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The Scope of the Tibetan Astro Sciences. The astro sciences of calendar-making, astronomy, astrology, and mathematics touch many aspects of Tibetan life. Their tradition spread from Tibet to so-called Outer and Inner Mongolia, Manchuria, East Turkistan, the Russian republics of Buryatia, Kalmykia, and Tuva, and all the other areas of Tibetan cultural influence in the Himalayas, Central Asia, and present-day China. These sciences play a significant role in the Tibetan medical tradition. All medical students must study to a certain level the astro sciences, although astro students are not required to study medicine. This topic of knowledge presents the calculations for the ephemeris to give the position of the planets, as well as those for making the calendar and predicting eclipses. It also includes the astrological calculations for personal horoscopes and for the information found in the yearly almanac concerning which days are auspicious or not for starting various activities such as planting crops. It is a very wide field of study. There are two divisions: white and black calculations. White and black stand for Indian and Chinesederived materials in accordance with the predominant color of the clothing traditionally worn in each country. As is the case with Tibetan medicine, Tibetan astrology shares aspects similar to those found in Hindu India and China. They are modified and blended, however, and used in different ways to constitute the unique Tibetan system. {Tibetan Astro Sciences}

The philosophical contexts of the astro sciences are quite different in the Indian Hindu, Tibetan Buddhist, and Chinese Confucian worlds. The Tibetan context derives from the Kalachakra Tantra. "Kalachakra" means "cycles of time." In this tantra, Buddha presented a system of external, internal, and alternative cycles. The external ones deal with the motion of the planets through the heavens and various cycles or divisions of time measured by them in terms of years, months, days, and so forth. The internal ones treat the cycles of energies and breaths through the body. The alternative cycles consist of the various meditation practices of the tantra system involving the Buddha-figure called Kalachakra, used to gain control over or purify the former two cycles. {Tibetan Astro Sciences}

Black Calculations. The element calculation system correlates the calendar to cycles of sixty years, with each year ruled successively by one of twelve animals. The classical Chinese order begins with the rat, whereas the Tibetan sequence starts with the fourth Chinese animal, the hare. Thus, the place in the sequence at which the sixtyyear cycle begins is different ... Magic-squares are also employed, specifically the one in which there is a grid of three by three, with the numbers one through nine arranged, one in each box, such that whether one adds horizontally, vertically, or diagonally, the sum of any line is fifteen. The nine numbers combine with the sixty-year cycle so that every 180 years the same magic-square number will correlate with the same element-animal year. The sequence begins with the number one, and then proceeds in reverse order: nine, eight, seven, and so on. {Tibetan Astro Sciences}

The basic structure of the calendar has symbolic information applied to it, from both Indian and Chinese systems, and the naming of the months - together with their other characteristics - is clearly a critical part of this. The calendar developed by Zhonnu Pal seems to have been the only one developed in Tibet for which descriptions survive that would have met with the approval of both Indian and Chinese calendar makers ... Once the months and their attributes are settled, further symbolic information is added to the calendar, for the years and days. From the Chinese system this consists of the five elements and the twelve animals, the eight trigrams (known from the I Ching) and the nine numbers, all cycling through the years, months and double-hours (there are twelve of these in single day). {Astrology associated with Kalacakra}

The first magic square in history was created in China by an unknown mathematician, probably sometime before the first century AD. Called the Lo Shu square, it is a magic square of 3 that was said to have appeared on the back of a turtle that came up out of the river. Lo Shu supposedly means "river map" and the story of the appearance of the turtle had to do with a sacrifice to the river god. Right from the beginning we are seeing an essentially mathematical construction combined with the supernatural. I have not found an analysis of the story of the turtle and the Lo Shu square from the point of view of folklore or mythology that would shed more light on the story. The Lo Shu square is later associated with the floor plan of a mythical palace, that of Ming'tang. Again, this is fragmentary, I have seen a diagram that shows the floor plan, but no explanation as to what the thinking about the square was, why it was used as a floor plan for a palace, or other information to flesh out the picture. The Lo Shu square is also connected to the I-Ching, though there is no explicit plan of correspondence that I know of. The oldest documents that refer to the Lo Shu square are ambiguous, but one reference lists a Shu Ching in 650 BCE who makes a reference to the "river map" which may be the magic square of 3. In 500 BCE, and 300 BCE, the river map is mentioned, but no explicit magic square is given. In 80 AD Ta Tai Li Chi gives the first clear reference to a magic square. In 570 AD Shuzun gives an actual description of a magic square of 3. Not until 1275 do we hear of the Chinese making squares of order larger than 3. Norman Biggs says that this is because the Chinese regarded the Lo Shu square as an object of the supernatural, rather than as an object of human curiosity, and it was therefore not a subject for study. {History of Magic Squares}

