The Great Meaning of the Five Phases: Preface

夫五行者，蓋造化之根源，人倫之資始。萬品稟其變易，百靈因其感通。本乎陰陽，散乎精像，周竟天地，布極幽明。子午卯酉為經緯，八風六律為綱紀。故天有五度以垂象，地有五材以資用，人有五常以表德。萬有森羅，以五為度，過其五者，數則變焉。實資五氣，均和四序，孕育百品，陶鑄萬物。善則五德順行，三靈炳曜；惡則九功不革，六沴互興。原始要終，靡究萌兆。

The Five Phases are the fundamental sources of heaven and earth, and the original basis for human relationships and order. All things receive the vital energy of the Five Phases and thus undergo birth, death, and transformation. The various deities also communicate with humans through the energy of the Five Phases. It originates from the dual forces of yin and yang, spreads out as various subtle forms, pervading the entire universe, reaching even the underworld and the human world. The four cardinal directions of Zi, Wu, Mao, and You serve as its meridians and parallels. The eight winds and the six tones of the musical scale constitute its principles and regulations. Therefore, in the heavens there are the five stars indicating celestial phenomena, and on earth there are the five materials—metal, wood, water, fire, and earth—for human use. Humans possess the five virtues—benevolence, righteousness, propriety, wisdom, and faithfulness—expressed as the "Five Constants" to manifest moral conduct. All things, diverse and numerous, are measured by the number five; once the number exceeds five, it must be reset and transformed again. Heaven and earth regulate the four seasons, nurture all living beings, and shape all things through the energy of the Five Phases. When government and education are clear and just, the virtues of the Five Phases proceed in order, and the three celestial spirits—sun, moon, and stars—shine brightly. When government and education are corrupt, the nine functions—water, fire, metal, wood, earth, and grain—cannot be cultivated, and the six disruptive forces ("six disorders") will arise together. Yet, when tracing its origin and seeking its conclusion, humans remain unable to perceive the initial signs of its emergence.

是以聖人體於未肇，故設言以筌象，立象以顯事。事既懸有，可以象知。象則有滋，滋故生數。數則可紀，象則可形。可形可紀，故其理可假而知。可假而知，則龜筮是也。龜則為象，故以日為五行之元；筮則為數，故以辰為五行之主。

Therefore, the sage could perceive things before they occurred, and thus established words to capture images—like using bamboo nets to catch fish. He also established images to clarify principles. Once things actually exist in the world, they can be known through images; once images are formed, they proliferate, and proliferation gives rise to numbers. With numbers, one can record; with images, one can depict. Being able to depict shapes and record numbers, the principles of things can be known through these tools. The tools that can be used to know things are divination by oracle bones and divination by yarrow stalks. Oracle bone divination presents 'images', so the ten heavenly stems, representing 'days', are used as the beginning of the Five Phases. Divination by yarrow stalks deals with 'numbers', so the twelve earthly branches, representing 'terms', are used as the masters of the Five Phases.

若夫參辰伏見，日月盈虧，雷動虹出，雲行雨施，此天之象也。二十八舍，內外諸官，七曜三光，星分歲次，此天之數也。山川水陸，高下平汙，嶽鎭河通，風回露蒸，此地之象也。八極四海，三江五湖，九州島百郡，千里萬頃，此地之數也。禮以節事，樂以和心，爵表章旗，刑用革善，此人之象也。百官以治，萬人以立，四教修文，七德閱武，此人之數也。因夫象數，故識五行之始末；藉斯龜筮，乃辨陰陽之吉凶。是以事假象知，物從數立。

As for the alternation of the star Can and Chen, the rising and setting of the sun and moon, the thunder's rumbling, the appearance of rainbows, the movement of clouds, and the falling of rain and snow, these are the "images" presented by Heaven. The twenty-eight constellations, the stars within and outside the Purple Micro Enclosure, the seven luminaries consisting of the sun, moon, and five planets, the three bright lights of sun, moon, and stars, and the divisions of the constellations along with the years corresponding to the wandering star, these are the "numbers" that Heaven can measure. The mountains and rivers, the land and water, their high and low, flat and uneven, the five great mountains guarding their respective regions, the rivers and canals connecting distant places, the swirling winds and the rising mist, these are the "images" of the earth. The eight directions and the four seas, the three great rivers and five great lakes, the nine provinces and hundreds of states, and the thousands of square li of farmland, these are the "numbers" of the earth. Using rites to regulate human affairs, using music to harmonize people's hearts, using titles and banners to indicate hierarchy, and using punishments to guide people toward goodness, these are the "images" of human affairs. Establishing officials to govern the world, gathering the people to form a state, using the four teachings to cultivate culture, and using the seven virtues to examine military strength, these are the "numbers" of human affairs. It is precisely because there are images and numbers that we can understand the origins and transformations of the Five Phases. It is precisely because of divination through tortoise shells and yarrow stalks that we can discern the auspiciousness and inauspiciousness of yin and yang. Therefore, things are recognized through their images, and all things are established through their numbers.

吉每尋閱墳索，研窮經典，自羲農以來，迄於周漢，莫不以五行為政治之本，以蓍龜為善惡之先。所以《傳》云：天生五材，廢一不可。《尙書》曰：商王受命，狎侮五常，殄棄三政。故知得之者昌，失之者滅。

I often examine ancient classic texts such as the San Feng and Ba Suo, deeply studying the classics of previous dynasties. I have found that since Fuxi and Shen Nong up to the Zhou and Han dynasties, no dynasty failed to regard the Five Phases as the fundamental principle of politics and to use divination with yarrow stalks and turtle shells as the primary means of distinguishing good and evil. Therefore, the Zuo Zhuan says: Heaven produces five materials, and abandoning any one of them is unacceptable. The Shang Shu says: King Zhou of Shang, after receiving the Mandate of Heaven, despised and treated lightly the five constants, and destroyed three essential affairs ("Shou" is the name of King Zhou). From this we can see that a state which masters the Way of the Five Phases will flourish, while one that deviates from it will perish.

昔中原喪亂，晉氏南遷，根本之書不足，枝條之學斯盛。虛談巧筆，競功於一時；碩學經邦，棄之於萬古。末代踵習，風軌遂成。雖復占候之術尚行，皆從左道之說；卜筮之法恆在，爻象之理莫分。《月令》靡依，時制必爽。失之毫髮，千里必差。水旱興而不辨其由，妖祥作而莫知其趣。非因形像，罕徵窮者。觀其謬惑，嘆其學人，皆信其末而忘本，並舉其麤而漏細。

In former times, when chaos prevailed in the Central Plains, the Jin dynasty royal family moved south, and writings that explored fundamental principles became increasingly rare, while studies focusing on superficial details flourished. Hollow discussions and ornate writing vied for fame at that time; scholars who possessed knowledge for governing the state and pacifying the people were discarded by generations. Later generations followed suit, and such practices eventually became a prevailing trend. Although divination by observation of celestial phenomena remains popular, it mostly follows the doctrines of heretical schools; although divination by means of yarrow stalks has continued, the principles of the hexagram lines are no longer understood. Calculations are not based on the "Monthly Orders," so the timing of seasons and periods will inevitably be wrong. A slight error at the beginning leads to a great mistake in the end. When floods and droughts occur, the causes cannot be explained; when portents of calamity or auspicious signs appear, their meanings are not understood. Without verifying through concrete phenomena, few can thoroughly investigate the matter. Seeing these errors and confusions, I feel sorrow for these scholars: they all place importance on the superficial while forgetting the fundamental, grasp the crude while neglecting the subtle.

古人有云：登山始見天高，臨壑方覺地厚。不聞先聖之道，無以知學者之大，況乃五行幽邃，安可斐然。今故博採經緯，搜窮簡牒，略談大義。凡二十四段，別而分之，合四十段。二十四者，節數之氣總；四十者，五行之成數。始自釋名，終於蟲鳥。凡配五行，皆在茲義。庶幾使斯道不墜，知其始焉。若能治心靜志，研其微者，豈直怡神養性，保德全身，亦可弼諧庶政，利安萬有，斯故至人之所達也。昔人感物制經，吉今因事述義，異時而作，共軌殊途。嘆味道之不齊，求利物之一致。倚焉來哲，補其闕焉。

Ancient people have said: only by climbing a high mountain can one see how high the sky is, and only by standing at the edge of a deep valley can one realize how thick the earth is. Those who have not heard of the teachings of the ancient sages cannot know how vast the study of learning is; and how much more so, the principles of the Five Phases are so profound and subtle, how could they be easily explained with a moment's literary display? Therefore, I now widely collect the classics and the supplementary writings, exhaustively gathering all kinds of ancient texts, and briefly discuss their main meanings. The entire work consists of twenty-four sections, each of which is further divided into sub-sections, making a total of forty. The number twenty-four is taken because it represents the total number of the twenty-four solar terms in a year; the number forty is taken because it is the sum of the five numbers of the Five Phases (six, seven, eight, nine, ten). The whole book starts with explaining names and ends with discussing birds, beasts, and insects; all content that corresponds with the Five Phases is included within these meanings. I hope this study will not be abandoned, and people will understand its origin. If one can concentrate the mind and calm the will, to study its subtle aspects, it is not only for cultivating the spirit and temperament, preserving virtue and body, but also can assist in managing various affairs, benefiting all things in the world and bringing peace and stability. This is originally the realm that the sage can reach. Previous people created classics due to their feelings towards external things; today, I, Xiao Ji, explain the great meanings based on specific matters. Although the times are different and the paths taken are different, the ultimate goal is the same. I feel sorrow that people's understanding of this path varies greatly, yet all pursue the same thing, which is benefiting all things. I entrust this to future wise men, asking them to complete the deficiencies in my work.

