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Re: Mystic 153 calendar

by irvin bromberg :: Rate this Message:

Am 07.06.2012 um 02:32 schrieb Helios:
A Himalayan monastery reckoned time by a calendar with a year divided into
153 parts called gongs. Every gong, a monk would strike the temple gong.
The lama was asked about this method of time-keeping. He explained that
seeing M months transpire after N gongs would portend that N months would
transpire after M years. In effect, the gong-lunar cycle is analogous to the
luni-solar cycle. What is the mean year of this calendar?

On 2012 Jun 7, at 06:14 , Sepp Rothwangl wrote:

sqr 153 = 235/19

Irv replies:

sqr 153 = 3 sqr 17

That is almost 0.0009 greater than 235/19, which seems like a good approximation -- but let's see how good it is. It is the number of months difference!

If that is the average number of months per year, and each month has a specified mean lunar month length, then the mean year can be calculated.

Taking 29+451/850 as a contemporaneously accurate mean month approximation (52 yerms), we have a mean year of:

(29+451/850) * 235 / 19 = 365 + 797/3230 = 365d 5h 55m 19+43/323s, which despite the accurate mean month is a rather excessively long mean year due to the inaccuracy of the metonic cycle.

Using sqr 153 instead of 235/19 we obtain about 365d 6h 33m 24.8s, which is more than 38 minutes longer!

Thus even though the metonic cycle is a poor accuracy lunisolar cycle, using sqr 153 as the average number of months per year yields a much poorer cycle.

The sqr 153 cycle would be much better as a lunisidereal cycle.

-- Dr. Irv Bromberg, University of Toronto, Canada

<http://www.sym454.org/>

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