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Chapter 14 of 25
皇极经世
This chapter deduces the fundamental numerical framework of the cosmos, revealing the mathematical logic behind the generation and transformation of all things in heaven and earth 🌌.
The substantive number of Great Yang is ten, that of Great Yin is twelve, that of Lesser Yang is ten, and that of Lesser Yin is twelve; the substantive number of Lesser Firmness is ten, that of Lesser Yieldingness is twelve, that of Great Firmness is ten, and that of Great Yieldingness is twelve.
Using the substantive numbers of Great Yang, Lesser Yang, Great Firmness, and Lesser Firmness as the foundation, and subtracting the substantive numbers of Great Yin, Lesser Yin, Great Yieldingness, and Lesser Yieldingness, one obtains the functional numbers of Great Yang, Lesser Yang, Great Firmness, and Lesser Firmness; using the substantive numbers of Great Yin, Lesser Yin, Great Yieldingness, and Lesser Yieldingness as the foundation, and subtracting the substantive numbers of Great Yang, Lesser Yang, Great Firmness, and Lesser Firmness, one obtains the functional numbers of Great Yin, Lesser Yin, Great Yieldingness, and Lesser Yieldingness.
The substantive numbers of Great Yang, Lesser Yang, Great Firmness, and Lesser Firmness total one hundred and sixty; the substantive numbers of Great Yin, Lesser Yin, Great Yieldingness, and Lesser Yieldingness total one hundred and ninety-two; the functional numbers of Great Yang, Lesser Yang, Great Firmness, and Lesser Firmness amount to one hundred and twelve, and the functional numbers of Great Yin, Lesser Yin, Great Yieldingness, and Lesser Yieldingness amount to one hundred and fifty-two.
Using the functional numbers of Great Yang, Lesser Yang, Great Firmness, and Lesser Firmness to "initiate" (sing) the functional numbers of Great Yin, Lesser Yin, Great Yieldingness, and Lesser Yieldingness, the result is the transformation numbers of Sun, Moon, Stars, and Constellations; using the functional numbers of Great Yin, Lesser Yin, Great Yieldingness, and Lesser Yieldingness to "respond" (harmonize) with the functional numbers of Great Yang, Lesser Yang, Great Firmness, and Lesser Firmness, the result is the generation numbers of Water, Fire, Earth, and Stone.
The transformation numbers of Sun, Moon, Stars, and Constellations amount to 17,024, known as the numbers of motion; the generation numbers of Water, Fire, Earth, and Stone amount to 17,024, known as the numbers of vegetation. Multiplying the numbers of motion with the numbers of vegetation once more yields 289,816,576, known as the universal number of motion and vegetation 👇.
Sun, Moon, Stars, and Constellations govern the changes of heat, cold, day, and night; Water, Fire, Earth, and Stone govern the generation of rain, wind, dew, and thunder. The changes of heat, cold, day, and night act upon nature, emotion, form, and substance; the generation of rain, wind, dew, and thunder acts upon walking, flying, plants, and trees.
Specifically: Heat transforms the nature of flying, walking, plants, and trees; cold transforms the emotion of flying, walking, plants, and trees; day transforms the form of flying, walking, plants, and trees; night transforms the substance of flying, walking, plants, and trees; rain generates the walking category within nature, emotion, form, and substance; wind generates the flying category within nature, emotion, form, and substance; dew generates the plant category within nature, emotion, form, and substance; thunder generates the tree category within nature, emotion, form, and substance 🌱.
Nature, emotion, form, and substance are rooted in Heaven; flying, walking, plants, and trees are rooted in Earth. What is rooted in Heaven manifests as the division of Yin and Yang; what is rooted in Earth manifests as the division of Yieldingness and Firmness. The division of Yin and Yang and the division of Yieldingness and Firmness govern the fundamental principles of all things in heaven and earth. Yet the one who can fully embody the principles of all things in heaven and earth is only Humanity 🙏.
The core of this chapter lies in establishing a mathematicized model of cosmic generation. Shao Yong, through the advance-and-retreat calculations of "substantive numbers" and "functional numbers," derives the numbers of motion (celestial transformation) and numbers of vegetation (terrestrial generation), then multiplies the two to obtain the universal number of motion and vegetation, thereby explaining the constant of transformation for all things in the cosmos.
The underlying logic can be summarized as follows:
From a contemporary perspective, the numerical reasoning of this chapter can be viewed as a manifestation of early systems thinking. Shao Yong attempts to explain infinite natural change through finite numerical relations, and its essence is a cognitive paradigm of "observing phenomena through numbers."
This chapter implies a profound philosophical question: Do numbers precede things in existence? Shao Yong's answer is affirmative—numerical structure is the underlying code of cosmic operation, and all things are merely the unfolding of this code at different levels.
This numerical foundationalism bears a remarkable resemblance to Plato's "Theory of Forms." Meanwhile, the concept of "initiation and response" reveals the philosophical significance of asymmetric interaction: Heaven acts actively (initiating), Earth responds responsively (harmonizing), yet after Earth's response, new "generation numbers" emerge, which in turn enrich Heaven's "transformation numbers." This circularly progressive relationship transcends simple causal chains, pointing toward a self-organizing cosmic picture.
"The one who completes heaven and earth is humanity" converges the entire numerical system upon the human being. Humanity is not a passive observer of the cosmos but the bearer and fulfiller of cosmic numerology. This thought provides a metaphysical foundation for later learning of the mind and theories of nature and destiny: understanding the numerical structure of oneself is equivalent to understanding the operational laws of all things in heaven and earth.
| Concept | Definition |
|---|---|
| Substantive Number | The fixed base number in the priori, representing the essential determination of a thing |
| Functional Number | The actual number in posteriori operation, derived from advancing and retreating the substantive numbers |
| Number of Motion | The transformation number of Sun, Moon, Stars, and Constellations (Heaven), 17,024 |
| Number of Vegetation | The generation number of Water, Fire, Earth, and Stone (Earth), 17,024 |
| Universal Number of Motion and Vegetation | The total number of celestial-terrestrial change, 289,816,576 |
| Initiation and Response | Heaven actively initiates as "singing"; Earth responsively generates as "harmonizing" |
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