Chapter Ten: Conclusion -- The Spiral of the Cosmos

The Five Combinations of the Heavenly Stems appear on the surface as five simple equations, yet they contain the ancient Chinese people's ultimate reflections on the operating patterns of the cosmos.

They encompass:

1. A mathematical model: The rigorous derivation of Hetu numbers.
2. A physical model: The energy field of yin-yang opposites attracting.
3. An astronomical model: The correspondence of planetary conjunctions with the Twenty-Eight Lodges.
4. A meteorological model: The periodic oscillations of Earth's climate.
5. A philosophical model: The beauty of firmness and gentleness in harmony, the doctrine of the Mean, environmental determinism (meeting the Dragon brings transformation).

The various conjectures, though differently emphasized, converge upon the same destination. They point together toward one truth: All things in the cosmos are not isolated, but attract and transform one another within specific rhythms.

Jia is not merely Jia -- when it meets Ji, at the right time (Chen), it willingly relinquishes its self to transform into Earth and nourish all things. Bing is not merely Bing -- when it embraces Xin, at the right time, even blazing fire can transform into the softest water.

This is perhaps the most profound revelation the Five Combinations of the Heavenly Stems leave us: Change is eternal; and harmony is the ultimate purpose of change.

Appendix: Excerpts on the Five Combinations from Classical Texts Through the Ages

"The East's Jia-Yi Wood fears the West's Geng-Xin Metal. Jia gives his younger sister Yi in marriage to Geng, turning ill fortune into auspicious omen. ... The South's Bing-Ding Fire fears the North's Ren-Gui Water. Bing gives his younger sister Xin in marriage to Gui, turning ill fortune into auspicious omen. ... The Center's Wu-Ji Earth fears the East's Jia-Yi Wood. Wu gives his younger sister Ji in marriage to Jia, turning ill fortune into auspicious omen." -- Shiji, Tianguan Shu (Records of the Grand Historian, Treatise on the Celestial Offices)

This passage is most intriguing. It interprets the Five Combinations as a form of political marriage alliance (heqin policy). To avoid being conquered (warfare), one gives a sister in marriage to the enemy (the one who conquers me), thereby turning swords into plowshares. This explains from a sociological perspective why "Yi-Geng combine" and "Bing-Xin combine" (though the pairing logic in the Records differs slightly, focusing mainly on marriage alliances, the core idea is consistent).

"The transformation through combination of the Ten Stems is the proper qi of heaven and earth. ... Jia-Ji transforms into Earth, the combination of centrality and uprightness; Yi-Geng transforms into Metal, the combination of benevolence and righteousness; Bing-Xin transforms into Water, the combination of authority and control; Ding-Ren transforms into Wood, the combination of excess and concealment; Wu-Gui transforms into Fire, the heartless combination." -- Sanming Tonghui (Comprehensive Compendium of the Three Fates)

"The Five Combinations are precisely the 'five positions corresponding to each other, each having its combination.' In the Hetu, one combines with six, two with seven, three with eight, four with nine, five with ten. Speaking in terms of the Ten Stems: Jia is one, Ji is six; Yi is two, Geng is seven; Bing is three, Xin is eight; Ding is four, Ren is nine; Wu is five, Gui is ten. These are the combinations of number." -- Yuanhai Ziping (The Oceanic Mirror of Ziping)

May every friend who studies the metaphysical arts, while memorizing formulae, occasionally look up at the starry sky, and in the eternal motions of those celestial bodies, contemplate the grand significance behind these twenty characters.