Prof. V.K. Samaranayake Memorial Oration held on 12 June 2012

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RAMBLINGS IN MATHEMATICS

Desamānya Professor J.B. Disanayaka

My friend and colleague, late Prof. Kitsiri Samaranayake was,

undoubtedly, one of the greatest mathematicians of our country. Since I

am no mathematician, I am unable to assess his mathematical thought

and practice in any substantial way. What I propose to do in this paper is

to present some rambling thoughts about numbers so that you can decide

whether they make any sense.

My ramblings relate to three areas: (a) the duo-deciml system (b)

Sinhalese numerations and (c) Sinhalese supremacy in mathematics.

My interest in the duo-decimal system takes my memory back to

the time when I was doing a regular weekly radio programme titled

„Tumpat Rata‟ (Three-fold Patterns). Once I had the chance to interview

a lay priest who was performing the folk healing ritual known as „bulat

yaham madu kankariya‟ in Matale, in the Kandyan highlands.

He told me that he invokes a set of gods who are „tun-dolahak‟ (three-twelve) in number. The phrase „tun-dolahak’ is not in use today

and I did not know precisely how many gods he meant. I asked him

whether he meant „fifteen‟ (three + twelve) and he categorically said “no” and insisted that he meant nothing but „tun-dolahak‟!

It was only some years later when I was interviewing some

informants in the Maldive Islands that I understood what was meant by

the number „tun-dolahak’. Maldvians who have been counting in

twelves until recently use the phrase „ti:n-dolos‟ (three-twelve) to mean

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„thirty-six‟(three into twelve). Thus the Sinhala phrase „tun dolahak‟ meant 36!

This made me think. Today we count in sets of tens and it is thus

called the „decimal system‟. In the distant past, however, we seem to have counted in twelves, a system which may be called the „duo-decimal

system‟. What evidence have we got to say that the Ancient World used

the duo-decimal system?

This evidence comes from the sets of twelves that are still in use.

In the measurement of time, for example, 12 has been the dividing line.

A year has 12 months, a day has 12 hours and so does the night. Twelve

marks the middle: mid-day and mid-night dawn at twelve o‟clock. An hour has 60 (12 x 5) minutes, and a minute has 60 (12 x 5) seconds.

The zodiac, the imaginary path through space along which the sun

and other celestial bodies are believed to travel, is divided into 12 equal

segments, called „signs‟. Astrologers have named these 12 signs of the zodiac on the basis constellations of stars that were identified by the

astronomers.

Mesopotamians were the first to draw up multiplication and

division tables and made calculations using geometry. Their number

system used a base of 60 (12 x 5). From this came the system of dividing

a circle into 360 degrees and an hour into 60 minutes.

The Sinhalese and many other peoples of Asia also believe that the

Sun moves along this circular path and that it takes 12 months to

complete a full circle. They believe that the movement of the Sun begins

with Aries and passes through Taurus, Gemini, Leo, Virgo, Libra,

Scorpio, Sagittarius, Capricorn and Aquarius to reach the last of the

signs, Pisces.

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In measuring space, 12 has become equally important, because a

„foot‟ has 12 „inches‟.

In measuring quantities, we come across a set of 12 known as the

„dozen‟. A dozen dozens make a „gross‟. In common parlance, a dozen

is used to signify „a reasonably large amount‟ or „many‟ as when we complain “I‟ve told you a dozen of times”. Do we ever say “I‟ve told you six times” or “I‟ve told you ten times”?

A jury that is chosen to hear the evidence of a case in court of law

usually has twelve members.

The words for numerals in the English language retain the old duo-

decimal system. The words for the first 12 numbers are mono-syllables:

one, two, three, four, five, six, seven, eight, nine, ten, eleven and twelve.

It changes to compound nouns containing the word „ten‟ (pronounced „teen‟) only after twelve:

three + ten : thirteen

four+ten : fourteen

five+ten : fifteen

six+ten : sixteen

seven+ten : seventeen

eight+ten : eighteen

nine+ten : nineteen

The multiplication table which young children are made to learn by heart

to multiply one number by another number, is made of twelves: such as,

five times twelve, seven times twelve, and so on until you reach twelve

times twelve.

