Sinhala archaic numerals or Sinhala Illakkam

Abraham Mendis Gunasekera, in A Comprehensive Grammar of Sinhalese Language (1891), described a set of archaic numerals which were no longer in use. According to Mr. Gunesekera, these numerals were used for ordinary calculations and to express simple numbers. Gunasekera wrote:

The Sinhalase had symbols of its own to represent the different numerals which were in use until the beginning of the present century. Arabic Figures are now universally used. For the benefit of the student, the old numerals are given in the plate opposite (No. iii.).

Sinhala numerals did not have a zero and they also did not have zero concept holder. They included separate symbols for 10, 40, 50, 100, 1000.^[1]

These numerals were also regarded as Lith Lakunu or ephemeris numbers by W. A. De Silva in his Catalogue of Palm leaf manuscripts in the library of Colombo Museum. This set of numerals was known as Sinhala illakkam or Sinhala archaic numerals.

Sinhala numerals or Sinhala illakkam were used in the Kandyan convention which was signed between Kandyan Chieftains and the British governor, Robert Brownrig, in 1815. Eleven clauses were numbered in Arabic numerals in the English part of the agreement, and the parallel Sinhala clauses were numbered in Sinhala archaic numerals.

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  Archaic Sinhala numerals from Plate III of Gunasekera's A Comprehensive Grammar of Sinhalese Language.
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  Archaic Sinhala numerals from ‘Catalogue of Palm leaf manuscripts in the library of Colombo Museum’, Volume I, compiled by W. A. De Silva, published by the Government Printer in 1938.
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  A day had sixty Sinhala hora or hours. This watch, which belonged to the last king of Kandy, shows thirty horas or hours in Sinhala Illakkam. Even today, Sinhala astrologers express time of birth in Sinhala Hora or Hours for casting horoscopes.
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  The Kandyan Convention of 1815, using Sinhala archaic numerals.
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  The first page of Kandyan Convention. The first clause of the convention is numbered with Sinhala Illakkam. The numeral 'one' is marked with a red square.
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  The second page of Kandyan Convention. The second and third clauses of the convention are numbered with Sinhala Illakkam.
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  All eleven numerals found in the Kandyan Convention are given in the second row and the corresponding numerals which are given by Mendis Gunesekera are given below for comparison. Number 2 and 3 of Sinhala Illakkam have a slight variation.

Sinhala astrological numerals or Sinhala Lith Illakkam

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  Sinhala Lith Illakkam or Sinhala Astrological Numbers. Zero of Lith Illakkam is Halantha or Hal Lakuna. Hal Lakuna or Halantha removes the inherent vowel sound in a consonant. This is the first version of Sinhala Lith Illakkam and is the oldest version found. Please note Number 2, 3, and 9 are given by shapes which are similar to older Murthda 'Na'.
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  Abraham Mendis Gunesekera became famous for the Sinhala Grammar Book which was written by him in the latter part of the 18th century. This book also gave the shapes of Sinhala Illakkam. Here in a rare magazine Article, he describes Lith Illakkam and he further suggests instead of using Hallantha or Hal Lakuna for zero to use modern zero. He writes in this article large numbers with Lith Illakkam.
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  This Ola was found at Kandy museum and it contains Astrological calculations. The book have been written in the 17th century.
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  This is the second version of Lith illakkam found in the modern books.
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  An astrological text book found in the Kandy Museum with Lith Illakkam.
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  A rare horoscope which was cast in 1936 with mixture of Lith Illakkam and Arabic numerals. Please note 'Thunda Litha' in Lith Illakkam.
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  Page numbering with Lith Illakkam. Page numbers of Ola which are non buddhist topics are numbered with Lith Illakkam.

Although this numeral set was commonly used for casting horoscopes and to carry out astrological calculations, it had been found that this set had been used for numbering pages of Ola palm leaf books which covered primarily of non-Buddhist topics in Sinhala. Numbers of lith illakkam look Sinhala letters and vowel modifiers, and it had been discovered that there are mainly two versions of these illakkam according to the way numbers 2, 3 and 9 are written. The number six is known as ‘akma’ in the Lith Illakkam. These numerals were in use continuously for writing horoscopes on Ola leaf, the tradition of which continued till the beginning of the twentieth century. Both versions of Lith illakkam have a zero and the zero is the Halantha or Hal lakuna (kodiya) in the Sinhala language. Although it is not understood whether Sinhala mathematicians treated zero as a number, it was quite possible they had known the concept of zero. In Lith Illakkam, numbers greater than zero were written the same way as the Arabic numbers with the zero and the value of the number in the left was increased by ten. In other words, Lith illakkam had a zero and a zero place holder concept. Lith illakkum version 1 had for 2, 3 and 9, Sinhala letter ‘Murthda Na’ in 6 to 8th century. In the second version of Lith Illakkam as W. A. De Silva had depicted in his book, 2,3 and 9, Sinhala letter, ‘Na’ (න) with vowel modifiers.