夫萬物自有體質，聖人象類而制其名，故曰：名以定體。無名乃天地之始，有名則萬物之母。以其因功涉用，故立稱謂。《禮》云：子生三月，咳而名之。及其未生，本無名字。五行為萬物之先，形用資於造化，豈不先立其名，然後明其體用。

All things originally have their own forms and natures. Sages took their images according to their categories and gave them names, so it is said that names are used to determine forms. The Book of Dao and Virtue says that "nameless is the beginning of heaven and earth, and named is the mother of all things." It is precisely because we need to rely on the functions of things and their uses that we establish names. The Book of Rites, Inner Rules says: when a child is three months old, the father plays with him to make him laugh and gives him a name. Before he was born, he had no name. The Five Phases are the pioneers of all things; their forms and functions are derived from the creative power of heaven and earth. How could we not first establish their names and then explain their forms and functions?

《春秋元命苞》曰：木者，觸也，觸地而生。許愼云：木者，冒也，言冒地而出，字從於中下，象其根也。其時春。《禮記》曰：春之為言蠢也，產萬物者也。其位在東方。《尸子》云：東者，動也，震氣故動。《白虎通》云：火之為言化也，陽氣用事，萬物變化也。許愼曰：火者，炎上也，其字炎而上，象形者也。其時夏。《尚書大傳》云：何以謂之夏？夏，假也。假者，方呼萬物而養之。《釋名》曰：夏假者，寬假萬物，使生長也。其位南方。《尙書大傳》云：南，任也，物之方任也。

The Wei texts "Chunqiu Yuanmingbao" say: Wood is "chu", meaning it touches the ground and grows out. Xu Shen's "Shuowen Jiezi" says: Wood is "mao", meaning it pushes through the ground. The character's structure, with a vertical line extending downward, symbolizes its roots. All of this is the Han dynasty's common "shengxun" method, using homophones or near-homophones to explain the original meaning of a character related to seasonal phenomena. Wood corresponds to the season of spring. The "Liji · Xiang Yinjiu Yi" says: The word "chun" (spring) is "chun", meaning it causes things to stir and produce all things. Wood corresponds to the direction of the east. The "Shizi" says: The direction of the east is "dong", meaning movement. The east is associated with the Zhen trigram, which represents movement, so it is called "dong". The "Baihu Tong" says: The word "huo" (fire) is "hua", meaning transformation. At this time, the yang energy is dominant and in charge, and all things change accordingly. Xu Shen's "Shuowen Jiezi" says: Fire is "yan shang", meaning it rises upward like flames. The character is a pictograph showing flames rising. Fire corresponds to the season of summer. The "Shangshu Dazhuan" says: Why is this season called "xia"? "Xia" means "jia", meaning it is calling and nurturing all things. The "Ximing" says: The reason "xia" is interpreted as "jia" is because it is generous and allows all things to grow freely. Fire corresponds to the direction of the south. The "Shangshu Dazhuan" says: The direction of the south is "ren", meaning all things are bearing the responsibility of growth.

《元命苞》云：土之為言吐也，含吐氣精，以生於物。許愼云：土者，吐生者也。王肅云：土者，地之別號，以為五行也。許愼云：其字，二以象地之下與地之中，以一直畫，象物初出地也。其時季夏。季，老也，萬物於此成就方老，王於四時之季，故曰老也。其位處內。內，通也。《禮斗威儀》云：得皇極之正氣，含黃中之德，能苞萬物。

The Spring and Autumn Original Mandate苞 says: The character "土" means "to emit," it contains and emits vital energy to nurture all things. Xu Shen says: "土" refers to the thing that gives birth to all things. Wang Su says: "土" is another name for the earth, and it is ranked among the Five Phases. Xu Shen also says: The character "土" is written with two horizontal strokes above and below to represent the ground and the layers beneath it, and a vertical stroke in the middle to symbolize all things breaking through the soil. The season corresponding to "土" is the last month of summer, which is June. "季" means old, and at this time, all things have matured and become old. "土" is also dominant in the last month of each of the four seasons, so it is called "old." The position of "土" is in the center. "内" has the meaning of being open and accessible. The "Rites of the Celestial Pole" says: "土" receives the central and upright energy of the Emperor's Pole, contains the virtue of the central yellow color, and thus can embrace all things.

許慎云：金者，禁也，陰氣始起，萬物禁止也。土生於金，字從土，左右注，象金在土中之形也。其時秋也。《禮記》云：秋之為言愁也，愁之以時察守義者也。《尸子》云：秋，肅也，萬物莫不肅敬恭莊，禮之主也。《說文》曰：天地反物為秋。其位西方。《尚書大傳》云：西，鮮也。鮮，訊也。訊者，始入之貌也。

Xu Shen said: Metal is "Jin", which means "prohibition". At this time, Yin energy begins to rise, and all things are restrained and no longer grow. Earth produces metal, so the character "Jin" includes "Tu" (earth) with two dots on either side, symbolizing the shape of a block of metal buried in the earth. The season corresponding to metal is autumn. The "Li Ji · Xiang Yin You Yi" says: The word "autumn" is "Chou", which refers to the solemn and severe season that causes people to feel anxious and alert, which is precisely the season for upholding righteousness. The "Shi Zi" says: Autumn is "Su", all things are solemn, respectful, and dignified, and it is the master of ritual. The "Shuo Wen" says: When the energies of heaven and earth reverse and all things transition from growth to decline, this is called autumn. The direction corresponding to metal is the west. The "Shang Shu Da Zhuan" says: West is "Xian", and "Xian" is "Xun", which refers to the state of being just newly gathered and stored.

《釋名》《廣雅》《白虎通》皆曰：水，準也，平準萬物。《元命苞》曰：水之為言演也，陰化淖濡，流施潛行也。故立字，兩人交，一以中出者為水。一者，數之始；兩人，譬男女，陰陽交以起一也。水者，五行始焉，元氣之湊液也。《管子》云：水者，地之血氣，筋脈之通流者，故曰水。許慎云：其字象泉並流，中有微陽之氣。其時冬。《尸子》云：冬，終也，萬物至此終藏也。《禮記》云：冬之為言中也。中者，藏也。其位北方。《尸子》云：北，伏也，萬物至冬皆伏，貴賤若一也。五行之時及方位，故分而釋之。

The Shiming, Guangya, and Baitu Tong all say that water is "zhun," which means it can level and measure all things, just as water surfaces are level. The Chunchou Yuanming Bao says that the character for water is "yan," meaning that the yin energy generates moist and muddy vapor, which flows and spreads, moving beneath the earth. Therefore, when the character for water was created, it took the shape of two people crossing each other with a vertical stroke passing through the middle: one represents the beginning of numbers, with two people symbolizing male and female, that is, the union of yin and yang producing "one." Water is the beginning of the Five Phases, a liquid formed from the condensation of the original qi. The Guanzi says that water is the blood of the earth, the fluid that circulates through its sinews, hence it is called water. Xu Shen says that the character for water resembles flowing spring water, with the central stroke containing a slight yang energy. Water corresponds to the season of winter. The Shizi says that winter is "zhong," meaning that all things reach their end and are stored away. The Li Ji says that the character for winter is "zhong," meaning that it is the time when things are stored internally. Water corresponds to the direction of the north. The Shizi says that north is "fu," meaning that all things become hidden in winter, regardless of their status. This is how the Five Phases correspond to the seasons and directions, so they are explained separately.

支干者，因五行而立之。昔軒轅之時，大撓之所制也。蔡邕《月令章句》云：大撓採五行之情，占斗機所建也。始作甲乙以名日，謂之干；作子丑以名月，謂之支。有事於天，則用日；有事於地，則用辰。陰陽之別，故有支干名也。

The "branch and stem" (i.e., the later term "gan zhi") were established based on the Five Phases. It is said that they were created during the time of the Yellow Emperor, Huangdi, by his minister Dazao. Cai Yong's "Chapter on the Monthly Ordinances" states: Dazao observed the characteristics of the Five Phases and also studied the direction indicated by the handle of the Big Dipper (the Dipper's handle), thus beginning to create the characters for the ten heavenly stems, such as Jia and Yi, to mark days, called "gan"; and the characters for the twelve earthly branches, such as Zi and Chou, to mark months, called "zhi". Matters related to heaven are marked with "day", which refers to the ten heavenly stems; matters related to earth are marked with "chén", which refers to the twelve earthly branches. Heaven belongs to yang, and earth belongs to yin, and because of the distinction between yin and yang, the terms "gan" and "zhi" were divided into two separate categories.