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Indian mythology, both Hindu and Buddhist, speak of gods who

have twelve eyes and twelve arms. The Hindu god, Skandha, is one of

them. Buddhist mythology says that there were 24 Buddhas before the

last Buddha, Siddhartha Gautama.

In consonance with the traditions of the Ancient World the

Sinhalese seem to have used the duo-decimal system of counting. The

Sinhala word for twelve is „dolaha‟ (base: dolos) which is related to the

Sanskrit word „dva-dasha‟ (two-ten).

Like in English, the words for numerals in Sinhala also retain the

old duo-decimal system. The words for the first 12 numbers are simple

nouns containing a single base:

base noun

ek eka

de deka

tun tuna

hatara hatara

pas paha

haya haya

hat hata

aTa aTa

nava navaya

daha dahaya

ekolos ekolaha

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dolos dolaha

It changes to compound nouns containing the word „daha‟ (ten) only after twelve:

daha + tuna ten-three : thirteen

daha + hatara ten-four : fourteen

daha + saya ten-six : sixteen

daha+ hata ten-seven : seventeen

daha + aTa ten-eight : eighteen

daha + navaya ten-nine : nineteen

The old duo-decimal system made the Sinhalese think in terms of

twelve. There are many sets of twelve that one comes across in

Sinhalese culture. They are basically two kinds of sets:

a. sets of beings, such as gods,

b. sets of sacred objects.

First let me tell you something about beings that form sets of twelve.

The Twelve Great Poets : dolos maha kivi:n

In the history of Sinhala literature, we are told that the reign of

King Aggabodhi (568-601 ACE) was one of great literary activity and

that there were 12 poets who flourished during this reign. They were

known as „dolos maha kivi:n’ (twelve great poets). Why was the number

limited to twelve?

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The Twelve Gods : dolaha deviyo

Sinhalese folk religion believes in supernatural beings such as gods

(devi) and demons (yakku). Among the gods is a set of twelve known as

„dolaha deviyo‟, the Twelve Gods. They are invoked during rituals held in honour of Pattini, the Goddess of Fertility. Among them are seven

gods who bear the name „Banda:ra‟: Devata: Bandara, Irugal Bandara,

Kiri Bandara, Ki:rti Bandara, Mangara Bandara, Maenik Bandara and

Vanniye Bandara.

The Twelve ‘Gara:’ Demons : doLos gara:

The Sinhalese invoke not only gods but also other supernatural beings

such as demons, „yakku‟. One set of demons are known as „gara: yakku‟, who are twelve in number. The set is headed by Ki:la Gara:

Ki:la gara: A^dun Oka^da

Jala Tota Mo:lan

PaTTi PuSpa Sa^dun

So:lan Sohon VaTa

The Twelve ‘Giri’ Goddesses : doLos giri

This is a set of goddesses who play an important role in folk ritual. It is

believed that this Goddess comes in the form of 12 incarnations

(avata:ra):

The Legion of Twelve Thousand Soldiers

The so-called Myth of Gajabahu deals with multiples of twelve. It

is said that the Cholas of India invaded this island and took away 12,000

Sinhalese to India. King Gajabahu retaliated by marching to India and

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bringing back 24,000 Indians who were settled in different parts of the

Island.

Now let me tell you something about things that come in twelves.

The God of Twelve-eyes : bara net

The famous god, who lives in the sylvan shrine by the Maenik Ga^ga at

Kataragama, has twelve eyes and twelve arms. He is thus called „bara

net‟ in Sinhala, meaning the „twelve-eyed one‟. The word „bara‟ is a synonymn of „doLos‟

The Lamp of Twelve Months: dolos mahe: pa:na

Every Buddhist temple has an oil lamp (pahana or pa:na ) that burns all

the year round and it is called „dolos mahe: pa:na‟ (the twelve month lamp). It is custom among Sinhala Buddhists to anoint their heads with

some oil taken from this lamp, for well-being and prosperity.

The Game of Twelve : dolaha keLiya

The Sinhalese and several other Asian nations celebrate their New

Year in April, when the Sun re-enters Aries after leaving Pisces. One of

the games that the Sinhalese play during their New Year is called

„dolaha‟ meaning „twelve‟. The Sinhala phrase „dolala da:nava:‟ means, literally, „to play twelve‟, that is, to play the game called twelve.

In other regions of Sri Lanka, it is called „pancha‟.

