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Modeling the Five Elements Using Angles
In a sense, the Five Elements relationship between two elements can be understood as an angular distance on a circle. Therefore, if two elements are known, the angle between them can in fact be computed. If the clockwise angle from A to B is between 0 and 72 degrees, then B and A are in a mutual (companion) relationship in the Five Elements; if it is between 72 and 144 degrees, A generates B. This way, the generating and overcoming cycles are simulated. The difficulty here is how to codify this — computing the angle between two vectors. The Python code is as follows.
On the Expansion and Contraction of Earlier and Later Heaven
The numbers of the Earlier Heaven are taken from Qian one through Kun eight. But how are the numbers of Heaven and Earth derived? Forty-five serves as the center; the calculation is centered and upright. Earlier Heaven is so called because it reveals the subtle; therefore it takes the center, and its numbers root in nine and transform. -2.5 -3.5 0.5 -1.5 1.5 -0.5 3.5 2.5. If gains and losses are halved, this becomes even clearer; what is removed is four point five, divided into yin and yang halves, so the total is nine.
When the Night Arrives the Bright Moon Appears in Heaven; When the Wind Blows, the Sea-Moon Is Born
I ask why the Earlier Heaven Eight Trigrams are ordered as they are. Looking at the square and circular arrangements of the sixty-four hexagrams, Kun likewise comes first: the upper trigrams follow the order of Kun, Gen, Kan, Xun, Zhen, Li, Dui, Qian, while the lower trigrams begin with “the ruler comes forth in Zhen,” proceeding Zhen, Li, Dui, Qian, Xun, Kan, Gen, Kun—and from Xun to Kun they follow this same sequence. If we divide them by the two solstices, the yang escape goes from Kun to Qian and the yin escape from Qian to Kun; both may be used. Yet Heaven is honored and Earth is lowly, so taking Qian and Kun as the beginning and the end follows the usual convention. Though it follows that convention, there is also principle to it...
Heavenly Virtue
Mnemonic one: first month Ding, second month Kun palace, third Ren and fourth Xin the same, fifth Qian and sixth at Jia, seventh Gui and eighth Gen meet, ninth Bing tenth in Yi, Zi month Xun and Chou month Geng in between. Mnemonic two: first month Ding, second month Shen palace, third Ren and fourth Xin the same, fifth Hai sixth on Jia, seventh Gui eighth Yin follow, ninth Bing tenth in Yi, Zi month Si and Chou month Geng meet. Only Kun-Shen, Qian-Hai, and Xun-Si differ. Another note: Yimao records: “The star of Heavenly Virtue begins at Hai in the first month and proceeds forward; the virtue and grace of Heaven descend from the Heavenly Gate—Hai is the Heavenly Gate, hence the name. The Heavenly Stem Heavenly Virtue is established on Ding in Yin month and on Shen in Mao month; human affairs and Heaven’s work, yin and yang assisting each other...
Divination TheoryA Little Research on the Numbers of the Nine Palaces
Nine-palace rotation 1, 8, 3, 4, 9, 2, 7, 6: computing a sequence formula for this periodic sequence yields a very complex result: 1/8 cos(1/4 π (n - 8)) + 1/8 cos(1/2 π (n - 8)) + 1/8 cos(3/4 π (n - 8)) + 1/8 cos(π (n - 8)) + 1/8 cos(5/4 π (n - 8)) + 1/8 cos(3/2 π (n - 8)) + 1/8 cos(7…
Fitting Taiyi Accumulated Numbers to the Three-Yuan Nine-Period and Two-Yuan Eight-Period Calculations
According to Wang Ximing's "Taiyi Golden Mirror Formula," as recorded: in the Jia-Zi year of the twelfth year of Kaiyuan, the upper yuan's accumulated years amount to 1,937,281 counts. This places CE 724 at 1,937,281 counts; because antiquity had no zero count, 1 count is taken as Jia-Zi. If one wishes to correct by the sequential ordinal of Jia-Zi, the upper yuan accumulated years for CE 724 become 1,937,280, and CE year 0 is 1,936,556 counts. The Three-Yuan Nine-Period and Two-Yuan Eight-Period are both derived from this. For example, the Three-Yuan Nine-Period year 2004: 1,936,556 + 2004, divide by 20, then take modulo 9, yielding the eighth period—identical to the present Three-Yuan Nine-Period calculation. Also, 180 years is precisely the cycle of three yuan or two yuan...
Divination TheoryAnswering a Zhihu Question: Why Are There Five Phases?
