Zongsheng Talks - Zengzi

古時象數，悉本河圖、洛書，是為易象之源。河圖負於龍馬，洛書呈於文龜；皆天地自然之象數，而聖人則之以演易；蓋所由來者遠矣！在天成象，在地成文，天地之象數，即由天地自呈於人前；神道之感應，為人道所昭彰；固上世常見之事。以地天猶通，神人時契；人習於道，無不通神；則神亦降其靈，資人以智，發人以道，非可異也；故圖書出，而人文以創；

In ancient times, the images and numbers were all based on the Yellow River Chart and the Luo Writing, which are the origins of the hexagrams in the Zhou Changes. The Yellow River Chart was brought forth by a dragon horse, and the Luo Writing was presented by a tortoise with cultural markings; both are natural images and numbers of heaven and earth. Sages took them as models to deduce the Zhou Changes. Their origin is indeed very ancient. The Great Treatise says, "In heaven, images are formed; in earth, forms are created." The images and numbers of heaven and earth were originally presented before people by heaven and earth themselves. Thesympathetic response of the divine path was manifested through human ways, which was common in ancient times. At that time, the qi of heaven and earth could still communicate, and the divine and human were constantly in harmony. People were familiar with the Dao, so none could not communicate with the divine. Thus, the divine descended its clarity, giving people wisdom and enlightening them with the great Dao, which was by no means surprising. Therefore, with the emergence of the Yellow River Chart and the Luo Writing, human civilization was thus established.

天地之道見，而人道以明；人之有文化教育，皆始於天地自然之象數文章；雖神而明之，存乎其人；而溯源探本，則有所自矣！故圖書者，易象之袓；欲明易象，必明圖書；如木本水源，不得其故；則枝流莫可究詰，是以夫子曰：「五十學易」，言由圖書以窮象數也。天五地十，五十為天地中心；

The way of Heaven and Earth becomes evident, and thus the way of human beings becomes clear. Human culture and education originate from the images and numbers of Heaven and Earth's natural phenomena and their principles. Although the Great Treatise says "to grasp the subtle and make it clear, it depends on the person," when tracing back to the source and exploring the root, there is always a beginning. Therefore, the Yellow River Chart and the Luo Writing are the ancestors of the hexagrams in the Zhou Changes. To understand the hexagrams of the Zhou Changes, one must first understand the Yellow River Chart and the Luo Writing. This is like a tree having roots and water having a source; if one does not clarify its origin, then the branches and streams cannot be pursued. Therefore, Confucius said in the Analects, "At fifty, one begins to study the Zhou Changes," meaning one should start with the Yellow River Chart and the Luo Writing to investigate the images and numbers. The Great Treatise mentions "Heaven is five, Earth is ten," and five and ten are the centers of Heaven and Earth.

天之道由此見，人道由此立。故五十為圖書之中數，猶易之太極也；太極在數曰一，在位曰中；在性曰至善，在氣曰純陽；為無始之始，萬有之宗；老氏之天下之母，即指此也；而其大包無外，廣盡萬類；故屬天地之中，亦天地所自成也。

The heavenly way is thus revealed, and the human way is thus established. Therefore, the numbers five and ten are the central numbers of the He Luo diagrams, just like the "Taiji" in the Zhou Changes. In terms of number, Taiji is called one; in terms of position, it is called the center; in terms of nature, it is called ultimate goodness; and in terms of energy, it is called pure yang. It is the beginning without a beginning, the master of all existence. The thing referred to by the Tao Te Ching as the "mother of the world" is precisely this. It is vast without boundaries, pervading all categories, thus belonging to the center of heaven and earth, and also the source from which heaven and earth naturally arise.

數雖自一至九，而其宗則五與十；五十分列，則乾坤定位；五十合用，則大衍成形；故曰五曰十，或五十，皆數之本體，其化則用也；乾用九，坤用六，九六為乾坤之用；乾數極於九九，坤數包於六六；人之數七，艮也；其數盡於七七，此大衍之用四十九，指人道也；

The numbers range from one to nine, but their master is five and ten. When five and ten are separated, the positions of Heaven and Earth are established; when five and ten are used together, the form of "the great derivation of numbers" is formed. Therefore, speaking of five, ten, or fifty, all refer to the essence of numbers, while their changes are called "use." The Qian hexagram has "use of nine," and the Kun hexagram has "use of six," with nine and six being the numbers used by Qian and Kun respectively. The number of Qian is limited to eight十一 (81), while the number of Kun is confined to thirty-six. The number of humans is seven, associated with the Gen hexagram. The number of humans ends at forty-nine, which is exactly the forty-nine used in "the great derivation of numbers," referring to the human way.

天地之道，由人而明；天地之數，由人而用；故大衍之數，以七七為用；而天地之數在其中矣。合則成用，分則為位；交錯則變化生，乘除則盈虛見；而其本始，莫外乎圖書之數也。河圖、洛書之象數，為自然象數；易之象數，則本圖書而推其變化之象數也；易與圖書有同異；但天地象數，終不外圖書所有者；

The principles of heaven and earth can only be explained through human effort, and the numbers of heaven and earth can only be applied through human effort. Therefore, the "Great Derivation Number" uses 49, which is seven times seven, as its basis, and the numbers of heaven and earth are included within it. When combined, they achieve function; when separated, they form positions. Through their intermingling, change arises; through multiplication and division,盈亏 (excess and deficiency) become apparent. Their origin lies entirely in the numbers of the Yellow River Chart and the Luo Writing. The images and numbers of the Yellow River Chart and the Luo Writing are naturally generated images and numbers. The images and numbers of the Zhou Changes (I Ching), however, are derived from the Yellow River Chart and the Luo Writing and further developed to show their transformations. The Zhou Changes and the Yellow River Chart and Luo Writing share similarities but also differences. However, the images and numbers of heaven and earth ultimately do not go beyond the scope already contained in the Yellow River Chart and the Luo Writing.

至其變化，雖推之無盡，仍不能有違於圖書之例；則由天地生成之數定，不可越也；自上而下，則二五賦形，而萬物以生；自下而上，則萬有歸一；由形返神；故圖書之數始一終九，五十在中；而二氣五行備具。其化生萬物，則以用言；以二五互交，推演為數；所謂二五構精是也。

As for their transformations, although they can be deduced infinitely, they still cannot violate the principles of the River Chart and the Lo Chart. This is because the numbers of heaven and earth have already been determined and cannot be exceeded. Looking from above, it is the interaction of yin and yang and the Five Phases that give form to things, thus generating all things. Looking from below, all things return to one, and from form they return to the spiritual. Therefore, the numbers of the River and Lo Charts begin with one and end with nine, with five and ten in the middle, thus completing the yin and yang and the Five Phases. As for their generation of all things, this must be understood in terms of application: through the interaction of the two energies and the Five Phases, numbers are generated, which is called "the combination of two and five to form essence."

故其數陽五陰五，陽以順行，陰以逆行；相交以生，相剋以變；而孤陰獨陽，則不生不變；易以乾坤交用，坎離相制；以成生克，而形變化；由數之用言，則陽者，一三七九順行，始一終九，其位在西；陰者，四二八六逆行，始四終六，其位始於西北；陽以九終交陰六，故陽數用九；陰數用六，九六相終始循環以生成變化；而五十主於中央，為天地中極；萬物樞紐。

Therefore, among these numbers, there are five yang numbers and five yin numbers: yang progresses in a forward direction, while yin moves in a reverse direction; they generate each other through mutual interaction and change through mutual control; if there is isolated yin or solitary yang, it cannot generate or change. The Zhou Changes uses the interaction of Qian and Kun, and the mutual restriction of Kan and Li, to form generation and control, thus revealing change. In terms of the use of numbers, the yang numbers are one, three, seven, and nine, progressing forward, starting from one and ending at nine, with the endpoint in the west; the yin numbers are four, two, eight, and six, moving backward, starting from four and ending at six, with the starting point in the northwest. When yang reaches nine, the terminal number, it meets the yin number six, so the yang number uses nine; the yin number uses six. Nine and six connect at their ends, continuing in a cycle to complete the process of generation and change. The numbers five and ten are central, serving as the axis of heaven and earth, and the key to all things.