The Twelve Acts : dolaha pela pa:liya

In the folk ritual known as Gam MaDuva, (Village Hall), held once a

year in villages in order to invoke the blessings of the gods, particularly

Pattini, the Goddess of Fertility, twelve items are offered to gods

accompanied by dancing. They items are:

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The Village of Twelve-Halves : dolos ba:ge

Near Kandy is a village named „Dolos Ba:ge‟ which means, literally, twelve halves or parts.

The County of Twelve Thousand Villages : dolos dahas raTa

In the South of Sri Lanka, there was a region (raTa) that was known as

dolos dahas raTa, meaning „a county consisting of 12,000 villages‟.

The Diagram of Twelve Stanzas

This is a diagram that is found among Sinhala verses, a verse that

is considered “an exceptionally clever feat in versification” (Godakumbura, p. 248). The intricate verse is called

n r k u . n i l

ba ra na ma ga ba sa ka

and it appears in a poem titled ndri ldjHh „Ba:rasa Ka:vyaya‟, a panegyric of the Buddha, composd by a Buddhist monk named Karatota

Dhamma:ra:ma in the Pre-modern Period.

Godakumbura states that this verse is “so called because the syllables are arranged in a diagram, embodying a dozen quatrains in the

Samudragho:sa..” (p.248).

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The verse runs as follows:

is is is is o h , ks ks ks ks ks

r c , , , ,

si si si si da ya la ni ni ni ni ni ra ja la la la la

is rs j , os h k j i j uq is k

o l= i l ,

si ri va la di ya na va sa va mu si na da ku sa ka la

is os n j .s u k r `. k . us k

m `M k i ,

si di ba va gi ma na ra ^ga na ga mi na pa lu na sa la

is rs . k ks r ; k u os us k j

K kq j ; , si ri ga na ni ra ta na ma di mi na

va na nu va ta la

(I worship the Buddha, who abstained from idle praise, was firm,

renowned like a precious gem, who extinguished the fire of

metempsychosis, who was the chief of the world, who was blessed with

properity, who, when born as King Kusa, was endowed with a voice like

the roar of a lion, in whom there was no allurement of sin and vice, who

was gentle as the moon, the benevolent savior of beings, and an ocean of

river-like wisdom, who destroyed the weakness of the heart by means

thereof‟ (Godakumbura‟p.249)

The syllables in this verse can be read in different ways in order to

produce 3 other verses of 4 lines.(12 lines)

Now let‟s come to multiples of twelve. The first multiple of twelve

that has attracted the imagination of the Sinhala speaker is 60, which is

called „haeTa‟ in speech and „saeTa‟ in writing. Maldivians, the

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islanders who used the duo-decimal system of counting, still say „fas

dolos’ (five into twelve) to denote 60.

Some idioms and phrases in Sinhala that highlight the significance

of sixty include the following :

Sixty Hour Day : haeTa paeya

In common usage, a day has 24 hours but in Sinhala usage, a day

had 60 hours : haeTa paeyak.

Passing Sixty : haeTa paeni:ma

A man is considered mature only when he reaches the age of sixty.

The Sinhalese have a proverb which says that even monkeys do not walk

on the ground once they reach sixty:

va^dura haeTa paennat bima yanne nae:

(monkey) (sixty) (even jumped) (ground) (go) (not)

The monkey does not go on the ground even if he reached sixty.

Sixty-mature speech : haeTa paehicca kata:

When a young man speaks like an elder, his speech is labeled haeTa

paehicca kata: (sixty) (ripened) (speech); Mature speech that has

reached sixty.

Sixty blindness : haeTa ae^diriya

A man who reaches sixty is also weak in his eye-sight (ae^diriya) .

This is the period known as „haeta aendiriya‟ (sixty blindness).

Sixty-day Paddy : haeTa da: vi:

This is a variety of paddy seed that yields in sixty days: haeta

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da: vi: (sixty)(day) (paddy); Sixty-day paddy

As fast as sixty : haeTa haete:

This is an adverbial phrase referring to speed, which is measured in

terms of sixties. To say that someone came or drove very fast, they say:

haeTaTa haeTe (for sixty) (sixty); Sixty for sixty; very very fast

The Legend of the Sixty Monks : sa^ga saeTa nama

This refers to a legend mentioned in the Pali commentaries about

60 monks who attained arahantship after listening to women who sang

praises of the Buddha in Sinhalese as they worked in the paddy fields.

