The Many Connections of a 50cm Tall Jade Buddha
Attempting to talk of the joys of
mathematics usually produces quizzical, if not downright unbelieving, looks. During
thirty-six years teaching the subject I never stopped learning and I always
took delight in the surprising links between apparently separate ideas - there's an example at the end.
The joys of travel are more widely – and
perhaps more easily - appreciated. Occasionally we find the same name or idea
popping up in different and sometimes widely separated locations and those
unexpected links give me the same pleasure as their mathematical analogues.
Introducing the Emerald Buddha
This post is about the Emerald Buddha, a fifty centimetre tall piece of carved jade ('Emerald' referring to its colour rather than the gemstone) that we encountered for the first, but by no mean last, time in Bangkok in 2012.
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| The Emerald Buddha, Wat Phra Kaew. Bangkok |
The Story Starts in Legend
Bangkok, though, is the end of a story
that starts in legend in 43BCE when the Buddhist sage Nagasena carved the image in
the northern Indian city now called Patna. There is a problem, though: modern
scholarship dates the writings that concern Nagasena to a hundred years earlier
and none mention his skills as a sculptor.
The Emerald Buddh Goes to Sri Lanka
The statue remained in Patna for 300
years until civil war necessitated moving it to a place of safety and the
Buddha was taken to Sri Lanka. Moving important objects a short distance for
safekeeping occurs regularly throughout history (see the Book of Kells for one example), but Sri Lanka is a very long way,
and the Sri Lankans, who are happy to claim any Buddha connections they can, fail to mention this one.
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| The Thuperama Dagoba, Anuradhapura, Sri Lanka, the Buddha's right collarbone is believed to be beneath this dagoba |
The Emerald Buddha is Sent to Burma but ends up in Cambodia
In 457 the Burmese King Anuruth requested
the Emerald Buddha to enhance the development of Buddhism in his country. There
are many stories of bits of the Buddha - hairs of which there were, presumably,
plenty and odd body parts that survived his apparently inefficient cremation -
being sent around Asia for this purpose, but giving away the Emerald Buddha sounds
like uncommon generosity. According to legend, the vessel carrying the Buddha
to Burma was shipwrecked on the coast of Cambodia and it fell into the hands of
the Khmer emperors.
The great days of the Khmer empire ended
in 1432 when Angkor Wat was sacked by the Thais. The Emerald Buddha was carried
off and after visiting several locations settled in Chiang Rai in the
northern Thai kingdom of Lanna.
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| Angkor Wat, the great temple of the Khmer Empire, Cambodia, |
Wat Preah Keo, (The Silver Pagoda) adjacent to Phnom Penh’s Royal Palace contains a 17th century replica known as the 'Emerald Buddha of Cambodia'. Although, according to the legend, the Emerald Buddha was in Cambodian keeping for almost a thousand years, it was only ever theirs because they found it. Cambodia in general - and Phnom Penh in particular - have little claim on the original but they seem happy enough with their replica and an almost life size solid gold Buddha figure made locally in 1908.
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| Wat Preah Keo, The Silver Pagoda, Phnom Penh I failed to take a satisfactory picture of the Silver Pagoda so I have borrowed this one from Wikipedia |
To Thailand and Legend Gives Way to History
Another legend states it became lost and was found in
Chiang Rai in 1434 inside a stupa that was split by a lightning strike. Whatever
the truth of the lightning story, the first incontrovertible evidence for the
Emerald Buddha’s existence is in Chiang Rai in 1434.
Chiang Rai was a major city in Lanna, but the capital was the confusingly similarly named Chiang Mai, 150km away. Objects like the Emerald Buddha gravitate towards capital cities, and it reached Chiang Mai in 1468.
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| South East Asia |
To Laos, First in Luang Prabang, then Vientiane
In 1546 the throne of Lanna became vacant and Prince Setthathirath, heir to the Lao kingdom of Lang Xan, was invited to sit on it. In due course he became king of Lang Xan as well and in 1552 he moved the Emerald Buddha to the Lang Xan capital of Luang Prabang, where he built Wat Xieng Thong.
