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|Positional systems by base|
|Non-standard positional numeral systems|
|List of numeral systems|
Sinhalese belongs to the Indo-European language family with its roots deeply associated with Indo-Aryan sub family to which the languages such as Persian and Hindi belong. Although it is not very clear whether people in Sri Lanka spoke a dialect of Prakrit at the time of arrival of Buddhism in Sri Lanka, there is enough evidence that Sinhala evolved from mixing of Sanskrit, Magadi (the language which was spoken in Magada Province of India where Lord Buddha was born) and local language which was spoken by people of Sri Lanka prior to the arrival of Vijaya in Sri Lanka, the founder of Sinhala Kingdom. It is also surmised that Sinhala had evolved from an ancient variant of Apabramsa (middle Indic) which is known as ‘Elu’. When tracing history of Elu, it was preceded by Hela or Pali Sihala.
Sinhala though has close relationships with Indo Aryan languages which are spoken primarily in the north, north eastern and central India, was very much influenced by Dravidian language families of Hindi.Though Sinhala is related closely to Indic languages, it also has its own unique characteristics: Sinhala has symbols for two vowels which are not found in any other Indic languages in India: ‘æ’ (ඇ) and ‘æ:’ (ඈ).
The Sinhala script had evolved from Southern Brahmi script from which almost all the Southern Indic Scripts such as Telugu and Oriya had evolved. Later Sinhala was influenced by Grantha writing of Southern India. Since 1250 AD, the Sinhala script had remained the same with few changes. Although some scholars are of the view that the Brahmi Script arrived with the Buddhism, Mahavamsa (Great Chronicle) speaks of written language even right after the arrival of Vijaya. Archeologists had found pottery fragments in Anuradhapura Sri Lanka with older Brahmi script inscriptions, which had been carbon dated to 5th century BC. The earliest Brahmi Script found in India had been dated to 6th Century BC in Tamil Nadu though most of Brahmi writing found in India had been attributed to emperor Ashoka in the 3rd century BC.
Sinhala letters are round-shaped and are written from left to right and they are the most circular-shaped script found in the Indic scripts. The evolution of the script to the present shapes may have taken place due to writing on Ola leaves. Unlike chiseling on a rock, writing on palm leaves has to be more round-shaped to avoid the stylus ripping the Palm leaf while writing on it. When drawing vertical or horizontal straight lines on Ola leaf, the leaves would have been ripped and this also may have influenced Sinhala not to have a period or full stop. Instead a stylistic stop which was known as ‘Kundaliya’ is used. Period and commas were later introduced into Sinhala script after the introduction of paper due to the influence of Western languages.
Although various scholars had mentioned about numerations in the Sinhala language in their writing on Sinhala language, a systematic study had not been conducted up to now on numerals and numerations found in Sinhala right before British occupation of Kandy. In modern Sinhala, Arabic numerals, which were introduced by Portuguese, Dutch and English, is used for writing numbers and carrying out calculations. Roman numerals are used for writing dates and for listing items or words in Sinhala though at present, Roman numerals are not commonly used and they were also introduced by Westerners who invaded Sri Lanka. It is accepted that Arabic numerals had evolved from Brahmi numerals. It had also been discovered by Sri Lankan archeologists that Brahmi numerals were used in the ancient Sri Lanka and it may have evolved into two sets of numerals which were known as archaic Sinhala numerals and Lith Illakkum which were found in the Kandyan period. This paper mainly covers numerals and numerations in Sri Lanka at the time of British occupation of the Kandyan Kingdom and their evolution to the forms which were found in 1815, the year the British occupied the whole of Sri Lanka. This article will also touch upon Brahmi numerals, which were found in Sri Lanka.
Numerals or numerations found immediately before the capture of the Kandyan Kingdom in Sri Lanka by the British
It had been found that five different types of numerations were used in the Sinhala language at the time of the invasion of the Kandyan kingdom by the British. Out of the five types of numerations, two sets of numerations were in use in the twentieth century mainly for astrological calculations and to express traditional year and dates in ephemeri des. The five types or sets of numerals or numerations are listed below.
Sinhala archaic numerals or Sinhala Illakkam
In “A Comprehensive Grammar of Sinhalese Language”, Abraham Mendis Gunasekera, the author of the book describes a set of archaic numerals which had not been in use even at the time of the publication of his book in 1891. According to Mr. Gunesekera, these numerals were used for ordinary calculations and to express simple numbers. These numerals had separate
- Archaic Sinhala numerals from Plate III of Abraham Mendis Gunasekera’s ‘A Comprehensive Grammar of Sinhalese Language’ book. These numerals did not have a zero and they also did not have zero concept holder.
- 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.
- A day had sixty Sinhala hora or hours. The watch shows thirty horas or hours in Sinhala Illakkam. Even today Sinhala Astrologers convert time of Birth to Sinhala Hora or Hours for casting horoscopes. This watch was owned by the last of king of Kandy.
