Why 108 beads

Below I have collected some other information that helps to explain in other ways the number 108. The first part is a quick read with point-form explanation while the additional article is extensive.

None of these reasons are being promoted here as more or less true than the others. However, you may notice that 108 appears to be somewhat like a road map of reality in general, and the human in particular. 

9 times 12: Both of these numbers have been said to have spiritual significance in many traditions. 9 times 12 is 108. Also, 1 plus 8 equals 9. That 9 times 12 equals 108. 

Powers of 1, 2, and 3 in math: 1 to 1st power=1; 2 to 2nd power=4 (2x2); 3 to 3rd power=27 (3x3x3). 1x4x27=108 

Harshad number: 108 is a Harshad number, which is an integer divisible by the sum of its digits (Harshad is from Sanskrit, and means "great joy") 

Desires: There are said to be 108 earthly desires in mortals. 

Lies: There are said to be 108 lies that humans tell. 

Delusions: There are said to be 108 human delusions or forms of ignorance. 

Heart Chakra: The chakras are the intersections of energy lines, and there are said to be a total of 108 energy lines converging to form the heart chakra. One of them, sushumna leads to the crown chakra, and is said to be the path to Self-realization. 

Sanskrit alphabet: There are 54 letters in the Sanskrit alphabet. Each has masculine and feminine, shiva and shakti. 54 times 2 is 108. 

Pranayama: If one is able to be so calm in meditation as to have only 108 breaths in a day, enlightenment will come. 

Upanishads: Some say there are 108 Upanishads, texts of the wisdom of the ancient sages. 

Sri Yantra: On the Sri Yantra there are marmas where three lines intersect, and there are 54 such intersections. Each intersections has masculine and feminine, shiva and shakti qualities. 54 times 2 equals 108. Thus, there are 108 points that define the Sri Yantra as well as the human body. 

Pentagon: The angle formed by two adjacent lines in a pentagon equals 108 degrees. 

Marmas: Marmas or marmasthanas are like energy intersections called chakras, except have fewer energy lines converging to form them. There are said to be 108 marmas in the subtle body. 

Time: Some say there are 108 feelings, with 36 related to the past, 36 related to the present, and 36 related to the future. 

8 extra beads: In doing a practice of counting the number of repetitions of the mala, 100 are counted as completed. The remaining are said to cover errors or omissions. The 8 are also said to be an offering to God and Guru. 

Chemistry: Interestingly, there are about 115 elements known on the periodic table of the elements. Most of those, around or higher than the number 100 only exist in the laboratory, and some for only thousandths of a second. The number that naturally exist on Earth is around 100. 

Astrology: There are 12 constellations, and 9 arc segments called namshas or chandrakalas. 9 times 12 equals 108. Chandra is moon, and kalas are the divisions within a whole. 

River Ganga: The sacred River Ganga spans a longitude of 12 degrees (79 to 91), and a latitude of 9 degrees (22 to 31). 12 times 9 equals 108. 

Planets and Houses: In astrology, there are 12 houses and 9 planets. 12 times 9 equals 108. 

Goddess names: There are said to be 108 Indian goddess names. 

Gopis of Krishna: In the Krishna tradition, there were said to be 108 gopis or maid servants of Krishna. 

1, 0, and 8: Some say that 1 stands for God or higher Truth, 0 stands for emptiness or completeness in spiritual practice, and 8 stands for infinity or eternity. 

Sun and Earth: The diameter of the Sun is 108 times the diameter of the Earth. The distance from the Sun to the Earth is 108 times the diameter of the Sun. 

Moon and Earth: The average distance of the Moon from the Earth is 108 times the diameter of the Moon. 

Silver and the moon: In astrology, the metal silver is said to represent the moon. The atomic weight of silver is 108. 

Numerical scale: The 1 of 108, and the 8 of 108, when added together equals 9, which is the number of the numerical scale, i.e. 1, 2, 3 ... 10, etc., where 0 is not a number. 

Meditations: Some say there are 108 styles of meditation. 

Breath: Tantra estimates the average number of breaths per day at 21,600, of which 10,800 are solar energy, and 10,800 are lunar energy. Multiplying 108 by 100 is 10,800. Multiplying 2 x 10,800 equals 21,600. 

Paths to God: Some suggest that there are 108 paths to God. 

Smaller divisions: The number 108 is divided, such as in half, third, quarter, or twelfth, so that some malas have 54, 36, 27, or 9 beads. 

Hinduism: 108 is said to refer to the number of Hindu deities. Some say that each of the deities has 108 names. 

Islam: The number 108 is used in Islam to refer to God. 

Jain: In the Jain religion, 108 are the combined virtues of five categories of holy ones, including 12, 8, 36, 25, and 27 virtues respectively. 

Sikh: The Sikh tradition has a mala of 108 knots tied in a string of wool, rather than beads. 

Buddhism: Some Buddhists carve 108 small Buddhas on a walnut for good luck. Some ring a bell 108 times to celebrate a new year. There are said to be 108 virtues to cultivate and 108 defilements to avoid. 

Chinese: The Chinese Buddhists and Taoists use a 108 bead mala, which is called su-chu, and has three dividing beads, so the mala is divided into three parts of 36 each. Chinese astrology says that there are 108 sacred stars. 

Stages of the soul: Said that Atman, the human soul or center goes through 108 stages on the journey. 

Meru: This is a larger bead, not part of the 108. It is not tied in the sequence of the other beads. It is the quiding bead, the one that marks the beginning and end of the mala. 

Dance: There are 108 forms of dance in the Indian traditions. 

Praiseworthy souls: There are 108 qualities of praiseworthy souls. 

First man in space: The first manned space flight lasted 108 minutes, and was on April 12, 1961 by Yuri Gagarin, a Soviet cosmonaut. 

Referenced from www.swamij.com

Why 108 ?

Dr     Koenraad ELST, Ph.D.

    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 6^th 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.

    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

            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

    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.

            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.

    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.

    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) http://koenraadelst.bharatvani.org/articles/misc/why108.html  

STILL INTERESTED? Magic squares and the origins of Math dating 1000BC

http://www.math.tamu.edu/~don.allen/masters/origins/1000bc.pdf