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

Part Three: Metaphysical Unification

Chapter 9: Information Capacity from the Viewpoint of the Heavenly Way

Section 1: The "Great Information Capacity" of the Heavenly Way

Chapter 25 of the Laozi states:

"There exists a thing, undifferentiated, born before Heaven and Earth. Silent! Empty! It stands alone and does not change; it circulates eternally and is never exhausted. It can be the mother of all under Heaven. I do not know its name; I style it the Dao. If I am forced to name it, I call it the Great (Dà). Great implies passing; passing implies distance; distance implies returning." (Yǒu wù hùnchéng, xiān tiāndì shēng. Jì xī liáo xī, dúlì ér bù gǎi, zhōuxíng ér bù dài, kěyǐ wéi tiānxià mǔ. Wú bùzhī qí míng, zì zhī dào, qiǎng wéi zhī míng yuē dà. Dà yuē shì, shì yuē yuǎn, yuǎn yuē fǎn.)

The Dao is "Great" (Dà); the meaning of "Great" lies not just in magnitude, but in the infinity of its information. "Stands alone and does not change"—the information of the Dao is constant, incompressible; "circulates eternally and is never exhausted"—the information of the Dao is cyclical and endless.

All arcane arts—Bazi, Qimen Dunjia, Liuren, Taiyi...—are partial extractions and encodings of the Dao's information. They extract from different "angles," with different "precisions," and cover different "ranges," but none can exhaust the entire information of the Dao.

Chapter 1 of the Laozi states:

"The Dao that can be told is not the eternal Dao. The name that can be named is not the eternal Name. Nameless is the beginning of Heaven and Earth; named is the Mother of the myriad things." (Dào kě dào, fēi cháng dào. Míng kě míng, fēi cháng míng. Wú míng tiāndì zhī shǐ, yǒumíng wànwù zhī mǔ.)

The Dao that "can be told" is not the "eternal Dao." Any arcane art is a "tellable Dao"—a finite information encoding system—not the entirety of the "eternal Dao."

Therefore, from the perspective of the Heavenly Way, the comparison between Bazi and Qimen Dunjia is like comparing a dipper and a bushel in measuring the ocean—both are finite.

But even within the finite, there are differences in size. Our comparison aims to distinguish this difference in "finitude."

Section 2: Temporality and Spatiality of the Heavenly Way

The operation of the Heavenly Way includes both temporality and spatiality.

Temporality—the "Movement" (Xíng) of the Heavenly Way:

The Book of Changes, Qian Trigram, Image Commentary states:

"The movement of Heaven is vigorous; the superior man strives ceaselessly." (Tiānxíng jiàn, jūnzǐ yǐ zìqiángbùxī.)

"Heaven's movement" (Tiān xíng)—the ceaseless circulation of Heaven, which is the passage of time.

The "Canon of Yao" (Yao Dian) in the Book of Documents—"calculate the ephemerides of the sun, moon, and stars, and diligently present the proper times to the people"—the essence of the calendar is the encoding of the temporal information of the Heavenly Way.

Spatiality—the "Position" (Wèi) of the Heavenly Way:

The Book of Changes, Kun Trigram, Image Commentary states:

"The disposition of Earth is yielding; the superior man supports all things with deep virtue." (Dì shì kūn, jūnzǐ yǐ hòudé zài wù.)

"Disposition of Earth" (Dì shì)—the configuration of the Earth, which is the expanse of space.

Bazi mainly encodes the temporality of the Heavenly Way ("Heaven's Movement"), while Qimen Dunjia encodes both the temporality and spatiality of the Heavenly Way ("Heaven's Movement" + "Earth's Disposition").

From the perspective of the Heavenly Way, temporality and spatiality are equally important aspects—neither can be omitted.

The Xici Zhuan states:

"Images are formed in Heaven, and forms take shape on Earth; transformations are thereby revealed." (Zài tiān chéng xiàng, zài dì chéng xíng, biànhuà jiàn yǐ.)

"Heavenly Images" (Tiān Xiàng) primarily relate to time (movements of the sun, moon, stars); "Earthly Forms" (Dì Xíng) primarily relate to space (distribution of mountains and rivers). "Transformation" (the generation and flow of information) must be revealed through the interaction of Heavenly Images and Earthly Forms.

Pure temporal information (Bazi) is like "Images formed in Heaven" but not yet "Forms taken shape on Earth"—the transformation may not be fully revealed.

Information that includes both temporal and spatial information (Qimen Dunjia) is like "Images formed in Heaven" and "Forms taken shape on Earth"—the "transformation is revealed"—the manifestation of information is more complete.

This provides a metaphysical basis for judging the difference in information capacity between the two: Because Qimen Dunjia incorporates both temporal and spatial dimensions, its coverage of the information of the Heavenly Way is more comprehensive.

Section 3: Heaven-Man Resonance and Information Transmission

The concept of "Heaven-Man Resonance" (Tiānrén Gǎnyìng) in pre-Qin thought is essentially a theory of information transmission—the information of the Heavenly Way can be transmitted to human affairs.

The Shangshu, Hongfan records Jizi's words:

"If the King is solemn, timely rain will fall. If he governs, timely sunshine will fall. If he is clear, timely warmth will fall. If he plans, timely cold will fall. If he is sage, timely wind will fall. Signs of calamity: If he is wild, constant rain will fall. If he is presumptuous, constant sunshine will fall. If he is complacent, constant warmth will fall. If he is urgent, constant cold will fall. If he is obscure, constant wind will fall."

There is a correspondence between the King's actions (Solemn, Governing, Clear, Planning, Sage) and meteorological phenomena (Rain, Sunshine, Warmth, Cold, Wind)—this is the specific expression of "Heaven-Man Resonance."

