《观物外篇》

The numbers of Heaven are five, and the numbers of Earth are also five. Together they make ten, the complete number. Heaven takes one number as its root and transforms it into four others; Earth likewise takes one as its root and transforms it into four others. Four of these numbers each have a definite form, while the remaining number has no definite form. This is the point at which “being” and “nonbeing” reach their limits.

Of Heaven’s four numbers of substance, three are put into actual use and one is not; the same is true of Earth. Thus the “one” without definite form serves as an analogy for nature, while the “one” that is not put to use serves as an analogy for the Dao. The three numbers put into actual use serve as analogies for Heaven, Earth, and humanity.

Things have eight changes in their substance and six changes in their function. Thus, among the figures of the Eight Trigrams (Bagua), four remain unchanged, while the others form two pairs of figures that are reversals of each other. Through the changes of six lines, the Eight Trigrams take shape.

Among the doubled hexagrams—those formed by placing two Eight Trigrams one above the other—eight remain unchanged, while the others form twenty-eight cases in which the figures reverse one another. Through thirty-six changes, the sixty-four hexagrams take shape.

Thus, the number of lines in a single hexagram ends at six, the number of trigram figures at eight, the changes produced by the yarrow stalks at thirty-six, and the number of doubled hexagrams at sixty-four. The Eight Trigrams consist of eight figures, while doubled hexagrams extend their number to sixty-four. Each hexagram has six lines; the changes produced by the yarrow stalks end at thirty-six, and the sixty-four hexagrams together have three hundred and eighty-four lines.

Heaven has four seasons, each season four months, and each month forty days. Multiplying four by forty, then subtracting one unit from each, gives three months in each season and thirty days in each month. The four seasons belong to the numbers of substance; three months and thirty days belong to the numbers of function. Although substance comprises four numbers, one is invariably left out of practical operation. The numbers of function therefore stop at three, with nine as their highest number. The numbers of substance are generally even, hence four and twelve; the numbers of function are generally odd, hence three and nine.

Why does a large number seem insufficient, while a small number often seems to have something left over? Because the larger part cannot be seen, while the smaller part can. Thus, the four seasons are bounded by four, the moon follows a cycle of thirty days, and a ten-day period has ten days. The human body has four limbs, while fingers and toes are counted by tens.

In people’s view, the sky appears in the south, while the scene in the north is hidden from sight. Its course reaches its limit at the sixth position, with something left over at the seventh. Thus, people can see what lies ahead but cannot make out what lies behind, and know only a little about what lies to either side.

The form of Heaven is reckoned by fours, the moon follows a cycle of thirty, and days are grouped into ten-day periods. Thus, the human body has four limbs, while fingers and toes are counted by tens.

In people’s view, the sky appears in the south, while the scene in the north is hidden from sight. Its course reaches its limit at the sixth position, with something left over at the seventh. Thus, people can see what lies ahead but cannot make out what lies behind, and know only a little about what lies to either side.

Heaven takes four as its form and three as its function; Earth, too, takes four as its form and three as its function. Heaven constrains Earth, and Earth also constrains Heaven. Yet the force of this constraint falls upon Earth, just as the extra portion of daylight falls upon the night. Hence it is said that Heaven’s number is three and Earth’s number is four: Heaven has three celestial lights—the sun, moon, and stars—while Earth has four circulating energies: Wood, Fire, Earth, and Metal. Earth, however, is vast, containing places that are exposed and visible as well as places that lie concealed from view. Perhaps this hidden portion is what is called the “remainder.”

The Qian trigram has seven sons, Dui has six, Li has five, Zhen has four, Xun has three, Kan has two, Gen has one, and Kun consists entirely of Yin lines, so it has no sons. Another account says that Qian has seven sons, Kun six, Dui five, Gen four, Li three, Kan two, and Zhen one; Xun has a firm line, so it has no sons. Yet another account says that Qian has seven sons, Kun six, Dui five, Gen four, Li three, Kan two, and Zhen one; Xun has a firm line, so it has no sons.

Heaven has two principal positions, and Earth has two as well. Together they employ two kinds of change to form the Eight Trigrams. Heaven has four principal positions, and Earth has four as well. Together they employ twenty-eight kinds of change to form the sixty-four hexagrams. Thus, among the lesser formed hexagrams, there are four principal positions and two changes, making six hexagrams in all; among the greater formed hexagrams, there are eight principal positions and twenty-eight changes, making thirty-six hexagrams in all. Qian, Kun, Kan, and Li are the roots of the thirty-six hexagrams; Dui, Zhen, Xun, and Gen are the roots of the twenty-eight.

Qian and Kun each undergo seven transformations, so the greatest number for day and night does not exceed seven. Gen and Dui each undergo six transformations, so the number of months ends at six, making twelve altogether. Li and Kan each undergo five transformations, so the number of days ends at five, making ten days altogether. Zhen and Xun each undergo four transformations, so the number for bodily forms ends at four, making eight altogether.

The primary and changed hexagrams together make thirty-six hexagrams, containing a total of 216 lines—the horizontal strokes that compose each hexagram. These are all used to represent numbers. Li and Kan each undergo five transformations, so the number of days ends at five, making ten days altogether; Zhen and Xun each undergo four transformations, so the number for bodily forms ends at four, making eight altogether.

