TianGan & DiZhi, aka Heavenly Stems and Earthly Branches. Vol 3
The Mathematical Logic of Stem-Branch Combinations
When Heavenly Stems combine with Earthly Branches, they form the so-called “Sixty Jiazi Cycle”—an ingenious mathematical arrangement. Ten Heavenly Stems pairing with twelve Earthly Branches requires sixty combinations before repeating, a practical application of the least common multiple principle.
The pairing method follows this sequence: Jiazi, Yichou, Bingyin, Dingmao… cycling continuously. Each combination serves as a unique temporal marker for recording years, months, days, and hours, forming a four-dimensional temporal network. This time-encoding system is precise without being cumbersome, easy to remember yet difficult to confuse.
Mathematically, the cyclic timekeeping method establishes a modulo-60 congruence system. Any point in time has a definite stem-branch representation within this system, allowing historical events to be precisely located across long time spans. This mathematical structure enabled ancient Chinese calendrical experts to handle complex calendar conversion problems.
The Internal Structure of the Four Pillars and Eight Characters
The stems-branches timekeeping evolved into the “Four Pillars” system—pillars for year, month, day, and hour—with each pillar containing one Heavenly Stem and one Earthly Branch, totaling eight characters (hence “Eight Characters”). This system precisely locates a person’s birth moment within cosmic space-time coordinates.
In the Four Pillars, the day stem serves as the “master” (subject), while the remaining stems and branches function as “favorable or unfavorable spirits” (environment). By analyzing the generating, controlling, restraining, and transforming relationships among these stems and branches, one can predict life circumstances. This analytical method essentially represents a structuralist symbolic calculation system built upon the systematic relationships of the Five Elements.
The Eight Characters structure also includes the “Naying” (Accepted Sound) system. Each stem-branch combination corresponds to a specific “Five Elements Sound,” such as “Metal in the Sea” for Jiazi and Yichou, or “Fire in the Furnace” for Bingyin and Dingmao. These correspondences, found in ancient texts like “The Comprehensive Book of Three Lives,” further refine the symbolic attributes of the stems and branches.
Najia Method and Directional Principles
The “Najia Method” combines stems-branches with the eight trigrams and directions. Its basic principle establishes fixed relationships: “Qian corresponds to Jiazi, Kun to Jiawu, Zhen to Jiayin,” and so on. This method finds applications in feng shui, divination, and other fields.
In the “Three Cycles and Nine Periods” theory, stems-branches divide time periods, with each period corresponding to different Flying Star combinations of the nine palaces. For example, the Seventh Cycle (1984-2003), Eighth Cycle (2004-2023), and Ninth Cycle (2024-2043) each last twenty years, with stems-branches years marking their boundaries. This division method reflects the traditional Chinese numerological understanding of time’s cyclical nature.
Feng shui’s “Division of Gold and Determination of Direction” method uses stems-branches to determine building orientations. The twenty-four mountain directions (twenty-four compass points) are assigned stems-branches combinations, such as “Ren Mountain Bing Direction” (north facing south) or “Jia Mountain Geng Direction” (east facing west). The core of this method combines abstract directions with the Five Elements attributes of stems-branches to judge auspiciousness.
Synchronization Logic of Stems-Branches and Calendar
When combined with the Twenty-Four Solar Terms, stems-branches form a precise seasonal observation system. Each solar term has fixed stem-branch combinations. For instance, “Beginning of Spring” typically occurs at the start of the Yin month (first lunar month), while “Summer Solstice” falls in the middle of the Wu month (fifth lunar month). These correspondences don’t represent fixed dates but reflect the sun’s position along the ecliptic, demonstrating the astronomical foundation of ancient Chinese calendars.
Traditional Chinese calendars defined a year as approximately 365.25 days. To handle this astronomical data, they developed intercalation systems. Working in conjunction with the stems-branches system, these intercalation methods ensured that the calendar wouldn’t deviate over long periods. Calendar designs like the “Shoushi Calendar” comprehensively considered both stems-branches cycles and astronomical observations.
Lunar months are based on the synodic month (approximately 29.53 days), which doesn’t naturally align with the stems-branches daily system (operating on a 60-day cycle). To coordinate these two systems, ancient calendar experts created complex calculation rules allowing stems-branches days and lunar months to operate relatively independently while synchronizing at specific points (such as solar terms).
Modern Challenges and Cultural Inheritance
In today’s technologically advanced world, we can calculate the precise movements of all celestial bodies in our solar system, giving us the capability to revise our calendars. However, the challenge isn’t technical but involves changing humanity’s deeply ingrained habits! I’ll later write an article discussing a calendar that completely abandons “political correctness” and “tradition.”
This extensively applied and complex stems-branches system remains largely unknown, not only to those outside the Chinese cultural sphere but even to most Chinese people today. Over 90% of people cannot even recite all ten Heavenly Stems and twelve Earthly Branches. This clearly signals the risk to Chinese cultural heritage. With current educational models and content, these cultural elements might become mere mythology within two or three generations. This would be a great loss not only for Chinese people but for all humanity—much like the civilizations we’ve already lost to time.