From an information theory perspective, this "resonance" is the "transmission" of information—the information of human affairs is transmitted to celestial phenomena through some mechanism, and the information of celestial phenomena is transmitted to human affairs through some mechanism—the transmission mechanism is the resonance of "Yin, Yang, and the Five Phases."

The path of Heaven-Man Resonance in Bazi: Temporal information of the Heavenly Way (Stems/Branches at birth) $\rightarrow$ Innate Endowment of the individual (Bazi Pattern) $\rightarrow$ Trajectory of the individual's destiny.

This path is: Heaven $\rightarrow$ Man (Unidirectional, mediated by Time).

The path of Heaven-Man Resonance in Qimen Dunjia: Time-Space information of the Heavenly Way (Bureau number and chart layout at the time of initiation) $\rightarrow$ Current state of the event (chart analysis) $\rightarrow$ Future direction and optimal course of action.

This path is: Heaven $\leftrightarrow$ Earth $\leftrightarrow$ Man (Multi-directional, mediated by both Time and Space).

The information flow of a multi-directional path is greater than that of a unidirectional path—this also supports the conclusion that the information capacity of Qimen Dunjia is greater than that of Bazi.

However, it must be pointed out: the "unidirectional" path of Bazi is not truly unidirectional—the addition of Great Cycles and Flowing Years gives it a certain characteristic of dynamic feedback. It is just that this feedback mainly occurs in the temporal dimension and does not involve the spatial dimension.

Section 4: "Counting the Past is顺 smooth/forward, Knowing the Future is 逆 reverse"—The Directionality of Information

The Shuogua Zhuan states:

"Counting the past is smooth (shùn); knowing the future is reverse (nì); therefore, Yi uses reverse counting." (Shù wǎng zhě shùn, zhī lái zhě nì, shì gù yì nì shù yě.)

This speaks of the direction of information in the Book of Changes—"reverse counting" means inferring backward, deriving causes from results, and the present from the future.

The direction of information in Bazi is mainly "smooth"—starting from the time of birth, flowing forward through the Great Cycles and Flowing Years to predict future fortune. This is the application of "Counting the past is smooth"—using the established past (moment of birth) as a basis to project the future.

The direction of information in Qimen Dunjia is mainly "reverse"—starting from the present question, inferring the pattern of Heaven and Earth, and finding the optimal course of action. This is the application of "Knowing the future is reverse"—aiming at the unknown future, designing actions in reverse.

"Reverse" information capacity is generally greater than "smooth"—because "reverse" requires considering more possibilities (inferring multiple possible causes from one result), whereas "smooth" only follows a single path forward.

This again supports the conclusion that the information capacity of Qimen Dunjia is greater than that of Bazi from another angle.

Section 5: The Dao of the Three Powers and the Hierarchy of Information

The Xici Zhuan states:

"There is the Way of Heaven, there is the Way of Man, there is the Way of Earth. Combining the Three Powers and multiplying them by two, thus we have Six. The Six are nothing else but the Way of the Three Powers." (Yǒu tiāndào焉, yǒu réndào焉, yǒu dìdào焉. Jiān sān cái ér liǎng zhī, gù liù. Liù zhě fēi tā yě, sān cái zhī dào yě.)

The Three Powers—Heaven, Earth, Man—are the three fundamental layers of cosmic information.

The correspondence of the Three Powers in Bazi:

• Way of Heaven: Heavenly Stems of the Great Cycles/Flowing Years (external environmental changes).
• Way of Earth: Earthly Branches of the Four Pillars (material basis of innate endowment).
• Way of Man: The Day Master and the Ten Gods (the individual's subjectivity and social relations).

In Bazi, these Three Powers are "folded"—compressed within the Four Pillars of Stems and Branches, requiring the interpreter to unfold them.

The correspondence of the Three Powers in Qimen Dunjia:

• Way of Heaven: Heaven Plate (Nine Stars + Heaven Plate Qiyi).
• Way of Earth: Earth Plate (Nine Palaces + Earth Plate Qiyi).
• Way of Man: Man Plate (Eight Gates).

Adding the Spirit Plate, it can be considered "Four Powers": Heaven, Earth, Man, Spirit.

In Qimen Dunjia, these Three Powers (or Four) are "unfolded"—each has an independent plate, and the information layers are clearly distinguished.

The difference between "unfolded" and "folded" relates to the readability of information:

• "Unfolded" information is easy to analyze layer by layer, but the interactions between layers require separate inference.
• "Folded" information is hard to layer, but its internal integration is stronger.

In terms of information capacity, "unfolded" information is no less than "folded"—because the process of "folding" might result in information loss (like lossy compression). But if the "folding" process incurs no loss, its information capacity is equal to that of the "unfolded" state.

Does the "folding" of Bazi involve no loss$4

The answer is: Generally no loss—because the rules of Bazi interpretation can restore the information of the Three Powers from the folded state. However, certain subtle pieces of information might be obscured during folding—for instance, spatial information like "This person develops better in the East." Bazi might infer this indirectly through the strength of Wood, but it is not as explicit as the direct directional indication in Qimen Dunjia.

Thus, from the perspective of the Dao of the Three Powers: Qimen Dunjia has slightly superior information in the "Man" and "Earth" dimensions compared to Bazi, while in the "Heaven" dimension, they are comparable.

Chapter 10: Information Capacity as Seen Through the Methods of the Sages

Section 1: Fuxi Drawing Trigrams—The Original Information Encoding

The Xici Zhuan states:

"In the time when Bao Xi ruled the world, he looked up to observe the images in Heaven, and looked down to observe the laws on Earth. He observed the patterns of birds and beasts and the suitability of the Earth. He took examples from his own person for what was near, and took examples from things far away. From this, he first created the Eight Trigrams, to connect with the spiritual virtue of Heaven and Earth, and to categorize the feelings (qíng) of the myriad things."