Why five? Here the complex mathematical proof is omitted so readers are not put off; those interested may derive it themselves. Suppose there is a set G: if we compare its elements pairwise and wish to establish a model to express their relations of difference, what happens? When things are compared, pairwise comparison necessarily yields difference. If we use the rule: A differs from B, A is the same as B—and try to express the features of this set—what problems arise? Everything identical with a belongs to one class; everything different from a belongs to another. If we take identity as 1 and difference as 0, a sample set like this is formed. T = {0,1,1,0,0,1,1,...}. But if we set a=1, b=2, c=3 and compare a with abc, b with abc, and c with abc, we get Ta={1,0,0}, Tb={0,1,0}, Tc={0,0,1}. Obviously for Ta, b and c are identical—which is clearly wrong, because Tc does not accept that b and c are the same.
On the Nature of Line Positions in the Eight Trigrams
In mantic arts and divination, the nature of line positions in the Eight Trigrams is extremely important, and different trigram lines represent different meanings. They can abstract the essential features of things; by taking the intersection of the line positions of the Eight Trigrams, one can discern subtle points. If one grasps these subtleties, one can immediately grasp the key through yin and yang. Among these four trigrams whose first line is yin—Water, Wind, Earth, Mountain—when the second line is yang, there is added yang activity, so both wind and water have a yielding nature.
How Information is Compressed in the Divination Model
This article is merely a collection of trivial remarks to fill space; reading is not necessary. If one only seeks to understand things through hexagrams, a problem easily arises: since a hexagram is an abstraction of a thing, how can it be guaranteed to perfectly represent details or truly outline the most important main thread of the thing? There must be information compression within the hexagram, so when interpreting a hexagram, one is essentially releasing this compressed information. This compression includes the hexagram itself and the relationships between hexagrams and their lines. Between hexagrams, there are 384 types of changes. However, given the vast variety of things, their subtleties cannot be fully expressed by merely 384 types of changes. But
Divination TheoryThe Five Elements Are the Only Minimum Complete Set That Expresses the Relations
This text was published on Zhihu. The bold text below is an editorial note for clarity. Those who have studied the I Ching know that the Five Elements focus on describing the relationships between things, rather than discussing five separate elements. This is entirely different from the Western theory of basic elements. If you do not understand this, your reasoning will be wrong, and naturally, you will find it difficult to understand what the Five Elements are about. There are generating and overcoming relationships among the Five Elements. However, these generating and overcoming relationships also depend on the subject, which distinguishes between the subject and the object. Other answerers on Zhihu have reversed a relationship. It is not that the Five Elements exist first and then the relationships are discussed; rather, the relationships exist first, and then the Five Elements are discussed. This is why explanations can be unclear. Here, we deduce how the relationships of the Five Elements arise.
数论
天一地二人三，三三而九，九九八十一。一主日，日数十，日主人，人故十月而生。八九七十二，二主偶，偶以承奇，奇主辰，辰主月，月主马，马故十二月而生。七九六十三，三主斗，斗主犬，犬故三月而生。六九五十四，四主时，时主彘，彘故四月而生。五九四十五，五主音，音主猿，猿故五月而生。四九三十六，六主律，律主麋鹿，麋鹿故六月而生。三九二十七，七主星，星主虎，虎故七月而生。二九十八，八主风，风主虫，虫故八月而化。
The Principle of the Five Combinations of Heavenly Stems
"The Dunjia Jing states: 'Between Xu and Hai lies the division of Kui and Bi; between Chen and Si lies the division of Jiao and Zhen. Therefore, the Five Movements all originate from Jiao and Zhen. In the years of Jia and Ji, the Qi of the Yellow Heaven (Wu and Ji) passes through Jiao and Zhen...'
The Twelve Stages of Longevity: Developmental Phases of All Things
Since ancient times, traditional metaphysics has used Heavenly Stems and Earthly Branches to simulate the changes of all things, identifying twelve states for the Heavenly Stems within the Earthly Branches. Regarding the "Twelve Stages of Longevity," descriptions are often vague, leaving many unclear on their true meaning. The Twelve Stages of Longevity actually represent twelve states, with modern terms being: Conception, Nourishment, Birth, Bathing, Dressing, Official Position, Imperial Prosperity, Decline, Illness, Death, Tomb, and Extinction. Older classics differ slightly; for instance, the state of Tomb should correspond to Extinction, explaining the saying "finding life in a desperate situation is auspicious." The current popular description has drifted somewhat from the original ancient meaning.
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