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凡万物之始，莫不始于无，而后有。是故易有大极，是生两仪，两仪生四序，四序，生之所生也。有万物滋繁，然后万物生成也。皆由阴阳二气，鼓舞陶铸，互相交感。故孤阳不能独生，单阴不能独成，必须配合以炉冶，尔乃万物化通。是则天有其象，精气下流，地道含化，以资形始。阴阳消长，生杀用成。明其道难明，非数不可究，故因数以辨之。数之显理，犹筌蹄之取鱼兔。阳顺唱始，阴佐其终。穷奇偶之数，备相成之道。极变化之源者，详于蓍策之数也。
七八为静，九六为动。阳动而进，变七之九，象气息也，明阳道之舒，以象君德，唱始不休，无所屈后，去极一等，而犹进之，故九动也。阴动而退，变八之六，象气消也，以明臣法有所屈后，唱和而已。蕝雾近君，则靖息以听命，必须退让，以明其义，故八静也。
《易》曰：分二以象两，挂一以象三，揲之以四，以象四时者。余手有四七，故名七也。有四八，故名八也。有此，则静爻之数。夏殷尚质，以用静爻占之。余有四九，故名九也。有四六，故名六也。此则动爻之数。周备质文，故兼用动爻。
凡大衍极天地之数，五十有五也。京房以十日、十二辰、二十八宿，合应五十，其一不用者，天之生气，将欲以虚求实，故用四十九焉。马融以易之大极，为北辰也。生两仪，两仪生日月，日月生四时，四时生五行，五行生十二月，十二月生二十四气。北辰居位不动，其余四十九，转运而用也。
郑玄曰：贞悔六爻，本有五十，定所用者四十有九。天地之数，本五十五。天五与地十通，天一与地六通，数之者气则有并，并则宜减焉。大衍减五，故有五十，其用减一，故四十有九。不并者，不可减也。今总其数五十者，天一至地十，凡五十五也。此合生成之数。若止言生数，唯十有五，从一至五也。《易》之所象，爻尽之，有邃。故自天地以下，日月等数，皆为蓍卦所摄，循环变转，万世无穷。而五十有五，五本并数，并数者，天之与地共，各有一体，体各有一正应敌对。今盈于五，则是气之并数，并不再用，是其配义。配则为虚，不当于实。不当于实，故事无所主。所以揲蓍不用。又虚其一者，挂一象无，无无可象。故有之用极，则无之功见。故曰：寻大业而得吉凶，寻吉凶而得八卦，寻八卦以得四时，寻四时以至两仪，寻两仪以至太极。太极者，大杀而极，穷无之致也。遣有以极邃，减多以就少，此之谓也。故曰：太极无所复象，明其空寂，非言象所诠也。
The origin of all things begins from "non-being" 🌌, from which "being" emerges. Thus, the Book of Changes introduces the concept of the Supreme Ultimate (Tai Chi), which generates the Two Modes (Yin and Yang). The Two Modes give rise to the Four Orders (the four seasons), and the Four Orders, in turn, catalyze the myriad things. As all things flourish and grow, they eventually take form, all stemming from the interaction of the two energies of Yin and Yang—like a bellows casting metal, they agitate and blend with each other. Therefore, Yang energy alone cannot generate, nor can Yin energy alone accomplish; they must cooperate like a furnace for all things to transform and permeate. Celestial phenomena reveal the flow of essential energy toward the earth, while earthly principles embody transformative power, supporting the inception of forms. The waxing and waning of Yin and Yang determine the completion of life and destruction. Understanding this principle is difficult and must be explored through mathematical reasoning, hence relying on numbers for clarification. Mathematical reasoning unveils truth, much like fishing gear catching fish or rabbits—a tool for revelation. Yang energy advances smoothly to initiate beginnings, while Yin energy assists in bringing about endings. Exhausting the laws of odd and even numbers completes the way of mutual complementarity. Those who delve deeply into the source of change will meticulously study the numerics of yarrow stalk divination.
Seven and eight are static numbers; nine and six are dynamic numbers. Yang energy moves forward, changing from seven to nine, symbolizing the growth of energy and indicating the expansion of the Yang principle, akin to the virtue of a ruler who advocates beginnings without ceasing, never submitting or retreating, advancing even near the limit, hence nine is dynamic. Yin energy moves and retreats, changing from eight to six, symbolizing the diminishment of energy to demonstrate the law of the minister, which involves submission and accord. Like mist approaching the ruler, it quietly heeds commands, necessarily yielding to clarify righteousness, hence eight is static.