- The Historical Convention which was signed in 1815 between the first British governor of whole of Sri Lanka and Kandyan Chieftains where Sinhala Illakkam or Sinhala archaic numerals had been discovered.
- The first page of Kandyan Convention. The first clause of the convention is numbered with Sinhala Illakkam. Number one of Sinhala Illakkam is marked with a Red Squaire.
- The second page of Kandyan Convention. The second and third clauses of the convention are numbered with Sinhala Illakkam.
- 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.
Symbols for 10, 40, 50, 100, 1000. 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. The following is an excerpt from “A Comprehensive Grammar of Sinhalese Language”, by Abraham Mendis Gunasekera describing Sinhala archaic numerals: “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.).
One of the major findings had been the discovery of Sinhala numerals or Sinhala illakkam in the Kandyan convention which was signed between Kandyan Chieftains and the British governor, Robert Brownrig in 1815. 11 clauses had been numbered in Arabic numerals in the English part of the agreement and in parallel Sinhala clauses were numbered in Sinhala archaic numerals.
Sinhala astrological numerals or Sinhala Lith Illakkam
- 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'.
- 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.
- This Ola was found at Kandy museum and it contains Astrological calculations. The book have been written in the 17th century.
- This is the second version of Lith illakkam found in the modern books.
- An astrological text book found in the Kandy Museum with Lith Illakkam.
- A rare horoscope which was cast in 1936 with mixture of Lith Illakkam and Arabic numerals. Please note 'Thunda Litha' in Lith Illakkam.
- 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 none 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.
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. The katapayadiya is mainly used for writing dates. This is numeration is known as Katapayadiya1 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.
Page numbering of Ola leaves using Sinhala ‘Swara (ස්වර)’
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.
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 Astronomer 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 If one were to write 130, he or she 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”, he describes Bhootha Anka as object-number metronomic expressions. 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.
Brahmi numerals found in Sri Lanka
Dr. Paranavithana (first Sri Lankan Commissioner of Archaeology) and Dr. Abaya Aryiasinha had independently found in their research that Sinhalese had used numerals which closely resembled Brahmi numerals of India in the early days of Sinhala civilization. The evidence for use of Brahmi numerals had been discovered primarily in rock inscriptions which were inscribed in between AD 200 and 400. These numerals were used to record donations given by royals and other people who were belonged to the upper echelon of ancient Sinhala society to Buddhist temples. Brahmi numerals are ancestors of Arabic numerals which are used presently worldwide. Brahmi numerals had symbols for 10,100, and 1000. Number 1 and 10 in Brahmi have not been found in Sri Lanka up to now. Therefore, shapes of these two numerals have been hypothesized taking into consideration of shapes of Brahmi Number 1 and 10 found in India without physical evidence . Sinhala rock inscriptions suddenly become barren of numerals from A.D. 400 onwards. Tradition of writing numbers in word becomes more prevalent from the above period.
- In Sri Lanka, number 1 and 10 have not been physically found. In addition, In Sri Lanka Brahmi numerals 30, 40, 80 and 90 seemed to have not been also discovered.
- Brahmi Numeral Four on a tile, Kandy Museum Sri Lanka
Research into Sinhala numerals
Although a few scholars had recorded the existence of Sinhala numerals after 1815, a comprehensive research was required to establish the past existence and precise shapes of these numerals.
The proposal, L2/07-002R (ISO/IEC JTC1/SC2/WG2 N3195R), which was submitted by Mr. Michael Everson to the Unicode consortium for encoding a set of numerals which he claimed were Sinhala numerals, initiated research into Sinhala numerals and numerations. Through the research which was carried out by Mr. Harsha Wijayawardhana of University of Colombo School of Computing (UCSC) under the aegis of the Information and Communication Technology Agency (ICTA) of Sri Lanka, it was discovered that other than the set of numerals submitted by Mr. Michael Everson for encoding, there were four other sets which were commonly used by Sinhala scribes, namely Sinhala Lith Illakkam (Astrological Digits) mainly used for writing horoscopes; Swara, (Sinhala Consonant and vowel modifier based numerals); Katapayadiya, a special Sinhala character based numeral set which was used for inscribing years in astrological writing, in ancient Ola and in rock inscriptions; and word based Bootha Anka or Samkaya used in Sinhala Poetry. Mr. Wijayawardhana identified the numeral set which was submitted by Mr. Michael Everson to UCS as Sinhala Illakkam (Sinhala Archaic Numerals).
Subsequently, Prof. K.D. Paranvithana of Raja Rata University, Sri Lanka, and Mr. Harsha Wijayawardhana carried out further research and the findings were presented at the National Archaeological Symposium held in July 2009, in Colombo, Sri Lanka, organized by the Department of Archaeology. The Synopsis of the paper was published in the Volume II of the Symposium’s proceedings. In October 2009, Mr. Harsha Wijayawardhana authored a book titled “Numerations in the Sinhala Language”.
