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.