The Book of Changes states: Dividing the yarrow stalks into two groups symbolizes the Two Modes; hanging one stalk symbolizes the Three Powers (Heaven, Earth, and Humanity); and counting by fours symbolizes the four seasons. If the remainder yields four groups of seven, it is called seven; if it yields four groups of eight, it is called eight. These are the numbers of static lines. The Xia and Shang dynasties emphasized simplicity and used static lines for divination. If the remainder yields four groups of nine, it is called nine; if it yields four groups of six, it is called six. These are the numbers of dynamic lines. The Zhou dynasty combined simplicity and refinement, hence using both dynamic and static lines.
The number of the Great Derivation exhausts the numbers of Heaven and Earth, totaling fifty-five. Jing Fang believed that the sum of the ten celestial stems, twelve earthly branches, and twenty-eight lunar mansions is fifty, with one unused to represent the vital energy of Heaven, aiming to seek substance through emptiness, hence forty-nine are used. Ma Rong believed that the Supreme Ultimate of the Changes is the North Star (Polaris), which generates the Two Modes, the Two Modes generate the sun and moon, the sun and moon generate the four seasons, the four seasons generate the five phases, the five phases generate the twelve months, and the twelve months generate the twenty-four solar terms. The North Star remains stationary, while the remaining forty-nine numbers circulate and are used.
Zheng Xuan said: The six lines of the hexagram, originally comprising fifty numbers, are determined to use forty-nine. The numbers of Heaven and Earth originally total fifty-five. Heaven’s five and Earth’s ten interconnect, Heaven’s one and Earth’s six interconnect; in numerology, energies merge, and merging necessitates reduction. The Great Derivation number is reduced by five, hence fifty; its use is reduced by one, hence forty-nine. Numbers that do not merge cannot be reduced. The total number fifty is derived from Heaven’s one to Earth’s ten, totaling fifty-five. This aligns with the numbers of generation and completion. If only the generative numbers are considered, there are only fifteen, from one to five. The symbolism of the Changes encompasses all lines, with profound implications. Therefore, from Heaven and Earth downward, numbers such as the sun and moon are all captured by the yarrow stalks and hexagrams, cycling and transforming endlessly through all ages. Among the fifty-five, five is inherently a merged number; merged numbers signify Heaven and Earth sharing, each having their own entity, and each entity having its proper correspondence and opposition. Now, exceeding five represents the merging of energies, which are no longer used—this is the principle of pairing. Pairing implies emptiness, not equivalent to substance. Not equivalent to substance, hence affairs lack a master. Therefore, the yarrow stalks are not used for this. Additionally, one is voided, hung to symbolize non-being, which cannot be symbolized. Thus, when the function of being reaches its extreme, the function of non-being manifests. Hence it is said: Seek the great undertaking to attain auspiciousness and inauspiciousness, seek auspiciousness and inauspiciousness to attain the eight trigrams, seek the eight trigrams to attain the four seasons, seek the four seasons to reach the Two Modes, and seek the Two Modes to reach the Supreme Ultimate. The Supreme Ultimate is the ultimate of great cessation, exhausting the extremity of non-being. Dispensing with being to reach profundity, reducing the many to approach the few—this is its meaning. Hence it is said: The Supreme Ultimate has no further symbol, indicating its emptiness and stillness, beyond the interpretation of words and symbols.
This text elucidates the numerological philosophy of the Book of Changes: the process of all things emerging from "non-being" to "being," based on the interaction and balance of Yin and Yang energies. Through the number of the Great Derivation (fifty-five) and the yarrow stalk divination method, mathematical reasoning is used to reveal cosmic laws, emphasizing the distinction between dynamic and static numbers (seven and eight static, nine and six dynamic), as well as the symbolic meaning of emptiness and substance in divination. Ultimately, it points to the nature of the Supreme Ultimate as emptiness, the ultimate source of all things.
In a modern context, this can be understood as a framework for systemic thinking and decision-making: Yin and Yang represent opposing yet unified forces (e.g., positive and negative, action and rest), while mathematical reasoning symbolizes data and logical analysis. Dynamic and static numbers (seven and eight static, nine and six dynamic) resemble dynamic and static states—static lines indicate stability or continuity, while dynamic lines signify change or turning points. The Great Derivation number fifty-five reflects the completeness of cosmic order, which, in today’s terms, could relate to holistic thinking in fields like ecology or psychology, where everything is interconnected. The idea of "using 49 out of 55" emphasizes practicality: in decision-making, we often focus on available data (the "real") while acknowledging unknown variables (the "void").
This text delves deeply into the philosophy of non-being and being: the Supreme Ultimate as the extremity of "non-being" reminds us that creativity stems from emptiness (e.g., the "blank canvas" theory in innovation). In contemporary terms, this echoes Eastern philosophies such as Daoist "governing by non-action" or Buddhist "emptiness," emphasizing that in a busy world, creating space (void) is necessary to produce substance (reality). Mathematical reasoning to discern the Dao shows that the universe can be explored rationally, but ultimate truth transcends symbols—encouraging us to embrace uncertainty and seek meaning beyond mere data.
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