Celestial Stems Unfolding and the Hidden Shield Transformed: A Unified Mathematical-Metaphysical Inquiry into the Information Volume of Bazi and Qimen Dunjia
Starting from the mathematical structure of Taiji, the Two Modes, Four Images, and Eight Trigrams in the Book of Changes, this article systematically explores the information-carrying capacity of Bazi and Qimen Dunjia as divinatory systems. Through analysis of Yin-Yang, the Five Phases, the Hetu and Luoshu, and other classical mathematical foundations, it seeks to provide a unified perspective for measuring and comparing the information volume of these two arts.
Part Two: Mathematical Analysis
Chapter Five: Detailed Analysis of the Mathematical Structure of Bazi
Section 1. The Combinatorial Mathematics of Four Pillars and Eight Characters
The theoretical number of Bazi combinations is approximately 518,400. The Year Pillar has 60 possible values; the Month Pillar, constrained by the Year Stem via the "Five Tigers Starting Month" method, has 12 independent choices; the Day Pillar has 60 independent values; and the Hour Pillar, constrained by the Day Stem, has 12 independent choices.
The total independent information volume of Bazi (first level):
= log base 2 of 60 + log base 2 of 12 + log base 2 of 60 + log base 2 of 12 = 5.91 + 3.58 + 5.91 + 3.58 = approximately 18.98 bits
This is the "first-level" static combinatorial information -- approximately 19 bits.
Section 2-4. Relational, Dynamic, and Total Information
The relational information (Stem relationships, Branch relationships, Stem-Branch interactions, Ten Gods system) adds approximately 80-120 bits. Dynamic information from Major Cycles, Annual Cycles, and finer temporal divisions adds approximately 100-200 bits. The estimated total information volume of Bazi is approximately 250-300 bits.
Chapter Six: Detailed Analysis of the Mathematical Structure of Qimen Dunjia
One configuration of Qimen Dunjia contains: 9 Earth Board Marvels/Ceremonies, 9 Heaven Board Marvels/Ceremonies plus 9 Stars, 8 Gates, and 8 Spirits -- totaling 43 symbols across 9 palaces with 4 layers. The independent input information is approximately 12 bits, but the multi-layer board superposition and inter-layer interactions amplify this to approximately 90-133 bits of static information, with dynamic information adding 100-300 bits. The estimated total is approximately 250-400 bits.
Preliminary Mathematical Comparison
| Bazi | Qimen Dunjia | |
|---|---|---|
| Input information | approx. 19 bits | approx. 12 bits |
| Static combinatorial information | approx. 19 bits | approx. 13 bits |
| Relational information | approx. 80-120 bits | approx. 77-120 bits |
| System-endogenous information | approx. 20-25 bits | approx. 40-60 bits |
| Dynamic information | approx. 100-200 bits | approx. 100-300 bits |
| Total | approx. 250-300 bits | approx. 250-400 bits |
Preliminary conclusion: Qimen Dunjia's information volume is, in mathematical terms, greater than or equal to that of Bazi.
Chapters Seven and Eight: Deep Analysis of Information Dimensions and Image
Qimen Dunjia has approximately 12 major information dimensions versus Bazi's 8. Bazi's information density (31-38 bits/character) far exceeds Qimen Dunjia's (5.8-9.3 bits/symbol). From the perspective of "image" (xiang), both systems have symbolic-meaning spaces tending toward infinity, though Qimen Dunjia's multi-layer recursive expansion provides a somewhat larger theoretical space.