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行言五者，明万物虽多，数不过五。故在天为五星，其神为五帝。孔子曰：昔丘闻诸老聃云：天有五行，木金水火土，其神谓之五帝。在地为五方，其镇为五岳。《物理论》云：镇之以五岳。人在为五脏，其候五官。《黄帝素问》云：五脏候在五官，眼耳口鼻舌也。
五行递相负载，休王相生，生成万物，运用不休，故云行也。《春秋繁露》云：天地之气，列为五行。夫五行者，行也。《易·上系》曰：天数五。王曰：谓一三五七九也。韩曰：五奇也。地数五。王曰：谓二四六八十也。韩曰：五偶也。五位相得。王曰：五位，金木水火土也。而各有合。王曰：谓水，在天为一，在地为六，六一合于北。火，在天为七，在地为二，二七合于南。金，在天为九，在地为四，四九合于西。木，在天为三，在地为八，三八合于东。土，在天为五，在地为十，五十合于中。故曰：五位相得，而各有合。谢曰：阴阳相应，奇偶相配，各有合也。韩曰：天地之数各有五，五数相配，以合成金木水火土也。
《尚书·洪范》篇曰：五行，一曰水，二曰火，三曰木，四曰金，五曰土，皆其生数。《礼记·月令》篇云：木数八，火数七，金数九，水数六，土数五，皆其成数。唯土言生数。天以一生水于北方，君子之位，阳气微动于黄泉之下，始动无二。天数与阳合而为一。水虽阴物，阳在于内，从阳之始，故水数一也。极阳生阴，阴始于午，始亦无二。阴阳二气，各有其始。正应言一，而云二者，以阳尊故。尊既括始，阴卑赞和，配故能生。而阳数偶阴在火中。火虽阳物，义从阴，配合阴始，故从始立义，故火数二也。
老子云：天得一以清，地得一以宁。是知皆有一义，唱和同始。是以云：木配阳动，而左长于东方。长则滋繁，滋繁则数增，故木数三也。阴佐阳消，阴道右转，而居于西，在阳之后，理无等义，故金数四也。阴阳之数，始乎一周，然后阳达于中，总括四行，苞则弥多，故土数五也。
此并生数，皆云据始，未明成数。数既未成，亦未能为用。《颖容春秋释例》云：五行生数，未能变化，各成其事。水凝而未能流行，火有形而未生炎光，木精破而体刚，金强而斫，土卤而斥。于是天以五临民，君化之。传曰：配以五成，所以用五者，天之中数也。
于是水得于五，其数六，用能润下。火得于五，其数七，用能炎上。木得于五，其数八，用能曲直。金得于五，其数九，用能从革。土得于五，其数十，用能稼穑。郑玄云：数若止五，则阳无匹偶，阴无配义，故合之而成数也。奇者，阳唱于始，为制为度。偶者，阴之本，得阳乃成。
故天以一始生水于北方，地以其六而成之，使其流润也。地以二生火于南方，天以七而成之，使其光曜也。天以三生木于东方，地以其八而成之，使其舒长盛大也。地以四生金于西方，天以九而成之，使其刚利有文章也。天以五合气于中央，生土，地以十而成之，以备天地之间所有之物也。
合之，则地之六为天一匹也。天七为地二偶也。地八为天三匹也。天九为地四偶也。地十为天五匹也。阴阳各有合，然后气性相得，施化行也。故四时之运，成于五行。土总四行，居时之季，以成之也。《五行传》及《白虎通》皆云：木非土不生，根核茂荣；火非土不荣，得木著形；金非土不成，入范成名；水非土不停，堤防禁盈。土扶微助衰，应成其道。故五行更互须土。土王四季，而居中央，不以名成时，故知同时俱起，但托义相生。
传曰：五行并起，各以名别，常从数义云：北方亥子，水也，生数一；丑，土也，生数五，一与五相得为六，故水成数六也。东方寅卯，木也，生数三；辰，土也，生数五，三与五相得为八，故木成数八也。南方巳午，火也，生数二；未，土也，生数五，二与五相得为七，故火成数七也。西方申酉，金也，生数四；戌，土也，生数五，四与五相得为九，故金成数九也。中央戊己，土也，生数五。又土之位在中，其数本五，两五相得为十，故土成数十也。
此阴阳两气各一周也，共一周，则为生数，各一周，则为成数。阳以轻清上为天，阴以重浊下为地。而阳至第五而入中者，其体躁疾，故共一周而入中。阴至第十方入中者，其体迟殿，故各一周而始入耳。然五行皆得中气而后成。土居中而王四季，并须土以成之也。
《洪范》是上古创制之书，故言生数。《礼记·月令》是时候之书，所贵成就事业，故言成数。唯土言生数者，土以能生为贵，且以成四行，足简之矣，是其能生能成之义也。郑玄曰：以天地相配，取阴阳之理，常从以支干数和合，取日辰为用。两说虽别，大意还同，终会《易经》天一至地十之义。《孝经·援神契》言：以一立，以二谋，以三出，以四孳，以五合，以六嬉，以七变，以八舒，以九列，以十钧。
五行以一立水，一为生数，以五配一，水之成数，故言一立而六嬉。嬉是兴义。二，是火之生数；七，是火之成数。故言二谋。火以变化为能，故曰七变。谋者，以其为变之始也。三，木之生数；八，木之成数。五行始于东方，故云三出。八而成长，故曰八舒。四，金之生数；九，金之成数。西方成就，故言四滋。品类不同，故称九列。五，是土之生数；十，是土之成数。以天之五，合地之十，数义斯毕。所以五言其合，十言其钧。钧是成备之义。
《春秋·元命苞》云：胎错舞，连以钧。一动，合于二，故阴阳受。成于三，故日月星序。张于四，故时起。立于五，故行动。布于六，故律踊。分于七，故宿改。萌于八，故风布。极于九，故州吐。毕于十，故功成数止。此并经纬共明，五行生成之数，不过十也。
Holistic Interpretation
This chapter systematically elaborates the Five Elements system and its numerical generation principles, revealing that although all things are complex, their fundamental laws can be summarized into the interactions of five basic elements 🌿🔥🛡️💧⛰️. The Five Elements are not only reflected in the five stars of celestial motion and the five sacred mountains representing spatial directions but also correspond to the five organs and five senses of the human body, forming a cosmology that interconnects "Heaven, Earth, and Humanity."