而名有總別，先論總名，次言別號。總名支干者，干字乃有三種不同：一作干，二作簳，三作干字。今解簳字者，此支簳既相配成用，如樹木之有支條莖簳，共為樹體，所以雲簳。又作干者，幹濟為義；支者，支任為義。以此日辰，任濟萬事，故云支干。又作干字者，亦是簳義，如物之在竿上，能豎立顯然，故亦云竿也。世書從易，故多干也。

The term has both a general name and specific names. First, the general name is given, then the individual alternative names. In terms of the general name "Zhi Gan," the character "Gan" has had three different forms throughout history: one is written as "Gan," another as "Gan" (meaning arrow shaft or main stem), and the third as "Gan." First, we explain "Gan": the Earthly Branches and the main "Gan" must be combined to be useful, just as a tree has both its branches and its central stem, together forming the whole tree, so it is written as "Gan." When written as "Gan," it takes the meaning of "Gan Ji" — capable of accomplishing things; "Zhi" takes the meaning of "Zhi Ren" — supporting and shouldering responsibilities: using these Day Branches to shoulder and accomplish all worldly affairs, hence called "Zhi Gan." When written as "Gan," it still refers to the meaning of "Gan": just as things are placed on a bamboo pole and thus stand upright and become visible, so it is also called "Gan." Because of the convenience of writing, common people often write it as "Gan."

次別號者。《詩緯推度災》云：甲者，押也，春則開也，冬則闔也。鄭玄注《禮記·月令》云：甲者，抽也。乙者，軋也。春時萬物皆解，孚甲自抽軋而出也。丙者，柄也，物之生長，各執其柄。鄭玄云：丙者，炳也。夏時萬物強大，炳然著見也。

Next, it explains the alternative names of each character. The esoteric text "Poetry Weave · Push and Measure Calamity" says: Jia is called "ya" (gate), opening in spring and closing in winter. Zheng Xuan's commentary on "Rites of the Monthly Ordinances" says: Jia is "chou" (to split open), Yi is "ya" (to press); in spring, the shells of all things split open, and the seeds' shells themselves split open and press their way out of the ground. Bing is "bing" (handle), as all things grow, each holding its own handle. Zheng Xuan says: Bing is "bing" (bright), in summer all things become strong and tall, clearly and brightly appearing. These explanations use homophones and near-homophones to indicate the phenological characteristics represented by each heavenly stem, belonging to the Han dynasty method of "sound interpretation" (shengxun).

丁者，亭也。亭，猶止也，物之生長，將應止也。戊者，買也，生長既極，極則應成買易前體也。己者，紀也，物既始成，有條紀也。鄭玄云：戊之言茂也，己之言起也，謂萬物皆枝葉茂盛，其含秀者抑屈而起也。庚者，更也。辛者，新也。謂萬物成代，改更復新也。鄭玄云：謂萬物皆肅然改更，秀實新成也。壬者，任也。癸者，揆也。陰任於陽，揆然萌牙於物也。鄭玄云：時維藏，萬物懷任於下，揆然萌牙也。

Ding is "ting," meaning to stop. Just as things come to a halt at this stage, the growth of all things reaches this point and is about to stop. Wu is "mai (trade)," meaning that growth has reached its peak, and at the peak, it should achieve completion and exchange the previous form. Ji is "ji (order)," meaning that after things have initially taken shape, they have order and structure. Zheng Xuan said: Wu refers to "mao (prosperous)," and Ji refers to "qi (arise)," meaning that all things have their branches and leaves flourishing, with the ears of grain first bent down and then rising up. Geng is "geng (change)," and Xin is "xin (new)," meaning that all things undergo generations of alternation and renewal. Zheng Xuan said: This refers to all things being solemnly renewed, with the ears of grain and fruits being formed anew. Ren is "ren (pregnancy)," and Gui is "kui (measure)," meaning that the yin energy is pregnant within the yang energy, and the budding can be vaguely measured. Zheng Xuan said: At this time, the main characteristic is gathering and storing, with all things pregnant beneath the earth, and the sprout can be vaguely measured.

子者，孳也，陽氣既動，萬物孳萌。《三禮義宗》云：陽氣至，孳養生。丑者，紐也。紐者，繫也，續萌而繫長也。故曰：孳萌於子，紐牙於丑。《三禮義宗》云：言居終始之際，故以紐結為名。寅者，移也，亦云引也，物牙稍吐，引而申之，移出於地也。《淮南子》云：寅，螾動生也。《三禮義宗》云：寅者，引也，肆建之義也。卯者，冒也，物生長大，覆冒於地也。《淮南子》云：丣，茂也。茂，然也。《三禮義宗》云：丣，茂也。陽氣至此，物生滋茂。

Zi means "zi," which refers to the sprouting of life. Yang energy has begun to stir, and all things start to sprout and grow. The "San Li Yi Zong" says: When yang energy arrives, it fosters the vitality of life. Chou means "nou," which refers to a knot or connection. It connects the sprouting buds and continues their growth, so it is said: sprouting occurs in Zi, and knotting occurs in Chou. The "San Li Yi Zong" says: Chou is at the junction of the end of a year and the beginning of the next, so it is named "knotting." Yin means "yi," or "yin," referring to the emergence of tender shoots, which stretch and extend, moving out of the ground. The "Huainanzi" says: Yin is the time when earthworms (ying) begin to move and live. The "San Li Yi Zong" says: Yin means "yi," which signifies striving to establish and exert. Mao means "mao," which refers to the flourishing of all things, covering the ground. The "Huainanzi" says: Mao (the ancient character for卯) means "mao," which means flourishing, indicating prosperity. The "San Li Yi Zong" says: Mao means flourishing, and at this point, yang energy reaches its peak, and all things flourish and grow vigorously.

辰者，震也，震動奮迅，去其故體也。《三禮義宗》云：此月之時，物盡震動而長。巳者，巳也，故體洗去，於是巳竟也。《三禮義宗》云：巳，起也。物至此時，皆畢盡而起。午者，仵也，亦云萼也。仲夏之月，萬物盛大，枝柯萼佈於午。《淮南子》云：午者，忤也。《三禮義宗》云：仵，長也，大也，明物皆長大也。未者，昧也，陰氣已長，萬物稍衰，體薆昧也，故曰：薆昧於未。《淮南子》云：未，味也。《三禮義宗》云：時物向成，皆有氣味。

Chen corresponds to "Zhen," which signifies movement and stirring, the shedding of old forms. The "Three Rituals: Meaning of the Categories" states: during this month, all things shake and grow. Si corresponds to "Si," meaning the complete shedding of old forms, at which point the process is concluded. The "Three Rituals: Meaning of the Categories" says: Si corresponds to "Qi," meaning that at this time, all things have exhausted their old forms and begin anew. Wu corresponds to "Wu" (opposition), also called "E." In the middle of summer, May, all things are flourishing, with branches and flower buds spreading out during the Wu month. The "Huainanzi" says: Wu corresponds to "Wu" (opposition), as the yin and yang energies begin to oppose each other. The "Three Rituals: Meaning of the Categories" says: Wu signifies growth and fullness, indicating that all things have grown large. Wei corresponds to "Mai," meaning that yin energy has grown, and all things slightly decline, with forms becoming hidden and obscure, hence "Mai Mei Yu Wei." The "Huainanzi" says: Wei corresponds to "Wei" (taste). The "Three Rituals: Meaning of the Categories" says: at this time, all things tend toward maturity, and have already developed their flavors.

申者，伸。伸，猶引也，長也，衰老引長。《淮南子》云：申，呻也。《三禮義宗》云：申者，身也，物皆身體成就也。酉者，老也，亦云熟也，萬物老極而成熟也。《淮南子》云：酉，飽也。《三禮義宗》云：酉，猶也。猶，倫之義也。此時物皆縮小而成也。戌者，滅也，殺也，九月殺極，物皆滅也。《三禮義宗》云：此時物衰滅也。亥者，核也，閡也，十月閉藏，萬物皆入核閡。《三禮義宗》云：亥，劾也，言陰氣劾殺萬物也。

Shen is "shen," meaning extension. Extension is like pulling and growing, indicating that things continue to stretch even as they age. The Huainanzi says that Shen is "shen," meaning to groan. The Sanli Yizong says that Shen is "shen," meaning body. At this time, all things have matured. You is "lao," also meaning "shu," indicating that things have aged to the extreme and have matured. The Huainanzi says that You is "bao," meaning full. The Sanli Yizong says that You is "you," meaning order and sequence. At this time, all things contract and become small, completing their form. Xu is "mie," meaning "sha," indicating that by September, the severe and killing force reaches its peak, and all things return to extinction. The Sanli Yizong says that at this time, all things decay and perish. Hai is "he," meaning "he" or "mo," indicating that in October, things retreat and are gathered into the core, closing off. The Sanli Yizong says that Hai is "he," meaning to investigate and punish, indicating that the yin energy investigates and punishes all things.