此圖書象數之大概，即為易所本者；乾之用九，坤之用六；即準河圖之陰陽數也。觀河圖所列之數，作為環形；則一三七九，由北而東而南而西；而四二八六，則自西北而西南而東南而東北；亦環而終始，唯五十在中焉。

That is the general idea of the two diagrams, the River Chart and the Lo Square, which form the basis of the Zhou Yi. The "All Nines" in the Qian trigram and the "All Sixes" in the Kun trigram are derived from the yin and yang numbers in the River Chart. If the numbers in the River Chart are arranged in a circular form, then one, three, seven, and nine run from north to east, east to south, and south to west; four, two, eight, and six run from northwest to southwest, southwest to southeast, and southeast to northeast, also forming a circular pattern that connects head to tail. Only five and ten are located at the center.

洛書亦然，不過其用有異，由方圓不同也；由北之一，東之三，則以接西之七，南之九，皆陽數也；其陰數，則西北六，東北八，西南二，東南四；亦由東南之四，西南之二，接東北之八，西北之六，相環以終始，正如河圖；而五在中焉，其不同者，圖屬先天，書屬後天；一體一用，一位一成，一位一時。故洛書之數，以相交而行；而河圖則相貫也。洛書之位，以東南與西北易數，而河圖則順逆依序也。

The Luo Shu is also arranged in this way, but its function differs because one takes the square and the other the circle. By connecting the number one from the north, three from the east, seven from the west, and nine from the south, these are all yang numbers. As for the yin numbers, they are six in the northwest, eight in the northeast, two in the southwest, and four in the southeast. These also connect from the southeast four and southwest two to the northeast eight and northwest six, forming a circular sequence that links the beginning and end, just like the He Tu. The number five is in the center. The difference between the two is that the He Tu belongs to the Earlier Heaven and the Luo Shu to the Later Heaven; one is about the main body, the other about application; one discusses position, the other discusses formation; one emphasizes direction, the other emphasizes sequence. Therefore, the numbers in the Luo Shu run across each other, while the numbers in the He Tu run in a straight line. The Luo Shu swaps the numbers between the southeast and northwest, while the He Tu follows its original order, proceeding in a straight line or in reverse.

河圖之數，本於天地生成之象；蓋自無入有，首為太極；一氣既動，兩儀以分；兩氣相蕩，五行以具；故河圖象之，其數自一至十；分為陰陽，陽奇陰偶，各得其半；而生化之本，必基於二氣之和；五行之分，即由於陰陽之變；其生化也，以一陰一陽相合而成；

The numbers in the Yellow River Chart are based on the image of the generation of heaven and earth. Heaven and earth began from nothingness to become something, and first there was the "Taiji" (Supreme Ultimate). When the single vital energy suddenly moved, the "Two Principles" (Yin and Yang) were divided. When the two energies interacted and clashed, the "Five Phases" were fully established. Therefore, the Yellow River Chart takes its image from this process: its numbers range from one to ten, divided into two categories, Yin and Yang. Odd numbers represent Yang, and even numbers represent Yin, each occupying half. The fundamental principle of generation and transformation must be based on the harmony of the two energies, Yin and Yang. The differentiation of the Five Phases comes from the changes of Yin and Yang, and their generation and transformation are all achieved through the mutual interaction of one Yin and one Yang.

乃於是數中，以陰合陽，以陽合陰；天生則地成之，地生則天成之；故一至五為生數，六至十為成數；生成二數，各居陰陽之半；如將籌比算之，自左設陽籌，右之陰籌；則左數為一三五七九，右數為二四六八十，左右各半也；更將其配合之，為左設生數，右設成數；則左為一二三四五，右為六七八九十，亦各半也；皆以相得而合，而後有物生焉。

Thus, among these ten numbers, yin is paired with yang and yang is paired with yin: what is generated by heaven is completed by earth; what is generated by earth is completed by heaven. Therefore, the numbers one to five are called "sheng shu" (generative numbers), and the numbers six to ten are called "cheng shu" (completed numbers); the generative and completed numbers each account for half of yin and yang. If we use counting rods as an analogy: place yang rods on the left and yin rods on the right, then on the left we have one, three, five, seven, and nine, and on the right we have two, four, six, eight, and ten, with each side accounting for half. Alternatively, if we arrange the generative numbers on the left and the completed numbers on the right, then on the left we have one, two, three, four, and five, and on the right we have six, seven, eight, nine, and ten, again each side accounting for half. Only when these are paired and harmonized can things be generated.

故自左之一陽，合右之六陰，而水生成；左之三陽，合右之八陰，而木生成；自右之二陰，合左之七陽，而火生成；自右之四陰，合左之九陽，而金生成；更餘陽之五，合陰之十，而土生成，此為五行生成之次序也。其生與成，恰為相當之位；故其數相得，如一居左首，六居右首；

Therefore, the yang number one on the left pairs with the yin number six on the right, and water is generated; the yang number three on the left pairs with the yin number eight on the right, and wood is generated; the yin number two on the right pairs with the yang number seven on the left, and fire is generated; the yin number four on the right pairs with the yang number nine on the left, and metal is generated; the remaining yang number five pairs with the yin number ten, and earth is generated. This is the order in which the Five Phases are generated. The generating and forming numbers are exactly in corresponding positions, so the two numbers match perfectly: for example, one is placed in the first position on the left, and six is placed in the first position on the right.

故恰相得，猶子與午對也；是為配偶之定例也。因其位相當，而數相得；始有合，而見其生成之功；此一六居北，二七居南；三八居東，四九居西；五十居中，以既合而後同居；亦如人之夫婦也。故其位之相配以次，數之相得以序；雖有一二之殊，卻非父子，而為兄弟，不得視為水生火也。

Therefore, they fit perfectly, just like the Earthly Branches "Zi" and "Wu" which are opposite to each other, this is the established pattern of pairing. Because their positions correspond and numbers match, there is a union, and thus the effect of generation is seen. Thus, one and six dwell together in the north, two and seven in the south, three and eight in the east, four and nine in the west, and five and ten in the center: they first match with each other and then dwell together, just like the "husband and wife" in human society. Therefore, the matching of positions has its order, and the matching of numbers has its sequence. Although adjacent pairs differ by only one or two numbers, they are not father and son, but brothers, and should not be regarded as water generating fire.

然五行之數，亦為二氣之量數；如一六為水生成數，亦即水之量數；以陽一陰六，為其分也。其所差五數者，繫以五之前為生數，即生氣；其氣能生不主成，而成氣必自五以下；猶之日與夜也，非至日落，不得為夜；以生氣未盡，不見成氣；故一必與六合，不能與二三四五合也；一六既合，其次則屬二與七；二為陰，七為陽；二屬生，七屬成；陽多陰少，乃為火之成分；亦如水之一六合也，以下皆同。

However, the numbers of the Five Phases are also the measures of the balance between yin and yang. For example, one and six are the numbers that generate water, which are also the numbers representing the quantity of water: yang accounts for one part, yin accounts for six parts, which is the ratio of its composition. The difference between them is five, because the numbers before five are called "sheng shu" or life numbers, which refer to life qi; life qi can only generate but not complete. The completed qi must be counted from five onwards. This is similar to day and night: until the sun sets, it cannot be called night; until the life qi is exhausted, the completed qi will not appear. Therefore, one must combine with six, and cannot combine with two, three, four, or five. Once one and six have combined, the next is two and seven: two belongs to yin, seven belongs to yang; two belongs to generation, seven belongs to completion; yang is more and yin is less, which is the composition of fire. This is the same principle as the combination of one and six. The following combinations are also the same.

蓋五行之數字，包括數義；一示陰陽之成分，一示生成之先後次序，一示五行之量數，一示二氣之分合總數，一示二五之化成原數也；其義甚廣，而無不相通；實天地間至數，不得移易者也；如天一地二，謂之為陽陰次序可，謂之為天地氣分量數亦可；論五行生成，則次序也；論五行成分，則量數也；論生成次序，兼示陰陽量數；而以紀二五之精氣所行，與天地之形氣所積，莫不一致。

The numbers of the Five Phases contain several layers of meaning: one refers to the proportion of yin and yang, another refers to the order of generation, another refers to the quantity of the Five Phases, another refers to the total amount of yin and yang qi, and another refers to the original numbers from which the Five Phases and the two qi energies were generated. Its meaning is very broad, and all these layers are interconnected. It is truly the most fundamental numbers in the universe, unchangeable and immutable. For example, the "Heaven one, Earth two" mentioned in the Great Treatise says it can refer to the order of yin and yang, or it can refer to the quantity of heavenly and earthly qi. In terms of the generation of the Five Phases, it refers to the order; in terms of the composition of the Five Phases, it refers to the quantity; in terms of the order of generation, it also indicates the quantity of yin and yang. Using it to record the movement of the refined qi of the two energies and the accumulation of the forms and qi of heaven and earth, it is entirely consistent.