Early Heaven and Later Heaven. Before going any further with the discussion of the eight trigrams, a discussion of the terms "Early Heaven" and "Later Heaven" is appropriate. These concepts have very deep meaning in Chinese thought and I would be remiss if I did not address the subject before turning to a discussion of the Fu Hsi (Early Heaven) and King Wen (Later Heaven) trigram arrangements. (Note: The Chinese terms Hsien T'ien (Early Heaven or Pre-Heaven) and Hou T'ien (Later Heaven or Post-Heaven), which describe the two trigram arrangements, also have been translated conveniently to English as "prenatal" and "postnatal," respectively.) In general terms, Early Heaven represents innate energies and Later Heaven represents acquired energies. Innate, or prenatal energy is genetic and hereditary in nature--it is life energy that represents life potentiality, or the possibility of life manifestation. The acquired, or postnatal energy is created by the prenatal energies after the manifestation of life. In the human, postnatal energies are formed upon conception. Early Heaven energies are not strictly related to the human, but represent all environmental elements that are involved in conception of new life and these elements remain active in guiding the growth and maturation of that life. When the Early Heaven energy has been exhausted, life in its material form will typically end. Movement launched by the Early Heaven energy is developed and nourished by Later Heaven energy. Later Heaven energy is manifest the moment life is conceived and is sustained by the Early Heaven force and nourished by the environment through the intake of food and air. The Early Heaven energies form a foundation for the Later Heaven energies to build upon. {The Eight Trigrams of the I-Ching}

When looking at the Later Heaven (King Wen) arrangement, we read the progressive pattern along the periphery in a clockwise rotation. Reading the trigrams in a circular arrangement symbolizes the elements of infinity and continuity. The movement in this arrangement flows from the superficial qualities to deep qualities, from new life to maturation of life, and from the physical existence to the spiritual existence. Whereas the Early Heaven (Fu Hsi) arrangement is based on a balance of opposing forces representing a primordial order based in stillness and beyond space and time parameters, the Later Heaven arrangement depicts the development of life in the time-spaced conditioned world. {The Eight Trigrams of the I-Ching}

The banner also represents the Square of Saturn for, as Kali regularly destroys the world grown corrupt, so also at the end of the Aeon, Saturn will again eat all his children to clear the boards, so to speak, for the new creation. Thus the three-by-three format of the banner represents magic square of order three, which is known in Chinese philosophy as the Square of Lo-Shu, and in the West as the Square of Saturn. Although this figure has enormous esoteric significance, here we'll restrict our attention to it as a symbol of cosmic completeness organized around the key numbers 4 and especially 5. (See 4 and 5 in the Minor Arcana.) Five, of course, is the number of Chinese elements and the number of elements in the West when Spirit (or the Quintessence) is combined with the four mundane elements. First observe that every row, column and diagonal of the square sums to 15, which is the divine exaltation (3) of 5. Next observe that the basal number of the square is 5: it is at the center of the square (representing the Quintessence) and opposing numbers balance to two 5s (4+6, 9+1, etc.). In Pythagorean numerology 5 is the first complete number, since it is the first number to comprise both female (2) and male (3). (my emphasis) The central cross corresponds to the five odd numbers 13579, and the background to the four even numbers 2468. The four odd numbers on the boundary (1379) add to 20 = 4 X 5, as do the four even numbers; 20 combines the two numbers of completeness (4, 5). {XVIIII. Nuntius - Angelos - Angel}

