WORDS AND SYMBOLS FOR NUMBERS


 

WORDS AND SYMBOLS FOR NUMBERS USED BY THE ANCIENT SINHALESE [3 Cent BC – 3 Cent AD].

Brig Siri Munasinghe.

We are fortunate that our ancestors left traces of these words and the symbols  for numbers on their rock inscriptions. These traces are extracted and listed for information of scholars interested in research. Few other numeration system existed and was practiced in Sri Lanka until the Portuguese reintroduced the numeral they obtained through the Arabs from India.

THE BASIC SINHALA  NUMBER WORDS [.S.Paranavitane – Inscription of Ceylon Volume I . 1970  Pg xlii

The  historical records  of  Twenty  basic words that are required to express  all numbers   is found on rock inscriptions of ancient Sri Lanka. The number words for one in   Ek patake meaning one lot of land , do– kahapana  to indicate  two silver kahapanas donated by the officer in charge of canals ,tini silapatani –the word for  three  stone steps donated by  Upasika Tisaya, catara –disa to indicate four directions mentioned often in the donations made to  the Sanga, the cave of the paca1  – batikana – of the five brothers, and  number words for saye [Six]sata[Seven], ata[Eight] is similarly found. Then a chief named Uba during the time of Mahasenpathi[  Dr S Paranavitane believes him to be King Dutugemeunu himself] builds a cave  for the Sanga or a King spending Nava [nine] lakhs for labour of hands and feet for construction of a cave  , a Princess whose father was King Gamini Uttiya donating  a cave in the memory of her father and mother to the Sanga of the dasa[ten] directions,  visiti[Twenty] appears in an inscription of King Lanjatissa in regard an donation of twenty five cool cave to the Sanga, other numbers such as of tisa [Thirty], catalisa  for Forty on Pg 337], panasa  [Fifty onPg 335 ], sati [Sixty on Pg 343], satati  [ Seventy on Pg 343 ], atasti   [ eighty for Pg 357], [The the pages given are those on Volume II Inscriptions of Ceylon- S Paranaviyane is published in two parts]Anu[Ninety- on Gold nugget Abeyagirri Vihare], sata  [Hundred], sahasa  [ Thousand] and an extra number word to indicate very large numbers –lak 1 [Lakh]of Money[ Kahapanas] or land measures[ Karihas]  are all in the two volumes of the  ‘Inscription of Ceylon’ Volume I by Dr S Paranavitane., the word for Ninety has not yet been traced in those Inscriptions available to the author . These words are similar to the words of  Sanskrit and Pali, that were  used in India and Sri Lanka during this ancient period. These words  later developed into Elu and these are  different to the early Dravadian words used by our closest neighbor. Those Dravidian number names  which are  described in the recently published book ‘Early Tamil Epigraphy’- I Mahadevan   2003  Pg 283,is listed alongside for comparison in Table I.

 

NUMBER WORDS FOR ROUND NUMBERS AND THEIR MULTIPLES.

The Number Words  for expressing multiples of Tens, Hundreds and Thousands  or the round numbers are also found on inscriptions from 3 Cent BC to 3 Cent AD was obtained from Dr Paranavitane’s three volumes ‘The  Inscriptions of Ceylon’. These words for numbers used express the measures of land in Karihsa , sums of money such as Ranas [ Gold Coins], Kahavanas{ Silver],  and Massas[ Copper or Alloy], dates of the lunar  Month, etc in the inscriptions. The words for the Multiples of Tens are a combine of the Initial letters of the nine digits  as the first member  with the words with sa in case of Tisa, Catalisa, Panasa or with ti in Visiti, Sati, Satati, Asati, as the second member.  The number word for ten ending with ti sounds more like the English Twenty, thirty, forty etc. Perhaps the rhythm made it easy to memorize the numbers.  The   Sinhala word for multiples Hundred and Thousands is a Compound of the Nine words for Sinhala Digits as the first member of the combined with the word for Hundred [ Sata] and Thousand[ Sahasa] as the second member. This way of expressing number names is similar to the present system adopted in present day Sinhala and English.

 

The construction of number words from 11 to 99.

The words for many numbers from eleven to eighty four  is recorded  on rock before the  3 Cent AD are shown on Table  II . These words were expressed as a  compound of the two word , the first word for  Units and then the word  for tens. The name for units as a rule came first. EK CATALISA  [41S.Paranavitane – Inscription of Ceylon Volume II Part II 2001. Pg 328] . It was One and forty instead of Forty and one . In the present day Sinhala this is different as its is a compound of  the word for Tens is expressed as the  first word  followed by the word for Units[ Hatalis eka], which is closer to the expression in English[ Forty One]. Both these system are in use in modern languages.