The author of „Lovaeda sa^gara:va‟, a didactic poem written in the Kotte period, refers to this legend thus:

“dahamaTa sari koTa eLuven pera ki:

kaviyaTa sita pahada: siTa nisae ki:

sihi koTa ka^da piLiveLa dos noye ki:

nivanaT sapaemiNi sa^ga saeTa nama ki:”(verse 5)

This says that in the past, sixty monks attained the highest blessing,

nirvana, after listening to the verses in Sinhala on the nature of the

human body. Why sixty monks?

The Village of Sixty Soldiers : hae:va haeTa

This is the name of a village in the Kandyan highlands where it is

said that 60 (haeTa) soldiers (he:va:) were settled.

The Whore of Sixty Bushes : haeTa pa^duri

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A woman who is known engages in promiscuous sexual

intercourse is sometimes referred to as a „haeta pa^duri‟ in folk speech.

The exact etymology of the phrase in uncertain but it is possible that it

refers to the idea that she is one who takes a man to the bushes

(pa^duru) and not to one bush but sixty of them!

Another multiple of twelve that attracted Sinhala thought was 84.

(twelve times seven). Eighty-four is asu: hatara or su:va:su: and, eighty

four thousand is called asu: ha:ra da:ha. What is the significance of 84

for the Sinhalese ?

Eighty-four Textiles : suva:su: saLu

Traditional Sinhala culture spoke of 84 kinds of textiles that were in use

in ancient times. Some of these names are archaic and obsolete. Among

them are varieties such as the following:

oluyal : isi oluyal tay oluyal

salu oluyal rat oluyal

bangle oluyal ra:muna:ra:yan oluyal

kacci : paTa kacci nilavanti kacci

paTa : sudu paTa leTa paTa

jina paTa kaNgam paTa

saLu : kasi: salu ko:ja saLu

jina saLu `divayina saLu

se:la : sin se:la dasaru se:la

tuDan se:la ran se:la

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The Corpus of 84,000 Teachings: asu ha:ra da:he dharma skanda

Sinhalese Buddhists believe that the corpus of teachings (dharma

skandha) of the Buddha consists of 84,000 elements. What is the source

of this mathematical calculation?

The source is the commentary on „Digha Nika:ya‟ where it is said that when monks planned to have the First Council (sanga:yana:) to

establish the text of the Buddha‟s teachings, they insisted that Venerable

Ananda should take part in it because he was the only disciple who knew

the entire corpus of eighty-four thousand dhamma-skandhas.

Legend also has it that Emperor Asoka who heard that the corpus

of the Buddha‟s teachings consisted of 84,000 elements, built 84,000

temples in His honour.

The Festival of 84,000 Lamps : asu ha:ra da:he pa:n pinkama

Buddhists light clay-lamps (pa:n) with oil as part of religious ritual that

brings about merit. Lighting a lamp is a symbol of bringing light, that is,

enlightenment, the process of shedding ignorance. On special days of

religious significance they light 84,000 lamps and this ritual is called

asu ha:ra da:he pa:n pinkama

(eighty) (four) (thousand)(lamp) (festival)

the eighty-four thousand lamp festival

The number of lamps is, no doubt, determined by the number of

elements of teachings, (dhamma skandhas) , one lamp for one element.

Losing temper at 84,000 : asu: ha:ra da:haTa naginava

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When a Sinhalese loses his temper and wanted to say that he got “really mad” he uses the following expression:

maTa asu: ha:ra da:hata naegga

(to me) (eighty-four-thousand) (lost temper)

I lost my temper at eighty-four thousand!

My temper was raised to 84,000!

It is clear from all this evidence that the Ancient World counted in

twelves, using the so-called „duo-decimal system‟ and that the Sinhalaese also followed it. When did it change to the „decimal system‟?

The decimal system is inextricably linked with the use of the zero.

Who discovered the zero? Of course, Arab mathematicians are generally

given the credit for using the zero in their system of numeration that

came to be called „Arabic numerals‟ but the history of the zero takes its origins to India, to the Gupta rulers, in particular.