Fuxi's method of drawing trigrams—"observing above and below"—was simultaneously collecting information from Heaven (observing above) and Earth (observing below). This method of information collection was inherently "encompassing Heaven and Earth."

Fuxi's encoding result—the Eight Trigrams—is a system of "Images," not purely "Number." This method of "Image" encoding allows a finite set of eight symbols to carry infinite information.

Bazi inherited Fuxi's Stems and Branches system (Stems + Branches), but it mainly utilizes the "Number" aspect (combination, inference).

Qimen Dunjia inherited Fuxi's Eight Trigrams system (Nine Palaces), and fully utilizes its "Image" aspect (the spatial image of each palace, the image of direction, the image of all things).

Therefore, from the perspective of the "quality" of information encoding (richness of symbolic meaning), Qimen Dunjia inherits the original encoding of Fuxi more completely.

Section 2: Wen Wang Developing the Yi—Expansion of Information

It is traditionally believed that when Wen Wang was imprisoned in Youli, he elaborated the Book of Changes, doubling the Eight Trigrams to form the Sixty-Four Hexagrams and attaching line statements and hexagram statements. This was the first major expansion of information.

Wen Wang's contribution was: expanding the original "Eight Images" system of Fuxi into a system of "Sixty-Four Images $\times$ Three Hundred Eighty-Four Lines," increasing the information capacity by about 48 times (on the order of $64/8 \times 384/24$).

Bazi's Four Pillar system can be seen as a "parallel development" of Wen Wang's Sixty-Four Hexagram system—both extracting information from combinations of Stems and Branches, but using different encoding methods (Hexagrams use Yin/Yang line superposition; Bazi uses Stems/Branches combination and sequence).

Qimen Dunjia's multi-layered chart system can also be seen as another "parallel development" of Wen Wang's system—the arrangement of the Nine Palaces is like the ordering of the Sixty-Four Hexagrams, and the multi-layer superposition is like the superposition of the Six Lines.

From the perspective of information expansion, both systems expand upon the original ancient encoding—but in different directions:

• Bazi's expansion direction: Refinement of the temporal dimension (Four layers: Year $\rightarrow$ Month $\rightarrow$ Day $\rightarrow$ Hour).
• Qimen Dunjia's expansion direction: Expansion of the spatial dimension (Nine Palaces) $\times$ Superposition of the layer dimension (Four layers: Earth, Heaven, Man, Spirit).

Information generated by "temporal refinement": $\approx 60^4 / \text{Constraints} \approx 518,400$ combinations.

Information generated by "spatial expansion $\times$ layer superposition": $\approx 18 \text{ (Bureau)} \times 12 \text{ (Hour)} \times 81 \text{ (Patterns)} \times 8 \text{ (Gates)} \times 8 \text{ (Spirits)} \approx 1,119,744$ combinations.

From this perspective, the combination space of Qimen Dunjia is about 2.16 times that of Bazi.

Of course, this factor of "nine times" mentioned earlier is only a rough estimate—the actual ratio depends on the correlation between the nine palaces. Since the information in the nine palaces is not completely independent—once the Heaven Plate Qiyi of one palace is determined, the Heaven Plate Qiyi of the other palaces are also determined (due to circular permutation)—the independent information capacity is lower, around 1.5 to 2 times that of Bazi.

This estimation roughly aligns with the results of the numerical analysis in the previous section.

Section 3: Duke Zhou's Establishment of Rites—Standardization of Information

Duke Zhou's establishment of rites and music integrated the principles of the Book of Changes into the social structure, transforming the information of the "Heavenly Way" into the norms of the "Way of Man."

The Zuo Zhuan, Duke Zhao Year 2 records the words of Han Xuanzi:

"Only now do I understand the virtue of Duke Zhou and why Zhou was able to reign."

Duke Zhou's system—rites, music, lineage laws, land division—are all standardized encodings of information. In this process of standardization, some of the original information is solidified (becoming institutions), and some is discarded (not incorporated into the institution).

The development of Bazi is similar—from ancient intuition to the systematization of Stems and Branches in the pre-Qin period, and then to the systemization of Ten Gods and Patterns later on. Each step of standardization makes the expression of information more precise, but it may also lead to the loss of some original information.

The development of Qimen Dunjia is similar—from ancient military intuition to the systematization of the Nine Palaces in the pre-Qin period, and then to the complete systemization of the four plates of Heaven, Earth, Man, and Spirit. Its degree of standardization is higher (more complex structure, clearer rules), so it likely retains more of the original information.

Section 4: Information Capacity in Pre-Qin Divination Cases

Let us compare the information capacity of "Four-Pillar style" inference versus "Multi-layer style" inference through actual pre-Qin divination cases.

Case: The Battle of Han Pass (Zuo Zhuan, Duke Xi Year 32-33)

Background: Before the battle between Qin and Jin at Han Pass, several divinations were performed within the Jin state.

"The tortoise said: 'Inauspicious.' The yarrow said: 'Auspicious.'"

Tortoise divination and yarrow divination gave opposite conclusions—a classic example of different information systems yielding different results.

Information from Tortoise Divination: One sign type (Inauspicious)—low information capacity, only one bit (Auspicious or Inauspicious).

Information from Yarrow Divination: Hexagram image, line text, hexagram change—high information capacity, potentially over ten bits.

Furthermore:

"They divined with yarrow, obtaining Gu (Corruption) transforming into Sui (Following). The diviner said: 'The firmness of Gu is Wind; its regret is Mountain. The year is Autumn, we are stripping its fruit and taking its wood. This is how we overcome. When the fruit is stripped and the wood is lost, what remains for failure$5'"

The interpretation process:

1. Obtaining Hexagram Gu—Xun (Wind) below, Gen (Mountain) above, Wind over Mountain.
2. Analyzing the inner trigram (Firmness) as Xun (Wind), the outer trigram (Regret) as Gen (Mountain).
3. Further symbolic inference based on the season (Autumn).
4. Symbolic action: Wind blowing down the fruit from the mountain—"stripping the fruit and taking the wood"—the image of overcoming the enemy.
5. But "fruit stripped and wood lost"—there will be losses after victory.