《爾雅》歲次云：大歲在寅，名攝提格。《淮南子》注云：格，起也，萬物承陽而起。卯名單閼。單，盡。閼，止也。言陽氣推萬物而起，陰氣盡止也。辰名執徐。執，蟄也。徐，舒也。言伏蟄之物，皆散舒而出也。巳名大荒落。荒，大也。言萬物熾盛而大出，落落而佈散也。午名敦。《淮南子》云：欃槍敦，盛，壯也。言萬物盛壯也。未名協洽。《淮南子》云：協，和也。洽，合也。言陰欲化，萬物和合也。

The *Erya* records the names of the years according to the movement of the Sovereign Star (Tai Su). When the Sovereign Star is in the Year of the Tiger (Yin), it is called "She Ti Ge." The commentary in the *Huainanzi* says: "Ge" means to begin; all things receive the yang energy and begin to flourish. When the Sovereign Star is in the Year of the Rabbit (Mao), it is called "Dan Yan." "Dan" means to reach the end, and "Yan" means to stop; this refers to the yang energy driving the flourishing of all things, while the yin energy reaches its end and stops. When the Sovereign Star is in the Year of the Dragon (Chen), it is called "Zhi Xu." "Zhi" means to be hidden, and "Xu" means to stretch out; this refers to hidden creatures spreading out and stretching themselves. When the Sovereign Star is in the Year of the Snake (Si), it is called "Da Huang Luo." "Huang" means great, indicating that all things are flourishing and bursting forth in great numbers. When the Sovereign Star is in the Year of the Horse (Wu), it is called "Dun." The original text has a missing character after "Dun," and the common version of this year name is two characters. The *Huainanzi* says: the name of the comet (Zhan Qiang) is "Dun," meaning fullness or strength; this refers to all things being strong and flourishing. When the Sovereign Star is in the Year of the Goat (Wei), it is called "Xie Xie." The *Huainanzi* says: "Xie" means harmony, and "Xie" means union. This refers to the yin energy about to take charge of nurturing, and all things harmonizing and uniting.

申名涒灘。《淮南子》云：涒灘，大修也。言萬物皆修其精氣也。酉名作鄂。《淮南子》云：作鄂，零落也。言萬物皆陊落也。戌名掩茂。掩，蔽也。茂，冒也。言萬物皆蔽冒也。亥名大淵獻。淵，藏。獻，迎也。言萬物終亥，大小深藏窟伏，以迎陽也。子名困敦。困，混也。敦，沌也。言陽氣混沌，萬物牙孽也。丑名赤奮若。奮，起也。若，從也。言陽氣奮迅萬物而起，無不順其性。赤，陽色也。《春秋緯》云：大陰所在之名，與《淮南子》《爾雅》不同。此並支干別名大意，終從氣解，故以具釋之。

The Tai Su is in Shen called "Tun Tan." The "Huainanzi" says: "Tun Tan" means great renewal. It refers to all things renewing their vital energies. The Tai Su is in You called "Zuo E." The "Huainanzi" says: "Zuo E" means withering. It refers to all things falling away. The Tai Su is in Xu called "Yan Mao." "Yan" means to cover, "Mao" means to cover over, meaning all things are covered and hidden. The Tai Su is in Hai called "Da Yuan Xian." "Yuan" means deep concealment, "Xian" means to welcome, meaning all things reach Hai and come to an end, regardless of size, they deeply conceal themselves in their holes to welcome the coming yang energy of the next year. The Tai Su is in Zi called "Kun Dun." "Kun" means confusion, "Dun" means turbid, meaning the yang energy is still in a confused state, and all things have just begun to sprout tender shoots. The Tai Su is in Chou called "Chi Fen Rao." "Fen" means to rise up, "Rao" means to follow, meaning the yang energy vigorously promotes the rise of all things, none does not follow its nature; "Chi" is the color of yang energy. The "Chunqiu Wei" records the names of the years corresponding to the Tai Su (the Tai Yin), which differ from those in the "Huainanzi" and the "Erya." These are the general meanings of the alternative names of the heavenly stems and earthly branches. In the end, they are all explained from the waxing and waning of yin and yang energy, so I have explained them in detail here.

體者，以形質為名；性者，以功用為義。以五行體性，資益萬物，故合而辨之。木居少陽之位，春氣和煦溫柔，弱火伏其中，故木以溫柔為體，曲直為性。火居大陽之位，炎熾赫烈，故火以明熱為體，炎上為性。土在四時之中，處季夏之末，陽衰陰長，居位之中，總於四行。積塵成實，積則有間，有間故含容；成實故能持。故土以含散持實為體，稼穡為性。金居少陰之位，西方成物之所，物成則凝強，少陰則清冷，故金以強冷為體，從革為性。水以寒虛為體，潤下為性。

"The 'body' refers to the form and texture, while 'nature' refers to the function and effect. The body and nature of the Five Phases can nourish and benefit all things, so they are analyzed together. Wood is in the position of 'Less Yang', with spring's warm and gentle energy, and a faint fire energy hidden within it. Therefore, wood has a body of gentleness and a nature of being flexible and straight. Fire is in the position of 'Sun', with intense heat, so fire has a body of brightness and heat, and a nature of rising upwards and burning. Earth is in the middle of the four seasons, at the end of the sixth month of late summer, when yang energy declines and yin energy increases. It occupies the central position and oversees the other four phases. Dust accumulates to form a solid mass, and when piled up, it leaves gaps. Because of the gaps, it can contain; because of the solid mass, it can bear. Therefore, earth has a body that can both contain and let things pass through, and a nature of sowing and harvesting. Metal is in the position of 'Less Yin', and the west is where things mature. Once things mature, they become firm and solid, and the energy of 'Less Yin' is cold. Therefore, metal has a body of firmness and coldness, and a nature of being shaped and transformed into objects according to models. Water has a body of coldness and softness, and a nature of moistening and flowing downward."

《洪範》云：木曰曲直，火曰炎上，土曰稼穡，金曰從革，水曰潤下。是其性也。《淮南子》云：天地之襲精為陰陽，陰陽之專精為四時，四時之散精為萬物。積陰之寒氣反者為水，積陽之熱氣反者為火。水雖陰物，陽在其內，故水體內明；火雖陽物，陰在其內，故火體內暗。木為少陽，其體亦含陰氣，故內空虛，外有花葉，敷榮可觀。金為少陰，其體剛利，殺性在外，內亦光明可照。土苞四德，故其體能兼虛實。

The Book of Documents, Hongfan section, says: The nature of wood is to be flexible and straight; the nature of fire is to rise upward and burn; the nature of earth is to till and harvest; the nature of metal is to follow the mold and change; the nature of water is to moisten and flow downward. This describes the 'nature' of the Five Phases. The Huainanzi, Tianwen Xun, says: The qi of heaven and earth accumulates and combines to form yin and yang; the qi of yin and yang concentrates to form the four seasons; the qi of the four seasons spreads to form all things; when the accumulated yin qi turns cold, it becomes water; when the accumulated yang qi turns hot, it becomes fire. Although water belongs to yin, it contains yang qi within, so its interior is clear; although fire belongs to yang, it contains yin qi within, so its inner part is dark. Wood is the lesser yang, and its form contains yin qi, so it is hollow inside, with flowers and leaves growing outside, appearing flourishing. Metal is the lesser yin, and its form is hard and sharp, with a severe nature expressed externally, and its interior is smooth enough to reflect images. Earth encompasses the virtues of the other four phases, so its form can have both emptiness and solidity.

《洪範傳》曰：木曰曲直者，東方。《易》云：地上之木為觀。言春時出地之木，無不曲直，花葉可觀，如人威儀容貌也。許愼云：地上之可觀者，莫過於木，故相字，目傍木也。古之王者，登輿有鸞和之節，降車有佩玉之度，田狩有三驅之制，飲餞有獻酢之禮，無事不巡幸，無奪民時，以春，農之始也，無貪慾奸謀，所以順木氣。木氣順則如其性，茂盛敷實，以為民用，直者中繩，曲者中鉤。若人君失威儀，酖酒淫緃，重徭厚稅，田獵無度，則木失其性，春不滋長，不為民用，橋樑不從其繩墨，故曰木不曲直也。

The *Hong Fan Wu Xing Zhuan* says: "So-called 'wood is flexible and straight,' wood is associated with the East. The *Zhou Yi* says that when there is wood on the ground, it is the image of the *Guan* hexagram — meaning that trees sprouting from the earth in spring are either flexible or straight, their flowers and leaves are for viewing, like the dignity and appearance of a person. Xu Shen said: the most worth viewing on the ground is wood, so the character 'xiang' (appearance) is written with 'mu' (wood) and 'mu' (eye) as a radical. Ancient kings had regulations on the sound of the bells on their chariots, and on the sound of jade when they walked, hunting had the system of driving from three sides and leaving one open, and banquets had the etiquette of toasting between hosts and guests. They would not go out without important affairs, nor would they interfere with the farming season of the people — because spring is the beginning of farming; they would not indulge in greed or schemes. Doing this would follow the wood energy. If the wood energy is smooth, the wood can maintain its nature, its branches and leaves flourish, and it bears much fruit, providing for the people. Straight wood conforms to the plumb line, and curved wood conforms to the compass. If the king loses his dignity, indulges in wine and women, and indulges in excess, imposes heavy labor and taxes, and hunts without restraint, then the wood loses its nature: spring does not flourish, cannot provide for the people, and the wood used for building bridges does not conform to the plumb line and compass. Therefore, this is called 'wood not flexible and straight.'"

