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 Franz Gnaedinger Posts: 330 Registered: 4/30/07
Posted: Apr 10, 2012 7:01 AM

(intermezzo, second part)

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 summmer,
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 8.

7 8 9 play a role in the old lunisolar calendar that goes
back to the era of the Göbekli Tepe: 7 x 9 periods of
thirty days correspond to 8 x 8 lunations.

7 8 9 also play a role in practical methods of squaring
a 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. A small drawing shows
a 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. The area of the square is 9, the one of
the quasi-circle 7. Also the numbers 1 2 3 4 5 6 7 8 9
of the Magic Square fill a grid of 3 by 3 small 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.

The Egyptians of the Old Kingdom developed
a systematic method for calculating 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. 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 of the Magic
Square, and again by the oblique cross of the
Yin numbers 2 4 6 8 around the heavenly 5.
Add the number 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 name the circle of hexagrams
in the I Ching. There is a rational core in the
Chinese instrument of divination.

Date Subject Author
11/17/11 Franz Gnaedinger
11/17/11 Milo Gardner
11/18/11 Franz Gnaedinger
11/18/11 Milo Gardner
11/19/11 Franz Gnaedinger
11/19/11 Milo Gardner
11/20/11 Franz Gnaedinger
11/20/11 Milo Gardner
11/20/11 Milo Gardner
11/21/11 Franz Gnaedinger
11/22/11 Franz Gnaedinger
11/22/11 Milo Gardner
11/23/11 Franz Gnaedinger
11/24/11 Franz Gnaedinger
11/24/11 Franz Gnaedinger
11/24/11 Franz Gnaedinger
11/24/11 Milo Gardner
11/25/11 Franz Gnaedinger
11/26/11 Franz Gnaedinger
12/2/11 Franz Gnaedinger
12/2/11 Milo Gardner
12/3/11 Franz Gnaedinger
12/4/11 Franz Gnaedinger
12/4/11 Milo Gardner
12/5/11 Franz Gnaedinger
12/5/11 Milo Gardner
12/7/11 Franz Gnaedinger
12/8/11 Milo Gardner
12/10/11 Franz Gnaedinger
12/12/11 Franz Gnaedinger
12/12/11 Milo Gardner
12/13/11 Franz Gnaedinger
12/13/11 Milo Gardner
12/15/11 Franz Gnaedinger
12/15/11 Milo Gardner
12/15/11 Milo Gardner
12/16/11 Franz Gnaedinger
12/16/11 Milo Gardner
12/18/11 Franz Gnaedinger
12/18/11 Milo Gardner
12/19/11 Franz Gnaedinger
12/20/11 Franz Gnaedinger
12/20/11 Milo Gardner
12/21/11 Franz Gnaedinger
12/22/11 Franz Gnaedinger
12/23/11 Franz Gnaedinger
12/24/11 Franz Gnaedinger
12/29/11 Franz Gnaedinger
1/2/12 Franz Gnaedinger
1/3/12 Milo Gardner
1/4/12 Franz Gnaedinger
11/28/11 Velev, Petyr
1/6/12 Franz Gnaedinger
1/6/12 Milo Gardner
1/9/12 Franz Gnaedinger
1/17/12 Franz Gnaedinger
1/19/12 Franz Gnaedinger
1/19/12 Milo Gardner
1/27/12 Franz Gnaedinger
2/10/12 Franz Gnaedinger
2/28/12 Franz Gnaedinger
3/2/12 Franz Gnaedinger
3/23/12 Franz Gnaedinger
3/24/12 Milo Gardner
4/9/12 Franz Gnaedinger
4/10/12 Franz Gnaedinger
4/13/12 Franz Gnaedinger
4/17/12 Franz Gnaedinger
4/18/12 Franz Gnaedinger
4/18/12 Franz Gnaedinger
5/5/12 Franz Gnaedinger
5/7/12 Franz Gnaedinger
5/7/12 Milo Gardner
5/8/12 Franz Gnaedinger
5/8/12 Milo Gardner
5/8/12 Franz Gnaedinger
5/8/12 Franz Gnaedinger
5/9/12 Franz Gnaedinger
5/10/12 Franz Gnaedinger
8/14/12 Franz Gnaedinger
1/13/13 Franz Gnaedinger
1/19/13 Franz Gnaedinger
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1/28/13 Franz Gnaedinger