Chinese knowledge of the Saturn Square is shown by the ground plan of the Ming-T'ang temple, which was built in A.D. 56. However, as Stapleton (Antiq. Alch. 15) says, "a much greater antiquity for this form of temple is indicated, firstly, by a temple of this plan being essential for Imperial worship, and, secondly, that in the 7th century B.C., during the time of the warring Lords, it was believed to have been used by Wu, the alleged founder of the Chou dynasty in 1025 B.C., when sacrificing to his ancestors. Moreover, if this tradition be correct, the Magic Square form of temple may ultimately be of Scythian origin, introduced at this time from Bactria, or ancient Iran, with the foreign mercenaries from the West, to whose help Wu owed his success in establishing a new dynasty." (From Bactria it may be traceable back to Mesopotamia.) The Ming-T'ang had twelve stations for the monthly "Proclamation of Space and Time." There is one station for each line segment on the perimeter of the square (or the banner), that is, two for each corner (even) square, one for each side (odd) square. The eight squares on the perimeter represent the eightfold year (3 = vernal equinox, 9 = summer solstice, 7 = autumnal equinox, 1 = winter solstice). The central square corresponds to the additional days of the year beyond the twelve lunar months represented by the twelve line segments of the outer squares. Thus the Son of Heaven visited the central room of the temple (numerically 5, the Emblem of the Center) at "the end of summer - a critical period when the transition was made from the yang seasons to the yin seasons" (my emphasis). Alternately, the twelve line segments of the perimeter can represent the solar year and the zodiac. Thus the representation of Time; the temple also represented Space by assigning 8+3 = east, 4+9 = south, 2+7 = west, 6+1 = north (the same four numbers as the elements, though not the same pairs of squares); opposing directions balance to 20, as do opposing elements. (Granet, Rel. Ch. 66-8; Stapleton, "Antiq. Alch.") Blofeld (I Ching, 218) says that mankind once understood how the Lo-Shu Square is connected with the (apparently illogical) Later Heaven Sequence of the I Ching, but that it has been forgotten and now only the gods know it. I certainly have not been able to find it. (The connection established by Hacker (41) seems to me to be contrived, although it is remarkable enough that any connection can be established at all.) {XVIIII. Nuntius - Angelos - Angel}

Illuminating the Eight Halls. The technique of residential fengshui known as Bazhai mingjing (Illuminating the eight halls), one of the most popular systems in use since the Qing dynasty, has been called the most obscure and difficult to understand of the different versions of the compass school. This is because there has never been a satisfactory explanation of the cosmological principles employed by this school, including, but not limited to, a justification for its apparently arbitrary assignment of good and bad fortune to the compass directions. This essay will first outline the rudiments of the technique as currently practiced, then suggest a possible derivation of its most baffling methodologies. {The Numerology of Nine Star Fengshui}

The Nine Stars and the Great Roving Year. The correlation of the luoshu numbers and bagua trigrams is the minimum requirement for conducting bazhai fengshui readings. A formula called the da you nian, "Great Roving Year" is the means by which number and trigram merge. First, the sequence of digits 1 through 9 is repeated 20 times to match three sixty-term, ganzhi cycles of 180 years called the sanyuan, "Tri-epoch." Since every year has a ganzhi designation, in the Tri-epoch everyone's year of birth has a digital correlate from 1 to 9. Each luo number has a unique trigram, derived from its houtian correlation (see fig. 2), so when the Tri-epoch digit is equated with the luo number, each person has a trigram that corresponds to his/her natal year. This is called the minggua, or the natal trigram, and it identifies the character of cosmic qi present at the person's birth. Finally, the natal trigram is paired with each of the eight directional trigrams in the houtian sequence (called zhaigua or hall trigrams). Each of the eight minggua therefore has a corresponding eight zhaigua, and these eight groups of eight trigrams complete the da you nian. This complement of a natal trigram and its set of hall trigrams represents a metaphysical interaction between the individual's natal qi and the qi of the environment that surrounds that individual. This conjunction is essentially thought of as a transformation of the minggua into the zhaigua and vice-versa (called biangua or bianyao), and each transformation is capable of generating good or bad fortune for the individual. The auspice generated by the conjunction is known as jiuxing, or the Nine Stars. {The Numerology of Nine Star Fengshui}