故河圖總數五十五，即由一六、二七、三八、四九、五十、相加之積；其屬天者二十五，即陽數之積；為最清輕之神，故居上而名天；其屬地者三十，即陰數之積；為重濁之精氣，故居下而名地；其實一陰一陽耳。其所間所差者五，此為元氣之未化者，雖在天地之中，卻非五十五數之內；

Therefore, the total number of the Yellow River Chart is fifty-five, which is the sum of each pair: one and six, two and seven, three and eight, four and nine, five and ten. Among these, the twenty-five belong to heaven, which is the sum of the odd numbers, representing the clearest and lightest divine energy, hence it is placed above and called heaven. The thirty belong to earth, which is the sum of the even numbers, representing the heavy and turbid vital energy, hence it is placed below and called earth. In the end, it is simply the interplay of one yin and one yang. The five in the middle, which is the difference between them, is the original energy that has not yet been transformed. Although it resides in the center of heaven and earth, it is not included in the total of fifty-five.

蓋可以名而無名，可以數而無數；故為中氣，即陰陽之間所差之數，然先天初見生化，無序可紀，無量可數；有差而無差，有積而無積；蓋以陽陰之異，祇在動靜之間；原同一氣，因其動靜，而後有始數可知；然未遽定也，必待五行次第生成；五十五數確定之後，始知其屬天者幾，屬地者幾；不可以後天之數。名先天之氣。

It can be named but has no fixed name, and can be counted but has no fixed number, so it is called "the middle qi," which refers to the number between yin and yang. However, at the very beginning when the Earlier Heaven first began to generate and transform, there was no order to record and no measure to count. Saying it has a difference, it actually has none; saying it has an accumulation, it actually has none. The distinction between yin and yang lies only in the movement and stillness; originally they were one qi, and only through the difference of movement and stillness did the first numbers become known. Yet at that time, the numbers were not yet fixed, and it was only after the Five Phases were generated in sequence and the total of fifty-five was determined that we could know how much belonged to heaven and how much to earth. Therefore, we cannot use the numbers of the Later Heaven to name the qi of the Earlier Heaven.

先天祇一團渾然之氣，分之為二；始為兩儀，然無量可數也；其為量者，乃五行生成之後，因而量之，始有其名；當初生之時，祇宜名曰：一陰一陽之化合；一、一也，六、亦一也；二、一也，七、亦一也；推之二十五與三十，初無異量，皆屬同氣；不過既分已久，生成已見；其氣已化，其行漸成；而後前之一中，變為有數可紀，有量可量；

The Earlier Heaven was originally a single mass of undivided energy. When it was divided into two parts, it was called the "Two Principles" or "Two Powers." But at that time, there was no measurable weight or quantity. The concept of weight and measure came into being only after the Five Phases were generated, and then it was used to determine their names. In the very beginning, it should be called the combination of one yin and one yang: one is a whole, six is a whole; two is a whole, seven is a whole. By this logic, twenty-five and thirty also originally had no difference in terms of quantity, as they all belonged to the same kind of energy. However, as the separation continued over time, the manifestations became evident, the energy changed, and its movement gradually took shape. It was only then that the originally undivided whole began to have numbers that could be recorded and quantities that could be measured.

如一六既成水，始有水成分可言；蓋以陰陽之偏，遂生差異之數；如冷與熱，升降異也，輕與重，上下殊也；於是有量有數，可以別其為何物；而物則因之更生他物，氣亦因之更化異氣，此後天數有一定者也。要知先天後天之分，本無多異；異者一有定，一無定；一有名有形，有象有數，故有定；一無名無形，無象無數，故無定；

For instance, when one and the Six Harmony become water, it is then possible to speak of the composition of water. Because yin and yang are unevenly distributed, differences arise: just as cold and heat represent upward and downward distinctions, and light and heavy represent being above and below. At this point, there is weight and number, allowing us to determine what kind of substance it is. And substances give rise to other substances, while qi transforms into other qi. This is why the Later Heaven numbers have a fixed standard. To understand the difference between the Earlier Heaven and the Later Heaven, there is not much difference in essence; the difference lies only in one being fixed and the other being unfixed: those with name, form, image, and number are fixed; those without name, form, image, or number are unfixed.

而介乎先後天之間，為初見生化之跡者；則可有可無之間，或定或否之類也；其象數，以上言之，先天也；以下言之，後天也；故其象數可量而不可量，可紀而不可紀；此以在上下之中，有無之界；如數之一，如位之中，如物之極是也。河圖之數亦如是，其數屬後天之始，其象屬初生之物；其氣仍純，其數仍簡，乃能為一切之母；故天地數止於十，而積之成五十五；其中之五十二數，即代示五十全數；而最中之五，即代示先天之中氣；

As for the section between the Earlier Heaven and Later Heaven, where the traces of generation and transformation first appear, it lies between existence and non-existence, belonging to a category that is both definite and indeterminate. Its images and numbers, when spoken of in relation to the Earlier Heaven, belong to that realm, but when spoken of in relation to the Later Heaven, they belong to this realm. Therefore, this section of images and numbers can be measured yet cannot be measured, can be recorded yet cannot be recorded. This is because it lies exactly in the middle between above and below, existence and non-existence, just like the number 'one' in numbers, the center 'zhong' in positions, and the extreme 'ji' in things. The numbers of the Yellow River Chart are also like this: its numbers belong to the beginning of the Later Heaven, its images belong to the initial stage of things. The qi is still pure, the numbers still simple, thus it can serve as the mother of all things. Therefore, the numbers of heaven and earth only go up to ten, adding up to fifty-five; among these, the numbers five and ten represent the full count of fifty. And the central number five represents the central qi of the Earlier Heaven.

先天中氣，本無五名；而名之五者，即由後天之五也；後天之五，亦主眾物，居中央，與先天同；故以其名先天之中氣。且因天地各五數，其積之差亦五，而生成之中數亦為五，天地之中心亦為五；故五者先後天之中位，亦先後天之中極；五為至中數，由其序言之，命曰一；由其量言之，命曰五；由其位言之，命曰極；由其方言之，命曰中；皆此數也。

The concept of the central energy in the Earlier Heaven originally did not have the name "five." It was given the name "five" by borrowing from the Later Heaven's five. The five in the Later Heaven also governs all things and resides in the center, which is the same as the central energy in the Earlier Heaven. Therefore, it was used to refer to the central energy of the Earlier Heaven. Moreover, both the heavenly numbers and earthly numbers each have five, and the difference between their accumulated totals is also five. The middle number generated by the Five Phases is also five, and the center of heaven and earth is also five. Thus, five is the shared central position and central extreme of both the Earlier Heaven and the Later Heaven. Five is the most central number: in terms of sequence, it is called one; in terms of quantity, it is called five; in terms of position, it is called extreme; in terms of direction, it is called center. All these refer to the same number.

故五者賅先後天之氣數，而獨立於其中者；且通先天中氣，立後天中極；謂之先天可，謂之後天亦可；以在後天直名曰土，實則土應有三個五；今僅曰中五者，即暗指先天之中氣矣！先天中氣，本無可名，無定居，無定方，無定形，無定數；而以五名之，以土位之，則以後天為主也，然此中氣，先後天同，而舉土亦可以代示中氣；因在後天五行，皆依於土而後成形；若無土，即無水火木金之質可見；

Therefore, the number five encompasses the qi of both the Earlier Heaven and Later Heaven, and stands independently between them; it connects upwards to the central qi of the Earlier Heaven and establishes downwards the central point of the Later Heaven. It can be said to belong to the Earlier Heaven, or to the Later Heaven. In the Later Heaven, it is directly called "earth," but originally, earth should have three fives. Now, when we refer to it as "middle five," it is implicitly pointing to the central qi of the Earlier Heaven. The central qi of the Earlier Heaven was originally nameless, without a fixed dwelling, direction, form, or number; using "five" to name it and "earth" to place it is a statement based on the Later Heaven. However, this central qi is essentially the same in both the Earlier and Later Heavens, so using "earth" can also represent the central qi. Because in the Later Heaven, the five elements all rely on earth to take form; without earth, the forms of water, fire, wood, and metal could not manifest.