火曰炎上。炎上者，南方，揚光輝在盛夏，氣極上，故曰炎上。王者嚮明而治，蓋取其象。古者明王南面聽政，攬海內雄俊，積之於朝，以助明也；退邪佞之人臣，投之於野，以通壅塞。任得其人，則天下大治，垂拱無為。《易》以離為火，為明；重離，重明，則君臣俱明也。明則順火氣，火氣順則如其性，如其性則能成熟，順人士之用，用之則起，舍之則止。若人君不明，遠賢良，進讒佞，棄法律，疎骨肉，殺忠諫，赦罪人，廢適立庶，以妾為妻，則火失其性，不用則起，隨風斜行，焚宗廟宮室，燎於民居，故曰火不炎上。

The phrase "fire is characterized by rising" refers to the nature of fire, which is associated with the south. In the height of summer, fire shines brightly and its energy rises strongly, hence it is called "rising." A ruler facing the light to govern the world takes this as a model. In ancient times, wise kings faced south to receive the court, gathering outstanding talents into the government to assist in their clear discernment; they expelled wicked ministers and sent them to the mountains and fields, thus opening up blocked channels of speech. When people are properly appointed, the world is well governed, and the ruler can rule by doing nothing. The "Zhou Changes" use the Li hexagram to symbolize fire and light. The Li hexagram has Li above and below, forming the image of "double brightness," meaning both the ruler and ministers are clear and upright. When politics are clear, it aligns with the nature of fire, allowing fire to maintain its essence. When fire maintains its essence, it can cook food, and when people use it, it burns; when it is abandoned, it goes out. If a ruler is dull, distant from the virtuous, and favors the deceitful, neglects laws, distances close relatives, kills those who speak truthfully, pardons criminals, removes the legitimate heir and installs the illegitimate one, and elevates concubines to the position of wife, then fire loses its essence. It burns on its own without being used, spreads wildly with the wind, burning temples and palaces, and spreading to the homes of the people. Thus, this is called "fire not rising."

土爰稼穡。稼穡者，種曰稼，斂曰穡。土為地道，萬物貫穿而生，故曰稼穡。土居中，以主四季，成四時。中央，為內事宮室夫婦親屬之象。古者天子至於士人，宮室寢處，皆有高卑節度。與其過也，寧儉。禹卑宮室，孔子善之。后夫人左右妾媵有差，九族有序，骨肉有恩，為百姓之所軌則也。如此順中和之氣，則土得其性；得其性，則百穀實而稼穡成。如人君縱意廣宮室臺榭，鏤雕五色，罷盡人力，親疎無別，妻妾過度，則土失其性；土失其性，則氣亂，稼穡不成，故五穀不登，風霧為害，故曰土不稼穡。

The phrase "土爰稼穑" means that the earth is responsible for planting and harvesting. Planting is called "稼," and harvesting is called "穑." The earth represents the principle of the great land, through which all things grow and emerge. Therefore, it is said that the earth governs planting and harvesting. The earth is located in the center, overseeing the last month of each season and completing the four seasons of the year. The center also symbolizes domestic affairs within the palace, representing the relationship between husband and wife and among relatives. In ancient times, from the Son of Heaven down to the common scholar, the height and rank of their dwellings were strictly regulated; it is better to be frugal than to be extravagant. King Yu lived in a simple dwelling, which Confucius praised. The queen mother and her attendants had their respective ranks, with the nine generations of relatives properly ordered in terms of closeness and distance, and affection among family members, becoming a model for the people to follow. In this way, the principle of harmony and balance is followed, and the earth retains its nature; when the earth retains its nature, all grains become full and abundant, and planting and harvesting are successful. If the ruler recklessly expands palaces and pavilions, adorns them with intricate carvings and colorful decorations, exhausts the people's strength, fails to distinguish between close and distant relatives, and has an excessive number of concubines beyond the proper limits, then the earth loses its nature. When the earth loses its nature, the earth's energy becomes chaotic, planting and harvesting fail, leading to poor harvests of the five grains, and disasters such as winds and mists follow continuously. That is why it is said that this is called "the earth not planting and harvesting."

金曰從革。從革者，革，更也，從範而更，形革成器也。西方物既成，殺氣之盛，故秋氣起而鷹隼擊，春氣動而鷹隼化，此殺生之二端。是以白露為霜，霜者，殺伐之表。王者教兵，集戎事以誅不義，禁暴亂以安百姓。古之人君，安不忘危，以戒不虞，故曰：天下雖安，忘戰者危；國邑雖強，盒摒必亡。殺伐必應義，應義則金氣順，金氣順則如其性，如其性者，工冶鑄作，革形成器。如人君樂侵凌，好攻戰，貪色賂，輕百姓之命，人民騷動，則金失其性，冶鑄不化，凝滯渠堅，不成者眾。秋時萬物皆熟，百穀已熟，若逆金氣，則萬物不成，故曰金不從革。

The phrase "gold is said to be 'from revolution'" means that "revolution" refers to change. Gold conforms to the mold and changes shape to be cast into objects. The west is the place where all things are fully formed, and the most severe cutting and killing energy is present. Therefore, when autumn comes, eagles and hawks attack their prey; when spring comes, eagles and hawks turn into doves—this represents the extremes of killing and nurturing. Thus, white dew condenses into frost, and frost is the manifestation of cutting and killing energy. A ruler trains his army, gathers military affairs to attack the unjust, and prohibits violence to stabilize the people. Ancient rulers remembered the dangers even in times of peace to guard against unexpected events. Therefore, it is said: although the world is peaceful, forgetting military preparedness is dangerous; although cities are strong, loving war will surely lead to destruction. Killing must be in accordance with righteousness; when it is in accordance with righteousness, the metal energy flows smoothly; when the metal energy flows smoothly, metal preserves its nature; when it preserves its nature, craftsmen can melt and cast it into objects. If a ruler likes to bully other countries, loves war, is greedy for women and bribes, and despises the lives of the people, causing the people to be restless and disturbed, then metal loses its nature: it cannot be melted, becomes stagnant and hard, and mostly cannot be cast into objects. In autumn, all things are mature, and the harvest of hundreds of grains is expected. If one goes against the metal energy, all things cannot be completed, so this is called "metal does not conform to revolution."

水曰潤下。潤下者，水流溼，就汙下也。北方至陰，宗廟祭祀之象。冬，陽之所始，陰之所終，終始者，綱紀時也。死者魂氣上天為神，魄氣下降為鬼，精氣散在於外而不反，故為之宗廟，以收散也。《易》曰：渙，亨，王假有廟。此之謂也。夫聖人之德，又何以加於孝乎。故天子親耕，以供粢盛；王后親蠶，以供祭服，敬之至也。敬之至，則鬼神報之以介福。此順水氣，水氣順，則如其性；如其性，則源泉通流，以利民用。若人君廢祭祀，慢鬼神，逆天時，則水失其性，水暴出，漂溢沒溺，壞城邑，為人之害，故曰水不潤下也。

The saying "water is characterized by its downward flow" means that water flows toward damp places and tends toward low-lying areas. The north is the place of utmost yin, symbolizing matters of worship and ancestral rites. Winter is the time when yang energy begins to emerge and yin energy reaches its end; this transition marks the key point in the cycle of time. After a person dies, their spirit ascends to heaven to become a deity, while their body descends to earth to become a ghost. Their vital energy disperses and does not return, so ancestral temples are built for the deceased to gather and contain this dispersed energy. The hexagram statement of "Huan" (Dispersal) in the Zhou Changes says: "Huan, smooth, the king goes to the temple." This refers to the king gathering scattered people's hearts and spiritual energies in the temple. What greater virtue is there than filial piety? Therefore, the Son of Heaven personally tills the籍田 to provide millet and millet for worship; the Queen Mother personally raises silkworms to provide ceremonial garments, showing the utmost reverence. When reverence is at its peak, the spirits and deities respond with great blessings. This aligns with the nature of water; when water's nature is unimpeded, it maintains its essence; when it maintains its essence, its source flows smoothly, benefiting the people. If a ruler neglects worship and shows disrespect to spirits, violates the natural order, then water loses its nature: it overflows, floods, destroys cities, and becomes a calamity for people. That is why it is called "water does not flow downward."