An exception is the  word for nineteen and twenty nine the word one less than twenty- ekuna visiti in Dakkina Stupa inscription and thirty- ekuna tisa is used[ S.Paranavitane – Inscription of Ceylon Volume II Part II 2001. Pg 329]. The One  less than twenty or one less than Thirty statement gives some indication of Number – sense such as less than or greater than.  The Sinhala name numbers was very flexible and akin to the Roman written numerals for 19 or 29 which was IXX or IXXX , placing  I to the left of XX or XXX for less than and to the right for one greater than .

 

CONSTRUCTION OF NUMBER WORDS FROM 101 TO 999

There are many records of the donations of allotments of land for temples and purchases or payment of money which provides an incite as to how the ancient Sinhala constructed name for numbers using Hundred ,Tens and Units free from ambiguities and misleading statements .The expression for land measurements are different to those expressing a  sum of money. Traces of these from inscriptions are separately shown below, and there had been a separate tradition for these different transactions.

When  expressing three digit numbers in the measurement of land, the   word  Karisha which was a measure equivalent of four acres is interspersed   between the word  for sata [hundred ] examples . eka Kiriha sataka, tini Kariha sata, catara ,kiraha sateka,Etc.  this is followed by the word Ca  the ancient word for and. The rest of the  numbers from 1 to 99 were constructed  in the manner described below.

These Written or Verbal notations seems to have a adopted a general rule in constructing  Thousands , Hundreds , Tens and Units into a precise mathematical language free of ambiguities and misleading statements. Was this a requirement for  the additions and subtractions of numbers, which was essential until the Zero was introduced  after the 3 Cent AD in India?.

The sentence for four hundred seventy seven was written as below.

Catari  Kariha            Sate     ca       sata       satati        Kariha     [S.Paranavitane – Inscription ofCeylon Volume II Part II ,2001. Pg 168]

Four     Kiraha       Hundred   and      seven  seventy    Kiraha

 

HOW KAHAVANAS WERE EXPRESSED.

An interesting observation made by Dr Paranavitane about expressing 600 as six times Hundred ‘The expression sata kala satekahas been taken to mean seven times hundred  i.e multiplied by seven[ Bakki Ala Inscription] .  He states that it is  interesting to find the same expression to denote the idea of multiplication in old Sinhalese as well as in modern English[S.Paranavitane – Inscription of Ceylon Volume II Part I 1983. Pg 19 ].

CONSTRUCTION OF NUMBER WORDS  ABOVE 1001.

There are interesting inscriptions where traces of names for Numbers consisting of thousands, Hundreds, Tens and units. These amounts on inscriptions give the cost of purchases and donations of Tanks to Monasteries. Few examples of these are shown below

The ancients were flexible in expressing these numbers specially in the case land measurements , they interspersed the units of measurement, the  Kariha in between the unit word and the word for  Hundred or thousand when expressing the number of Hundred or thousands. In case of expressing numbers over ten and up to ninety nine they sometimes used the Kariha  after the number word. How ever when large numbers expressing money  Kahapana  they wrote the whole word beginning with the highest denomination the thousand then hundred and the tens and units followed by the word Kahavana orMassa.

 

Page 8

LINKING NUMBERS WITH SYMBOLS.

The traces of symbols to express the written number were used on Inscriptions. Most of the  number words described in table 1 that is required to express any number was  represented  by  symbols. The traces of these symbols or Numerals of the ancient Sinhalese  found in the ancient inscriptions are shown in Table III. The two main inscription where these Numeral are seen are those of Situlpavu and of the Dakkina Stupa Inscriptions.  Others are shown under Inscriptions with numerals page.