是五行必賴土以成物，亦猶人物必賴中氣以為生；其義同也。如河圖中五，視為後天之數，則屬五行土之生數；若視為先天之氣，則屬中極之氣；故由河圖一變為洛書，僅留此中五不移；由河洛一變為八卦，則連此中五亦隱；所謂：「易無體」，即隱此中五；而將土之成數，暗附於四方，與洛書同；此皆示中極之地，為先後天中氣所在；而先後天所以變，而不離其宗；生化，而不失其本；皆賴有此中五也。

It can be seen that the Five Phases must rely on earth to accomplish all things, just as human beings and objects must rely on the central qi to survive. The principle is the same. For example, the number five in the center of the Yellow River Chart, if regarded as the Later Heaven number, belongs to the earth's generating number among the Five Phases; if regarded as the Earlier Heaven qi, it belongs to the central vital qi. Therefore, when the Yellow River Chart transforms into the Luo Writing, only this central five remains unchanged. When the River and Lake diagrams transform into the Eight Trigrams, even this central five disappears. The passage in the Great Treatise says, "The spirit has no fixed form and the Book of Changes has no definite body," where "no definite body" refers to hiding this central five and secretly assigning the earth's completed number to the four directions, following the same method as the Luo Writing. All this shows that the place of the central vital point is exactly where the central qi of the Earlier Heaven and Later Heaven lies. The reason why the Earlier Heaven and Later Heaven can change yet not depart from their origin, can generate and transform yet not lose their essence, is entirely due to the presence of this central five.

故天地之差止五，而大衍與天地之積之差亦五；此五彼五，與先天之中氣，後天土之生數，皆二而一也；能通而一之，始能明生化之源，造化之機；天人之道，道器之途；莫不豁然貫通焉！夫子講義，特提出此五，以為讀者告，其旨至深切矣！

Therefore, the difference between the numbers of Heaven and Earth is exactly five, and the difference between the "Great Derivation Number" and the total numbers of Heaven and Earth is also exactly five. The five here and the five there, together with the central qi of the Earlier Heaven and the generating number of Earth in the Later Heaven, may seem different, but they are actually the same thing. Only by integrating them can one understand the origin of generation and transformation, and the key to creation and change; the principles of Heaven and humanity, as well as the path of Dao and objects, will then all become clear. Confucius deliberately emphasized this number five in his teachings, with a very profound intention.

先天之氣，無形無名，因其動靜而後生成五行；故生之數五，成之數五，合為十；猶先天之一也。先天之一分為十，又分為陰陽各半；更由其生成次序，分為生成各半；故生之初為一屬陽，其次為二屬陰；其次為三為四為五，以奇偶而分屬陰陽；皆生之數也，然生者初見之氣，必賴成者而後成物；

The primordial qi is formless and unnamed, but because it has movement and stillness, it gives rise to the Five Phases. Therefore, the numbers of origin are five, and the numbers of completion are also five, making a total of ten. This ten is still the original "one" of the Earlier Heaven. The original one divides into ten, which then splits into yin and yang each comprising five. Following the order of generation, the numbers of origin and completion each make up half. Thus, the first to emerge is one, belonging to yang; the second is two, belonging to yin; then three, four, and five, which are divided between yin and yang according to their odd and even nature. These are all numbers of origin. However, what is called "generation" is merely the initial qi, which must rely on "completion" in order to form actual things.

故初成者六，屬地陰；其次七，屬陽；其次八九十，亦以奇偶而分陰陽，其次序恰與生數相得；故一與六合，二與七合，三與八合，四與九合，五與十合；而其生或成，亦以陰陽各得其一為序；故一六為水，則陽生而陰成之；二七為火，則陰生而陽成；其下木金亦然。至五與十，又屬陽生陰成；則陽占生者多之，陰居成者眾；以此為後天生化之大則，即必先陽而後陰也。

Therefore, the first to be formed is six, which belongs to the earth and is yin; next comes seven, which belongs to yang; then eight, nine, and ten follow, each assigned to yin or yang according to their odd or even nature, and their order exactly matches the sequence of the generating numbers. Thus, one combines with six, two with seven, three with eight, four with nine, and five with ten. Whether in generation or formation, the order is always that yin and yang each take one position: one and six are water, with yang generating and yin forming; two and seven are fire, with yin generating and yang forming; the same applies to wood and metal. As for five and ten, they are also yang generating and yin forming. In this way, yang predominates in the 'generating' aspect, while yin predominates in the 'forming' aspect. This becomes the great principle of the later heaven's transformation and generation, which necessarily follows the order of yang first and then yin.

此生成之次序共五，而陰陽不等，其意實為深微；果將此中數提出，而不與四方之數並列，則陰陽始平。土雖為五行之一，且居生成之終；卻能獨承先天之氣，而為後天之根；其兼備五行之數，合陰陽之德者，實有自也；故自五行生成之後，其數已定，其量始明；而其為二氣之差，亦恰此五；因其兼備先後天之氣，而包含陰陽之德；恆能齊所不齊，足所不足；而在後天之五，等於先天之元氣；

The sequence of generation consists of five groups, yet the numbers of yin and yang are not equal, and the intention behind this is profound and subtle. If the central group of numbers is taken out and not placed among the four directions, then yin and yang will be balanced. Though earth is only one of the Five Phases and is placed last in the sequence of generation, it alone can receive the qi of the Earlier Heaven and becomes the foundation of the Later Heaven. It is able to encompass the numbers of the Five Phases and conform to the virtues of yin and yang, which has a definite reason. Therefore, after the Five Phases have been generated, their numbers are already determined, and their proportions become clear. The difference between the two qi of yin and yang also corresponds exactly to this number five. Because it encompasses the qi of the Earlier and Later Heavens and includes the virtues of yin and yang, it is able to harmonize the uneven and make up for the deficiency. The number five in the Later Heaven is equivalent to the original qi of the Earlier Heaven.

作陰陽之中樞，物所資生，人所資育，初無限量；故在河洛之象，獨以之置於中央，而不與他數並列。且陰逆陽順之序，他數皆易其次，獨中五之次不移；明其為後天之極，即先天之精也；以數量言，屬後天者，本有多寡之殊，輕重之別；在先天則無殊無別，以皆一氣也；

It serves as the central axis of yin and yang, through which all things are generated and humans are nurtured. It has no limits. Therefore, in the diagrams of the Yellow River Chart and the Luo Writing, it is placed alone in the center, not listed together with other numbers. Moreover, in the order where yin moves against and yang moves in accordance, other numbers change their positions, but the central number five remains unchanged. This indicates that it is the ultimate point of the Later Heaven, which is also the subtle essence of the Earlier Heaven. In terms of quantity, those belonging to the Later Heaven have distinctions of more and less, light and heavy; but in the Earlier Heaven, there are no distinctions, since they are all the same kind of qi.

後天之異，而必求其同，則亦唯此五是賴；其所差者亦恰是此五數，果欲齊其不齊，足其未足，亦唯以此劑之；此由後天觀測者也，苟明乎五行生成，原由二氣之有多寡輕重；若其無也，則所生同一物矣！故所生之異，在乎數之不同；而其不同，即所差之五。

In the Later Heaven, differences have already arisen, yet one must seek unity within these differences, which can only be achieved through the number five. The difference between them is precisely this number five. If one wishes to harmonize the uneven and make up for the lacking, it can only be done by using this number five to adjust. This conclusion is drawn from observing the Later Heaven. To understand the generation of the Five Phases, we must recognize that they arise from the interaction of yin and yang energies, which vary in quantity and weight. If there were no such variations in quantity and weight, then only one thing would be produced. Therefore, the reason different things are generated is due to differences in number, and this difference is exactly the number five.

如以此中五調劑之，固可齊一；此係後天之例。以一陰一陽，而後為道。故河洛之後，變為大衍；其數始齊，若在河圖，猶陽少陰多；變為洛書，則陰少陽多；皆不齊。待易大衍，截長補短，而成各半之數；然大衍與河洛所差，亦皆此五數；以其恰合於中數，為陰陽之樞；故少則可加之。多則可減之；以歸於齊一。若其它數，則不得加減之也；

If we use this central five to adjust, it could make everything harmonious, which is the usual practice in the Later Heaven. It is necessary for yin and yang to be paired, only then can it be called the Dao. Therefore, after the Yellow River Chart and the Luo Writing, it became the "Great Derivation Number," and the numbers became complete. In the Yellow River Chart, there is still more yin than yang; when it became the Luo Writing, it turned into more yang than yin: neither is balanced. It is only when the Great Derivation Number of the Zhou Changes adjusts by taking from the long and adding to the short that the numbers become equal, with equal parts of yin and yang. However, the difference between the Great Derivation Number and the numbers of the Yellow River Chart and the Luo Writing is also this five. Because it exactly matches the central number, being the pivot of yin and yang, it can be added to when there is a deficiency, or subtracted from when there is an excess, thus achieving harmony. If another number were used, it could not be adjusted so freely.

