In the Hindu-Buddhist civilizational
sphere, the number 108 is among the most sacred and appears as the true or
fictitious cardinal number of all manner of philosophical sets and religious
series. What makes this number so
special? We will try to position
ourselves as best as possible into the minds of profundity-oriented symbolists
in order to extract their kind of meaning from this unusual number.
Insufficient reasons
Since matters of religious symbolism
typically attract self-styled esotericists who have a dislike for serious
logical ratiocination, the usual explanations of the sacred status of the
number 108 don’t amount to much. Just as
those people “explain” the status of the number 12 by merely enumerating “the
12 months, the 12 apostles” etc., they will merely enumerate a number of
instances where the number 108 is in evidence.
Thus, I
have seen it claimed by Western esotericists that 108 = 6² + 6² + 6², the sum
of the squares of the three equal numerals making up the Biblical-Apocalyptic
“number of the Beast”, 666. The
calculation isn’t incorrect, but it remains unclear why squares should be
counted, or why 666 should be of any importance. This number has some strange numerical
properties in its own right, but they are not the reason for its popularity
among the mystery-minded. The real
reason is that through a numerical-alphabetical manipulation best known by its
kabbalistic name gematria, the number refers to a Roman emperor disliked by the first
Christians who called him “the Beast”.
Emperor or “Caesar” seems to be the meaning of the component 60, this
being the numerical value of the Greek letter Ksi, shorthand for its Greek
rendering Kaisar. This probably
doesn’t refer to Nero, as has been assumed for long, but to “Divus Claudius”,
the 6th emperor, who came after Julius Caesar, Octavian August, Tiberius,
Germanicus (who received the imperium maius but was murdered; his
caesarian status is shown by the fact that the succession devolved to his
son:), Caligula. Even Claudius’ mother
considered Claudius ugly like a beast, and his initials DC were read in Latin
as the number 500 + 100 = 600. So,
probably 666 means “the 6th Caesar/60, named D.C./600”.
Admittedly, there are other explanations, but
whatever the details, the reference to “the number of the Beast” is merely an
expression of the abysmal hatred of Rome by some early Christians, a mere
footnote in history. At any rate, the
abusive religio-political slogan “666” is totally irrelevant to any serious
philosophy. It is equally irrelevant to
Hindu-Buddhist culture, and relating it to the status of 108 is anachronistic
since it appeared on the scene centuries after the number 108 gained its
aura of sacredness.
Even where the explainers try to
prove their point with proper Hindu-Buddhist examples, they fail to get to the
bottom of the matter. Thus, the
Upanishads (philosophical texts completing the Vedic corpus) are classically
counted as 108, eventhough their actual number, depending on which ones you
include, can range from 13 to more than 200.
Rosaries east of the Indus have 108 beads, the Nepalese parliament has
108 seats. The poses of Bhârata
Natyam dancing, the number of gopî-s (cowgirls) enamoured of
Krishna, the number of sacred sites in the tradition of Vishnu worship, the
number of Buddhist arhat-s (realized saints), and many other sacred sets
are all conventionally counted as 108.
Likewise with derived numbers, e.g. the Rg-Vedic verses are
conventionally counted as very approximately 10800, the Purâna-s as 18,
the Bhagavad-Gîtâ has 18 chapters, and many Hindu monks carry titles
like “Swâmi 1008 Padmânanda”.
All very fine, but that list doesn’t explain
anything. The number 108 has been chosen
in these instances, and often forced upon rather unwilling sets as their
cardinal number, because it was already a sacred number to begin with. We need something more objective as a basis
for the special status of this number.
Among attempts to find a more solid
basis, we still have to be wary of cheap and easy proposals. Thus, I have seen it claimed that “108 x 20 =
2160, the number of years spent by the equinox in each Zodiac sector”, on the
assumption that the total precessional cycle takes 2160 x 12 years, i.e. 25,920
years or neatly 1° per 72 years (and the extra assumption that the Vedic seers
knew and cared about the precessional cycle).
But in reality, the cycle takes ca. 25,791 years, which doesn’t yield
any round number when divided by 108.