Most of these symbols for numbers [Numerals] appear next to and  are attested by written number words. These are well described in Dr Abya Aryasinghe in ‘A Short Study of  Brahmi Numerals in Sri Lanka- ’SAMSKRTI Cultural Quarterly Vol 17 No 3. 1983. Pg 31-50. These numerals bear a close resemblance to the Indian counterparts. The Sinhala numbering system  in written form or in numerical representation was based on the powers of Ten[ Decimal]. It was similar to the Indian counterpart and to the Egyptian Hieratic Script. All three  had 20 symbols or numerals which could be written  in free form on Palm leaves/ Papyrus.The simple additions and Subtractions may have been the  same as the present day arithmetic where it was necessary only to collect numerals of the same order and exchange ten like symbols for the next higher order[ David M Burton-History of Mathematics, 1997 Pg 12.] and subtraction was performed by the same process in the reverse order. Some times borrowing was used when the a symbol was exchanged for a larger number was exchanged for ten lower order symbol to provide enough for the smaller number to be subtracted.  Multiplications and Divisions were additive according to the Rhind’s Papyrus , where the product of two numbers was obtained by repeated doubling of one of the  numbers and then adding the appropriate duplications to from the products. Division  was multiplication in the reverse and was not easy when fractions were involved. To divide one would begin by doubling the divisor to a point at which the next duplication would exceed the dividend, then he would start halving the divisor in order complete the remainder.The construction of large Dagobas, the construction of Tanks and Canals, the creation of the Calendar,

Surveying of land and the record keeping for commerce required a  numerical system and precise mathematical language free of ambiguities and misleading statements. All these subjects should be studied in greater detail, as a lot of factors could be deduced from Rock Inscriptions, Ancients Texts and other evidence.

One such  example is the  constructions of a Stupa of the magnitude of the Maha seya at Anurhadapura. This stupa is     tall and  where a  truncated hemisphere rests  on three concentric short cylinder of descending diameters. On top of the this is placed a  Cube    and on which is built a spire in the shape of Cone. All from of two and three dimensional shapes available to the ancient has been utilized in its construction. Precise  formulas for their areas and volumes  would have been available either those of the Greeks , but more so the Hindu Mathematics. To quote one such formula that the Hindus and perhaps the Sinhalese used was that for  the area of a Circle. This   was Half the circumference multiplied by the half the Diameter34. This eliminated the value of Phi which is now 22/7 an approximate. This would not be  that accurate when  large diameters are considered. Perhaps they had there own Geometrical treaties now lost to us.

Perhaps King Sadhatissa was aware of the Thales of Miletus[625-547 BC] method of measuring the height of the pyramid35. The King may have measured the length of the Shadow from the Dagabo  to the tip of  the Pinnacle of the Maha- seya,  when his own shadow equal in length  to his own height. He had only to add the half the diameter at the base to get the true height of the Maha- seya.


34 David M Burton-History of Mathematics, 1997 Pg 59

35 ibid, 1997 Pg 86

 

 

51 S.Paranavitane – Inscription of Ceylon.Volume II Part I ,1983.Pl XXIII  No 48

52 ibid.Pl XXIV  No 49

53  S.Paranavitane – Inscription of Ceylon.Volume II Part II ,2001.Pl VII to XII & Siri Munasinghe- The Island-Midweek Review 16.02. 2005, Pg IV

54 A. Aryasinghe- SAMSKRTI Cultural Quarterly Vol 17 No 3. 1983. Pg43

55 S.Paranavitane – Inscription of Ceylon.Volume II Part I ,1983.Pl XXXI  No 65

56 ibid.Pl XXXI No 146

57 MH Sirisoma & Gita Amerasinghe- Has Ebu Kahavana 1986, Pg 148

58 DMDe Silva Wickremasinghe- Epigraphia Zeylanica Vol I 1912 Pl 13(b).

59 S.Paranavitane – Inscription of CeylonVolume II Part II ,2001.Pl XLVII No 168

60 S.Paranavitane – Inscription of CeylonVolume II Part I ,1983.Pl VIII No 14(2)

61 Rev Habarakada Varira- Abeyagiri Inscription Sankrutika Puranaya 1994 Jan-March Pg 12

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2 thoughts on “WORDS AND SYMBOLS FOR NUMBERS

  1. The inscription that says “sata kala sataka” is vry important. It means multiplication not addition.

    Do you know the date of that inscription?

    Its in the above table “How kahavans expressed?

    This could be the oldest decimal notation if it goes to BC times

    • The Bakki-Ala inscription is a grant of King Lajaka Tissa [59-50 BC], as you said is important in the history of mathematics of ancient Sri Lanka, it also mentions fractional shares or water rates that need be calculated and paid up, as many inscriptions of the period. This includes of interest paid for deposits of Kahavanus and grain to monasteries. Very Interesting, any way I placed the scans of the pages on the blog for your info.Please call me Mune. Thanks.
      sorry the page you read is a big mess, I have corrected a little of it, I need to put the tables etc and also placed a brief note on Katapaya Numeration system with the Zero, used in SL before the Portuguese reintroduced the numeral to the Island.

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