河圖之數，原象也；洛書之數，變象也；大衍之數，例象也；言為後天生化之例，包含天地之數，而得陰陽之平者也；故日：大衍。衍者，演也；與古道字術近，即一陰一陽之謂道，由此而演其用，以明生化之例耳；故齊者，人齊之；演者，人演之；以便於推算耳。如歷之制閏，與歲月相齊也。

The numbers of the Yellow River Chart represent the original forms, while the numbers of the Luo Writing represent changing forms. The "Great Derivation" numbers represent the principles of regulation. By "principles of regulation," it means that it serves as the general rule for the later heaven's generation and transformation, encompassing the numbers of heaven and earth and achieving the balance of yin and yang. Therefore, it is called "Great Derivation." "Derivation" refers to deduction and inference, which is similar to the ancient usage of the term "Dao." This is the meaning of "One yin and one yang is called Dao" from the Great Treatise: by deducing its function, it is used to clarify the principles of generation and transformation. Therefore, when it says "alignment," it refers to the human making it aligned; when it says "derivation," it refers to the human deducing it. This is done for convenience in calculation, just as the calendar sets intercalation months to align the seasons with the years and months.

且大衍之數雖五十，而用則四十九；此中妙義，亦多未知；蓋本於象也。五十之象，雖陰陽各半；而其中一數，為二者共有；亦中數也。故用數止四十九，以陰陽分別數之，則各得二十五；若合數之，則各止二十四又半；故其用祇宜於合，不宜於分；苟分用時，則當更減去一數；即中數之一。而各二十四，於是陰陽之數始平均；

Furthermore, the "Great Derivation Number" is fifty in total, but only forty-nine is actually used. The profound meaning behind this is not well understood by most people. In fact, it is based on symbolic representation. The number fifty, although seemingly representing yin and yang each taking up half, includes one number that is shared by both yin and yang, which is the central number. Therefore, the number used in practice is forty-nine. If yin and yang are counted separately, each gets twenty-five; but when counted together, each only has twenty-four and a half. Therefore, its use is more appropriate when combined rather than divided. If it is to be used separately, one should subtract the central number, which is one, so that yin and yang each have twenty-four, making the numbers balanced.

若一歲之月十二，氣侯二十四；以合日之行度，而月之三旬，有晦朔望上下弦，亦見月光者，止二十四日；上半月十二日，下半月十二日；為得日照時，餘日則無光；是陽之合於陰，亦止二十四，與陽之度數同；雖河圖象陰陽之數，共五十五；而至大衍之用，僅四十九；及其分用時，則止四十八；此由先天易為後天數之差也。

For example, a year has twelve months and twenty-four solar terms, used to correspond with the sun's movement. Within a month, there are three ten-day periods, with new moon, full moon, and the waxing and waning phases. Only twenty-four days in a month actually have moonlight: twelve days in the first half and twelve days in the second half, when the moon is illuminated by the sun. On other days, there is no light. This shows that yin and yang combine to form only twenty-four days, matching the measure of yang. Although the Yin-Yang numbers represented by the Yellow River Chart total fifty-five, in the actual process of the Great Derivation, only forty-nine are used. When they are further divided, only forty-eight remain. This is precisely the numerical difference caused by the transition from the Earlier Heaven to the Later Heaven.

其差者，因欲齊其不齊，足其未足；故恆截長補短，以劑於平；此後天之數，以平為歸；而陰必後陽，天必包地；日必先月，女必順男；此皆後天一陰一陽之道，由河圖變易而來者。河洛之數，則異乎是；天地之數不齊，陰陽之象各異；為其初化，各物未具；數量猶混，不如後天之朗然若定；規然不移者也。

This is why there are these differences; it is to adjust the uneven, to supplement the deficient, so that things may be balanced by taking from the long to make up for the short. The later heaven numbers aim at balance, so yin must necessarily follow yang, heaven must necessarily encompass earth, the sun must necessarily precede the moon, and women must necessarily obey men. All these are the principles of yin and yang in the later heaven, derived from the changes in the Yellow River Chart. The numbers of the He Luo are different: the numbers of heaven and earth are not uniform, and the images of yin and yang differ. At that time, things had just begun to take form, and all things were not yet complete, so the numbers and measures were in a confused and undifferentiated state, unlike the clear, definite, and fixed numbers of the later heaven.

故在河圖之時，一六同級，二七等觀；三八如鄰，四九若親；五十為偶，皆自相得；不多不少，而以成其五行也；若既生成五行，次序已明，數量以定；始得其所差，而辨其數；再因其中數，而求其齊；於後天陰陽之道始明，生化之機乃定；故自河圖一變為洛書，再變為大衍；其數同而不同，與自太極兩儀四象八卦之變易，其例正同；八卦定而後後天之象見，大衍用而後後天之數明；

Therefore, in the stage of the Yellow River Chart, one and six are placed on the same level, two and seven are treated equally, three and eight are like neighbors, four and nine are like close relatives, and five and ten are paired as spouses. Each pair is matched appropriately, neither too many nor too few, thus forming the Five Phases. When the Five Phases have already been generated, their order is clear, their numbers fixed, then their differences can be discerned, and their quantities can be distinguished. Then, by relying on the central number, unity can be achieved. At this point, the principle of later Heaven yin and yang becomes clear, and the pivot of generation and transformation is established. Therefore, from the Yellow River Chart, it changes into the Luo Writing, and then into the "Great Derivation Number," whose numerical appearance seems the same but is actually different. This is consistent with the evolution from "Taiji" to "Two Principles," then to "Four Symbols," then to "Eight Trigrams." Only after the Eight Trigrams are established does the image of later Heaven appear; only after the Great Derivation Number is applied does the number of later Heaven become clear.

本末始終，各有所紀；通而一之，推而化之；則數不盡數，象不盡象；是在精研其自來，而貫澈其有無耳。至於五行之生成，與夫先天元氣之初化；何以如是生成？及天地之數，何以分生與成。是皆造化之階，為自無入有經歷之級；其理微，其義深；初非一二言所可盡，茲就大略言之：夫先天之氣，光明純潔，密緻剛健；凝然不動，晶然透澈；本無可名，無可形；

The beginning and the end, the root and the branch, each have their own records; when they are connected as a whole and extended with transformation, the numbers are not limited to the existing ones, and the images are not confined to the present ones. The key lies in carefully studying their origins and thoroughly understanding their existence and non-existence. As for how the Five Phases are generated, how the original qi of the Earlier Heaven first came into being, why it takes precisely this form of generation, and why the numbers of heaven and earth are divided into birth numbers and completed numbers, these are the steps of creation, the stages from nothingness to experience, whose principles are subtle and meanings profound, not something that can be fully explained in a few words. Now I will briefly explain. The qi of the Earlier Heaven is bright, pure, dense, strong, still, clear and transparent, originally nameless and indescribable.

乃因含有熱性，溫氣氤氳，光流渾圓；以成其動，動則氣搖；先熱乃布，布則氣分；於是渾圓者漸漸變化，光明者漸漸暗然；此由動而生變，即由一而成兩之機也。故無極而太極，直一氣之轉移；動則有靜，陰陽始分；陰為陽化，陽為陰復；二者相施，兩儀乃判；其始判也，一陰一陽，猶甚純簡；以旋迴之故，交合乃成；故陰陽漸離，其氣時接；此則四象之漸成也。

Because it contains warmth, the warm energy becomes diffused and misty, with light flowing smoothly and circularly, thus creating movement. Once movement begins, the energy begins to stir and fluctuate. The warmth spreads out first, and once it spreads, the energy differentiates. Thus, what was originally round and unified gradually begins to change, and what was originally bright gradually turns into darkness. This is the process of change caused by movement, which is the beginning of transformation from one into two. Therefore, the transition from "wuji" (formless) to "taiji" (primordial energy) is merely a transfer of the same energy; when there is movement, there must be stillness, and thus yin and yang become distinct. Yin arises from yang, and yang arises from yin, and the two alternate and interact, leading to the division of "liang yi" (two principles). At the moment of their initial division, yin and yang were still pure and simple. Due to their rotation and intermingling, they combine to form a union, and thus yin and yang gradually separate, yet their energies constantly connect: this is the process by which the "si xiang" (four images) gradually take shape.