It is already better to note that 108 lurks in
a corner of the Hindu (or actually Indo-European) number 432 with any number of
zeroes added. Thus, 432,000, the number
of years sometimes attributed to a Yuga, a world age, which happens to
be equal to the number of guardians of the Germanic Walhalla or heaven
(viz. 800 for every one of its 540 gates), can be analysed as 108 x 4000. Or as 18 x 24000, for that matter. This is true, but is it important? Many numbers are related to other
numbers. Is it relevant to anything?
So, we will try to do better than that and give
correct data which underlie the special status of our sacred number in a more
compelling manner. We will distinguish
between a pair of contingent astronomical facts singling out the number 108 and
four mathematical properties of the number 108, two of these conditional and
two unconditional.
Solar and lunar distances
It could have been otherwise, but it so happens
that the distance between the earth and the sun equals about 108 (actually
107-odd) times the sun’s diameter. Likewise,
it so happens that the distance between the earth and the moon equals about 108
(actually 109-odd) times the moon’s diameter.
That sun and moon look equally big in the earthly sky is the immediate
result of their having the same ratio between distance and diameter. Moreover, it so happens that the sun’s
diameter approximately equals 108 times the earth’s diameter.
These are contingent data, which means that
they could have been different. And they
are subject to change, meaning that if you look deep enough into the past or
the future, you find values considerably different from the present ones of ca.
108. While the distance between the sun
and its planets is fairly stable, the distance between the earth and the moon
is subject to steady and ultimately very sizable changes. In the times of the dinosaurs, the moon was
so close to the earth that a lunar revolution (i.e. a month) took only a few
earthly days, with the days themselves also being shorter than today. In the future, the lunar revolution will take
thirty days, forty days, etc. Its
distance from the earth will then equal 110 lunar diameters, 120 etc.
It is a cosmic stroke of luck that the solar
and lunar distances happen to match the number 108, a remarkable number for
non-contingent reasons we will discuss below, right at the time when life on
earth was reaching a level of intelligence sufficient to start astronomical
observations and wonder at this coincidence.
Just as it is a cosmic stroke of luck that in this same age, the moon is
at such a distance from the earth that its annual number of revolutions is
approximately 12, another number with unique non-contingent properties.
Can we be sure that this remarkable
astronomical state of affairs has played a role in the selection of 108 as a
sacred number? Did the ancient Indians
know about the moon’s diameter or its distance from the earth? According to Richard L. Thompson (Mysteries
of the Sacred Universe, Govardhan Hill Publ. 2000, p.16, p.76), the
medieval Sûrya-Siddhânta gives an unrealistically small estimate for the
distance earth-sun, but the estimate for the distance earth-moon and the lunar
diameter differs less than 10% from the modern value. The ratio between distance and diameter of
the moon is implicitly given there as 107.5, admittedly a very good
approximation.
However, I have never heard of any text,
whether from the Vedic or the medieval period, that explicitly derives the
importance of the number 108 from these or any other astronomical data. But this is merely an argument from silence,
with limited proof value. For on the
other hand, the estimation of the relative distance of sun or moon isn’t that
difficult to calculate even without 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.” (Subhash Kak: “Shri 108 and Other
Mysteries”, Sulekha.com, 27 Nov. 2001)
Also, in some respects the Vedic-age astronomers were more advanced than
their medieval successors, who had jettisoned part of their own tradition in
favour of Hellenistic import.
So, it remains speculative but quite possible
that the solar and lunar data were estimated with a good degree of accuracy at
the time when 108 was selected as a sacred number. But it is also possible that the selection
was made purely on the basis of the non-astronomical considerations discussed
in the following sections.
Big 1,
little 8
One of the arithmetical properties
of 108 is dependent on the choice of counting system. In the near-universally used decimal counting
system, the quantity 108 is expressed as “108”, meaning “1 hundred, 0 tens, 8
units”. In other counting systems, it
would look different, e.g. in a duodecimal (12-based) system, it would be
written as “90”, and in the binary system, it is written as “1101100”. Assuming the conventional decimal system,
what is remarkable about “1-0-8”?
Like 18, it brings together the
numerals 1 and 8, with the former in the leading and the latter in the lowly
position. The main difference (valid
even more in subsequent numbers like 1008) is merely that an abyss of
worshipful distance is created between the regal 1 and the servile 8. So, let us briefly focus on this symbolism of
1 and 8. It is chiefly remarkable as a
reference to yet other important symbols.
