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The Evolution of the Heavenly Stems and Earthly Branches and the Transformation of Dun Jia: A Unified Mathematical Metaphysical Study of the Information Capacity in Bazi and Qimen Dunjia

This paper systematically investigates the information-carrying capacity of Bazi (Eight Characters) and Qimen Dunjia (Mystical Gates) as divination systems, starting from the mathematical structure of Taiji, Liangyi, Sixiang, and Bagua in the *Book of Changes*. By analyzing the classical mathematical foundations such as Yin-Yang, Five Phases, the River Chart, and the Luo Script, it aims to provide a unified perspective for measuring and comparing the information density of these two divination arts.

Tianwen Editorial Team February 7, 2026 85 min read PDF Markdown
The Evolution of the Heavenly Stems and Earthly Branches and the Transformation of Dun Jia: A Unified Mathematical Metaphysical Study of the Information Capacity in Bazi and Qimen Dunjia

Chapter 11: Information Capacity Verification in Historical Cases

Section 1: The Battle of Muye—Information Needs in Ancient Military Decision Making

The Shangshu, Oath of Muye records King Wu's oath before attacking Zhou:

"The King said: 'Alas! My allied feudal lords, magistrates, ministers of instruction (Sītú), ministers of war (Sīmă), ministers of works (Sīkōng), adjutants (Yǎlǚ), officers of the divisions (Shīshì), commanders of a thousand, commanders of a hundred, as well as the men of Yong, Shu, Qiang, Mao, Wei, Lu, Peng, and Pu peoples. Raise your spears, hold your shields, set up your spears; I shall now swear the oath.'"

King Wu's military decisions required the following information:

  1. Temporal Information: When to depart, when to arrive, when to engage.
  2. Spatial Information: Where to assemble, which route to march, where to deploy.
  3. Celestial Information: Whether the celestial signs were auspicious.
  4. Human Information: The morale of the troops, intelligence on the enemy.
  5. Geographical Information: The terrain of Muye.

These five categories of information—Time, Space, Celestial, Human, Geography—correspond exactly to the five layers of Qimen Dunjia: Shí Chén (Time), Nine Palaces (Space), Nine Stars (Celestial), Eight Gates (Human Affairs), Earth Plate (Geography).

Bazi can provide only the first category (Time) and the third (Celestial, indirectly via the Five Phases of the Stems and Branches)—it is insufficient to meet all information needs for military strategy.

The Shiji, Basic Annals of the Five Emperors records the divination before King Wu's attack on Yin:

"When King Wu attacked Yin, he first embarked a boat to cross the River. His army had three hundred war chariots, three thousand tiger guards, and forty-five thousand armored soldiers. While crossing the river, a white fish jumped into the King's boat... After crossing, a fire descended from above onto the King's roof, turning into a black bird whose color was red... Although the Yin army was numerous, none had the will to fight."

This record shows that King Wu received various "Heavenly Omens" (Tiānzhào) while crossing the river (white fish jumping, fire turning into a bird), which were interpreted as auspicious signs—an instance of "Heaven-Man Resonance" information transmission.

Case Analysis:

If we assume the moment of departure could be calculated into a Bazi chart, and a Qimen Dunjia chart could also be initiated.

Bazi information provided:

  • Five Phases strength/weakness at the time of departure.
  • Strength/Weakness of the Day Master.
  • Favorable direction inferred indirectly (Utility).
  • Trend of Great Cycles and Flowing Years.

Qimen Dunjia information provided:

  • The complete pattern of the chart at the time of departure.
  • The auspiciousness of each direction.
  • The optimal direction for advancement.
  • The state of the enemy (auspiciousness of the Guest Palace).
  • Favorable/unfavorable aspects of Heavenly timing (Heaven Plate information).
  • Advantages/disadvantages of terrestrial location (Earth Plate information).
  • Presence or absence of human accord (Man Plate information).
  • Warnings about unexpected factors (Spirit Plate information).

Clearly, Qimen Dunjia provides far more information than Bazi—especially in scenarios requiring comprehensive information like military strategy.