This process of inference involves multiple information layers:

• Hexagram Image Layer (Wind, Mountain).
• Seasonal Layer (Autumn).
• Material Image Layer (Fruit, Wood).
• Human Affairs Layer (Overcoming the enemy, suffering losses).

The interaction of these four layers produces a judgment of far richer meaning than the hexagram image itself.

This pattern of inference closely resembles the multi-layer interactive analysis of Qimen Dunjia—rather than the single-line temporal projection of Bazi.

Case: Divination of Nan Kuai before Rebellion (Zuo Zhuan, Duke Zhao Year 12)

"When Nan Kuai was about to rebel, someone in his village knew of it, sighed as he passed by, and said: 'So worried! What will come of it$6' Nan Kuai divined with yarrow repeatedly, obtaining Kun (Yielding) transforming into Bi (Clinging/Alliance). He said: 'Yellow skirt, fundamentally auspicious.' Thinking this meant great luck, he showed it to Zifu Huibo. Huibo said: 'I have studied this. If the matter involves loyalty and trust, it is possible; otherwise, it will surely fail. Yellow means the color of the center. Skirt means the adornment of the lower part. Fundamentally auspicious means the greatest good. If the center is not loyal, one cannot attain the color. If the lower part does not share, one cannot attain the adornment. If the undertaking is not good, it cannot be great. Furthermore, Kun transforming into Bi says, "To remain firm in peace brings auspiciousness," and its changing line says, "Straight, square, and great; without deviating from this, nothing is unfavorable." Thus, those who study this and do not deviate are auspicious. If one proceeds with disloyalty and untrustworthiness into great danger, can one escape$7''

Here, Zifu Huibo's interpretation is brilliant—not only interpreting the literal meaning of the hexagram and line texts but also judging based on moral dimensions like "center," "lower part," and "goodness." The depth of information extraction here is far beyond simple auspicious/inauspicious judgment.

Dimensions of information required for such a deep interpretation:

1. Hexagram Image Dimension (Kun, Bi).
2. Line Text Dimension ("Yellow skirt, fundamentally auspicious").
3. Color Image Dimension (Yellow—color of the center).
4. Adornment Image Dimension (Skirt—lower adornment).
5. Moral Dimension (Loyalty and Trust).
6. Situation Dimension (Rebellion—disloyalty and untrustworthiness).

The judgment based on the interaction of these six dimensions is closer to the multi-dimensional analysis of Qimen Dunjia than the simple analysis of Bazi.

This suggests that multi-dimensional interactive judgment was common practice in pre-Qin divination—not just simple fortune-telling as later simplified. Both Bazi and Qimen Dunjia emerged from this multi-dimensional tradition, but Qimen Dunjia retained this tradition more explicitly through its multi-layered structure.

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.

Chapter 12: Constructing the Unified Conclusion

Section 1: Re-examining the Core Question

The core question of this paper is: "Between Bazi and Qimen Dunjia, which one carries a greater volume of information$10"

After detailed analysis in the preceding chapters, we have reached the following preliminary conclusions:

1. From the Mathematical Combination Perspective: Qimen Dunjia's combination space is slightly larger than Bazi's (about 1.5-2 times).
2. From the Information Dimension Perspective: Qimen Dunjia's dimensions (12) exceed those of Bazi (8).
3. From the Information Density Perspective: Bazi's density (31-38 bits/character) exceeds that of Qimen Dunjia (5.8-9.3 bits/symbol).
4. From the Effective Information Perspective: This depends on the question asked—Bazi is superior for fate calculation, Dunjia is superior for decision-making.
5. From the Image Semantic Space Perspective: They are roughly comparable, with Qimen Dunjia slightly larger.
6. From the Heavenly Way Coverage Perspective: Qimen Dunjia is more comprehensive as it encompasses both time and space.

These conclusions seem to point toward the conclusion that "Qimen Dunjia's information capacity is greater than Bazi's"—but this needs a more rigorous distinction of the different meanings of "information capacity."

Section 2: The Triple Meaning of "Information Capacity" in Pre-Qin Context

In the pre-Qin context, "information capacity" can be understood in three layers:

First Layer: Number (Shù) (Quantity)

"Number" refers to quantifiable information—combination counts, bit counts, permutation counts.

From this perspective: Qimen Dunjia $\geq$ Bazi.

Reason: Qimen Dunjia's multi-layered plate structure (Heaven, Earth, Man, Spirit) and its simultaneous encoding of time and space produce a larger combinatorial space than Bazi's four-pillar structure.

Second Layer: Image (Xiàng) (Quality)

"Image" refers to perceptible information—material images, implied meanings, symbolism.

From this perspective: The two arts each have their own strengths, making direct comparison difficult.

Reason: Each character in Bazi carries extremely rich symbolic meaning (high information density), capable of mapping to countless things; Qimen Dunjia's individual symbols carry relatively simpler meanings, but the cross-mapping of multiple symbols generates an extremely rich set of combined meanings. Overall semantic space is roughly comparable.

Third Layer: Principle/Application (Lǐ) (Utility)

"Principle" refers to applicable information—the scope and depth of problems that can be answered.

From this perspective: Qimen Dunjia > Bazi.

Reason: Qimen Dunjia can answer a far wider range of questions than Bazi—not only destiny calculation but also military strategy, choosing directions, selecting auspicious times, judging events, finding lost objects, assessing illness, etc. (hence its title as the "Art of the Emperor"). Bazi is primarily used for questions centered on "Man"—destiny, marriage suitability, career choice, etc.