8 1 6
3 5 7
4 9 2
In the magic square of 9, there is 1
little square in the middle and 8 on the periphery. Also, the 1 central number is 5, the sum of
the 8 peripheral numbers is 40, yielding a ratio of 1:8. The magic square itself, with equal sums of
the three numerals on every line, is an important symbol of cosmic order,
balance and integration. Painted on walls
or wrought into little metal plates it is used as a luck-charm.
Moreover, consider the sums in the magic
square, adding the central number and a number in the middle of the sides,
yielding the number in an adjoining corner (counting only the units): 5 + 1 = 6; 5 + 7 = 2 (12 modulo 10, as it
were); 5 + 9 = 4 (14 modulo 10); 5 + 3 = 8.
If you draw lines following the numerals in these sums, you get the Swastika,
yet another lucky symbol in Hindu-Buddhist culture.
The “nine planets” of Hindu
astronomy are also often depicted in a square arrangement for ritual purposes
such as the Navagraha Agnihotra (nine-planet fire ceremony), with the
sun in the middle and the 8 others around it: moon, Mercury, Venus, Mars,
Jupiter, Saturn, Râhu (northward intersection of lunar orbit and
ecliptic, “Dragon’s head”) and Ketu (southward intersection, “Dragon’s
tail”). So, 18 or 108 may add some
detail to the symbolism of 9 as representing the planets. This is, however, of lesser importance than
the magic square because the number of planets is contingent and changeable
whereas mathematical properties are intrinsic and forever.
The
Golden Section and 108°
A conditional geometrical property
of 108 is dependent on the conventional division of the circle into 360°. This division is arithmetically very
practical, it also alludes to the division of the year in ca. 365 days, it is
now universally accepted, yet it is contingent and essentially only the result
of a human convention. At least one
alternative division is known, viz. the division into 400° introduced during
the French Revolution on the assumption that the division into religion-tainted
numbers like 7 and 360 was less “rational” than the division into 10 or 100 or
their multiples. Hence also the
Revolutionary replacement of the 7-day week by a 10-day week and the
definitional choice of the meter as one hundred-thousandth of one “decimal
degree” measured on the earth’s equator of 40,000 km.
But for now, we may settle for the
division in 360°. In that case, the
angle of 108° has a unique property: the ratio between the straight line uniting
two points at 108° from each other on a circle’s circumference (in effect one
of the sides of a 10-pointed star) and the radius of that circle equals the
Golden Section. Likewise, the inside of
every angle of a pentagon measures 108°, and the pentagon is a veritable
embodiment of the Golden Section, e.g. the ratio between a side of the
5-pointed star and a side of the pentagon is the Golden Section. So, there is an intimate link between the
number 108 and the Golden Section. But
why should this be important?
The Golden Section means a
proportion between two magnitudes, the major and the minor, such that the minor
is to the major as the major is to the whole, i.e. to the sum of minor and
major. The general equation yielding the
Golden Section is A/B = (A + B)/A, or alternatively but equivalently, X = 1 +
1/X. In numbers, X = (1 + square root
5)/2; or decimally, X = 1, 618… This
infinite series of decimals can be replaced with a more predictable infinite
series of numbers, viz. X equals the limit of the series G/F in which F is any
member and G is the very next member of the Fibonacci series, i.e. the series
in which every member equals the sum of the two preceding members: 1, 1, 2, 3,
5, 8, 13, 21, 34, 55, 89, 144,… This
means that every next fraction G/F, i.e. 1/1, 2/1, 3/2, 5/3, 8/5 etc. forms a
better approximation of the Golden Section, whose value can be approximated to
any desired degree of precision if fractions of sufficiently highly-placed
members of the Fibonacci series are considered.
In art and architecture, it is found
that the Golden Proportion is naturally pleasing to our inborn tastes. In living nature, there are plenty of
sequences where every member stands to the preceding member in a Golden
Proportion or its derivatives (square root etc.), e.g. the distances between or
the sizes of the successive twigs growing on a branch, the layers of petals on
a flower, the rings of a conch, the generations of a multiplying rabbit
population, etc. What this symbolizes is
the law of invariance: in every stage of a development, the same pattern
repeats itself. The son is to the father
as the father was to the grandfather.