Section 2: The Battle of Chengpu—Example of Pre-Qin Military Divination

The Zuo Zhuan, Duke Xi Year 28 records the divination before the Battle of Chengpu between Jin and Chu:

"Marquis Jin dreamed of grappling with the Duke of Chu; the Duke of Chu pinned him down and scraped his brain, causing him to be frightened. Zifan said: 'Auspicious. We have received Heaven; Chu has pinned down its guilt, and we shall treat it gently.' "

Here, Zifan interpreted the ominous dream image ("pining down and scraping the brain") as auspicious by transforming it through "Images"—"receiving Heaven" and "Chu admitting guilt"—this is the flexible application of the multi-faceted nature of "Image."

Furthermore:

"Marquis Jin sent Buyan to divine; he said: 'Auspicious. It resembles the sign of the Yellow Emperor fighting at Banquan.'"

The tortoise divination yielded the sign of "Yellow Emperor fighting at Banquan"—this sign directly referenced the ancient battle against Chiyou, predicting that Marquis Jin would win like the Yellow Emperor. This method of "using ancient events to symbolize present events" adds a historical dimension to the information.

Furthermore:

"Zifan said: 'We fight. If we win quickly, we will certainly gain the allegiance of the feudal lords. If we do not win quickly, we have mountains and rivers guarding us internally and externally, and there will be no harm.'"

Zifan's judgment synthesized multiple pieces of information:

  1. Divination information (Auspicious omen).
  2. Geographical information (Mountains and rivers guarding Jin—a territorial advantage).
  3. Political information (Victory ensures allegiance of feudal lords).
  4. Risk assessment (Even if defeated, there is no major harm).

This pattern of multi-dimensional comprehensive judgment closely matches the multi-layer analysis of Qimen Dunjia.

The Zuo Zhuan also records specific tactics during the Battle of Chengpu:

"Jin's army had seven hundred chariots, fully equipped with harnesses and traces. The Marquis of Jin ascended the heights of You Shen to observe the army, saying: 'The young and old have proper rites; they can be used.' He then ordered wood to be cut to augment the troops. On the Day Ji Si, the Jin army formed up north of Shen; Xu Chen and others commanded the auxiliary forces against Chen and Cai. Ziyu, commanding the six battalions of the central army, said: 'Today, Jin shall surely be ruined!' Zixi commanded the left wing, Shangfu commanded the right wing. Xu Chen covered his horses with tiger skins and charged first against Chen and Cai. Chen and Cai fled, and Chu's right wing collapsed. Hu Mao set up two banners and retreated, while Luan Zhi ordered carts to drag burning wood in a feigned retreat. The Chu army charged; Yuan Zhen and Xi Zhen, commanding the central army's clansmen, attacked horizontally. Hu Mao and Hu Yan attacked Zixi's central army from both flanks, and Chu's left wing collapsed. The Chu army was routed."

The information processing in this battle was extremely detailed:

  • Temporal Information: "Ji Si" (Exact date—can be used to deduce Stems and Branches).
  • Spatial Information: North of Shen, Heights of You Shen (Specific terrain).
  • Military Strength Information: 700 chariots.
  • Morale Information: Young and old have proper rites.
  • Tactical Information: Horses covered in tiger skins, setting up banners to retreat, dragging burning wood in a feigned retreat, central army attacking horizontally, upper army attacking from flanks.

If analyzing this battle with Qimen Dunjia:

  • Day Ji Si—Value Symbol/Embodiment can be determined.
  • North of Shen—the direction corresponds to a specific Palace.
  • Direction of Jin army movement, location of Chu army—can be pinpointed on the Nine Palaces.
  • Auspiciousness of the Heaven Plate Stars—corresponds to the benefit of Heavenly timing.
  • Opening/Closing of the Eight Gates—corresponds to the appropriateness of action.
  • State of the Enemy (Guest Palace).
  • Unexpected factors (Spirit Plate).

If only analyzing with Bazi: One could only determine the strength/weakness of the Day Stem Ji Earth on that day, and the general auspiciousness of the day—far insufficient to guide specific tactical deployment.

