Why do we chant mantras 108 times?

At the Yoga Australia teacher's retreat in South Australia recently we took the opportunity to chant the Gayatri Mantra 108 times. This is a traditional practice which is why there are 108 beads on a mala. The fingers are run over the beads to facilitate counting while chanting. There is also a tradition in yoga of doing 108 sun salutations.

The question arose later in conversation, why 108? What is it about 108 that makes it chosen as the number of times to chant a mantra or  do sun salutations?

108 is a number that is ascribed mystical significance in Indian traditions but other traditions as well. Here are some attributions:

• The deities of Hinduism often have 108 names. 
• There are 54 letters in the Sanskrit alphabet; with each letter being attributed with a masculine and a feminine aspect, or more accurately Shiva and Shakti, 54 x 2 = 108. 
• There are said to be 108 Gopis or servants of lord Krishna
• In symbolic terms 1 stands for the one Universal Consciousness from which all arises; 0 stands for completeness or perfection which is also fully spacious (empty, void) that is the goal of the spiritual path; 8 stands for Infinity (laid on its side it is a universal symbol for infinity
• In numerology 9 is considered the number of completion and 12 is the cosmic number. their product 9 x 12 = 108, 108 is the Universal number
• 1+0+8 = 9; in numerology 9 represents unconditional love
• Some schools of Buddhism say there are 108 feelings, multiplying the six senses of taste, hearing, smell, sight, touch and consciousness by the three attributes of  painful, pleasant or neutral, multiplied again by the two factors of whether they are internally or externally generated, and again by the three time divisions of past, present or future. 6 x 3 x 2 x 3 = 108
• 18 is a revered number in Judaism. Gifts and charitable donations are given in multiples of 18 (18 x 6 = 108) and in the number 108 the fullness of zero sits inside 18.
• Many Buddhist temples have 108 steps

But none of this really satisfactorily explains why.

The ancient Indians were keen astronomers (and astrologers) and great mathematicians, so I wondered if all the magical mystical significance comes about due to their understanding of the maths and science of it. And it turns out that there are indeed some pretty amazing things about 108 when we turn to science and mathematics. Like this:

• The average distance of the earth from the sun is 108 times the diameter of the sun
• The average distance of the earth from the moon is 108 times the diameter of the moon

At least it would have been as far as the ancients could observe and calculate it - with modern instruments and computers it is a bit off, but still, I am already going wow!

Now for the mathematics.  I have to admit to quite a lot of  "glazing over" when researching this for I am not noted as a mathematician. But it turns out to be a pretty cool maths idea too. See if you can get your head around these:

• 1¹ x 2² x 3³ = 108 (1 x 4 x 27 = 108) - that is called hyperfactorial. But wait there's more!
• 108 is a refactorial number meaning that it is divisible by the count of its divisors, that is it has 12 divisors, 1 and 108, 2 and 54, 3 and 36, 4 and 27, 6 and 18, 9 and 12, and it is divisible by 12
• The measure in degrees of the internal angle of a regular pentagon is 108 (Euclidean space) - this relates back to metaphysical excitement about the number as pentagons are also considered a magical shape.
•  2 sin (^108°/₂) = ᵩ (the Greek symbol phi which means the golden ratio )

• Apparently it is also a "self number", an "abundant number", a "semi-perfect number" and a "tetranacci number" but this about where my mathematical capabilities resulted in a headache.

I do not know if all of this has resulted in an answer, really, as to why we chant the mantras 108 times and do 108 sun salutes, or why the deities have 108 names, however with such an amazing number, why not?

Many thanks to my daughter Chaitanya Shettigara for her mathematical input ... she actually does understand it all and was most helpful in researching this article.