Wheels within wheels: every whole consisting of parts is itself likewise
part of a larger whole. And the
principle of order: the underling obeys the orders of his master to the same
extent that the master obeys the requirements of the whole. Or with a pre-feminist maxim: “he for God
alone, she for God in him”, i.e. the wife serves the husband because (and to
the extent that) the husband serves the cosmic order defining his duties. As Confucius said, the authority of the
ruler, his capability of making the people willingly obey him, is that he
himself obeys the Laws of Heaven.
So, the Golden Section is a
meaningful symbol in the cosmological, aesthetical and ethical realms. And somewhere in a corner of Golden Section
lore, in the pentagon and decagon, we see the number 108 participating. This is meritorious though perhaps a bit too
indirect to count as sensational.
Sacred 9
times sacred 12
An intrinsic and ever-unchangeable property of
108 is that it equals 9 times 12, the product of two smaller sacred
numbers. It is the number of divisions
in the Zodiac in the so-called Navamsha horoscope, a horoscope which
Hindu astrologers always calculate along with the basic horoscope, and in which
all original positions expressed in angular distance from the beginning point
of the Zodiac are multiplied by 9. This
implies, for example, that a planet at 8° Aries is projected to 72°, meaning
12° Gemini. In effect, the whole sector
between 6°40’ and 10° Aries is projected onto Gemini (i.e. between 60° and 90°)
and given a Gemini colouring, just as the sector between 10° and 13°20 Aries is
navamsha-projected onto Cancer, etc.
This way, every one of the 12 signs is subdivided into 9 sectors, or 108
in total. But of course, this doesn’t
explain the status of 108, as the idea of subdividing the Zodiac this way
apparently results from the awe in which 108 or 9 x 12 was already held.
As we have seen, 9 is the Hindu number of
planets, and 12 is the Zodiac, so 108 is the total number of
planet-in-Zodiacal-sign combinations.
This makes it into the total set of all possible planetary influences
taken separately, or in a more generalized symbolism, the matrix containing all
possibilities. However, to purists, 9 as
the number of planets isn’t good enough.
For one thing, the Hindu definition of a planet is pre-heliocentric,
counting sun and moon and their two eclipse points as planets all while failing
to count the earth as a planet (though it so happens that planets by the modern
astronomical definition are again counted as 9, from Mercury to Pluto including
the earth). Also, planets may be added
through empirical discovery, as some have indeed been in astronomy and in
Western astrology; and in some rare but not-impossible catastrophe, a planet
may disappear. They are only creatures, born from dust and returning to
dust. If we’re looking for intrinsic
properties of numbers, we should not settle for contingent data such as the
present number of Hindu “planets”.
To the unique properties of 12, revealing it to
be a logical symbol of cosmic order, we have devoted a separate paper, Why
Twelve?, where we have focused on its unconditional properties, both
arithmetical and geometrical. We may add
that, conditional upon the choice of the decimal system, 12 is structured as 1
tenfold plus 2 units: 1 big, 2 small.
Which to a freely-associating symbolist mind can mean: 1 precedes 2 (as
indeed it does, in fact it is the most elementary observation to be made in the
number series, e.g. long preceding the realization that there must be a zero),
unity is superior to division, oneness precedes and underlies polarity, the
odd/yang dominates the even/yin.
Note however that for all their inequality, the numbers 1 and 2 and all
that they symbolize are at any rate united and synthesized in the number
12 and in whatever the latter symbolizes.
Meanwhile, this conditional arithmetical property of 12 must remain
inferior to the unconditional properties of 12, especially those of 12
conceived geometrically as the regular dodecagon, e.g. the fact that its
construction uniquely flows automatically from the construction of the circle,
keeping the same compass width; and the fact that it bridges the gap between
straight/radius and round/circumference by dividing both rationally in a single
move (the radius into 2, the quarter-circumference into 3).
