RAMBLINGS IN MATHEMATICS - ucsc.cmb.ac.lk · last Buddha, Siddhartha Gautama. I n consonance with...
Transcript of RAMBLINGS IN MATHEMATICS - ucsc.cmb.ac.lk · last Buddha, Siddhartha Gautama. I n consonance with...
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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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.