Synthesizing the analysis across the three layers:

From the perspective of the three layers: If measured by "breadth," Dunjia is greater; if measured by "density," Bazi is greater; if measured by "total quantity," Dunjia is slightly greater; if measured by "origin," both come from the Dao and are incomparable.

Section 3: Unifying the Conclusion with the Principles of the Book of Changes

The Xici Zhuan states:

"One Yin and one Yang is called the Dao. What follows it is Goodness; what completes it is Nature. The benevolent see it and call it benevolence; the wise see it and call it wisdom. The common people use it daily yet do not know it, thus the Way of the Superior Man is rare."

"One Yin and one Yang is the Dao"—the essence of the Dao lies in the interaction of Yin and Yang. Both Bazi and Qimen Dunjia are built upon Yin and Yang—this is their commonality.

"The benevolent see benevolence, the wise see wisdom"—the same Dao, seen from different angles by different people—results in different understandings. Bazi "sees the Dao" from the time perspective; Qimen Dunjia "sees the Dao" from the time-space perspective—the scope of what they see differs, thus their information capacities differ.

The Xici Zhuan further states:

"The Yi has four ways of the Sage: those who speak value its diction; those who act value its change; those who fashion implements value its image; those who divine value its judgment."

"Diction" (Cí), "Change" (Biàn), "Image" (Xiàng), "Judgment" (Zhàn)—These four aspects: Diction pertains to textual information (verbal layer); Change pertains to dynamic information (temporal layer); Image pertains to structural information (spatial layer); Judgment pertains to decision-making information (application layer).

Bazi excels in "Change" (dynamic temporal inference). Qimen Dunjia excels in "Image" (multi-layered structural presentation) and "Judgment" (multi-dimensional decision support).

Comparing the four aspects:

• Bazi coverage: Diction (partial, e.g., pattern names) + Change (Great Cycles/Years) = 2/4.
• Qimen Dunjia coverage: Diction (partial) + Change (chart rotation/bureau change) + Image (Nine Palaces multi-layer) + Judgment (comprehensive application) = 4/4.

From the perspective of coverage of the "Four Ways of the Sage," Qimen Dunjia is more comprehensive.

However, the Xici Zhuan immediately follows by saying:

"Therefore, when a Superior Man is about to act, about to proceed, he asks about it and receives the response as an echo. There is no distance near or far, hidden or deep, whereby he comes to know the future. If it is not the utmost subtlety of the world, who can participate in this$1"

"About to act," "about to proceed"—this specifically refers to moments requiring action and decision-making. At these times, one needs to "ask and receive the response as an echo"—requiring a comprehensive information system to support decision-making. "No distance near or far, hidden or deep"—regardless of spatial distance or hidden depth—information is provided. This description aligns more closely with the characteristics of Qimen Dunjia.

If the objective is not "action" or "acting," but purely understanding a person's inherent destiny pattern—then Bazi's specialized depth is more appropriate.

The Xici Zhuan also states:

"Interspersing Threes and Fives brings change, interweaving their numbers. By penetrating their changes, one completes the patterns of Heaven and Earth. By exhausting their numbers, one determines the images of the world below. If it is not the utmost change in the world, who can participate in this$2"

"Interspersing Threes and Fives brings change, interweaving their numbers"—the complex numerical operations involving variation and interweaving. This precisely describes the multi-layered interwoven operation of Qimen Dunjia—the "interweaving" (Cuò) of Heaven Plate and Earth Plate, the "interlacing" (Zōng) of the Man Plate and Spirit Plate, and the "interspersing" (Cānwǔ) of the Nine Palaces.

"Penetrating their changes, one completes the patterns of Heaven and Earth"—by mastering all changes, one completes the texture (the entirety of information) of Heaven and Earth.

This suggests: The size of the information capacity is directly related to the richness of the "Change"—and the more varied the "Change," the greater the information capacity.

Bazi's "Change": The sequential change of Heavenly Stems and Earthly Branches in the Great Cycles and Flowing Years—a one-dimensional change (linear progression along the time axis).

Qimen Dunjia's "Change": The rotation and superposition of multi-layered plates—a multi-dimensional change (cross-progression of Time and Space).

Multi-dimensional change is richer than one-dimensional change—thus, from the perspective of "Change," the information capacity of Qimen Dunjia is also greater than that of Bazi.

Chapter 13: Further Reflections and Deep Questions

Section 1: Why Did the Ancients Create Multiple Arcane Arts Instead of Just One$3

This question is very important. If one arcane art could "vastly and fully encompass" (guǎngdà xī bèi) the entire information of the Heavenly Way, why would multiple arts need to be created$4

The Xici Zhuan states:

"All under Heaven have the same destination but follow different paths; they have one goal but a hundred considerations." (Tiānxià tóng guī ér shū tú, yī zhì ér bǎi lǜ.)

"Same destination but different paths"—the goal is the same (to attain the Dao of Heaven), but the paths are different (various arcane arts). The reason multiple arts are needed is precisely because no single arcane art can completely carry the entire information of the Heavenly Way.

This is a mathematical necessity. As analyzed previously: The information of the Heavenly Way tends toward infinity ("the greatest without outside"), while the information capacity of any arcane system is finite—Bazi about 300 bits, Qimen Dunjia about 400 bits—both are only small fragments of the Heavenly Dao.

Therefore, multiple arcane arts are needed to "extract" the Dao's information from different angles—like needing multiple cameras to film a scene from different viewpoints to restore its entirety.

Bazi extracts information from the "Time" angle. Qimen Dunjia extracts information from the "Time-Space" angle. Liuren extracts information from the "Human Affairs" angle. Taiyi extracts information from the "National Destiny" angle.

Using multiple arts together can approximate (but never achieve) the full information of the Heavenly Dao.