This case clearly demonstrates that in military (action-oriented) scenarios, the information capacity and dimensions of Qimen Dunjia far exceed those of Bazi.

Section 3: The Battle of Xiao—The Interaction of Time-Space Information

The Zuo Zhuan, Duke Xi Year 32-33 records the Battle of Xiao between Qin and Jin.

Jian Shu's Warning:

"Jian Shu wept and said: 'Mengzi! I saw the army depart but have not seen its return.' The Duke sent someone to ask him: 'What do you know$8 If you are of middle age, the trees on your grave will already be fully grown!' Jian Shu's son was with the army. Jian Shu wept as he sent him off, saying: 'The Jin people will certainly ambush the army at Xiao. Xiao has two ridges: the southern ridge is the tomb of Gao of the Xia Dynasty; the northern ridge is where King Wen first sheltered from wind and rain. They will surely die between them. I will collect your bones there.'"

Jian Shu's judgment was precisely localized to a spatial orientation—"certainly at Xiao," "surely die between them"—this is not merely derived from temporal projections (though the day of departure could be analyzed for fortune), but relies more on spatial analysis (the dangerous terrain of Xiao).

This spatial judgment is precisely the strength of Qimen Dunjia—analyzing the auspiciousness/inauspiciousness of the Nine Palaces and Eight Directions.

The facts proved Jian Shu entirely correct—the Jin army indeed ambushed at Xiao, and the Qin army was annihilated.

Analyzing this from an information capacity perspective:

Information used by Jian Shu:

  1. Temporal Information: Unfavorable time of departure (possibly based on Stems/Branches).
  2. Spatial Information: Terrain of Xiao as a deadly location.
  3. Enemy Information: Jin would certainly set an ambush (based on political analysis).
  4. Comprehensive Judgment: Both time and space conditions are unfavorable; defeat is certain.

This comprehensive judgment based on four layers of information cannot be fully provided by a single arcane art—but Qimen Dunjia can provide most of the required elements (Time + Space + Enemy Intelligence—reflected by the auspiciousness of the Guest Palace), whereas Bazi can only provide part of the temporal dimension.

Section 4: The Exile of Chong'er—Validation of Fate Information

The Zuo Zhuan records the story of Duke Chong'er of Jin, who was exiled for nineteen years before returning to rule.

"When he reached Cao, Duke Gong of Cao heard of his fused ribs and wished to see him naked. After bathing, he looked at him thinly. The wife of Xi Fuzi said: 'I observe Duke Chong'er's followers; all are capable of being prime ministers. If you treat them as ministers, the Duke will surely regain his state. When he regains his state, he will surely attain influence over the feudal lords. If he punishes those without propriety, Cao will be the first. Why not attach yourself to him earlier$9'"

The wife of Xi Fuzi's judgment was based on "Human Image" (analysis of personnel information)—analysis of human talent and destiny, which has corresponding elements in the Bazi system (Bazi can infer a person's talent, destiny) and in Qimen Dunjia (auspiciousness of the Man Plate Eight Gates).

Chong'er's Bazi chart (if calculable) must necessarily show an extremely noble fate—the image of an emperor. And his nineteen-year exile, his Great Cycles must show a turning point from initial misfortune to later fortune. This type of "life trajectory" information is precisely the specialty of Bazi—Qimen Dunjia is not skilled in such long-term fate divination.

Thus, this case demonstrates: In the domain of long-term destiny (the pattern of a person's entire life), the information specialization of Bazi surpasses that of Qimen Dunjia. Although Qimen Dunjia has a larger total information volume, it is less profound in this specific area.

This leads to an important correction—the comparison of information capacity cannot only look at the total volume but must also consider the effective information capacity for a specific question:

  • On the question of "A person's destiny throughout life": Bazi's effective information capacity > Qimen Dunjia.
  • On the question of "Decision making for a specific time-space event": Qimen Dunjia's effective information capacity > Bazi.
  • On "Comprehensive questions concerning Heaven, Man, and Earth": The two arts each have their strengths, and the total volume is roughly comparable.