The research into Sinhala numerals were carried out from the both linguistic and mathematical perspectives. In their research, the researchers had looked specifically for the existence of zero in any form of numerations in the Sinhala language, since the invention of zero had been a major demarcation point in mathematics and advancement in modern pure mathematics would have not been possible without having the concept of zero. Although zero had been discovered and re-discovered independently by various civilizations in the world, it is now accepted that zero as an independent number was discovered and used for the first time by the Indian mathematicians and it had been taken to the west by the Arabs with the rest of numerals which were developed in India from Brahmi numerals. E.T. Bell in his book, the development of Mathematics, describes of the development of zero by Indian mathematicians in the following manner: “The problem of numeration was finally solved by Hindus at some controversial date before A.D. 800. The introduction of zero as a symbol denoting the absence of units or of certain powers of ten in a number represented by the Hindu numerals has been rated as one of the greatest practical inventions of all time”.
In their research into Sinhala numerals or numerations, the authors had looked into the following:
- Papers or publications on Sinhala numerals
- Original documents which had some of form of numerals or numerations
- Rock inscriptions
- Ola leaf page numbering
- Any evidence for zero in Sinhala numerals or numerations
Shapes of several numeral sets which belong to Indic languages were compared with of the numerals sets which were identified as numerals or numerations in the Sinhala language. The Indic numerals sets which were studied extensively were Thai, Lao, Burmese, and Malayalam numerals. Colombo and Kandy museum were visited many instances to study Ola leaf pagination by the researchers. Colombo museum library hosts to an Ola leaf collection which is known as W. A. De Silva Collection and this sizable collection amounts to be 5000. Some of the original and older Ola leaf collections were found to be outside of Sri Lanka. A major collection is located in Britain and is known as Hue Neville collection and the catalogue of this collection is available in Sri Lanka. Other country museums that are reputed to host to Sinhala Ola leaf collections are in Arizona, US, Brussels, Belgium and Netherlands.
Sinhala numerals were added to the Unicode Standard in June, 2014 with the release of version 7.0.
The Unicode block for Sinhala numerals, called Sinhala Archaic Numbers, is U+111E0–U+111FF:
| Sinhala Archaic Numbers|
Official Unicode Consortium code chart (PDF)
- Dissanayaka, J.B. (2006). Sinahala Graphology. Sumitha Publication.
- Mahanama, Thera. Mahavamsa: The Great Chronicle of Sri Lanka. Vijith Yapa.
- Gunasekera, Abraham Mendis (1891). A Comprehensive Grammar of Sinhalese Language. Sri Lanka Sahitya Mandalaya (Academy of Letters). pp. 144–150.
- ගුණසේකර ඒබ්රැුහැම් මෙන්දිස් ග්රේණ්ථාන්වය, කතෘ – (පිටු අංක 3 සිට 10 දක්වා). 1891.
- Epa Panchanga (Epa Ephemeris). Epa Printers. 2007.
- De Silva, W.A. (1938). Catalogue of Palm leaf manuscripts in the library of Colombo Museum. 1. Government Printer.
- Filliozat, Pierre-Sylvain (2004). Ancient Sanskrit Mathematics: An oral tradition and a written literature, book 147, History of Science, History Text by Karine Chemla.
- අභිලේඛන, සමරු පොත් පෙළ, දෙවන වෙළුම, ප්ර,ධාන සංස්කාරක – පණ්ඩිත ආචාර්ය නන්දදේව විජේසේකර, පුරාවිද්යා දෙපාර්තමේන්තුව. 1990. p. 90.
- Everson, Michael (2007). "N3195R: Proposal to add archaic numbers for Sinhala to the BMP of UCS" (PDF). Retrieved 4 July 2014.
- "N3888: Proposal to include Sinhala Numerals to the BMP and SMP of the UCS" (PDF). Retrieved 4 July 2014.
- Bell, Eric Temple (1940, 1945). Development of Mathematics (2nd ed.). McGraw Hill Book Company. p. 51. Check date values in:
- Wijayawardhana, Harsha. Numerations in the Sinhala Language. Strategic Communications and Media Unit – ICTA. ISBN 978-955-1199-05-0.
- Hettigoda; De Silva, Hendrick (1987, first print in 1967). Life and Planets, Vishwa Lekha, Sarvodaya. pp. 34–36. Check date values in:
- Indian Epigraphy: A Guide to the Study of Inscriptions in Sanskrit, Prakrit, and the Other Indo-Aryan Languages. Oxford University Press US. 1998.
- "Numeration by Kularathne P.D.S.". Sinhala Encyclopedia. 1967.
- Menninger, Karl; Broneer, Paul (1992). Number words and number symbols: A cultural history. Courier Dover Publications.
- Samaranayake, V.K.; Nandasara, S.T.; Dissanayake, J.B.; Weerasinghe, A.R.; Wijayawardhana, H. (2003). "An Introduction to UNICODE for Sinhala Characters" (PDF). University of Colombo School of Computing. Retrieved 4 July 2014.