The provenance of the concept of Nine Stars is unknown, but the scant textual evidence suggests at the very least that it was religious in origin. The unusual nouns (see table 1 below) supposedly name the seven stars of Beidou, the Northern Ladle (Big Dipper), plus two secret "companions" to the penultimate star of the handle. There is a considerable body of legend attached to the stars of Beidou, which were recognized as deities by Daoist priests of the 4th century. {The Numerology of Nine Star Fengshui}

The Fortune of Five and the Hetu Key. The supposition of orthodox fengshui is that when the five phase value of the natal trigram is matched with the five phase value of the directional trigram, good fortune is indicated when the two exhibit a relationship of xiangsheng, or "mutual production," while bad fortune is indicated when the two exhibit a relationship of xiangke, or "mutual conquest." ... Up to now we have seen how the houtian trigrams correlate with the luoshu numbers to provide the characteristics of a person's natal qi. But the resolution of the mystery of auspice determination requires the juxtaposition of five factors, not just two. In order to facilitate the reader's comprehension of the numerology underlying bazhai fengshui, I have prepared a heuristic device in fig. 5, patterned after the early Han dynasty cosmograph (click on the link to the left to view the illustration). This numerical dial juxtaposes the following four factors: the xiantian and houtian sequences of trigrams, the luoshu numbers, and the directions. Around the inner dial are arrayed the xiantian trigram names with their luoshu correlates. On the square grid are arranged the trigrams of the houtian sequence, along with their luoshu numbers from the xiantian dial. On the outer square I have placed the cardinal directions. From just these factors, in other words, without five phase theories and their mutual orders, we can conduct fengshui readings as sophisticated as those outlined above. What makes this possible, however, is the fact that there lies embedded within this number dial one more hidden factor, the hetu system of numbers mentioned briefly above. More importantly, however, this board will reveal a most intriguing phenomenon that may have begun as a well-guarded secret centuries ago but was eventually forgotten. From a numerological standpoint good fortune always and without exception reveals itself as 5 or a multiply of 5. (author's emphasis) {The Numerology of Nine Star Fengshui}

There is considerable evidence, both immanent and historical, that the chinese I Ching and the Nma numogram share a hypercultural matrix. Both are associated with intricate zygonomies, or double-numbering systems, and process abstract problematics involving subdivisions of decimal arrays (as suggested by the Ten Wings of traditional I Ching commentary). Digital reduction of binary powers stabilizes in a six-step cycle (with the values 1, 2, 4, 8, 7, 5). These steps correspond to the lines of the hexagram, and to the time-circuit zones of the Numogram, producing a binodecimal 6-Cycle (which is also generated in reverse by quintuplicative numbering). In both cases a supplementary rule of pairing is followed, according to a zygonovic criterion (9-twinning of reduced values: 8:1, 7:2, 5:4, mapping the hexagram line pairs). The numogram time-circuit, or I Ching hexagam, implictly associates zero with the set of excluded triadic values. It is intriguing in this respect that numerous indications point to an early struggle between triadic and binary numbering practices in ancient chinese culture, suggesting that the binary domination of decimal numeracy systematically produces a triadic residue consistent with nullity. The hexagram itself exhibits obvious tension in this respect, since it reinserts a triadic hyperfactor into the reduced binodigital set (compounded by its summation to twenty-seven, or the third power of three). An ancient binotriadic parallel to the I Ching, called the T'ai Hsuan Ching (or Book of the Great Dark) consisted of eighty-one tetragrams, reversing the relation of foregrounded and implicit numerical values. The division of Lao Tse's Tao Te Ching into eighty-one sections suggests that this numerical conflict was an animating factor in the early history of Taoism. {Numogram and I Ching}

Usually Arabic ABJAD table (from now ‘ABJAD’) is arranged in Powers of 9 ... The ABJAD values of all levels are based on the connections between the ABJAD order and the ABJAD value of each letter at the first level (1-9) in which ABJAD value of each letter is equal to its ABJAD order ... all ABJAD (and values) and Arabic letters perfectly correspond to the 9 zones of the numogram. There is no redundancy or deficiency. {The ABJAD version of the Numogram | ABJAD Table (ABJAD-e Kabir) | ABJAD Installation of the Numogram (ABJAD-e Kabir)}

Links: The Classic of Magick Squares | Tibetan Astrology (Michael Erlewine) | The Parkha: Eight Trigrams of Tibetan Astrology | Magic square | Lo Shu Square

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