Section 2: Does Greater Information Capacity Mean Greater Accuracy$5

This question is also crucial. Greater information volume does not equate to higher accuracy.

The Zuo Zhuan, Duke Xiang Year 9 records the divination of Lady Mu before her death:

"Lady Mu died in the Eastern Palace. When first they divined about her leaving, they obtained Gen transforming into Sui. The official said: 'This is called Gen transforming into Sui; it means she will leave. The Lord must leave quickly.' Lady Mu said: 'No. In the Zhou Yi, it says: "Sui, supremely prosperous, beneficial and firm, without blame." Yuan means the greatest in body. Heng means the confluence of good fortune. Li means the harmony of righteousness. Zhen means the foundation of affairs. Possessing the four virtues, following leads to no blame. Now I, a woman, am involved in chaos. I am in a low position and lack benevolence, so I cannot be Yuan. I do not settle the state, so I cannot be Heng. Acting rashly harms the body, so I cannot be Li. Abandoning my position for adultery, so I cannot be Zhen. I lack all four virtues, how can I follow without blame$6 I embrace wickedness, how can I be blameless$7 I shall surely die here and not get out.'"

This passage is extremely classic. The divination yielded Gen not changing (fixed Gen, or Gen transforming into Sui), and the official advised her to leave the Eastern Palace quickly. But Lady Mu, deeply understanding the doctrine, argued that she lacked the Four Virtues of Yuan, Heng, Li, and Zhen, so even if the hexagram implied "Following," she could not avoid blame—she ultimately died in the Eastern Palace as predicted.

This case reveals: The same hexagram image, interpreted by different readers, yields different conclusions—the accuracy of the interpretation depends on the reader's "Clarity" (mastery of doctrine), not the sheer "amount" of information.

By extension: Although Qimen Dunjia has a greater information volume than Bazi, if the interpreter cannot correctly process this large amount of information, they might be less accurate than an interpreter who has mastered the precision of Bazi.

The Laozi, Chapter 71, states:

"Knowing what one knows and knowing what one does not know—this is true knowledge. Not knowing what one knows and knowing what one does not know—this is delusion."

The information capacity of any arcane art, no matter how large, has its boundaries. Understanding these boundaries is the key to using the arts effectively.

Thus, the size of the information capacity is an objective mathematical problem, while the accuracy of the application is a subjective problem of skill. The two should not be conflated.

Section 3: Why is the Information Density of Bazi So High$8

This question deserves deep investigation. We previously established that Bazi's information density is about 2-3 times that of Qimen Dunjia—carrying extremely rich information with only 8 characters. Whence does this high density come$9

The answer lies in the "encoding efficiency" of the Stems and Branches.

A Heavenly Stem (Jia, Yi, Bing, Ding, etc.) carries information:

• Five Phases (one of 5 types).
• Yin/Yang (one of 2 types).
• Sequential Position (one of 10 positions).
• Direction (one of 5 directions).
• Season (one of 5 seasons).
• Five Tastes (one of 5 tastes).
• Five Colors (one of 5 colors).
• Five Tones (one of 5 tones).
• Five Viscera (one of 5 viscera).
• ...

Each Heavenly Stem carries information across at least 10 dimensions—each dimension being about 1-3 bits. Totaling about 10-20 bits/Stem.

An Earthly Branch carries even more information (due to Hidden Stems, Three Combinations, etc.), about 15-25 bits/Branch.

Thus, one Pillar (one Stem and one Branch) carries about 25-45 bits of information. Four Pillars total about 100-180 bits (after deducting redundancy).

The root of this high density lies in this: The Stems and Branches are a form of "multi-dimensional encoding"—a single symbol encodes information across multiple dimensions.

This is similar to a modern barcode—a single barcode encodes product category, origin, sequence number, etc. But the dimensions encoded by the Stems and Branches are far more numerous—and the dimensions have rigorous internal logical relationships (generation/overcoming of Five Phases, correspondence of Yin/Yang), making the encoding extremely compact.

This efficient encoding demonstrates the profound wisdom of the ancient Sages—to carry the richest information in the simplest form. The Xici Zhuan's statement "Simplicity leads to the understanding of the Dao under Heaven" (Yì jiǎn ér tiānxià zhī lǐ dé yǐ) refers precisely to this meaning.

Section 4: Why Does Qimen Dunjia Require Such a Complex Structure$10

Since the encoding efficiency of Stems and Branches is so high, why didn't Qimen Dunjia adopt a concise form like Bazi$11 Why construct the complex structure of four plates and nine palaces$12

The answer is: Because the problems Qimen Dunjia seeks to address are an order of magnitude more complex than those addressed by Bazi.

Bazi primarily addresses the core question: "What is the innate destiny pattern of this person$13"—a problem centered on "Man" and primarily utilizing the "Time" axis. The problem dimensions are about: 1 (Person) $\times$ 1 (Time Axis) = 1 Dimension.

Qimen Dunjia primarily addresses the question: "At this time and in this place, what action should be taken, and which direction should be pursued$14"—a problem centered on "Event" and utilizing "Time + Space" as dual axes. The problem dimensions are about: Multiple (types of events) $\times$ 2 (Time + Space) = Multi-dimensional.

The higher the dimensionality of the problem, the more complex the required information structure—this is inevitable.

Use the "Five Factors" from Sunzi's Art of War as an analogy:

"Hence the five fundamental factors must be compared when making plans: First, the Way (Dào); second, Heaven (Tiān); third, Earth (Dì); fourth, the Commander (Jiāng); and fifth, Method (Fă)."

The Five Factors—Dao, Heaven, Earth, Commander, Method—represent at least five dimensions. If one tries to address a five-dimensional problem with a simple structure like Bazi, the information is insufficient to support decision-making. Qimen Dunjia's four-plate structure—Heaven Plate (Heaven), Earth Plate (Earth), Man Plate (Commander/Man), Spirit Plate (Dao/Spirit)—coincidentally corresponds to most of the dimensions required by the Five Factors.

