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#Bazi #Qimen Dunjia #Information Theory #Mathematical Metaphysics #I Ching Foundations

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 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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