In „A History of the World‟ it is said that “ the Gupta rulers were Hindu, but Buddhism was still influential. Some monasteries had

developed into universities with large libraries. Buddhist scholars came

there from China and other countries to which Buddhism had spread.

Astronomy, mathematics, and surgery in Gupta India were far ahead of

the rest of the world at that time. Probably the most impressive

contributions were made by Gupta mathematicians. They established the

decimal system, the idea of the zero, and the beginnings of algebra.

Although Arab mathematicians later were given the credit for the so-

called Arab numerals, the Arabs themselves called mathematics “the Indian art” (p.239).

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The role of the Muslims in mathematics is no less impressive. “The spread of Islam gave Muslim mathematicians and scientists access to the

works of earlier thinkers in many lands. From India they acquired the

concept of the zero and „Arabic‟ numerals, passing these ideas on to the West” (A History of the World, p. 214)

Indian philosophers, both Hindu and Buddhist, dwelt with the

concept of the zero, „su:nya‟ (Y+kH) in Sanskrit and „sunna‟( iq[a[ ).

It carried meanings such as „empty, void, nothing, devoid of reality, unsubstantial and phenomenal‟.

Indian grammarians, such as Pa:nini, also made use of the concept

of the zero when they spoke of a „zero suffix‟ (shu:nya pratya).

“Panini is also to be credited with the device of zero in linguistic description, by which part of an apparently irregular set of

morphological forms can, by positing an analytic entity without actual

exponents as an element of their structure, be brought into line with the

regular forms.” (R.H.Robins, General Linguistics: An Introductory Survey, p. 378)

For those who are not familiar with the grammatical concept of the

„zero suffix‟ let me explain it with an example from Sinhala. It related to the structure of the noun in Sinhala. In terms of the concept of „number‟, all Sinhala nouns are three-fold: singular definite, singular indefinite and

plural. Each category is realized by a „number suffix‟ that is placed after a noun base:

base: kavi (poet) base suffix noun

singular definite: kavi a: kaviya: the poet

singular indefinite: kavi ek kaviyek a poet

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plural: kavi o: kaviyo: poets

With some bases, however, the plural suffix is a zero:

base: ali (elephant)

singular definite ali a: aliya: the elephant

singular indefinite ali ek aliyek an elephant

plural ali - ali elephants

base: pot (book):

singular definite : pot a pota (the book)

singular indefinite : pot ak potak (a book)

plural : pot - pot (books)

Now let me move into the field of Sinhalese numerations. Being

mathematicians of the highest caliber, the Sinhalese had not one but

many sets of numerations that can be called their own. Of these, some

were without a zero and some were with a zero.

The most popular set without the zero is called:

isxy, b,lalus [sinhala ilakkam] Sinhala

Numerals

This is the set of numerals introduced by Abraham Mendis Gunasekara

in his „A Comprehensive Grammar of the Sinhalese Language‟ (first published in 1891) are the „Sinhala ilakkam.‟

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Says

Gunasekara: “The Sinhalese 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” (p.147).

Sinhalese have two sets of numerals that have a zero. They are two

versions of the same type:

,s;a b,lalus [lit ilakkam] Ephemeris

numerals

This set is used basically for astrological calculations such as

casting horoscopes and other needs of the almanac (lit). The numerals

are some of the letters of the Sinhala alphabet. W.A.De Silva presents

„lit ilakkam in his „Catalogue of Palm leaf Manuscripts‟:

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Michael Everson, an Irish expert on signs and symbols, was the

first to draw the attention of Western IT-experts to the existence of

Sinhala numerals. In his proposal of the Sinhala UNICODE to the ISO

in 1998, he suggested that these numerals be included. The system of

numerals he proposed was the set of Sinhala ilakkam cited by

Gunasekara in his Grammar (p. 144). At the request of the Sri Lanka

Standards Institute, the proposal to include the Numerals was postponed

for a future data.

Since the with-drawl of the proposal by Michael Everson to

include the Sinhalese numerals in the UNICODE, new research on

Sinhala numerals was undertaken by a few Sri Lankan scholars. Harsha

Wijayawardhana of the University of Colombo School of Computer

Studies, in particular, brought into light that the Sinhala numerals

contain a zero. Hence the need to include the revised set of Sinhala

numerals in addition to Everson‟s set which has no zero.

