Page 3.

Spheres of 64 hexagrams of the Chinese Book of Changes i-ching. The third page shows five spheres or spatial arrangements in which hexagrams of the Book of Changes i-ching are compared to astrological circle of zodiac signs and five substances of Chinese philosophy. And also third page shows numerical mathematical ratio according to which spatial spheres and consecutive order of hexagrams i-ching are organized in the Chinese Book of Changes. Information of this page can be interesting for academic scientists whose sphere of interests is occult philosophy and culture of ancient China, and also for independent researchers who are interested in esoteric  knowledge of Chinese astrology and numerology. Because the question about consecutive order of 64 hexagrams i-ching in the Chinese Book of Changes is one of the most mysterious and inexplicable in modern occultism, and also in the academic sinology science which studies culture and philosophy of ancient China.

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Spheres of hexagrams and astrological circle.
Sequence of symbols in the Book of Changes.

In addition to annual chronological cycle of the sun and geodetic lines of terrestrial globe it is possible to correlate hexagrams of the Book of Changes i-ching to traditional Chinese chronologic system or otherwise to tell classical cyclic calendar which has duration of 60 years which are connected with 12 zodiacal animals. Namely with the cyclic Chinese calendar in which twelve zodiacal animals are interconnected with five substances, that in the sum is a basis of 60-years chronological cycle, as 12x5=60.
Because sixty hexagrams within the logic system of binary symbols of the Chinese Book of Changes form five spheres which correspond with five 12-years chronological periods. And four hexagrams with serial numbers 1, 2, 63, 64 form a cross outside of chronological cycle, that is shown on the chart.

Cross of hexagrams i-ching symbolizes four geographic directions or spatial coordinates, and also four world elements from the view point of astrology and classical Greek philosophy. Ground - north - winter - 1st hexagram consists of three digrams in which all lines are entire, that corresponds to number 9 of Chinese numerology. Air - south - summer - 2nd hexagram consists of digrams in which all lines are break, that corresponds to number 6 of Chinese numerology. Water - west - autumn - 63rd hexagram consists of digrams in which top lines are break and bottom are entire, that corresponds to number 8 of Chinese numerology. Fire - east - spring - 64th hexagram consists of digrams in which top lines are entire and bottom are break, that corresponds to number 7 of Chinese numerology.

Sixty hexagrams i-ching in five spheres symbolize five substances of Chinese philosophy, that is shown on following charts.
Dark figures on charts specify serial numbers of hexagrams according to sequence in the Book of Changes, and white figures in dark circles correspond to numerical values. And also these charts show physiognomic symbols of human facial emotions which correspond with hexagrams i-ching.

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Hexagrams of the Chinese Book of Changes i-ching in the shown five spheres correspond with zodiac signs and astrological circle which symbolizes current of time, or otherwise to tell celestial movement of heavenly bodies and sequence of historical events.
Ratio of hexagrams with zodiac signs and astrological circle are certain by physiognomic symbols of human facial emotions. Namely spheres are organized according to ratios of physiognomic symbols with quarters or quadrants of astrological circle.
Spring quarter of astrological circle - zodiac signs Aries,Taurus, Gemini - joyful emotions of eyes.
Summer quarter of astrological circle - zodiac signs Crab, Leo, Virgo - open emotional expressions of eyes.
Autumn quarter of astrological circle - zodiac signs Libra, Scorpio, Sagittarius - sad expressions of eyes.
Winter quarter of astrological circle - zodiac signs Capricorn, Aquarius, Pisces - quiet emotions of eyes.
Emotional expressions of eyebrows and mouth in the shown charts too are organized according to rules of astrology, namely according with ratio of zodiacal signs with triangles which correspond to four elements or have angular sizes of 150x60x150 degrees.
For example, emotional expressions of eyebrows and mouth in the fifth sphere correspond with zodiacal signs as shown in following two charts.

Left chart - emotional expressions of eyebrows.
Joyful eyebrows - red triangle - zodiacal signs of fire element: Aries, Leo, Sagittarius.
Quiet eyebrows - dark triangle - signs of zodiac in ground element: Taurus, Virgo, Capricorn.
Sad eyebrows - green triangle - zodiacal signs on element of air: Gemini, Libra, Aquarius.
Open eyebrows - blue triangle - zodiac signs of water element: Crab, Scorpio, Pisces.
Right scheme - emotional expressions of a mouth.
Sad mouth - red triangle - signs of zodiac Aries, Virgo, Scorpio.
Quiet mouth - blue triangle - signs of zodiac Crab, Sagittarius, Aquarius.
Joyful mouth - green triangle - signs of zodiac Libra, Pisces, Taurus.
Open mouth - dark triangle - signs of zodiac Capricorn, Gemini, Leo.
Physiognomic symbols of human emotions in different spheres correspond with triangles of zodiacal signs differently.
It is impossible to formulate logical principle according to which hexagrams i-ching and corresponding physiognomic symbols of facial emotions are organized in spatial spheres and are compared to zodiacal signs. But this logical principle can be seen on following charts where numerical values of 64 hexagrams in cells of a magic square are shown. Namely grey color specifies positions of hexagrams of five spheres in cells of a magic square.