凡萬物之始，莫不始於無而後有。是故易有大極，是生兩儀，兩儀生四序。四序，生之所生也，有萬物滋繁，然後萬物生成也。皆由陰陽二氣，鼓舞陶鑄，互相交感。故孤陽不能獨生，單陰不能獨成，必須配合以爐冶，爾乃萬物化通。是則天有其象，精氣下流；地道含化，以資形始。陰陽消長，生殺用成。明其道難明，非數不可究，故因子以辨之。數之顯理，猶筌蹄之取魚兔。陽順唱始，陰佐其終，窮奇偶之數，備相成之道，極變化之源者，詳於蓍策之數也。

All beginnings of things are first "non-being" and then "being." Therefore, the Great Treatise of the Zhou Changes says: The Book of Changes has the Taiji, from which the two principles of yin and yang arise. The two principles generate the four seasons. The four seasons, being generated, go on to generate other things, thus giving rise to the proliferation of all things. Then all things are formed. All this comes from the movement and shaping of the two principles of yin and yang, which interact with each other. Therefore, isolated yang cannot generate things, and isolated yin cannot form things. They must be combined, like the smelting of metal in a furnace, so that all things can be transformed and developed. Thus, heavenly phenomena appear, and the vital energies descend. The earth's way is to contain and nurture, aiding in the formation of forms. The mutual increase and decrease of yin and yang lead to the processes of growth and decline. To explain this principle is difficult, and without the use of numbers, it cannot be fully understood. Therefore, numbers are used to distinguish it. Using numbers to show meaning is like using a bamboo basket to catch fish or a rabbit net to catch rabbits; it is a tool for obtaining things. Yang energy proceeds smoothly and initiates the beginning, while yin energy supports and completes the end. To exhaust the odd and even numbers, to fully embody the principle of mutual support, and to trace the origin of change, the most complete is found in the counting of the yarrow stalks used in divination.

七八為靜，九六為動。陽動而進，變七之九，象氣息也。明陽道之舒，以象君德，唱始不休，無所屈後，去極一等，而猶進之，故九動也。陰動而退，變八之六，象氣消也。以明臣法有所屈後，唱和而已。蕝霧近君，則靖息以聽命，必須退讓，以明其義，故八靜也。

In divination, the numbers seven and eight represent 'static lines' (unchanging lines), while nine and six represent 'moving lines' (changing lines). When a yang line moves, it advances, changing from seven to nine, symbolizing the growth and flourishing of yang energy. This indicates the expansion of yang, representing the virtue of a sovereign: initiating action without hesitation, unwilling to lag behind others; even when approaching the extreme point (nine is close to ten), it still moves forward, hence nine is considered the number for yang movement. When a yin line moves, it retreats, changing from eight to six, symbolizing the reduction of yin energy. This indicates the conduct of a minister should involve yielding and retreating, merely responding to orders. Attendant ministers close to the sovereign must remain quiet and wait for commands, needing to yield to demonstrate the meaning of the relationship between sovereign and minister, hence eight is considered the number for yin stillness.

《易》曰：分二以象兩，掛一以象三，揲之以四，以象四時者。餘手有四七，故名七也；有四八，故名八也。有此，則靜爻之數。夏殷尚質，以用靜爻占之。餘有四九，故名九也；有四六，故名六也。此則動爻之數。周備質文，故兼用動爻。

The Great Treatise of the Zhou Changes explains the method of divination using yarrow stalks: fifty stalks are divided into two groups, symbolizing the two principles of heaven and earth. One stalk is then set aside, symbolizing the three principles of heaven, earth, and humanity. Then, the remaining stalks are counted in groups of four, symbolizing the four seasons. After counting, if the remaining stalks form four groups of seven (twenty-eight), it is called seven; if they form four groups of eight (thirty-two), it is called eight—these two numbers are the numbers for static lines. The Xia and Shang dynasties valued simplicity, so they used static lines for divination. If the remaining stalks form four groups of nine (thirty-six), it is called nine; if they form four groups of six (twenty-four), it is called six—these two numbers are the numbers for moving lines. The Zhou dynasty combined simplicity with refinement, so both static and moving lines were used.

凡大衍極天地之數，五十有五也。京房以十日、十二辰、二十八宿，合應五十。其一不用者，天之生氣，將欲以虛求實，故用四十九焉。馬融以易之大極為北辰也，生兩儀，兩儀生日月，日月生四時，四時生五行，五行生十二月，十二月生二十四氣。北辰居位不動，其餘四十九，轉運而用也。

The total number of lines in the Great Derivation (Da Yan) exhausts the numbers of heaven and earth, originally fifty-five. Jing Fang used ten heavenly stems, twelve earthly branches, and twenty-eight constellations to add up to fifty. He left one line unused, symbolizing the heavenly vital energy that is ever-renewing. This is to indicate that seeking the real through emptiness, the actual number used is forty-nine. Ma Rong believed that the Taiji (Supreme Ultimate) in the Zhou Yi is the North Star. Taiji gives rise to the two principles (Yi), the two principles give rise to the sun and moon, the sun and moon give rise to the four seasons, the four seasons give rise to the Five Phases, the Five Phases give rise to the twelve months, and the twelve months give rise to the twenty-four solar terms (adding one and two, two and four, five and twelve, twenty-four, totaling fifty). The North Star remains stationary in its position, while the other forty-nine elements rotate and move, used for divination with the yarrow stalks.

鄭玄曰：貞悔六爻，本有五十。定所用者，四十有九。天地之數，本五十五。天五與地十通，天一與地六通。數之者氣則有並，並則宜減焉。大衍減五，故有五十；其用減一，故四十有九。不併者，不可減也。

Zheng Xuan said: The inner trigram (Zhen) and outer trigram (Hui) together consist of six lines, combining to form a total of fifty numbers. However, the number actually used is forty-nine. The original numbers of heaven and earth are fifty-five: the number five of heaven and the number ten of earth belong to the same category and are connected (both belong to earth); the number one of heaven and the number six of earth also belong to the same category and are connected (both belong to water). Whenever numbers are connected and combined, their energies overlap, and overlapping should be subtracted. Therefore, the number of Da Yan (Great Derivation) subtracts five for the overlapping numbers, resulting in fifty. Then, when actually using it, one more is subtracted, resulting in forty-nine. As for numbers that are not connected, they should not be subtracted.

今總其數五十者，天一至地十，凡五十五也。此合生成之數。若止言生數，唯十有五，從一至五也。易之所象，爻盡之，有邃，故自天地以下，日月等數，皆為蓍卦所攝，循環變轉，萬世無窮。而五十有五，五本並數。並數者，天之與地共，各有一體，體各有一正應敵對。今盈於五，則是氣之並數，並不再用，是其配義。配則為虛，不當於實；不當於實，故事無所主，所以揲蓍不用。

Nowadays it is commonly said that the number is fifty, because counting from heavenly one to earthly ten adds up to fifty-five, which is the total of the generating numbers and the completing numbers combined. If we only speak of the generating numbers, they total fifteen, which is the sum of one to five. The images taken by the Zhou Changes are already fully expressed through the six lines of a hexagram, and their meaning is profound, so all numbers from heaven and earth down to sun and moon are included within the divination rods and the lines of the hexagram, changing in a cycle without end. Among these fifty-five numbers, the number five is originally a number that is doubled. By "doubling," it is meant that heaven and earth together have this number: each of heaven and earth has its own essence, and each essence has a corresponding counterpart that is equal and opposing. The extra five now is the number of the two energies overlapping; since it is overlapping, it is not used again, which is the meaning of "pairing." Since it is only pairing, it is in a virtual position, not a real one; not being real, it cannot serve as a basis for action, so it is not used when divining with the divination rods.

又虛其一者，掛一象無。無無可象，故有之用極，則無之功見。故曰：尋大業而得吉凶，尋吉凶而得八卦，尋八卦以得四時，尋四時以至兩儀，尋兩儀以至太極。太極者，大殺而極，窮無之致也。遣有以極邃，減多以就少，此之謂也。故曰：太極無所復象，明其空寂，非言象所詮也。

Another stick is left unused, which is called 'hang one' during the process of divination with yarrow stalks. It symbolizes 'nothingness.' Since 'nothingness' has no form to take as a symbol, the function of 'something' must be pushed to its extreme so that the function of 'nothingness' can be revealed. Therefore, following the great affairs one can seek good fortune and misfortune; following good fortune and misfortune one can seek the Eight Trigrams; following the Eight Trigrams one can seek the four seasons; following the four seasons one can trace back to the Two Principles; following the Two Principles one can trace back to the Supreme Ultimate. The Supreme Ultimate refers to reducing layer by layer until it reaches the extreme, exhausting emptiness to reach the ultimate state. Discarding 'something' to reach the deepest level, reducing multiplicity to return to simplicity, is exactly this. Therefore, the Supreme Ultimate has nothing to take as a symbol, indicating it is empty and formless, beyond words and images.