其太陽太陰，全然兩儀之象，是為水火之生；太者，言其大也；然非純陰陽也，以各得其多者為名；故水為天生地成，火為地生天成；斯為兩儀之後，四象之初；太陰太陽之所象也。繼之者，則少陽少陰，亦出於兩儀；而其所得者少，所成者弱，是為木與金；此木亦天生地成，金亦地生天成；四者既具，生成之氣未盡，於是土乃成焉。故土者、生成之末，而備兩儀之精；全後天之象；接先天之氣；此其生成之序也。然亦非如此簡單者，蓋氣蕩無停，精流不見；生機既啟，成數斯應；

Among them, "Taiyang" and "Taiyin" fully inherit the image of the two principles, and what they generate are water and fire. The term "Tai" means that they possess a large share. However, they are not purely yin or purely yang; they are named according to the principle that dominates more. Therefore, water is born of heaven and formed by earth, while fire is born of earth and formed by heaven. This is the essence represented by Taiyin and Taiyang, which comes after the two principles and before the four images. Then come "Shaoyang" and "Shaoyin," which also originate from the two principles, but they possess a smaller share and weaker force, resulting in wood and metal. Wood is born of heaven and formed by earth, while metal is born of earth and formed by heaven. Once these four elements are in place, the generating qi has not yet been fully exhausted, so earth is subsequently generated. Thus, earth comes last in the order of generation but encompasses the essence of both principles, completing the Later Heaven image and receiving the qi of the Earlier Heaven. This is the order of their generation. However, the actual situation is not so simple: qi is constantly stirring and never ceasing, while the essence flows continuously and invisibly; once the vital force is activated, the numbers of generation respond accordingly.

天生於上，地乃應之；地生於下，天乃應之。以兩儀初分，力足精強，行走至速，各含生機，均有成德，此生彼成。如電與雷，不差毫黍。其分之為氣者十，生成各半，以與陰陽奇偶，相見而合。故水之生於陽也，而陰成之；火之生於陰也，而陽成之，其所應至捷也。

Heaven's energy first arises above, and Earth responds below; Earth's energy first arises below, and Heaven responds above. This is because when the two principles were first divided, the energies of yin and yang were strong, pure, and vigorous, moving very quickly, each containing the function of growth and each possessing the virtue of completion. Therefore, when one side begins to arise, the other side immediately completes it, as swift as lightning and thunder following each other without the slightest delay. The energies derived from the two principles total ten numbers, with the "generative numbers" and "completing numbers" each taking up half, exactly matching the odd and even numbers of yin and yang to combine. Thus, water is generated by yang energy but completed by yin energy; fire is generated by yin energy but completed by yang energy—when one side begins to arise, the other side's response arrives immediately.

然陽者，所生必陰；陰者，所生必陽。陽者下，而陰者上；陰者熱，而陽者涼；皆以動而變，得其反也。故天動生水而流於地，地乃成之；地動生火而炎於天，天乃成之。皆氣變自然而合，初無為之序，而自成序也。

However, what is produced by yang must belong to yin, and what is produced by yin must belong to yang. Yang is originally above, yet the water it produces flows downward; yin is originally below, yet the fire it produces rises upward. Yin is naturally cold, yet fire is hot; yang is naturally hot, yet water is cool. This is because once the qi is activated, it must change, and the result of this change is precisely its opposite. Therefore, when heaven activates, it produces water, which flows down to the earth, and the earth completes it; when the earth activates, it produces fire, which rises upward to the heaven, and the heaven completes it. All these are the natural transformations of qi that then come together. Initially, there was no one to arrange an order, yet an order naturally formed.

水火既生，其氣已弱，故木為陽之微，金為陰之微，氣自至焉。生成既眾，強弱皆見；精復其始，德返於初。於是土乃生成，而得氣獨全，以其值氣之復也。土生於天，成於地，與先天初生同，而土質厚德凝，為後天萬有之本。其氣全，其數中，此五行所獨有者，亦萬物所同母。

After water and fire have been generated, the sharpness of the two energies has already weakened, so the wood that comes next is merely a faint remaining yang energy, and metal is merely a faint remaining yin energy. This is the natural decline of energy. When the number of generated elements has become numerous, the differences in their strength become apparent, and the refined energy returns to its original state, while the virtue reverts to its source. At this time, earth is generated, receiving a complete energy, because it coincides with the moment when the energy returns to its original state. Earth is generated by heaven and formed by earth, which is the same as the original way of generation in the Earlier Heaven. However, earth has a heavy quality and a concentrated virtue, becoming the fundamental basis for all existence in the Later Heaven. Its energy is complete, and its number is in the center — this is unique to earth among the Five Phases, and it is also the common mother of all things.

故其用周於天地，利於四行；雖在生成之終，卻居後天之首，乃位中央而數中極。此其生化之妙，有非人之所能知；而後天生化無窮，莫不本於此土者，其得氣固不同也。先天生化之序，至土而止；而後生化之功，自土而成。是為先後始終之樞，恰當道器上下之紐，其為此世界之所貴者，自過於一切矣！

Therefore, the function of earth extends throughout heaven and earth, and it can benefit the four other elements, water, fire, wood, and metal. Although it comes last in the order of generation, it holds the first position in the Later Heaven, located in the center, and occupies the middle number. The subtlety of this process of generation and transformation is not something humans can fully comprehend. Yet the process of transformation in the Later Heaven is endless, and nothing is not based on earth, because the qi it receives is fundamentally different from the other four elements. The order of generation in the Earlier Heaven ends with earth; the function of transformation in the Later Heaven begins with earth. Thus, earth becomes the hub connecting the Earlier Heaven and the Later Heaven, linking the beginning and the end. It is precisely situated at the junction between the ultimate principle of "Dao" and the physical "qi" of things. Its value in this world naturally surpasses all others.

故先後天之生化次序，均不同也，而皆以土為貫通之機。舍土則不獨後天之生化不成，既先天之生成，亦無由竟其用。故言後天與先天同異，必自土溯其根源；此天地萬物，莫不依土而後生存變化也。

Therefore, although the sequence of generation and transformation in the Earlier Heaven and the Later Heaven differ from each other, both take earth as the key element connecting the two ends. Without earth, not only can the transformation in the Later Heaven not be completed, but the generation in the Earlier Heaven also cannot fully realize its function. Therefore, whenever one discusses the similarities and differences between the Later Heaven and the Earlier Heaven, one must trace back to earth as the root. All things in heaven and earth depend on earth to exist and to change.

五行之氣，水本太陰，而根於陽；火本太陽，而根於陰；以所生之屬與所成異也。故水火木金，皆陰體陽用，陽體陰用；唯土則兼陰陽體用，以得氣全也。氣始動為陽生陰，既復則仍返於陽；氣之初行，為陰隨陽，既定則仍抱於陰。

In terms of the Five Phases, water originally belongs to 'Taiyin' but its root is in the yang; fire originally belongs to 'Taiyang' but its root is in the yin. This is because the aspect that generates it and the aspect that completes it belong to different energies. Therefore, the four phases of water, fire, wood, and metal all have yin as their substance and yang as their function, or yang as their substance and yin as their function, with substance and function on opposite sides; only earth possesses both yin and yang as its substance and function, because it receives a complete energy. When the energy first begins to move, it is yang that produces yin; when it returns, it still reverts to yang. When the energy first starts to flow, yin follows yang; when it becomes stable, it is still embraced by yin.