The numerical system, through the pairing of "generative numbers" (1–5) and "completion numbers" (6–10), fully illustrates the transformation process of Yin and Yang energy from potential to actualization: Water (generative number 1 → completion number 6) moistens and descends, Fire (2 → 7) flares upward, Wood (3 → 8) bends and straightens, Metal (4 → 9) yields and reforms, and Earth (5 → 10) sows and reaps. Particularly noteworthy is the central role of the Earth element—it serves as the foundation of generative numbers and, through the synthesis of "five + five = ten," oversees the other four elements, becoming the ultimate force for the realization of all things.
The Five Elements generative number system is essentially an ancient Chinese mathematical expression of systemic laws:
In a modern context, this is similar to: any complex system (🔧 society, 💻 organization, 🧬 ecosystem) requires a core regulatory mechanism (Earth) to coordinate the interactions of various elements, transforming theoretical design (generative numbers) into practical results (completion numbers).
The generative number system reveals the philosophical relationship between "potential and actuality": all existence undergoes a process from "mathematical possibility" to "actual manifestation," with the key to transformation lying in finding the appropriate medium and method of integration. The special role of the Earth element reminds us that achieving ideals cannot focus solely on the goal itself but must also emphasize the platform and ecological environment for realizing those goals.
Contemporary systems science has found that complex systems often exhibit interactive patterns of 5–10 key variables, remarkably aligning with the ancient theory of Five Elements generative numbers. This reflects the highly abstract systemic thinking wisdom of ancient people.
Generative Numbers Correspondence Table
| Element | Direction | Generative Number | Completion Number | Generation Principle | Property |
|---|---|---|---|---|---|
| Water🌊 | North | 1 | 6 | Heaven generates Water, Earth completes it | Moistening and descending |
| Fire🔥 | South | 2 | 7 | Earth generates Fire, Heaven completes it | Flaring upward |
| Wood🌿 | East | 3 | 8 | Heaven generates Wood, Earth completes it | Bending and straightening |
| Metal🛡️ | West | 4 | 9 | Earth generates Metal, Heaven completes it | Yielding and reforming |
| Earth⛰️ | Center | 5 | 10 | Heaven generates Earth, Earth completes it | Sowing and reaping |
Please translate the above content into English while maintaining the original format and structure.