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Replies: 86   Last Post: Jan 28, 2013 5:19 AM

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 Franz Gnaedinger Posts: 330 Registered: 4/30/07
Posted: Apr 9, 2012 4:51 AM

(intermezzo)

Mapping the River of Time - a lunisolar calendar
encoded in the Yellow River Map Ho-T'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.
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 Ho-T'u. A dragon-horse
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.
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

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 Ho-T'u was complemented by
the Magic Square Lo-Shu 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.

Date Subject Author
11/17/11 Franz Gnaedinger
11/17/11 Milo Gardner
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