ANCIENT NUMERALS OF SRI LANKA-[3 CENT BC- 4 CENT AD]


WORDS AND SYMBOLS FOR NUMBERS USED BY THE ANCIENT SINHALESE [3 Cent BC – 4 Cent AD].

Brig Siri Munasinghe.

The early Sinhalese and those of the Indians Continent appear to have developed their words and symbols for numbers from a common source. We are fortunate that our ancestors left traces of these words and the symbols  on their rock inscriptions. These traces are extracted and listed for information of scholars interested in research .

THE BASIC SINHALA  NUMBER WORDS .

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 1meaning one lot of land , do 1– kahapana to indicate  two silver kahapanas donated by the officer in charge of canals ,the tini1 silapatani –the word for  three  stone steps donated by  Upasika Tisaya, catara1 –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 [1] [Six], sata1 [Seven], ata1 [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 Nava1 [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 dasa1 [ten] directions,  visiti1 [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  tisa2 [Thirty], catalisa 3[Forty], panasa 4[Fifty], sati 5[Sixty], satati 5 [ Seventy], atasti 6 [ eighty, ?[Ninety], sata 7 [Hundred], sahasa 1 [ 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’ by Dr S Paranavitane.[The Volume II is published in two parts], 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  8is 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 9[41] . 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 10in Dakkina Stupa inscription and thirty- ekuna tisa 10is used. 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.

LAND MEASURE

108 eka sataka Kiriha ata11 100 KA 8
300 tini kariha sata ca12 3 KA 100 and
367 tini Kariha sata ca sati-sataka Kiriha13 3 KA 100 and 67 KA
400 catara kiraha sateka14 4 KA 100
420 Catara Kriha sata ca visiti kariha ca15 4KA 100 and 20 KA
477 Catari Kariha Sate ca sata satati Kariha16 4KA 100 and 77 KA
500 paca kiraha sati17 5 KA 100
603 Kariha Sa-sata ca tini kariha18 KA 600 and 3
884 ata kiraha sata ca catu-asati kiriha19 8 KA 100 and 84 KA
904 Nava Kariha sate ca catara Kiriha ca20 9 KA 100 and 4 KA
950 nava kiriha sata ca panasa Kiraha21 9 KA 100 and 50 KA

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 22

Four     Kiraha       Hundred   and      seven  seventy    Kiraha

HOW KAHAVANAS WERE EXPRESSED.

100 eka sataka 23kahavana One hundred
500 Paca sata23a Kahavana Five Hundred
600 sata kala stataka 24Kahavana 6 times 100
600 sa sata 24a kahavana   Six hundred
833 Ata sate tetisa 25kahavana   Eight hundred thirty three

An interesting observation made by Dr Paranavitane about expressing 600 as six times Hundred ‘The expression sata kala sateka 24has been taken to mean seven times hundred  i.e multiplied by seven .  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 English24.

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 or Massa.

Number Thousands Hundreds Tens/units
1120 Eka Kariha Sahasa25

KA 1000

ca eka Kariha sata

and 1 KA 100

ca visiti .

and 20.

2041 Sari ca do karihi Sahasa26

An assessment of  2 KA 1000

ca eka catalisa

and 41 KA

4000 Catara sahasa27
5000 paca sahasa 28

Five thousand

100663 Sata  sahasa29

Hundred Thousands

ca ana sata sate

and another 600

ca ana se sate ca

and another 63.

[ Kahapanas]

LINKING NUMBERS WITH SYMBOLS.

The traces of symbols to express the written number were used on Inscriptons. 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.  Some 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 Lanka30’. 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 order31 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 products32. 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 remainder33.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.


[1]S.Paranavitane – Inscription of Ceylon Volume I . 1970  Pg xlii

3 S.Paranavitane – Inscription of Ceylon Volume II Part II 2001. Pg 337

4 ibid. Pg 335

5 ibid. Pg 343

6 ibid. Pg 357

7 ibid. Pg 327

8 Iravatham .Mahadevan – Early Tamil Epigraphy 2003  Pg 283

9 S.Paranavitane – Inscription of Ceylon Volume II Part II 2001. Pg 328

10 S.Paranavitane – Inscription of Ceylon Volume II Part II 2001. Pg 329

11 Rev Habarakada Varira- Abeyagiri Inscription Sanskrutika Puranaya 1994 Jan-March Pg 12

12 S.Paranavitane – Inscription of Ceylon Volume II Part II 2001. Pg 168

13 ibid. Pg 165

14 ibid 2001.

