Shri
108 and Other Mysteries
http://www.sulekha.com/column.asp?cid=155230
Subhash Kak
~ Nov 27, 2001
The Golden Ratio,
1.618033989, is at the basis of stock-market data, petal patterns
of flowers, and even the planet periods. It is the ratio obtained
by dividing consecutive elements, the larger by the smaller, of
the Fibonacci series: 1, 1, 2, 3, 5, 8, 13, 21... where the next
term is the sum of the preceding two terms. The Golden Ratio is
the solution to the equation x = 1 + 1/x. When raised to the powers
-3, -1, 0, 1, 5, 7, the Golden Ratio gives the periods of Mercury,
Venus, Earth, Mars, Jupiter, and Saturn in years, suggesting that
the solar system must be viewed as a single whole.
For the physicist,
the number 137, the inverse of the fine structure constant, is more
mysterious. It is a dimensionless ratio that equals the product
of the Planck's constant and the speed of light divided
by the square of the electron's charge. Actually, the number is
slightly larger (137.0359895), but it is sufficiently close to the
integer 137 that people have wondered if it is related to some deep
property of nature. This number shows up at many places in atomic
physics, and it has been even seen in the motions of Jupiter's satellites.
Some of the greatest minds of the physics of the last century have
sought formulae for it. One theorist considered it particularly
significant that 137 equals 128+8+1, each of which factor is a power
of 2.
A less esoteric
and more interesting number is 108, the number of beads of a rosary
and of many other things in Indian cosmology. I first heard of it
in the title of swamis in India, as in Shri 108 so-and-so, which
irked me not only because of its pretentiousness but also because
no one seemed to know why it was 'holy'. I also had heard of 1,008,
another equally mysterious number used by swamis.
Much, much later,
I asked professors about these numbers. One gentleman told me that
its secret lay in the 'holiness' of the number 18, as evidenced
by the eighteen Puranas, and the eighteen chapters of the Bhagavad
Gita; and the number 108 was obtained from 18 by slipping a zero
in between, and doing this again led to 1,008. But this explanation
didn't convince me. Why is 18 holy, to begin with?
And if it is, why doesn't slipping a zero in between 1 and 8 destroy
that holiness? If it doesn't for whatever reason, leading to 108
and 1,008 in two stages, why doesn't it lead to 10,008 and other
larger numbers?
Another gentleman
said that 108 was 27 times 4, that is 27 nakshatras (constellations
in the moon's monthly circuit) multiplied by four of the four cardinal
directions. But why should this be important? Also,
in reality, the moon takes 27 and one-third days to complete its
circuit, and not exactly 27.
I ultimately
found the answer to the mystery of these numbers while researching
early Indian astronomy. I discovered that the Indians took this
to be the distance between the earth and the sun in sun-diameter
units, and the distance between the earth and the moon in moon-diameter
units.
Three facts
that any book on astronomy will verify:
* Distance between
earth and sun = 108 times sun-diameter,
* Distance between
earth and moon = 108 times moon-diameter, and most
remarkably,
* Diameter of
the sun = 108 times the earth diameter.
That the Indians
knew of the first two shouldn't surprise, because it can be calculated
by anyone without the need for any instruments. Take a pole, mark
its height, and then remove it to a place 108 times its height.
The pole will look exactly of the same angular size as the moon
or the sun.
I don't believe
Indians knew the third fact, that the sun is 108 times as large
as the earth, because there is no evidence of that in the old astronomy
manuals. If they did, it would be as amazing a coincidence as the
knowledge of the correct speed of light before modern measurements.
Indian thought
takes the outer cosmology to be mirrored in the inner cosmology
of the human. Therefore, the number 108 is also taken to represent
the 'distance' from the body of the devotee to the God within. The
chain of 108 'links' is held together by 107 joints, which is the
number of marmas, or weak spots, of the body in Ayurveda.
We can understand
that the 108 beads of the rosary (japamala) must map the steps between
the body and the inner sun. The devotee, while saying beads, is
making a symbolic journey from the physical body to the heavens.
The number 108
joined to the name is merely a boast that one is a spiritual adept,
a master of the journey of 108 steps through the intermediate regions
of danger.
The other number
1,008 has a slightly different basis. Early Indian astronomy divides
the kalpa -- the total period within a creation, the day of Brahma,
which is part of an infinite cycle -- into 1,008 yugas. The use
of this number as a title is to boast that one knows the mystery
of time from creation to annihilation.
The number 108
appears in many settings in the Indian tradition. The Natya Shastra
of Bharata speaks of the 108 karanas -- combined movements of hand
and feet -- of dance. A few months ago in Chennai,
Padma Subramaniam, the great dancer and dance theorist, told me
a story of discovery connected with this number.
In the 1960s,
Padmaji had come to the realization that the four hands of the Shiva
figures in Thanjavur represented animation. Then, in 1980, Sri Chandrasekharendra
Saraswati Swamigal, the Shankaracharya of the Kanchi Peetham --
who was to pass away at the age of 100, fourteen years later --
asked her to design a fresh set of karana figures for the panels
of the new Uttara Chidambaram Nataraja Mandir in Satara, Maharashtra,
based on the Natya Shastra descriptions. Each panel had to show
Shiva and Parvati.
She first had
to decide whether to use Shiva with four arms as at Thanjavur or
Shiva with two arms as at Kumbakonam, together with Parvati with
two arms as at Chidambaram. She took pictures for advice
to the Swamiji, but he said there was to be no copying of existing
images. Ultimately, she chose four arms for Shiva and two for Parvati,
and created the 108 new designs.
Later in the
1990s, Padmaji was approached by Alessandra Iyer, an Italian scholar,
who wished to study the influence of the Natya Shastra on the Far
East. They discovered that the Satara temple panels of Padmaji were
similar in form to the 53 surviving dance panels of the 9th century
Prambanam temple of Java, Indonesia, that was largely destroyed
by earthquake in the 15th century.
This established
that Padmaji's choices were right and her understanding of the four-armed
poses as frozen movements was correct. Since her reconstruction
were based on brief description, it also suggests that the karanas
are archetypes of motion.
The idea of
archetypes brings me to Wolfgang Pauli and Carl Jung who, in a book
they wrote in 1952 called The Interpretation of Nature and the Psyche,
argued that our discoveries are a consequence of the
preexisting patterns in our mind. Pauli wrote once, "I prefer
to say that mind and matter are governed by common, neutral ordering
principles 'that are not in themselves determinable'." The
idea of archetype, borrowed by Jung from Yoga, makes it possible
for us to see how different people can come to the same discovery
independently. Parenthetically, Jung took the idea of divinity as
male-female (Harihara), suggesting that each man had a female within
(anima), and each woman had a male within (animus).
In his contribution
to the book, Pauli indicated how the great Kepler had come by his
three laws of planetary motion upon the use of Fibonacci sequences.
From there the next step was the Newtonian
synthesis that viewed the universe as a machine. But now we have
come full circle in our realization that if the universe is a machine,
it is one where the components are all connected together -- it
is a holistic machine.
Reading: To
get an overview of the astronomy and cosmology of the ancient world,
see Subhash Kak, The Astronomical Code of the Rgveda.
Munshiram, 2000.
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