土之生成數，雖有陰陽，而五則備二氣；十又五之倍，亦陽之所用。故其體用兼二氣，以為後天之母，四氣之長。五行雖分，莫不依土而生變化；是土者，直二氣之精，五行之本，萬物之源也。按之易卦，以艮為土，故曰：「成始成終」。以居先天生成之終，為後天生化之始；在後天卦位，艮與坤對，在連山易序，艮為首位，即洛書之象。二八易位，亦以艮坤相易，以明後天之土代地之用，為生化之本也。

The numerical values associated with earth, known as the generating number five and the completing number ten, also belong to yin and yang—five is yang and ten is yin. However, the number five itself already contains both yin and yang energies. Since ten is a multiple of five, it also belongs to yang. Therefore, earth possesses both yin and yang energies in its nature and function, making it the mother of all things in the later heaven system and the master of the four seasons. Although the five elements are divided into five, none of them can change without earth. Thus, earth is the essence of yin and yang, the foundation of the five elements, and the origin of all things. According to the hexagrams of the Book of Changes, the hexagram Gen is associated with earth. Therefore, the Commentary on the Hexagrams refers to Gen as the hexagram of "beginning and end." This is because Gen is at the end of the sequence of generation in the earlier heaven system, and also the beginning of generation in the later heaven system. In the later heaven hexagram positions, Gen and坤 are opposite each other. In the sequence of the Linked Mountains Changes, Gen is the first hexagram, which corresponds to the image of the Luo Writing. In the Luo Writing, the numbers two and eight have exchanged positions, which also corresponds to the exchange of Gen and坤. This indicates that in the later heaven system, earth has taken over the role of the earth element, becoming the fundamental source of all generation and transformation.

夫艮卦屬土，而異於坤之地也，乃能代坤之用，履地之位；其因氣之異，德之充也。在先天艮為山象，居西北隅；在後天則移東北，與坤對位，而其原位為乾所居。明後天之土，即先天之坤，足與天同功，與地同德，此連山易所以推為首也。後天之艮，當坎震之交，明生化之源；其成萬物終始者，即以其能代地而配天也。故艮在後天，非僅山之象，實土之總名也。

The Geng hexagram, although belonging to the earth element, differs from the Kun hexagram representing the earth. Because of this difference, it is able to take on the role of Kun and occupy the position of the earth. This is due to the distinct nature of the qi it possesses and its fullness of virtue. In the Earlier Heaven arrangement, Geng takes the image of a mountain and occupies the northwest corner. However, in the Later Heaven arrangement, Geng moves to the northeast, facing opposite the Kun. Its original position in the northwest is taken by the Qian hexagram. This shows that the earth in the Later Heaven is actually the Kun of the Earlier Heaven, capable of sharing the function of heaven and the virtue of the earth. This is why the Linked Mountains Changes places Geng as the first hexagram. In the Later Heaven arrangement, Geng is located at the junction of Kan and Zhen, indicating the source of generation. It is able to accomplish the beginning and end of all things because it can both replace the earth and harmonize with heaven. Therefore, in the Later Heaven, Geng is not merely a symbol of a mountain, but the general term for earth.

既以山言，亦對海洋而論，以出海面也。故其代地之德，多見於陸，而其象繫大陸也。因地之用，有陸水之別；而土之德，則見於陸；即水亦陸所載所防，而後成其用也。故五行之水，受制於土；而八卦之坎，與艮連居；其義至深切矣。

Since "mountain" is used to represent the trigram Gen (Geng), then mountain is also relative to the ocean, because mountain rises out of the sea surface. Therefore, the virtue displayed by Gen in place of earth is mostly manifested on land, and its image is actually the continent. The function of earth originally has a distinction between land and water, and the virtue of soil is only manifested on land; even water needs land to carry it and to build dikes before it can fulfill its function. Therefore, in the Five Phases, water is restrained by soil; in the Eight Trigrams, the position of Kan is adjacent to Gen—this meaning is extremely profound.

土之在後天，實為一切主，無論何物，莫不因地以為生化；即空中之氣，亦附於地面而後殖；其它有形之物無論矣！凡生在天地間者，無能離土以存以變；不獨人物之生也，即植物等或無生之物，亦必賴土以存以變。此可以見土之德，為造化之本源所寄，亦即氣數之根株所在；故土之數五，實為萬數之基。

In the Later Heaven, earth is indeed the master of all things. Whatever exists, whether it is something tangible or intangible, depends on the earth for its growth and transformation; even the air in the sky needs to rely on the ground to flourish and multiply, let alone other physical substances. All things existing between heaven and earth cannot exist or change without the earth. This is not only true for humans and animals, but also for plants and even inanimate objects. Therefore, the virtue of earth is the place where the origin of creation is entrusted, and it is the root of both qi and numbers. Hence, the number of earth is 'five', and this five is indeed the foundation of all numbers.

而足通天地之用，為人物之權衡；是五者，等於一，言其用廣，而能通一切數也。在河圖證之，一六居北，二七居南，三八在東，四九在西，五十處中；四方之數，均仰中央，而其差皆此五；已可見此中數所寓，即中氣所存。

The number five is sufficient to encompass the functions of heaven and earth, becoming the standard for measuring people and things. Saying 'five equals one' refers to its wide range of applications and its ability to integrate all numbers. Using the Yellow River Chart as evidence: one and six are in the north, two and seven in the south, three and eight in the east, four and nine in the west, and five and ten in the center. The numbers of the four directions all depend on the center, and the difference between each pair of numbers in the directions is exactly five. From this, it is evident that the number in the center embodies the essence of the 'central vital force'.

又以陰陽順逆言之，一三七九，由北而西；四二八六，由西反北；兩者循環，以相終始；五獨居中，以運其樞，不隨之移易。十以二五，亦同在中，皆氣之妙用，數之妙合也。故陰數皆逆，而十不動；由先天之本序言，則二四六八應為次，今以行之逆，故變四為首，六為終。

Looking at the progression and retrogression of yin and yang: the yang numbers one, three, seven, and nine move from the north to the west in sequence; the yin numbers four, two, eight, and six move from the west back to the north in reverse. They cycle continuously, mutually marking the beginning and end. Only the number five remains in the center, rotating as the central hub, not shifting with the numbers of the four directions. Ten is two fives, so it also remains in the center. These are the subtle workings of qi and the harmonious combination of numbers. Therefore, although the yin numbers generally move in reverse, the number ten remains stationary. Following the original order of the Earlier Heaven, the yin numbers should be arranged as two, four, six, and eight in sequence; but because they move in reverse, they now start with four and end with six.

六者為陰數始終之數，在成數為始，在用數為終。陽始一終九，陰始四終六；展轉相合，皆為五；亦即中數所寄，中氣所存也。一四同行，至九六相交；莫非五數，以明中氣之無不通也。五行之數，固如上述；先天後天各殊，即其方位，亦有此異。當五行之初見於數也，雖有南北東西之分，實則所指屬虛空之象。如以中國論，自當北為水，南為火，木居東，金居西，而土在中央；若合天下言之，則有不然。

Six is the number that combines both the beginning and the end within the yin numbers. In the "cheng shu" (completed numbers), it comes first, but in the "yong shu" (used numbers), it comes last. The yang numbers start from one and end at nine, while the yin numbers start from four and end at six. When these are paired together, the result always relates to the number five—adding one and four gives five, and adding nine and six gives fifteen, which is still a multiple of five. This is the place where the central number is embodied and where the central qi (vital energy) resides. The yang number one and the yin number four begin together and continue until nine and six meet, with no point failing to conform to the number five, showing that the central qi is present everywhere. The numbers of the Five Phases are as described above. The Earlier Heaven and Later Heaven differ, and so do their directions. When the Five Phases first appeared in terms of numbers, although they were assigned to the directions north, south, east, west, and center, they actually referred to the atmospheric phenomena in the void, not to specific places on the earth. If we consider China specifically, the north is associated with water, the south with fire, the east with wood, the west with metal, and the center with earth. But if we consider the whole world, this may not necessarily be the case.

蓋赤道南，則反其寒熱方位矣！此理原易明，蓋所云方位者，為其氣之所宜也。今以土為本，土之所在，當以大陸屬之。則凡赤道以北，大陸為多，而南則少；故當以北溫帶為中央，而順是以次南北焉。若果赤道南之大陸，則正與北反，即宜以南之北，當北之南，而反其五行之位。

Because in the southern hemisphere, the positions corresponding to cold and heat are exactly reversed. This principle is not hard to understand: what is meant by direction refers to the suitability of the qi, not to fixed directions on a map. Now that we take earth as the foundation, the place where earth resides should be considered as the continent. Since there is more land in the northern hemisphere than in the southern, the north temperate zone should be regarded as the center, and then the south and north should be determined accordingly. If we are discussing the continent in the southern hemisphere, the situation is exactly opposite to that in the northern hemisphere. Therefore, the northern part of the southern hemisphere should be regarded as the southern part of the northern hemisphere, and the five elements' directional arrangement should be completely reversed.

