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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: May 8, 2012 3:11 AM

River Map Ho-T'u and Magic Square Lo-Shu
of Early China (revised and illustrated version)

3) River of Time and Change

Where is the river in the Yellow River Map?

I explained how the Yin number 10 can be arranged as
a circle around the domino five in the center of the map.
Now imagine that circle in motion, turning in clockwise
direction, round and round, making the seasons change,
from winter to spring to summer to autumn, from cold
to warm to hot to cool, bringing about changes of every
sort, as the waters in a river rise and sink and rise in
perpetual motion.

The number 10 of the river circle is also the sum of the
pairs opposing each other via the heavenly domino five
in the Magic Square

4 9 2
3 5 7
8 1 6

1 and 9, north and south, winter and summer, water and fire;
3 and 7 east and west, spring and autumn, wood and metal;
4 and 6, wood and metal; 2 and 8, earth. East and west also
invoke morning and evening. Wood and metal are organic
and anorganic materials. Earth makes the plants grow and
in turn takes up the fallen leaves. Consider also the colors,
the yellow of dawn and violet of dusk, blue water and orange
fire, green leaves and rusty red iron ore, turning into a glowing
red when molten with fire made of wood ? The elements of
the Magic Square, paired in opposites, evoke a host of
meanings.

We could say that the eight numbers around the heavenly
domino five in the center of the Magic Square are the frozen
River of Time and Change that flows around the domino five
in the center of the River Map.

Here again the numbers of the modified reconstruction of
the Ho Map: outer square 20 by 20, inner square 16 by 16,
diameter of a small circle 1, distance of the centers of two
adjacent small circles on a straight line 2, radius of the river
circle 4, diameter 8. Those are middle numbers, relevant
for the positions of the centers of the small circles. 8 is the
middle diameter of the river circle. The outer diameter is 9,
the inner diameter 7.
http://www.seshat.ch/home/china03.GIF

7 8 9 play a role in practical methods of squaring the circle
in the Rhind Mathematical Papyrus of Ancient Egypt. A circle
of diameter 9 and a square of side 8 have practically the
same area.
http://www.seshat.ch/home/china04.GIF
A small drawing shows a square with a virtual or imaginary
grid of 3 by 3 squares whose corner squares are halved
along diagonals, generating a quasi-circle, an octagon
that is close to the circle inscribed in the square 3 by 3.
Also the numbers 1 2 3 4 5 6 7 8 9 of the Magic Square
fill a grid of 3 by 3 squares. Their sum is 45. Halve the
numbers of the corner squares 2 4 6 8 and the sum is
reduced to 35. The ratio 45 to 35 equals 9 to 7.
http://www.seshat.ch/home/china05.GIF

The Egyptians of the Old Kingdom developed a systematic
method for the calculation of the circle on the basis of the
Sacred Triangle 3-4-5. The numbers of this triangle are
prominent in the River Map: 3 on the left side of the inner
square, 4 on the right side of the inner square, 5 in the center.
http://www.seshat.ch/home/china06.GIF
The first Egyptian circle of radius 5 in the square 10 by 10
is defined by the triple 3-4-5 that marks 8 rational points
of the circumference. The second circle of radius 25 is
defined by the triple 15-20-25, enlarged version of the basic
triple 3-4-5, and the new triple 7-24-25 that marks 8 more
points of the circumference. And so on. Every multiplication
by a factor of 5 yields one more triple that marks 8 more points
on the circumference. Now the numbers 5 and 8 and 10 are
present in the River Map and the Magic Square. The number
25 is given by the sum of the Yang numbers of the cross
1 3 5 7 9, and again by the oblique cross of the Yin numbers
2 4 6 8 around the heavenly 5. Add the numbers 25 of the one
cross and the number 25 of the other cross and you get 50.

While the calendar concerns time, the squaring of the circle
concerns a change of form, a shift of shape, justifying the
?River of Time and Change? that could also have named
the circle of hexagrams in the I Ching. There is a rational
core in the Chinese instrument of divination.

(to be continued)

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