行言五者，明萬物雖多，數不過五。故在天為五星，其神為五帝。孔子曰：昔丘聞諸老聃云，天有五行，木金水火土，其神謂之五帝。在地為五方，其鎭為五嶽。《物理論》云：鎭之以五嶽。在人為五藏，其候五官。《黃帝素問》云：五藏候在五官，眼耳口鼻舌也。五行遞相負載，休王相生，生成萬物，運用不休，故云行也。《春秋繁露》云：天地之氣，列為五行。夫五行者，行也。

The term "行" emphasizes the number "five" to indicate that although things are numerous, they can be categorized into five types. In the heavens, this is manifested as the five planets (the wandering star, the red star, the stationary star, the white star, and the dim star), whose spirits are called the Five Emperors. Confucius said: I once heard Lao Dan say that heaven has the Five Phases, which are wood, metal, water, fire, and earth, and their spirits are called the Five Emperors. On earth, this is manifested as the five cardinal directions—southeast, northwest, and the center—guarded by the Five Mountains. The "Treatise on Things" says: the Five Mountains are used to guard the world. In the human body, this is manifested as the five internal organs, whose symptoms are expressed through the five senses. The "Su Wen" section of the "Huang Di Neijing" says: the symptoms of the five internal organs are expressed through the five senses, namely the eyes, ears, mouth, nose, and tongue. The Five Phases support each other, take turns to be active or inactive according to the seasons, and in sequence generate each other, thus producing all things, continuously operating without ceasing, hence it is called "行." The "Chun Qiu Fan Lu" says: the energies of heaven and earth arranged in order are the Five Phases; the term "Five Phases" is precisely derived from the meaning of "running" or "movement."

《易上繫》曰：天數五。王曰：謂一三五七九也。韓曰：五奇也。地數五。王曰：謂二四六八十也。韓曰：五偶也。五位相得。王曰：五位，金木水火土也。而各有合。王曰：謂水，在天為一，在地為六，六一合於北；火，在天為七，在地為二，二七合於南；金，在天為九，在地為四，四九合於西；木，在天為三，在地為八，三八合於東；土，在天為五，在地為十，五十合於中。故曰：五位相得而各有合。謝曰：陰陽相應，奇偶相配，各有合也。韓曰：天地之數各有五，五數相配，以合成金木水火土也。

The Great Treatise of the Zhou Changes says, "Heaven has five numbers." Wang Bi explains that these refer to the odd numbers one, three, five, seven, and nine. Han Kangbo says they are simply the five odd numbers. It also says, "Earth has five numbers." Wang Bi says these refer to the even numbers two, four, six, eight, and ten. Han Kangbo says they are simply the five even numbers. It also says, "The five positions are in harmony." Wang Bi says the five positions refer to the five directions of metal, wood, water, fire, and earth. It also says, "Each has a corresponding match." Wang Bi says water is one in the heavenly numbers and six in the earthly numbers, and one and six combine in the north. Fire is seven in the heavenly numbers and two in the earthly numbers, and seven and two combine in the south. Metal is nine in the heavenly numbers and four in the earthly numbers, and nine and four combine in the west. Wood is three in the heavenly numbers and eight in the earthly numbers, and three and eight combine in the east. Earth is five in the heavenly numbers and ten in the earthly numbers, and five and ten combine in the center. Therefore, it says, "The five positions are in harmony and each has a corresponding match." Xie says: Yin and Yang correspond to each other, odd and even numbers match each other, and each has a corresponding match. Han Kangbo says: Heaven has five numbers and Earth has five numbers, these five pairs of numbers correspond to each other, and are used to form the five elements of metal, wood, water, fire, and earth.

《尚書·洪範》篇曰：五行，一曰水，二曰火，三曰木，四曰金，五曰土。皆其生數。《禮記·月令》篇云：木數八，火數七，金數九，水數六，土數五。皆其成數，唯土言生數。天以一生水於北方。君子之位，陽氣微動於黃泉之下，始動無二，天數與陽合而為一。水雖陰物，陽在於內，從陽之始，故水數一也。極陽生陰，陰始於午，始亦無二。陰陽二氣，各有其始，正應言一，而云二者，以陽尊故。尊既括始，陰卑贊和，配故能生，而陽數偶陰在火中。火雖陽物，義從陰，配合陰始，故從始立義，故火數二也。

The Book of Documents, the Hongfan section, says: The Five Phases, the first is water, the second is fire, the third is wood, the fourth is metal, and the fifth is earth. These numbers one to five are the "generative numbers" of the Five Phases. The Book of Rites, the Yueling section, says: Wood has the number eight, fire has the number seven, metal has the number nine, water has the number six, and earth has the number five. These are all "completed numbers," except for earth, which is still the generative number five. Heaven uses the number one in the north to generate water. The north is the position of the gentleman, where yang energy quietly begins to stir beneath the yellow earth. Since it is the initial movement, it can only be one and not two. The heavenly number and yang energy combine to form one. Although water is a yin substance, yang energy is contained within it, following the beginning of yang, so the generative number of water is one. When yang reaches its extreme, yin is generated. Yin energy begins at the position of wu. As the beginning, it is also one. Both yin and yang energies have their own starting points, and by principle, they should both be one. However, here fire is said to have the number two, because yang is esteemed. The esteemed one has already taken the "beginning" as one, and yin, being in a humble position, can only support and harmonize from the side. Because there is a spouse, life is generated, so yang number combines with yin number to form an even number. Yin energy is hidden within fire: although fire is a yang substance, its meaning follows yin, used to harmonize with the beginning of yin energy. Therefore, based on the concept of beginning, the generative number of fire is two.

《老子》云：天得一以清，地得一以寧。是知皆有一義，唱和同始。是以云：木配陽動，而左長於東方，長則滋繁，滋繁則數增，故木數三也。陰佐陽消，陰道右轉，而居於西，在陽之後，理無等義，故金數四也。陰陽之數，始乎一周，然後陽達於中，總括四行，苞則彌多，故土數五也。此並生數，皆云據始，未明成數。數既未成，亦未能為用。

The Tao Te Ching says: Heaven receives the "One" and becomes clear, Earth receives the "One" and becomes tranquil. From this we know that Heaven and Earth both contain the meaning of "One," which is like a call and response, starting from the same point. Therefore, wood combines with the movement of yang energy, growing to the left in the East; when it grows, it proliferates, and as it proliferates, its numbers increase, so the number of wood is three. Yin energy assists yang energy in retreating, and the yin path turns to the right and resides in the West, coming after yang, and by nature cannot be equal to yang, so the number of metal is four. After the yin and yang numbers complete the first cycle, yang energy reaches the center, encompassing the remaining four elements; the more it encompasses, the greater the number, so the number of earth is five. All of these are birth numbers, discussing the beginning of each element, without yet involving completed numbers. Since the numbers have not yet "become complete," they are still unable to function.

穎容《春秋釋例》云：五行生數，未能變化，各成其事。水凝而未能流行，火有形而未生炎光，木精破而體剛，金強而斫，土滷而斥。於是天以五臨民，君化之。傳曰：配以五成。所以用五者，天之中數也。於是水得於五，其數六，用能潤下；火得於五，其數七，用能炎上；木得於五，其數八，用能曲直；金得於五，其數九，用能從革；土得於五，其數十，用能稼穡。

Ying Rong's "Commentary on the Spring and Autumn Annals" says: When the Five Phases only have the numbers of generation, they are still unable to change and accomplish their respective functions: water is stagnant and cannot flow, fire has form but cannot emit light, wood's vital energy is scattered and its form is stiff, metal is only hard and can be carved, and soil is alkaline and repels crops. Therefore, Heaven uses the number "five" to illuminate the people below, and the ruler uses it to carry out education. The transmission says: Only by combining with five can things be completed. The reason for taking five is that five is the central number among the heavenly numbers. Thus, water, when combined with five, becomes six, and can moisten and flow downward; fire, when combined with five, becomes seven, and can become hot and rise upward; wood, when combined with five, becomes eight, and can be bent or straightened; metal, when combined with five, becomes nine, and can be shaped into objects; soil, when combined with five, becomes ten, and can be cultivated and harvested. This is the method of adding the number of generation to five to obtain the number of completion.

鄭玄云：數若止五，則陽無匹偶，陰無配義，故合之而成數也。奇者，陽唱於始，為制為度；偶者，陰之本，得陽乃成。故天以一始生水於北方，地以其六而成之，使其流潤也；地以二生火於南方，天以七而成之，使其光曜也；天以三生木於東方，地以其八而成之，使其舒長盛大也；地以四生金於西方，天以九而成之，使其剛利有文章也；天以五合氣於中央生土，地以十而成之，以備天地之間所有之物也。合之，則地之六為天一匹也，天七為地二偶也，地八為天三匹也，天九為地四偶也，地十為天五匹也。陰陽各有合，然後氣性相得，施化行也。

Zheng Xuan said: If numbers only go up to five, then yang would have no counterpart, and yin would have no way to match. Therefore, the generating numbers must be combined with five to form the completing numbers. Odd numbers belong to yang, initiating at the beginning and establishing principles; even numbers are the foundation of yin, which can only be completed through yang. Therefore, heaven uses one in the north to generate water, and earth uses six to complete it, allowing water to flow and moisten; earth uses two in the south to generate fire, and heaven uses seven to complete it, allowing fire to shine and illuminate; heaven uses three in the east to generate wood, and earth uses eight to complete it, allowing wood to grow and flourish; earth uses four in the west to generate metal, and heaven uses nine to complete it, allowing metal to be hard, sharp, and have luster; heaven uses five in the center to combine and generate earth, and earth uses ten to complete it, to fully include all things in the universe. When viewed together: six is the counterpart of one, seven is the counterpart of two, eight is the counterpart of three, nine is the counterpart of four, and ten is the counterpart of five. Both yin and yang have their counterparts, then the qi and nature can harmonize and the process of generation and nurturing can proceed. Zheng Xuan's words point out two calculation rules: first, the five generating numbers from one to five, when each is added to the central earth number five, result in the completing numbers from six to ten in order; second, whatever is generated by heaven's odd numbers must be completed by earth's even numbers, and whatever is generated by earth's even numbers must be completed by heaven's odd numbers. Odd and even numbers alternate and match, allowing the five phases to both generate and complete.