Thus, the complex structure of Qimen Dunjia is not over-engineering—it is necessitated by the complexity of the problem it aims to solve.

Section 5: Can the Two Arts Be Used Concurrently$15

Since Bazi and Qimen Dunjia each have their strengths, can they be used together$16

The answer is Yes, and this practice existed in antiquity.

In pre-Qin divination practice, there are examples of "using multiple methods concurrently":

The Zuo Zhuan, Duke Xi Year 4 records:

"Initially, Duke Xian of Jin wished to make Li Ji his principal wife, and divined about it: inauspicious. He used yarrow, which was auspicious. The Duke said: 'Follow the yarrow.' The diviner said: 'Yarrow is short, tortoise is long; it is better to follow the long one. Moreover, the line text says: "Focusing on deviation, pushing away the Lord's strength. One fragrance, one stench; after ten years, the smell remains." It must not be done.' The Duke did not listen."

This is an example of using both tortoise divination (Gui) and yarrow divination (Shi) simultaneously. The two methods gave contradictory conclusions—Tortoise inauspicious, Yarrow auspicious—the diviner advocated "following the long" (the tortoise), but Duke Xian chose the "yarrow"—and the result proved the tortoise divination correct.

This case shows that using multiple arcane arts concurrently can verify and supplement each other—when conclusions align, confidence increases; when they contradict, it signals the need for more cautious judgment.

Combining Bazi and Qimen Dunjia:

• Use Bazi to determine a person's innate pattern—to know the essence of their fate.
• Use Qimen Dunjia to determine the optimal time and space for action—to choose the advantageous path.

The combined information capacity = Bazi Info + Qimen Dunjia Info - Overlapping Information.

If the overlapping information is about 30% of each, then: Combined Capacity $\approx 300 + 400 - 0.3 \times \min(300, 400) \approx 300 + 400 - 90 = 610$ bits.

This is far greater than using either art alone—about twice that of Bazi and 1.5 times that of Qimen Dunjia.

Therefore, combining the two arts can yield the maximum information capacity and the most comprehensive decision support.

Section 6: The Limit of Information Capacity—The Boundary of Arcane Arts

Any arcane system has an upper limit to its information capacity. This limit is determined by its mathematical structure.

Bazi Information Limit: $\approx 518,400$ combinations $\times$ Ten Gods relations $\times$ Great Cycles/Years $\approx 10^8-10^{10}$ states.

Qimen Dunjia Information Limit: $\approx 18 \text{ Bureaus} \times 60 \text{ Hours} \times 81 \text{ Patterns} \times 8 \text{ Gates} \times 8 \text{ Spirits} \approx 10^6-10^8$ states.

However, the existence of an upper limit does not imply the inadequacy of the system—because the number of distinguishable states in the real world is also finite.

The number of distinct temporal segments in a human lifetime (using shí chén as the unit) is about 345,000—far less than the state limit of Bazi. The number of different decision options for a military engagement is a few hundred to a few thousand—far less than the state limit of Qimen Dunjia.

Therefore, in their respective fields of application, the information capacity of both arts is "sufficient"—the difference lies only in the amount of "redundancy" beyond what is sufficient.

Bazi Redundancy $\approx$ State Limit / Actual Need $\approx 10^8 / (3.5 \times 10^5) \approx 286$ times.

Qimen Dunjia Redundancy $\approx$ State Limit / Actual Need $\approx 10^7 / 10^3 \approx 10,000$ times.

Qimen Dunjia has much greater redundancy than Bazi—this implies that Qimen Dunjia has a larger margin for error in application; even if the interpretation has some error, it is less likely to lead to a catastrophic misjudgment.

Greater redundancy also means lower precision requirements—in some cases, Qimen Dunjia might not need to reach the level of detail required by Bazi to satisfy the need.

This confirms the conclusion from before: Bazi is deep but narrow, Dunjia is broad but wide—each is suited for its purpose.

Section 7: Returning to the "Dao"—The Ultimate Answer to the Information Capacity Question

Ultimately, we must return to the level of the "Dao" to examine the question of information capacity.

The Laozi, Chapter 1:

"The Dao that can be told is not the eternal Dao. The name that can be named is not the eternal Name. Nameless is the beginning of Heaven and Earth; named is the Mother of the myriad things."

All the information in arcane arts—whether the 300 bits of Bazi or the 400 bits of Qimen Dunjia—is "tellable Dao," "namable Name"—not the "eternal Dao," not the "eternal Name."

What is the information capacity of the "eternal Dao"$17 It is infinite.

No matter how much it is expanded, any arcane art can never reach the "eternal Dao"—this is a mathematical necessity (a finite number is always less than infinity) and the profound truth of metaphysics (the "Dao" cannot be completely encoded).

Therefore, when comparing the information capacities of Bazi and Qimen Dunjia, on the level of the "Dao," the comparison is between two finite quantities—and compared to infinity, both are effectively zero.

The Zhuangzi, Autumn Floods Chapter states:

"One cannot speak of the ocean to a frog in a well, for it is constrained by its habitat. One cannot speak of ice to a summer insect, for it is bound by its season. One cannot speak of the Dao to a narrow scholar, for he is constrained by his teachings."

The "teachings" (jiào) of the arcane arts, while individually marvelous, are all teachings of "narrow scholars"—partial knowledge, limited views. To "speak of the Dao"—to achieve a complete understanding of the Heavenly Way—is beyond the capacity of any single arcane art.

Thus, the final unified conclusion must add one final sentence:

On the level of the "Dao"—the information capacity of both Bazi and Qimen Dunjia is zero—compared to infinity, all finite quantities equal zero.