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20

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As Wijayawardhana says “the research into Sinhala numerals was carried out from both linguistic and mathematical perspectives. The

researchers looked specifically for the existence of zero in any form of

numeration in the Sinhala language, since the invention of zero had been

a major demarcation point in mathematics. Advancement in modern

pure mathematics would not have been possible without the concept of

the 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 other numerals which were developed in India from

Brahmi numerals.” (p.18).

Wijayawardhana quotes E.T.Bell, the author of „The Development of Mathematics‟, on the significance of the discovery of the zero.

“The problem of numeration was finally solved by Hindus at some controversial date before AD 800. He 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” (Bell, p.51)

Wijayawardhana studied and compared the “shapes of several numeral sets which belong to the Indic languages” with “numeral sets which were identified as numerals or numerations in the Sinhala

language.” (p.19).

Wijayawardhana found that the system known as lit ilakkam had a

zero, as cited by W.A.De Silva. As a result of this discovery, it was

decided to make a new proposal to the ISO to include the Sinhala

numeral system with zero. I am told that it is now encoded in the third

revision of the Sri Lanka Sinhala Character Code for Information

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Exchange which has been approved by the Sri Lanka Standards Institute

as a Sri Lanka Standard, SLS 1134: 2011

That the Sinhalese were among the greatest mathematicians of the

Ancient World is proved by two facts: that they had their own system of

numerals, containing a zero, and that they excelled in many areas that

needed mathematical precision.

The system of numerals and the mathematical thought based on it

made the Sinhalese produce a civilization that was on par with any of the

other great civilizations of the Ancient World, such as that of China,

India, Babylonia, Egypt, Greece and Rome.

What achievements have the Sinhalese made with their

mathematical knowledge? Let me confine myself to a few instances

where they have shown their mathematical genius:

(1) the discovery of the centre of the island

(2) the development of a super hydraualic civilization, involving

(a) the invention of the valve-tower

(b) the discovery of the ancient sluice at Maduru Oya

(c) the degree of slope of the Jaya Ganga

(d) the water gardens of Sigiriya

(3) the design of the stupa

(4) the design of the Buddha image at Aukana

Among the many achievements is the discovery of the exact centre

of the Island of Sri Lanka. According to their mathematical calculations,

the exact centre of the Island is located in the village of in the Matale

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District. It lies about a km. off the main road that links Matale and

Dambulla.

To identify this location, a unique edifice known as a „gedi-ge‟ has been built. This building has been described as “a little gem of a building and one of the most unusual monuments in the Cultural Triangle” (The Rough Guide to Sri Lanka, p.316).

This Gedige is an image house of an unusual nature. Its uniqueness

stems from two factors. First: it is not part of a Buddhist monastery but a

building of its own. Second: it has the only erotic sculpture that is found

in any Sri Lankan building.

The greatest achievement of the Sinhalese mathematicians was

perhaps the development of an advanced hydraulic civilization. Only a

few nations of the Ancient World could claim achievements of hydraulic

engineering. Among these nations were Mesopotamia and Egypt, Greece

and Rome, India and China.

Joseph Needham, the author of „Science and Civilization in China‟, who speaks of the achievements of the Chinese in glowing terms, has this to say of the achievements of the Sinhalese:

Nalanda

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“It will be evident even from the roughest of sketches that the achievements of Indian civil engineers in ancient and medieval times are

quite worthy to be compared with those of their Chinese colleagues,

though not to win the palm. Yet it was never in India that the fusion of

the Egyptian and Babylonian patterns achieved its most complete and

subtlest form. That took place in Ceylon, the work of both cultures,

Sinhalese and Tamil, but especially the former” (Needham, p. 368).

What exactly are the achievements of the Sinhalese in hydraulic

engineering? Needham mentions “some of the more interesting special devices of the Sinhalese engineers.” (p.372)