故四時之運，成於五行。土總四行，居時之季，以成之也。《五行傳》及《白虎通》皆云：木非土不生，根核茂榮；火非土不榮，得木著形；金非土不成，入範成名；水非土不停，堤防禁盈。土扶微助衰，應成其道。故五行更互須土，土王四季而居中央，不以名成時，故知同時俱起，但托義相生。傳曰：五行並起，各以名別。

Therefore, the operation of the four seasons depends on the Five Phases to be completed, and earth oversees the other four phases, residing in the last month of each season to perfect them. Both the "Transmission of the Five Phases" and the "White Tiger Treatise" state: wood cannot grow without earth; its roots depend on earth to flourish and bloom. Fire cannot be vigorous without earth; it requires wood to take form. Metal cannot become an object without earth; it needs to be cast into a mold to take shape. Water cannot be contained without earth; it relies on embankments to control its overflow. Earth supports the weak and assists the declining, and should complete their paths. Therefore, the Five Phases alternate in operation and cannot do so without earth. Earth is strong in the last month of each season and resides in the center, yet it does not use its own name to denote a particular season. From this we can understand that the Five Phases actually arise simultaneously, but they are arranged in order through the concept of "mutual generation." The transmitted text says: the Five Phases arise together, differing only by their names.

《常從數義》云：北方亥子，水也，生數一；丑，土也，生數五。一與五相得為六，故水成數六也。東方寅卯，木也，生數三；辰，土也，生數五。三與五相得為八，故木成數八也。南方巳午，火也，生數二；未，土也，生數五。二與五相得為七，故火成數七也。西方申酉，金也，生數四；戌，土也，生數五。四與五相得為九，故金成數九也。

The book "Chang Cong" discusses the principles of numbers, stating that in the north, the branches Hai and Zi belong to water, with the generating number one; Chou belongs to earth, with the generating number five. One and five combine to make six, so the completed number of water is six. In the east, the branches Yin and Mao belong to wood, with the generating number three; Chen belongs to earth, with the generating number five. Three and five combine to make eight, so the completed number of wood is eight. In the south, the branches Si and Wu belong to fire, with the generating number two; Wei belongs to earth, with the generating number five. Two and five combine to make seven, so the completed number of fire is seven. In the west, the branches Shen and You belong to metal, with the generating number four; Xu belongs to earth, with the generating number five. Four and five combine to make nine, so the completed number of metal is nine. Thus, after each pair of branches in each direction comes an earth branch. It is precisely through this earth number five that the generating numbers are transformed into the completed numbers.

中央戊己，土也，生數五。又土之位在中，其數本五，兩五相得為十，故土成數十也。此陰陽兩氣各一周也。共一周，則為生數；各一周，則為成數。陽以輕清上為天，陰以重濁下為地。而陽至第五而入中者，其體躁疾，故共一周而入中；陰至第十方入中者，其體遲殿，故各一周而始入耳。然五行皆得中氣而後成，土居中而王四季，並須土以成之也。

The central heavenly stems 戊 (Wu) and 己 (Ji) belong to the earth element. Their birth number is five, because the earth element is located in the center, and its number is naturally five. When the two numbers five combine, they total ten, so the earth element's completed number is ten. This is the result of the interaction of yin and yang energies each completing one cycle: when the two energies together complete one cycle, they produce the birth number; when each energy individually completes one cycle, they produce the completed number. Yang energy is light and clear, rising to form heaven, while yin energy is heavy and turbid, sinking to form earth. Yang reaches the center at the fifth position because it is impetuous and swift, so it completes one cycle and enters the center. Yin reaches the center at the tenth position because it is slow and lagging, so it completes one cycle before entering the center. In summary, all five elements depend on the earth's energy at the center to be completed. The earth element is located at the center and is most vigorous in the last months of the four seasons; each element must rely on it to be fully realized.

《洪範》是上古創制之書，故言生數；《禮記·月令》是時候之書，所貴成就事業，故言成數。唯土言生數者，土以能生為貴，且以成四行，足簡之矣，是其能生能成之義也。鄭玄曰：以天地相配，取陰陽之理；《常從》以支干數和合，取日辰為用。兩說雖別，大意還同，終會《易經》天一至地十之義。

The *Hong Fan* is a book on the early establishment of institutional systems, so it discusses the generating numbers; the *Liji · Yue Ling* is a book recording seasonal changes and natural phenomena, and it focuses on the accomplishment of affairs, so it discusses the completed numbers. Among these, only earth still discusses the generating numbers, because earth is valued for its ability to generate, and it also uses this to complete the other four elements. The generating numbers are sufficient to summarize this, which precisely reflects the meaning of earth's ability to both generate and accomplish. Zheng Xuan said: one interpretation is to pair the heavenly numbers with the earthly numbers, drawing on the principles of yin and yang; the *Chang Cong* uses the numbers of the heavenly stems and earthly branches to harmonize, taking the day branches for practical application. Although these two interpretations differ, their general meaning is the same, ultimately both returning to the principle of the *Yijing* that "heaven one to earth ten."

《孝經援神契》言：以一立，以二謀，以三出，以四孳，以五合，以六嬉，以七變，以八舒，以九列，以十鈞。五行以一立水，一為生數，以五配一，水之成數，故言一立而六嬉。嬉是興義。二，是火之生數；七，是火之成數，故言二謀。火以變化為能，故曰七變。謀者，以其為變之始也。三，木之生數；八，木之成數。五行始於東方，故云三出；八而成長，故曰八舒。四，金之生數；九，金之成數。西方成就，故言四滋；品類不同，故稱九列。五是土之生數，十是土之成數。以天之五，合地之十，數義斯畢。所以五言其合，十言其均。均是成備之義。

The "Xiao Jing Yuan Shen Qi" says: "With one, it is established; with two, it is planned; with three, it emerges; with four, it proliferates; with five, it harmonizes; with six, it thrives; with seven, it changes; with eight, it spreads out; with nine, it is arranged; with ten, it is balanced." These ten sentences correspond to the generating and completing numbers of the Five Phases. The Five Phases use one to establish water, and one is the generating number of water; using five to pair with one, we obtain the completing number of water, which is six, so it is said "one is established" and "six thrives" — "thrive" means prosperity. Two is the generating number of fire, and seven is the completing number of fire; thus it is said "two is planned," and since fire is characterized by change, it is also said "seven changes." The reason it is called "planning" is because two is the beginning of change. Three is the generating number of wood, and eight is the completing number of wood; since the Five Phases begin from the east, it is said "three emerges"; when it grows to eight, it becomes mature and spreads out, so it is said "eight spreads out." Four is the generating number of metal, and nine is the completing number of metal; since the west is associated with harvest, it is said "four proliferates (grows and achieves); since myriad things are different, it is called "nine arranged (arranged in order)." Five is the generating number of earth, and ten is the completing number of earth; combining the five of heaven with the ten of earth, the meaning of numbers is complete here, so five refers to "harmony," and ten refers to "balance" — "balance" means completeness and achievement.

《春秋元命苞》云：胎錯儛，連以鈞。一動，合於二，故陰陽受；成於三，故日月星序；張於四，故時起；立於五，故行動；佈於六，故律踴；分於七，故宿改；萌於八，故風布；極於九，故州吐；畢於十，故功成數止。此並經緯共明五行生成之數，不過十也。

The Spring and Autumn Original Mandate says: The primordial qi moves like a fetus, intertwining and dancing, forming a harmonious whole. When there is movement, it combines with two, thus allowing yin and yang qi to receive the vital breath and be generated; it is completed through three, thus the sun, moon, and stars have their order; it is spread through four, thus the four seasons arise; it is established through five, thus the five phases operate; it is dispersed through six, thus the six tones produce sound; it is divided through seven, thus the seven star constellations succeed each other; it emerges through eight, thus the winds of the eight directions spread; it reaches its peak through nine, thus the nine regions give birth to all things; it concludes through ten, thus the achievements are completed and the number ends here. This is the common explanation of both the canonical and the esoteric texts: the numbers of the generation of the five phases do not exceed ten.