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| Wat Xieng Thong, Luang Prabang |
In 1564 he moved his capital to Vientiane, taking the Emerald Buddha with him. We first encountered Setthathirath dressed like a big boy scout, sitting in front of That Luang in the centre of Vientiane.
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| King Setthathirath in front of That Luang, Vientiane |
He built his personal temple, Wat Pha Keo, to
house the Buddha
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| Wat Pha Keo, Vientiane |
In time Vientiane became a vassal state of Siam. In 1779, the Thai General Chao Phraya Chakri put down an insurrection and carried off the Emerald Buddha. General Chakri later became King Rama I of Thailand (the current king is the ninth of the Chakri dynasty [Update: Rama IX died in 2016, the current king is the tenth of that dynasty]) and in 1784 installed the Emerald Buddha in Wat Phra Kaew in Bangkok where it remains to this day.
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| Wat Phra Kaew, Bangkok |
Anyone (or at least anyone who can afford
the entrance ticket) may go and see the image. They must behave respectfully
and sit quietly on the floor, remembering to arrange themselves in the eastern
fashion with legs folded backwards. To point your feet towards the Buddha is extremely
ill-mannered and will quickly earn an unobtrusive but nonetheless stern rebuke
from one of the stewards.
And so the Emerald Buddha is in Bangkok, which is where, mathematics apart, this post started. The Thais consider it the palladium of their country and it is touched only by the monarch when he changes the Buddha's vestments three times a year. The sage Nagasena, who (allegedly) made, it (allegedly) said the Emerald Buddha would bring "prosperity and pre-eminence to each country in which it resides." Laos would like it; Wat Pha Keo, destroyed in 1828 has been rebuilt and awaits its return, but is doomed to remain a museum that is missing its main exhibit. The Cambodian are sentimentally attached to it but are content with their replica, while the Sri Lankan are hardly aware they ever had it – if they ever did.
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| Finishing where we started with the, Emerald Buddha in Bangkok This is the uncropped version of the photograph at the start, taken, of course, from outside the hall of the Emerald Buddha. Taking photographs inside would bring down the wrath of god - or at least of the stewards |
Yet to be established is where
in the long journey from 50BCE Patna to modern Bangkok does legend turn into
fact. Art historians say the carving style is that of 14th century Lanna,
suggesting India, Sri Lanka and the Cambodian shipwreck are firmly in the
realms of myth and legend. Whether it was ever in Cambodia is problematic and
it may well have originated in Chiang Rai, though the lightning strike story is
unlikely. It was, it seems, made in northern Thailand and now resides in
southern Thailand, and that, for the foreseeable future, is where it will stay.
And to Finish a Little Mathematics
Everybody knows that for all circles, the circumference divided by the diameter gives a constant known as π.
π = 3.142.... the dots indicating that the numbers go on, never stopping and never falling into a pattern.
Anybody who took (and remembers) A level maths, should also know that if you work out the little sum below and then multiply the answer by 4, then
the more terms you use the closer the answer gets to π. If you take an infinite
number of terms, then it is exactly π.
1-1/3 + 1/5 - 1/7 + 1/9 -1/11 + ....
Of course, calculating an infinite number of terms is impossible, but you can get π to as many decimal places as you want by taking enough terms.
The proof is well within the scope of year 12/13 mathematics, but the proof (which does not involve radii or circumferences) does not explain why it is true. What is the connection between this simple sequence of
fractions and a circle? I do not know, I not sure anyone knows, but the
connection exists.
There are actually a number of infinite series which converge to π. This one, known as the Gregory-Leibniz series, is the simplest. Should you pick up a calculator to check I am telling the truth, be warned that it converges painfully slowly; after 5 terms you get to 3.396…. , others can be much quicker.