Needham says that “perhaps the most striking invention was the

intake-towers or valve-towers (bisi-kottuva) which were fitted in the

reservoirs, perhaps from the – 2nd

century onwards, certainly from the +

2nd. K.M.De Silva also notes that “the Sinhalese were the first inventors

of the valve-pit (bisokotuva), counterpart of the sluice which regulates

the flow of water from a modern reservoir or tank. The engineers of the

third century BC or earlier who invented it had done their work with a

sophistication and mastery that enabled their successors of later

centuries merely to copy the original device with only minor adaptations

or changes, if any. Sri Lanka owes more to the unknown inventors of

this epoch-making device than to all but a handful of kings whose

virtues are extolled in the Mahawamsa and Culawamsa. Without the

technological break-through which the biso-kotuva signified, irrigation

works on the scale required to maintain the civilisation of ancient Sri

Lanka – the construction of artificial lakes of outsize dimensions like

Minneriya and Kalavaeva, where vast expanses of water were held back

by massive dams – would have been all but impossible.”(p.28)

Needham and De Silva use two terms to refer to this valve-tower in

Sinhala. Needham uses the term „bisi-kottuva‟ and De Silva uses the

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more popular term „biso-kotuva‟. Has this difference any significance? The word „kotuva‟ signifies a box or an enclosure. What does „bisi‟ or „biso‟ mean? The most popular meaning of „biso:‟ is „queen‟ but that does not seem to have any relevance to the valve-tower. On the other

hand, „bisi‟ ( singular: bissa) refers to the small structure for storing rice

paddy in traditional villages in the dry zone. Paddy is deposited in it

from the top and paddy is taken out from the bottom. The valve-tower

performs the same function: water that enters the tower from top is

released from the bottom.

Another instance to prove that the Sinhalese engineers had reached

exceptional heights in hydraulic engineering due to their knowledge of

mathematics relates to the construction of the sluice in Maduru Oya, an

ancient reservoir in the Dry Zone. Since this reservoir was damaged by

time, the government of Sri Lanka requested a Canadian company of

engineers in 1978 to construct a new sluice at Maduru Oya, under the

accelerated Mahaveli programme.

The company, using all modern mathematical techniques at its

disposal over a period of about two years, calculated the exact location

of the proposed sluice. When they began work at the proposed site, they

were surprised to find that beneath it was the sluice constructed by the

ancient Sinhalese engineers many centuries ago. At the request of the

Government, the Canadians shifted the location of the new sluice by a

few meters so that the ancient sluice could be preserved.

Another achievement was the construction of a canal, described by

historians “as an amazing technological feat” (De Silva, p. 30). It took water from the Kala:-vaeva, one of the most impressive achievements of

this period, to tanks in Anuradhapura, such as Tisa: Vaeva. This was

done in the fifth century during the reign of King Dhatusena (455-73

ACE).

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“The Kala: vaeva had an embankment 3.25 miles long and rising to a height of about 40 feet. Its bund was constructed of blocks of dressed

granite morticed together to enable a very close fitting. Through a canal

50 miles in length – the Jaya Ganga – its waters augmented the supply in

tanks at Anuradhapura and its environs such as Tissa, Nagara and

Maha:da:regatta, apart from irrigating an area of about 180 square miles.

This canal was an amazing technological feat, for the gradient in the first

seventeen miles of its length was a mere 6 inches to a mile” (De Silva, 30).

Conserving water for domestic and agricultural purposes was not

the only concern of the hydraulic engineers of ancient Sri Lanka.

Landscape gardening also found in water a natural resource that added to

its aesthetic beauty.

In ancient Sri Lanka, Sri Lanka had produced some of the most

remarkable water-gardens of Asia. A study of the layout of the royal

gardens in Anuradhapura, the first royal capital, such as the Maha:

Me:gha Vana (The Garden of the Great rain-Cloud), the Nandana Vana

(The Pleasure Garden) and the Ran Masu Uyana, (The Golden Fish

Park) unmistakably point to the existence of a highly developed art of

landscape gardening that is now lost.

As Senaka Bandaranayake says, “one of the oldest landscaped gardens in the world” was the water-garden at Sigiriya, the Rock

Citadel. It is a legacy par excellence of Sri Lanka‟s hydraulic civilization.

“A water-garden is, in the final analysis, a harmonious synthesis of

hydraulic engineering, landscaped gardening and aesthetic finesse. The

large reservoirs and canals of the Dry Zone bear silent testimony to the

achievements of hydraulic engineering that the ancient Sinhalese had

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attained by the early years of the Christian Era.” (Disanayaka, Water Heritage of Sri Lanka‟, p.97)

The water gardens at Sigiriya occupy the area to the west of the

Rock. Recent excavations at Sigiriya, under the auspices of the

UNESCO Cultural Triangle project, have unearthed a large corpus of

archaeological data pertaining to the plans and structure of these garden

types.

