
Re: Ariadne's thread
Posted:
Apr 9, 2012 4:51 AM


(intermezzo)
Mapping the River of Time  a lunisolar calendar encoded in the Yellow River Map HoT'u of ancient China that inspired the I Ching or Book of Changes
The Stone Age way of counting lunations was to lay out pebbles, 30 29 30 29 30 29 30 ... pebbles for 1 2 3 4 5 6 7 ... lunations or synodic months.
15 and 17 lunations counted that way yield 443 and 502 days respectively, together 945 days for 32 lunations, doubled 1890 days for 64 lunations.
The Göbekli Tepe lunisolar calendar had a month of 30 days and a basic year of 12 months or 360 days. Add 3 days of midsummer and 2 days of midwinter and you get a regular year of 365 days. Add 3 midwinter days instead and you get an occasional leap year of 366 days.
63 periods of 30 days are 1890 days and correspond to 64 lunations, as found above. One lunation, calculated that way, lasts 29 days 12 hours 44 mintues, exact value 29 d 12 h 44 m 2.9 s. (average from 1989 AD), mistake of the ancient value less than one minute per lunation, or half a day in a lifetime.
Now for the River Map HoT'u. A dragonhorse emerged from the Yellow River Ho, bearing a map on its back: the Yang numbers 1 3 5 7 9 given in light circles and the Yin numbers 2 4 6 8 given in dark circles arranged in a square. Inner square 1 3 2 4 sum 10, outer square 6 8 7 9 sum 30, individual numbers given as lines of light or dark circles, beginning with 1 at the bottom of the inner square, in clockwise direction. The center is held by a domino five in light circles; below and above a line of five dark circles each, together the Yin number 10. (You may google for "river map" "i ching" in the sector Images for an illustration.)
The number 10 represents a basic year of ten periods of 36 days, in all 360 days. Add the vertical line of the domino five for 3 midsummer days and the remaining circles for 2 midwinter days and you get a regular year of 365 days. If you add instead the horizontal line of the domino five for 3 midwinter days you obtain an occasional leap year of 366 days.
25 years require 6 leap years (in all 9131 days). The number 6 is given as sum of the vertical line and horizontal line of the domino five (central circle counted twice). The number 25 is the sum of the Yang numbers 1 3 5 7 9.
The number 36 of the calendar period is the sum of the numbers 1 2 3 4 5 6 7 8. The square of 8 equals 64. Outer square of the River Map 6 8 7 9 sum 30. The product of the Yang numbers 7 and 9 equals 63, times 30 days 1890 days or 64 lunations or 2 by 2 by 2 by 2 by 2 by 2 lunations, mirrored in the cycle of 64 binary hexagrams in the I Ching.
64 lunations correspond to 63 periods of 30 days, 128 lunations to 126 periods of 30 days or 105 periods of 36 days, yielding the l/p ratio 128/105. Simpler ratios are 6/5 or 12/10 and 11/9. Generating additive number sequences of more l/p ratios:
6/5 (plus 11/9) 17/14 28/23 39/32 50/41 61/50 ...
Best value: 50 periods of 36 days for 61 lunations.
12/10 (plus 11/9) 23/19 ... 78/64 89/73 ...
Best value: 73 periods of 36 days for 89 lunations.
89/73 (plus 128/105) 217/178 345/283 473/388 ...
Best value: 388 periods of 36 days for 473 lunations, mistake not even six seconds per lunation, a good hour in a lifetime.
The period of 36 days offers many practical, good, very good and excellent values for counting lunations over long periods of time  mapping the river of time, as it were.
(The River Map is a reconstruction. I'd like to make a suggestion: instead of halving the Yin number 10 one might arrange it as a circle around the domino five. Outer square 20 by 20, inner square 16 by 16, diameter of a small circle 1, distance between the centers of two small circles on a straight line 2, radius of the circle of the basic year 4, diameter 8, outer diameter 9, inner diameter 7  my drawing looks fine.)
The River Map HoT'u was complemented by the Magic Square LoShu on the back of a tortoise that also emerged from the Yellow River Ho:
4 9 2 3 5 7 8 1 6
5 heaven (domino five)
1 north and winter and water 3 east and spring and wood 9 south and summer and fire 7 west and autumn and metal
2 earth 4 wood 6 metal 8 earth
The Magic Square is a world map and includes time insofar as the cardinal directions are linked with the four seasons of the year.