15 ibid. Pg 168

16 ibid. Pg 168

17 ibid. Pg 168

18 ibid. Pg168

19 ibid. Pg 167

20 ibid. Pg 167

21 ibid. Pg 167

22 S.Paranavitane – Inscription of Ceylon Volume II Part II ,2001. Pg 168

23 ibid. Pg  259

23a S.Paranavitane – Inscription of Ceylon Volume II Part I 1983. Pg 61

24 ibid. Pg 19

24a S.Paranavitane – Inscription of Ceylon Volume II Part II 2001. Pg

25 ibid. Pg 126

24 S.Paranavitane – Inscription of Ceylon Volume II Part I 1983. Pg 19

25 S.Paranavitane – Inscription of Ceylon Volume II Part II ,2001. Pg168

26 ibid. Pg160

27 S.Paranavitane – Inscription of Ceylon Volume II Part I 1983.   Pg 98

28 ibid.   Pg 92

29 S.Paranavitane – Inscription of Ceylon Volume II Part II ,2001. Pg 146

30 A. Aryasinghe- SAMSKRTI Cultural Quarterly Vol 17 No 3. 1983. Pg 31-50

31 David M Burton-History of Mathematics, 1997 Pg 12.

32 ibid. Pg 35

33 ibid .Pg 36.

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

35 ibid, 1997 Pg 86

ANCIENT SINHALA , SANSKRIT, PALI AND TAMIL WORDS FOR NUMBERS

3  CENT BC TO 3  CENT AD

Reference-Inscriptions of Ceylon Vol I- S Paranavitane SINHALA SANSKRIT PALI ELU TAMIL

ReferenceEarly Tamil Epigraphy 9– I Mahadevan

One No 786,815 EKA1 EKA EK
Two Nos791, 208 DO/DUVA1 DUVU DO IRU

-2CentBC-1 Cent AD

Three Nos 95,123,314,540,1152 TE /TINI/TI1 TRINI TINI TIN
Four Nos 9 , 331,1120 CATARA1 CATVARA CHATTRO SATARA
Five Nos 294, 428,978 PACA1 PANCA PAS
Six No 150 SA/SAYE1 SAT CHATTRO SATARA AIM       -5-6 Cent AD
Seven Kanitha tissa

2 CentAD

SATA1 SAPTA SATTA SAT EL         -5-6 Cent AD
Eight Nos 538,502 ATA1 ASTAN ATTHA ATA
Nine Nos 851,1199 NAVA1 NAVAM NAVA NAVA
Ten Nos 34,251 DASA1 DASAN DASA PATIN/PAT

2CentBC-1Cent AD

Twenty VISITI1
Thirty TISA2
Forty CATALISA4 CATVARI-MSAT CATTALI-SA SATALIS
Fifty PANASA5 PANCASA PANNASA PANAS
Sixty SATI/SATA6 SASTI SATTHI SATA
Seventy SATATI7 SAPTATI SATTATI SATTA
Eighty ASATI8 ASITI ASITI ASU
Ninety
Hundred No 857 SATA1 SATA SIYA NARU    -5-6 Cent AD
Thousand Nos 251,1199 SAHASA1 SAHASRA SAHASSA DAHAS
Lakh No 1199 LAKA1

NUMBER WORD FROM 10 TO 100

10  TO 19 20  TO 29 30  TO 39 40  TO 49
DASA         10 VISITI               20 TISA          30 CATALISA           40


EKA DASA36 1 & 10 EKA TISA36 EK CATULISA36   1 & 40
DO DASA37 2 & 10 DO VISITI 37       2 & 20 DO TISA37
TERASA38 3 & 10 TE VISITI 38 3& 20
CATARA VISA 4 & 20 CATA CATALISA43 4 & 40
PACA VISITI42 5 & 20
SOLASA 39 6 & 10
ATA DASA/atalosa40 8&10
EKUNA VISITI 36

1 LESS THAN 20

EKUNA TISA36

1 LESS THAN 30

50  TO   59

60  TO  69

70  TO  79 80  TO 89 90 to 99
PANASA44 50 SATI47 60 SATATI49 70 ASITI50 80 None
SESATI48 3 AND 60
CATA PANASA45 CATA ASITI46 4 & 80
PASA PANASA46
SA SATI48 6 & 60 SATA SATATI49 7 & 70

