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.