Like 12, the number 9 has its unusual
properties. Once more, we cannot be satisfied
with simply enumerating instances where 9 has been used in a sacred context:
the 9 worlds of Germanic cosmology, the 9 Muses, etc. We want objective properties, and when
looking for these, we must again distinguish between conditional and unconditional
properties. Thus, it is often remarked
that 9 is the highest among the decimal numerals, and hence symbolizes anything
that is highest, including God, who, in comparison with anything you may
propose, is always Greater. However,
this property is conditional upon our choice of numeral system, i.c. decimal
rather than binary or any other: in the binary system, the number 1 would have
this property, and in the duodecimal one, the number eleven would. Likewise, 9’s property of equalling the sum
of the numerals in its own multiples (e.g. in 9 x 8 = 72, we find that 7 + 2 =
9) is again dependent on our choice of the decimal system.
For unconditional properties, we might look at
some characteristics of the enneagon (9 x 40°).
This is the first polygon with a non-prime base (as distinct from the
heptagon, 7 being a prime number) that eludes construction with ruler and
compass. This contrasts sharply with the
division of the circle into 4 or 6 or 12, which is so simple and natural, or
with its division into 5 or 10, which is more complicated but very rewarding
(yielding the Golden Section) and at any rate possible. So, 9, though analysable as 3 x 3, is
elusive. Does anyone care to read some
symbolism into this property? If 7
represents the mystical eluding the rational, what should be represented by 9,
which is more structured yet equally eludes rational construction? Let’s see: how about God, who always eludes
our concepts? Allahu Akbar, God
is greater!
But we need not look that far. Whatever else 9 may be, its most immediate
arithmetical property is certainly that it equals 3², or 3 x 3. Unlike the neat balance of even numbers like
2 or 4, suggesting stability and a waiting matrix of potentialities, the number
3 expresses motion, as even the most vulgar book on number symbolism will tell
you. The number 9, therefore, is a
movement affecting the movement, i.e. acceleration. It is dynamic par excellence, Shakti as the
dynamic expression of static Shiva. The
primal form of acceleration is the change from rest to motion, i.e. setting
things in motion, starting the whole process from zero. This, of course, is the doing of the Creator
who is Greater. Or as the Scholastics
used to say: God is not Potency, God is pure Act.
So, whereas 12 represents synthesis of
opposites within an ordered cosmos (3 x 4, time-space, motion-structure) and
harmonization of self and non-self, 9 represents unfettered dynamism, pure
self-expression riding roughshod over the non-self, the joy of being entirely
oneself. It transcends and leaves behind
all compromise in favour of purity and absorption. Its structure as 3 x 3 actually explains its
elusiveness: whereas divisions of any angle into 2 and its multiples are always
feasible and simple, the division into 3 is impossible, though very good
approximative techniques have been developed.
Even folding a letter into three requires a manual jump, an
approximation rather than a slow but sure technique guaranteeing an exact
division into equal parts. The enneagon
is the first regular polygon which requires for its construction the trisection
of a known angle (120°, itself easily constructed though not by trisecting the
“angle” of 360°), an impossible operation with ruler and compass. Likewise, according to poets, the Absolute
cannot be caught in a conceptual net but can only be approximated, hinted at,
spoken of in parables and metaphors.
Let’s put ourselves into the mood of
god-seekers in order to understand this.
As 9 x 12, the number 108 infuses the cosmic order represented by 12
with the god-drunkenness, the enthusiasm free of all doubts, the pure
dedication represented by 9. That makes
it an excellent number for the prayer-wheel or rosary, which is used in a
disciplined and systematic manner in order to lift up the spirit towards
god-absorption.
Square
times cube
Among other intrinsic and ever-unchangeable
properties, it may be hard to choose which one is sufficiently relevant. Thus, 108 equals the sum of the first 9
multiples of 3, viz. 0, 3, 6, 9, 12, 15, 18, 21 and 24. This reconfirms its intimate relation with the
richly symbolic number 9, but then, so what?
Slightly more remarkable is that 108 equals the
product of the second power of 2 and the third power of 3, i.e. the first
non-trivial even and odd numbers multiplied by themselves as many times as
themselves. In figures: 108 = 2² x 3³,
or 108 = 2 x 2 x 3 x 3 x 3. This way, it
unites on their own terms the polar opposites of even and odd, the numerical
counterparts of female and male, yin and yang, etc. If nothing else, at least it’s cute, is it
not? That may well be the most we can
expect of number symbolism.
(copyright:
author, October 2003)
(in case we
have missed some important symbolically-charged properties of the number 108,
we welcome feedback)