This is not nihilism—it is a reminder to those who study arcane arts to maintain humility. The arts are useful, but finite; they have areas where they reveal spiritual efficacy, but also areas where they fail to reach.

The final teaching of the Xici Zhuan:

"The Spirit has no fixed place, and Yi has no fixed form." (Shén wú fāng ér yì wú tǐ.)

The marvelous aspect is not confined to any one direction (it is not limited to the timeline of Bazi, nor to the Nine Palaces of Qimen Dunjia). The true essence of Yi resides not in any concrete structure (neither the form of the Four Pillars nor the body of the Four Plates).

To transcend the form and directly grasp the body of the Dao—this is the highest realm of arcane art cultivation.

Chapter 14: Summary of Mathematical Parameters

Section 1: Summary of Bazi Mathematical Parameters

Section 2: Summary of Qimen Dunjia Mathematical Parameters

Section 3: Comparative Summary Table

Chapter 15: Conclusion

Section 1: Concluding Remarks

This article has traced the origins from pre-Qin classics and ancient traditions, using mathematical structure as the warp and metaphysical doctrine as the weft, to systematically compare the information capacities of Bazi and Qimen Dunjia.

After fourteen chapters of detailed analysis, we arrive at the following unified conclusion:

Conclusion 1 (Mathematical Perspective): Qimen Dunjia's information capacity (total volume) is greater than Bazi's, by about an order of magnitude. This difference primarily stems from Qimen Dunjia's multi-layered plate structure (Heaven, Earth, Man, Spirit) and its encoding method that encompasses both time and space.

Conclusion 2 (Metaphysical Perspective): Bazi, through the method of "Simplicity" (Yì Jiǎn), embodies the essence of fate calculation with extremely high information density; Qimen Dunjia, through the method of "Vastness" (Guǎng Dà), covers the comprehensive information of Heaven, Earth, and Man with extreme breadth. The two arts grasp different aspects of the Yi and are mutually indispensable.

Conclusion 3 (Unified Perspective): The size of the information capacity depends on the standard of measurement—Dunjia is greater in "breadth" and "total volume"; Bazi is greater in "density"; in terms of "applicability," each has its strengths; on the level of the "Dao," both are finite.

Conclusion 4 (Practical Perspective): For questions of fate calculation, Bazi is superior—using simplicity to derive profound insight. For questions of action, Dunjia is superior—using vastness to master transformation. Using both arts concurrently yields the maximum information capacity and the most comprehensive judgment.

Section 2: Concluding with the Words of the Sages of Pre-Qin

The final words of the Book of Changes, Great Treatise (Part II) are aptly suited to conclude this paper:

"The Yi as a writing, traces the origin and grasps the end, serving as its substance. The six lines intermix, corresponding only to the time and the object. Its beginning is difficult to know, its culmination is easy to know—this is the beginning and the end. If one is to interweave the myriad things and record their virtues, distinguishing right from wrong, then the middle lines must be fully prepared."

"Tracing the origin and grasping the end" (yuánshǐ yàozhōng)—tracing the origin (the birth moment of Bazi), grasping the end (the action result of Qimen Dunjia).

"The six lines intermix, corresponding only to the time and the object" (liù yáo xiāngzá, wéi qí shí wù yě)—the intermixing of multiple layers of information (the multi-plate superposition of Qimen Dunjia) only reveals its meaning in specific time and circumstances.

"Its beginning is difficult to know, its culmination is easy to know" (qí chū nán zhī, qí shàng yì zhī)—the beginning of a matter is hard to predict (the profound nature of innate Bazi destiny is difficult to fathom), while the end result is relatively easy to know (the action outcome in Qimen Dunjia is easier to determine).

"Interweaving myriad things and distinguishing right from wrong, then the middle lines must be fully prepared"—to integrate various things and distinguish right from wrong, one must rely on complete information—and "complete" information requires both the "depth" of Bazi and the "breadth" of Dunjia.

Finally, concluding with a sentence from the Xici Zhuan:

"Thus the Yi is Image; Image is likeness." (Shì gù yì zhě, xiàng yě. Xiàng yě zhě, xiàng yě.)

All arcane arts are "Images" (Xiàng) of the Heavenly Dao—likenesses of the Heavenly Dao. The clarity of the likeness (information capacity) depends on the size and precision of the "mirror." Bazi is a small, precise mirror; Qimen Dunjia is a large, broad mirror. Using both mirrors together allows for a more complete reflection of the whole picture of the Heavenly Dao.

And the Heavenly Dao itself—that which the "Image" "likens"—always transcends the reflection of any mirror.

This is the final unified expression of the conclusion from mathematics and metaphysics.

References Cited:

The Book of Changes (Complete Text of Classic and Commentaries) The Book of Documents (Canon of Yao, Grand Plan, Oath of Mu Ye, Oath of Gan) The Zuo Zhuan (Duke Zhuang Year 22, Duke Xi Years 4, 15, 28, 32-33, Xuan Gong Year 3, Duke Xiang Year 9, Duke Zhao Years 2, 7, 12) Guoyu (Discourses of the States, Zhou Yu) Laozi (Chapters 1, 25, 42, 57, 71) Zhuangzi (Discussion on Making Things Equal, Heaven and Earth, Transcending Things, Autumn Floods) Guanzi (Inner Cultivation, Five Phases, Four Seasons, Minor Officials) Sunzi's Art of War (Laying Plans, Maneuvering for Position, Nine Grounds) Lüshi Chunqiu (Twelve Records, Records of Origin) Erya (Distinctions of Heaven) Heguanzi (Circular Flow Chapter) Shiji (Basic Annals of the Five Emperors, Basic Annals of Zhou) Shangshu Dazhuan (Relevant Chapters)

Drawn up by the Xuanji Editorial Department

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