The network of underground conduits, originating from the tank

known as Sigiriya Vaeva, and feeding the moats and fountains, exhibit

that the Sinhalese engineers of this period had a highly sophisticated

knowledge of hydraulics. Observes Bandaranayake “The water gardens at Sigiriya seem to have been the playground not only of the court but

also of the ancient engineers, who applied here on a micro-scale the

principles of the macro-hydraulics which formed the essential

technological basis of the Sri Lankan civilization during the Early and

Middle Historical Period” (p. 6)

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The effective control and management of water in a water garden

assumes that the engineers had understood the different functions of

water in a purely ornamental and recreational context. Bandaranayake‟s observation that “the total conception involves the knitting together of a number of hydraulic structures of varied scale and character in a single

intricate network - a complex masterpiece of irrigation engineering

design that formed the hydrological skeleton of the landscaped gardens” help us to understand “the uniqueness of this fifth century creation of the Sri Lankan master builders” (p.7)

Sinhalese architects and engineers, who were thorough in their

mathematical knowledge, were able to build three of the tallest edifices

of the Ancient World. These are the three tallest stupas in Anuradhapura,

the first royal capital of the Island kingdom. They are the three stupas:

Jetavana (400 ft), Abhayagiri (370 ft) and Ruvanvaeli (300 ft). Today,

they have been declared UNESCO heritage sites.

“This town flourished during the hey-day of Athens and Rome and

ambassadors were exchanged between Rome and Anuradhapura in the

period of Augustus Caesar. The township of Anuradhapura compares in

grandeur and extent to those of Rome or Athens. With the fall of the

Roman Empire in the 4th

century AC Sri Lanka had three edifices that

were much larger than the largest buildings of Rome. The Jetavana

Stupa (400 feet) constructed in the 4th

century AC, the Abhayagiri Stupa

(370 feet) constructed in the 1st century BC and the Ruvanvalisaya (300

feet) constructed in the 2nd

century BC were the 4th

, 5th

and 6th

tallest

buildings of the Ancient World, being only smaller than three largest

pyramids in Egypt.” (Ancient Buddhist Monuments Triangle, Sri

Lanka)

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In height, the tallest edifices of the Ancient World were the three

tallest pyramids in Giza, the most important royal necropolis of the

Fourth Dynasty (c.2613-c.2494 BCE). The structure and design of the

stupa, however, was more intricate and sophisticated than that of the

pyramids.

Sinhalese Buddhist sculpture also bears evidence to the fact that

the sculptor possessed a wealth of intricate mathematical knowledge.

The best example is the Buddha Image in the village of Aukana,

between Dambulla and Anuradhapura.

The image is carved in the round out of natural rock. It is 40 feet in

height above its pedestal. Carving an image out of natural rock is

difficult because it has to done with utmost precision. The sculptor who

carved this image had done so with such mathematical precision that a

drop of water that falls from the tip of the nose (of the Buddha) falls

exactly between his feet! A visit to Aukana will clarify any doubts about

this statement.

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If the Sinhalese had reached such heights of mathematical thought

and skill, where was this corpus of knowledge stored?

As Prof. Arasaratnam rightly concludes, “there must have been some theoretical knowledge, some manuals on this science on which

practical building could be based. The selection of rivers and points at

which to dam them, the calculation of gradients for the sloping of

channels must have demanded technical knowledge and the use of

instruments of a nature comparable to modern hydraulics” (Arasaratnam,

Ceylon, p.67)

Needham to comes to a similar conclusion. “Finally” says Needham “the Sinhalese engineers were not without their charts, though hardly any have survived. We possess, however, a rare map of the

Elahera anicut and canal leaving the Amban Ganga, with a contribution

from the Kalu Ganga by way of the Yodiye-bendi-ela (one of those

canals planned to arrive at anicuts), and making its way across a number

of tributaries in the usual manner towards the great Minneriya-

wewa”(p.373).

May I now invite my colleagues in the Departments of

Mathematics, Statistics and Computer Studies to complete this saga of

the Sri Lankans who ranked among the super-nations of the Ancient

World on par with Egypt, Babylonia, Greece, Rome, India and China.