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The number 108
There is a curious historical/cultural footnote to Jas's post about the precise size relationship of the sun and moon so as to bring about eclipses as we see them. I lived a long time in the India Subcontinent regions, and there the number 108 figures very large in cultural thinking. There are 108 beads in a Hindu priest's rudrushka (the equivalent of the western rosary first devised in 1440). When people donate money at charity events, it is not an even 100 rupees or whatever, but always 108. There are 108 tones in the Carnatic equivalent of the western musical octave. The Bharata Natyam 'classical' dance form (equivalent to ballet) has 108 postural poses and 108 finger flexions each with its own meaning. The number 108 figures prominently in astrological computation, especially as related to determining the auspices of a hopeful couple's wedding day based on their natal birthdays. It is a perplexing number to turn into a cultural icon—it doesn't fit in well as a prime number in base-8, decimal, or base-12 computations. Why has it such a strong hold on cultural thinking? One would think 64 in a base-8 or 144 in a base-12 system makes sense, but why 108? Then one day a Hindu astronomer told me that way back in India's history, somebody noticed the moon's average distance from the Earth is 108 times the moon's diameter and the sun's distance is also 108 times its diameter as seen from Earth. Today we know these proportions have no relation to the complex ellipses of real orbits, but I still marvel that so long ago in history, somebody managed to calculate what they observed in the moon and sun's diameter-orbit relationship and attributed to that number a profound mysticism.
I mention this only as a historical curiosity, and not as my idea of the vital force which gives astronomy its meaning.
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