pictorial motifs, the latter identifying the commodity.

                        A serious objection to Subbarayappa’s solution is that it is highly unlikely that the large and beautifully carved stone seals, apparently very expensive to make, would be used to record quantities of commodities varying with each transaction. It would have been much simpler to make use of cheaper and readily available material like cloth, palm leaves or clay for daily accounts not required to be preserved for posterity. Another equally serious objection is that notwithstanding his claim to the contrary, the great complexity of the system would render it quite unsuitable for unambiguous recording of transactions for handing out daily rations or despatch of goods.
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