9 Iravatham .Mahadevan – Early Tamil Epigraphy 2003 Pg 283

2 S.Paranavitane – Inscription of Ceylon Volume II Part II ,2001. Pg

4 ibid. Pg 335

5 ibid. Pg 343

6 ibid. Pg 358

7 ibid. Pg 357

8 ibid. Pg 327

36 S.Paranavitane – Inscription of Ceylon Volume II Part II ,2001. Pg 329

37 ibid. Pg 339

38 ibid. Pg 337

43 ibid, Pg 111

42 ibid. Pg 341

39 ibid. Pg 360

40 ibid. Pg 324

44 ibid. Pg 169

47 ibid. Pg 357

49 ibid. Pg 358

50 ibid. Pg 327

48 ibid. Pg 146

45 ibid. Pg 334

46 ibid. Pg 167

46 ibid. Pg 167

48 ibid. Pg 359

49 ibid. Pg 357

DAKKINA STUPA INSCRIPTION.

This is the largest inscription in the Island ,inscribed on 17 slabs. These are 17   of many slabs which are placed around the stupa,  People walk on this inscription  when worshiping the Caitiya which on this inscription was known as the Tisa- maha- cheitiya. This inscription is of the period  King Sirinaga of 2 Cent AD and lay buried under the debris, which is now cleared. Most visitors to this site is unaware of the historical importance of this inscription. I visited this site in November 2004 and I asked the Watcher about this inscription, unfortunately he was unaware of its existence. I walked around this Stupa on the stone pavement which ran around its circumferance.  I notice to my horror  that I was walking on the inscription which is on 17 of the slabs that make up the pavement. All visitors walk over this inscription most without even noticing it. A few photo are attached , there were remnants of pieces of bottles broken on the inscription.

The traces of the Numbers or Numerals used by our ancestors is found  on this inscription. These numbers symbols are similar to the Indain Numerals which the Arabs copied and introduced to the west about the 14 Cent AD. The trace of 6 Numbers are found an Asokian inscription at Nanghat in Bombay. Which is the earliest available, The  Nasik Inscription dated to the 2 Cent AD is also famous for the ancient Hindu numerals.

This inscription which is about the same period as of Nasik and is of great significance to the Sri Lankans. There are many other inscription of the Island where traces of ancient Numerals, these are dated from 2 Cent BC to 3 Cent AD. Except for that at Situlpavu which is of the 1 Cent AD, the other has only one to three ancient Numerals to express symbolically the number of Kahapanas[ Silver Coins] and Karisa[ Measure of land- 4 Acres in extent]  transacted for various purposes.  The Situlpavu Inscription has traces of fair amount of numerals depicting Tens and Hundred.

This inscription is a lengthy account of a large number allotments of lands which are named by various personalities including Royalty . The extent of land is given in the ancient measure of land the Karisa which is equivalent to about 4 acres in extent. In addition to the Numerals an symbol for karisha   is  always placed  beside it. The placement of this symbol follows a uniform set proceedure. These allotments of  lands and Fields to this Monastery for its upkeeps is described in detail by Dr Paranavitane in Inscriptions of Ceylon Vol II Part 2.

Slab No V.Line 1.

The Karisa Symbol followed by Numeral 100 symbol 6   Karisa symbol Numeral 3. Drparanavitane identifies the worn letters in line 4 end as kariha sa sata ca tini kariha , which is 603 karihas.

Slab VII line 2.

Kariha symbol Numeral 100  Numeral 4  karina symbol sybol 70 and symbol 7. Line 5and continued to 6 is catara kariha ca sata satati Kariha, which is four hundred and seventy seven karihas.

Slab 9 line 7

Kariha symbol  Numeral 100 Numeral 9 Kariha symbol Numeral 4. Line six is Nava kiriha sata ca catara kiriha ca, which means Nine Hundred and four karahas.

Slab XI line 5/6.

The  Kariha symbol[ line 5]  Numeral 50 Kariha symbol Numeral 5. These symbol are preceded by words Pasa panasa kiraha, which fifty five karihas..

Slab XII line 3 / 4.

The Kariha symbol Numeral 100 and Numeral 4 Kariha symbol              then Numeral 20 . These symbol are preceded by the words in Line

catara kiraha sata ca visiti kiraha ca. This is Four hundred and twenty karahas.

SlabXIII line 6

Kariha symbol Numeral 1000 kariha symbol Numeral 100 Kariha symbol Numeral 9. Words in line 3 eka krahi sahasa sata ca …….

Which means One thosand and one hundred  and …. Kariha.

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