First and fifth spheres have mathematical sums of numerical values 316 and 464, that in aggregate forms number 316+464=780.
Second and fourth spheres have mathematical sums of numerical values 476 and 304, that too forms total number 476+304=780.
Third sphere has mathematical sum of numerical values 402. But if to add to the third sphere numerical values of four hexagrams which form a cross outside of chronological cycle of five spheres then total number is 402+1+25+50+42=520.
Numbers 520 and 780 correspond with mathematical sums of numerical values on verticals and horizontals of magic square, as 520/2=260 and 780/3=260.
Number 260 corresponds to quantity of days in the chronological cycle of Tzolkin in the ritual or sacral calendar of Mayan civilization.
Look information about 260 days of the chronological cycle Tzolkin in Mayan calendar within other website www.wordgame.64g.ru on the seventh page in section which is named as letters of gods.
If other so-called associative magic square will be used then mathematical sums of numerical values in five spheres will be ideal, that is shown on the following chart.

Numbers symmetric concerning the center in the associative magic square form identical sums. For example, 01+64=65 or 29+36=65, also mathematical sums of numbers in all spheres have size 390 or otherwise to tell are ideal, that differs from the previous usual magic square.
Also pay attention that opposite hexagrams and physiognomic symbols in five spheres correspond to numbers which are symmetric concerning the center in the associative magic square.
The shown associative magic square can be applied instead of usual in the conjectural mantic game which is presented on pages of this website, also for analyses of mathematical laws according to which traditional sequence of 64 hexagrams of the Chinese canon i-ching is organized. But it is necessary to consider that ratio of numbers of the usual magic square with serial numbers of hexagrams i-ching allow to see mathematical laws which are unobvious according to numbers of associative rectangular digital matrix of magicians.
Or it is possible to tell that comparative analyses of logic ratios of diverse magic squares with serial numbers of hexagrams i-ching allow to see mathematical laws according to which structural sequence of the ancient Chinese Book of Changes is organized.
Also serial numbers of 64 hexagrams of the Chinese Book of Changes i-ching form mathematical laws according to which five spheres are organized. Namely if 64 hexagrams are located in cells of a magic square according to numerical values then serial numbers form total numbers which are shown on following charts.

Mathematical sums of serial numbers in the second and fourth spheres are 409.
Mathematical sums of serial numbers in the first and fifth spheres are 444 and 374. But in the first and fifth spheres there are especial numerical ratios.
444-374=70/2=35.
444-35=409.
374+35=409.
Mathematical sum of serial numbers in the third sphere is 314. But if third sphere has addition of serial numbers of four hexagrams which form a cross then total sum is equal to the cipher of first sphere, as 1+2+63+64=130+314=444.
These numerical ratios allow to speak that the shown spatial spheres correspond to mathematical laws according to which sequential order of 64 hexagrams of the Chinese Book of Changes i-ching is constructed. And also these numerical ratios allow to speak that consecutive order of hexagrams i-ching in the Chinese Book of Changes is not casual.
Because symbols of i-ching in five spheres are organized according to quarters of astrological circle. And also according with triangles which correspond to four elements or have angular sizes of 150x60x150 degrees within astrological circle, and as a result numerical values of hexagrams form regular ciphers or natural figures which correspond with mathematical sums of numbers on verticals and horizontals of magic square. And also serial numbers of hexagrams i-ching in five spheres form regular ciphers or natural numerical ratios as a result of coordination with astrological circle and magic square.
I cannot explain the law or logic principle according to which consecutive order of hexagrams i-ching in the Chinese Book of Changes is constructed. I only pay your attention that the sequence is not casual.
It is a question of sequence which has been established by legendary King Wen, or which has been received by the Chinese civilization from other unknown sources.

Following page shows parities of hexagrams of the Book of Changes i-ching in five spheres with zodiacal circle of twelve animals which form chronological cycle of traditional Chinese calendar and astrology.

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On other pages in this section of website it is possible to find information about natural phenomena and atmospheric processes, geodetic lines of the Earth and primordial deities of Egyptian cosmology, chronology of New Age and celestial birth map of French artist, constellations and stars of heavenly sphere, precious gem stones and minerals, divination charts of Lian Shan and Gui Cang.

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