蓋河圖五行，本無定方，僅有定位。上火下水，左木右金；若在北溫帶，則下為北，上為南；若移南溫帶，則下為南，上為北。此固就所居地而定，不過水與火對，金與木配，乃不易耳。更推言之，水雖居北，而中國北方皆陸；火雖在南，而中國南方多水；東方亦為水居，西方則多高地；是即按之吾國，亦難以物質求之。

The Five Phases listed in the Yellow River Chart originally had no fixed directions, only fixed relative positions: fire is above, water is below, wood is to the left, and metal is to the right. If one is in the Northern Temperate Zone, the bottom of the chart would correspond to north and the top to south; if moved to the Southern Temperate Zone, the bottom would correspond to south and the top to north. Although directions depend on the location, the relationship that water and fire are opposite, and metal and wood are compatible, remains unchanged. Going further down: although water is said to be in the north, China's northern region is mostly land; although fire is said to be in the south, China's southern region is actually water-rich; the east is where the sea lies, while the west is mostly highlands and mountains. This shows that even when checking against China's geography, it is difficult to confirm the specific substances corresponding to the Five Phases' directions.

況水雖屬陰，而根於陽；火雖屬陽，而根於陰；是寒熱亦未盡水火之體用。木在山多，金出水內；東海無森林之地，西陲少金石之丱；則東西以配木金，亦非一定之理。故五方雲者，乃就氣而言；就先天之氣言，與一歲所合同；初非一一按之實物也。

Moreover, water though belonging to yin has its root in yang, and fire though belonging to yang has its root in yin. This shows that using only the terms cold and hot is insufficient to fully explain the nature and function of water and fire. Trees often grow on mountains, and metal is commonly found in water; the eastern sea area has no forests, and the western frontier has few mineral deposits. Therefore, associating the east with wood and the west with metal is not an unchanging principle. Hence, the concept of the five directions is based on qi, specifically the qi of the Earlier Heaven, which corresponds with the seasonal changes of cold and heat. Originally, it was not intended to match each direction with specific physical objects.

不然，春溫秋涼，冬寒夏熱，皆氣之變耳；物或隨之或否，不得以物執其說也。然若謂此言無定，而不信五行之說，則不可，蓋五行正同於二氣，無地無時不見之，其分別亦至明晰。如水之流下，火之炎上，與春夏之溫熱，秋冬之涼寒，皆一定不移者。雖至何地何時，仍可驗者；故其分別，得氣之殊，成象之異；實有至理，毫無可疑，不過學者宜會通其意，勿泥其辭。

If we do not look at it this way, then the warming in spring, cooling in autumn, severe cold in winter, and extreme heat in summer would merely be changes in qi; specific things may change with it or not, and we cannot rigidly apply this theory to individual things. However, if we reject the theory of the Five Phases simply because their positions are not fixed, that would be wrong. The Five Phases are just like yin and yang; they are present everywhere and at all times, and their distinctions are very clear. For example, water always flows downward, fire always rises upward, spring and summer are always warm and hot, and autumn and winter are always cool and cold. These are all unchanging; they can still be verified anywhere and at any time. Therefore, the Five Phases have distinct differences because they are influenced by different kinds of qi and form different appearances. There is real principle here, without any doubt. The scholars should understand its meaning thoroughly and not be stuck to its literal words.

貫徹其精，勿執其表；則天地之大，日月之明；山川之遙，草木之庶；無不可候其氣數，而得其類別也。故言五行，重在其生化之功，而探研生克之理；以求其象數，通乎天道耳。近世科學漸已近於是理之討論，果假以時日，讀吾中土之書，精以求精，自有會歸一途之日；

To grasp its essential meaning, one should not be fixated on its superficial aspects. In this way, the vastness of heaven and earth, the brightness of the sun and moon, the remoteness of mountains and rivers, and the abundance of grass and trees, none of these would be beyond the ability to perceive their qi and numbers, thus determining their categories. Therefore, when discussing the Five Phases, the key lies in understanding their function of generation and transformation, and then exploring the principles of mutual generation and mutual control. Through this, one can seek out their symbolic representations and numerical patterns, connecting them to the heavenly way. Modern scientific discussions have gradually approached this principle; if researchers continue to study our traditional texts with diligence and refinement, they will eventually reach the same conclusion through different paths.

蓋五行之說，乃古人探本生化之源；格物致知，窮理盡性；通天地鬼神之道，立人生修養之方；順吉凶禍福之常，為日用起居之則；固與科學之義同，初非惝況無據之談，迷離莫詰之論。故中國一切文物制度，無不准是而成；人倫綱紀，世道規範；以及醫卜之技，言行之箴；政教所成，禮法所制；初無不由是而出，所謂規法是也。

The theory of the Five Phases is originally a study by ancient people to trace the origin and investigate the fundamental principles of generation and transformation. It is like the saying in the "Great Learning" that "investigate things to gain knowledge," and like the saying in the "Book of Changes · Explanation of the Trigrams" that "exhaust the principles and fully understand the nature," it connects the principles of heaven and earth and spirits, establishes methods for personal cultivation, follows the regularities of good fortune and misfortune, and sets guidelines for daily life. This is fundamentally consistent with the purpose of science, and is not mere empty talk without foundation or obscure and indeterminate metaphysical speculation. Therefore, all cultural and institutional practices in China were established according to this principle: human relationships and social order, moral standards, as well as medical and divination techniques, guidelines for speech and action, achievements in politics and education, and the formulation of rites and laws—all originated from this—this is what is called "rules and standards."

如天文之軌度，地理之紀程；各有規矩方圓，以應乎二五氣數；故欲深通古時文化，必先自易探索；而易之仿始河洛圖書，以準天地之道，明鬼神之德；其精義入神，初非言文所盡；今所論者，尚其大略耳；望世之讀者，更由是以深求之；庶乎有通於古，有造於今；而不獨中國文化之得傳，無負聖人之教矣！

For example, the measurements of celestial orbits and the methods of recording distances on earth each have their own rules and standards, used to correspond with the principles of yin and yang and the numbers of the Five Phases. Therefore, to deeply understand ancient culture, one must first start with the Book of Changes to explore its principles. The Book of Changes was modeled after the Yellow River Chart and the Luo Writing, used to accurately grasp the way of the heavens and earth's movement, and to clarify the virtues of the transformations of ghosts and spirits. The subtle and profound aspects of it are not fully expressible through words and texts. What is discussed today is only a general overview. I hope that readers of the world will pursue further understanding from here, so that they can both comprehend the ancients and benefit the present generation. In this way, not only will Chinese culture be passed down, but also the earnest efforts of the sages in establishing teachings will not be in vain.

又曰：天地之間，萬物並生；而所憑者，多在地土；則以土為後天生化之母，備五行之氣，而為兩儀之所合化也。其德全而用宏，居中而運眾；雖天之高，星辰之遠；日月之明，風雨之降；寒暑之往復，關於天時氣候者，若不在地；而莫不自地見其用也。

It is also said that all things grow together in the space between heaven and earth, and most of them rely on the earth. This shows that the earth is the mother of all things generated in the Later Heaven, possessing the energies of the Five Phases. It is formed from the union of the two principles. The earth's virtue is complete and its functions are great, residing in the center and governing all things. Although heaven is high, the stars are far away, and the brightness of the sun and moon, the falling of rain and wind, the coming and going of cold and heat, these are all phenomena of heaven and climate, which seem not to be on the earth. Yet none of them can manifest their effects without the earth.

地者，萬物之中樞；為一切氣數之機衡，生變之爐冶；而人亦隨之生長死沒，至於無窮；故後天之土，雖居五行之末，實策生化之源。而本數則五，故其用亦五；以五應天，則天數成，此十乾之為二五也；以五應時，則時令備，此歲序之分為五時也。

The earth is the central hub of all things, the mechanism and scale for the movement and transformation of qi and numbers, the furnace where generation and change occur. Humans also grow and die in accordance with it, in an unending cycle. Therefore, although the Later Heaven's earth element is placed last among the Five Phases, it actually controls the source of generation and transformation. The number of earth is five, so its application follows the number five: using five to correspond with heaven, the numbers of heaven become complete, which is why the ten heavenly stems are divided into two fives; using five to correspond with the seasons, the sequence of the year becomes complete, which is why the annual cycle is divided into five periods.