One of the most interesting articles which had been discovered is an article on numerals and numerations in Sinhala language, the authorship of which has been attributed to Abrham Mendis Gunesekera. In this article, he refers to Lith Illakam as well as to Sinhala Illakkam. For Sinhala illakkam, he produces the same shapes which had been given in his English book. Abraham Mendis Gunesekera uses modern Sinhala letters and vowel modifiers which is the Version 2 of Lith illakkam. In this article, he clearly mentions that Hal lakuna or ‘Kodiya’ is the zero. In other words, ‘Sunayathana’ is filled with a kodiya will multiply by ten of the number which is on the left side of Sunayasthana. Abrham Mendis Gunesekera clearly states that instead of Hal lakuna of the Sinhala language, a ‘Shunaya binduawa’ (zero) can be used to fill the ‘Shunayasthana’ (Zero Place Holder). In other words, Lith Illakkum uses duality of zero to write numbers greater than 9.^[2]

Katapayadiya

Even to this day, years are given in the front page of popular ephemeris in Sri Lanka, ‘Panchanga Lith’ using ‘Katapayadiya’. Katapayadiya is a unique numbering scheme where numbers 1 to 9 and 0 have been depicted by Sinhala consonants.^[3] The katapayadiya is mainly used for writing dates. This is numeration is known as Katapayadiya since number one is allocated with the Sinhala letters ‘Ka’ (ක), ‘Ta’ (ට), ‘Pa’ (ප ) and ‘Ya’ (ය) . In this tradition of writing numbers, the year 2007 can be written with for instance ‘Ka’ (ඛ) ‘Na’ (න) ‘Na’ (න) ‘Sa’ (ස). Traditionally, 2007 will be written from right to left: 7002. Ordinarily, using vowel modifiers, a word in Sanskrit will be created for the year 2007 (7002 right to left) with the allocated letters for 7002. When reading, one has to remove the vowel modifier. Katapayadiya was widely used by South Indian astrologers and some of Chola rock inscriptions in Sri Lanka have dates inscribed in Katapyadia.

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  Katapayadiya

Page numbering of Ola leaves using Sinhala ‘Swara’

The method of page numbering of Ola using Sinhala Swara with consonants had been common tradition in the ancient and recent history of Sri Lanka. The author had found that using Sinhala Swara in place of numeration could be traced back to Aryabhata's (the great Indian Mathematician and Astronomer) numbering system where he used Sanskrit Swaras in place of numerals. Sinhala scribes had developed its own numeration based upon Sinhala characters according to the order of the position of consonants and vowels in the Sinhala Alphabet without the modern two vowels: ‘Ae’ (ඇ) and ‘Ae:’ (ඈ) in the Sinhala Alphabet (the Sinhala alphabet without the above-mentioned two vowels is known as ‘Pansal Hodiya’ or the alphabet of the temple). The numeration method which is similar to the use of Sinhala Swara is found in Burmese Ola collection.

The tradition of Swara as numeration in page numbering in Ola had been commonly used for Buddhist manuscripts. The authors had the opportunity of examining several Ola palm leaf books which are in the Colombo Museum and the catalogues of Hugh Neville collection in the London Museum. Having investigated paging of Ola leaves, the majority of palm leaf manuscripts which are in the museum had Sinhala consonants with ‘swara’ (ස්වර) (combinations of sounds) for numbering. The number of combinations which can be made out of consonants is 544 and once the first 544 finishes, paging begins with the second cycle of 544 with the word ‘dwi:’ (ද්වී) or second in English. If the second cycle does not end the palm leaf book, it goes into third cycle of 544 which begins with the word ‘three’ (ත්රීp) or Three in English.^[4]

Bhootha Anka or Butha Samkaya

In Sinhala literature, certain words in the language were used to denote numbers. For instance, sky is associated with zero or ‘Sunaya’, and a number which was denoted by words is known as Bhuta Anka. Bhootha Anka was created by ancient Sanskrit mathematicians and astronomers prior to the invention of a symbol for zero. Some of the words which are associated with numbers are

• Moon = one
• Eye = two
• Fire = three

To write 130, one would place moon, fire, sky together to form the number.

Pierre-Sylvain Filliozat, in his article ‘Ancient Sanskrit Mathematics: An oral tradition and a written literature”, describes Bhootha Anka as object-number metronomic expressions.^[5]

As it was mentioned previously, knowledge was transferred through memory rather than writing it down. In order to make memorization easier, it is natural that the numbers are placed as words and the words are formulated sequentially that they would sound rhythmical. The Indian tradition of Bhootha anka was imported to Sri Lanka as it was used in India and the tradition continued with Sinahala words that had same meanings.