The primary and changed hexagrams together make thirty-six hexagrams, containing a total of 216 lines. These are the numbers of yarrow stalks used in calculation—the counts employed when deriving the numbers of the Yi with yarrow stalks. Subtract four from thirty-six to get thirty-two; subtract four again to get twenty-eight; subtract four once more to get twenty-four. Thus, the hexagram number has thirty-two positions, obtained by subtracting four from thirty-six; the number of Heaven has twenty-eight positions, obtained by subtracting eight; and the number of Earth has twenty-four positions, obtained by subtracting twelve. Here, “four” refers to Qian, Kun, Kan, and Li. “Eight” means these four hexagrams together with Yi, Zhongfu, Daguo, and Xiaoguo. “Twelve” means these eight hexagrams together with Dui, Zhen, Tai, and Jiji.

The sun has eight positions, but its number in actual use ends at seven; this is calculated by leaving out the Qian hexagram. The moon has eight positions, but its number in actual use ends at six; this is calculated by leaving out the Dui hexagram. The stars have eight positions, but their number in actual use ends at five; this is calculated by leaving out the Li hexagram. The chen—an ancient unit of time, also referring to the periods associated with the movement of the stars—has eight positions, but its number in actual use ends at four; this is calculated by leaving out the Zhen hexagram.

The sun has eight positions, but its number ends at seven; this is calculated by leaving out the Tai hexagram.

The count of the months begins with the Dui hexagram because the moon’s course does not reach the sun’s number. Thus, when the twelve months are added together, there is generally a remainder of twelve days.

Qian belongs to Yang within Yang and cannot change, so the year is described in terms of twelve months. Zhen belongs to Yin within Yang and cannot change, so the division of a day into twelve shichen is fixed.

The count of the months begins with the Dui hexagram because the moon’s course does not reach the sun’s number. Thus, when the twelve months are added together, there is generally a remainder of twelve days.

Qian represents pure Yang, so it cannot change further. A year is represented by twelve months. Zhen represents Yang Qi held within Yin, so the twelve double-hours of a day and night cannot emerge from it. Dui is Yang held within Yin, while Li is Yin held within Yang. Both can change, so the numbers of the sun and moon can be counted separately. The Yin count begins with twelve, and the Yang count with thirty; throughout, both contain the number “two sixes.”

The month can be seen through the year, the day through the month, and the double-hour through the day. This is the relationship in which Heaven governs Earth. Thus, the four changes of Heaven contain the four changes of Earth; the changes of the sun also contain those of the moon and stars. Therefore, one hexagram, the basic figure in the Yi, contains four hexagrams.

The sun, moon, stars, and double-hours each occupy one position, and each in turn has four positions. This is the change of four times four. Therefore, one hexagram contains four hexagrams.

The sun, moon, stars, and double-hours each occupy one position, and each in turn has four positions. The four categories have four positions apiece, making sixteen positions in all. After this cycle of change, the numbers of the sun and moon reach their limit.

Heaven has four changes, and Earth has four changes as well; change brings both increase and decrease. After sixteen changes, the numbers of Heaven and Earth reach their limit.

The sun’s number begins with one, the moon’s with two, the stars’ with three, and the double-hours’ with four. From this, the numbers unfold: Yang always has six, and Yin always has two. Thus, the changes operating across both the greater and lesser ranges are fully worked out.

Three hundred and sixty changes unfold into 129,600.

129,600 changes unfold into 1,679,616,000.

1,679,616,000 changes unfold into 28,211,099,074,560,000.

Taking 360 as one unit of time—that is, one unit in the calculation—one can derive 129,600 … then 1,679,616,000 changes, which in turn unfold into 28,211,099,074,560,000.

Set three hundred and sixty as one “period,” one hundred and twenty-nine thousand six hundred as one “day,” and sixteen billion seven hundred ninety-six million sixteen thousand as one “month.” Then set two hundred eighty-two trillion one hundred nineteen billion nine hundred ninety million seven hundred forty-five thousand six hundred as one year. This establishes the numbers used to calculate the great and lesser cycles.

Divide this number of years into twelve parts: the first six represent increase, and the last six, decrease, corresponding to the twelve months of the year. Following this pattern of advance and retreat, the three hundred and sixty days likewise advance and retreat.

Divide the number for one month into thirty parts, corresponding to the thirty days in a month. As the great cycle waxes and wanes, these parts advance or retreat by sixty days. Divide the number for one day into twelve parts, corresponding to the twelve double-hours of the day, and it advances or retreats by six days. Three hundred and sixty, in turn, corresponds to one double-hour; as the lesser cycle advances or retreats, it marks the changing hours of day and night.

Following the number of “sixteen transformations,” subtract the overlapping portions and take the values that remain in effect. This gives two hundred eighty-two trillion one hundred nineteen billion nine hundred ninety million seven hundred forty-five thousand six hundred. Divide this into twelve limits to serve as the basis for the calculations above.

Likewise, following the number of “sixteen transformations,” subtract the overlapping portions and take the values that remain in effect to obtain the total given above. Divide it into twelve limits, with the first six representing increase and the last six, decrease. Each limit is sixteen billion seven hundred ninety-six million sixteen thousand, or one-twelfth of the total.

For every sixteen billion seven hundred ninety-six million sixteen thousand years that pass, one portion opens and advances by sixty days. Across six limits, six portions open, advancing by three hundred and sixty days. Since one portion still remains, a seventh opens, advancing by three hundred and sixty-six days. The amount of retreat during decrease is calculated in the same way.

From the total of 129,600, subtract three-tenths to obtain the “exchange number,” the base number for the meeting and cyclical movement of Heaven and Earth. Take the remaining seven-tenths as the “operational number,” the number used in practice. Multiplying the operational number by three gives six; adding the remainder makes seven-tenths. Calculated on this basis, it comes to 90,720 years. Taking half gives 45,360 years, used to calculate an increase of six days.

A day consists of daylight and darkness. The calendar also accounts for the moon’s varying speed, which creates differences in its reckoning. Together these make twelve days. One day is added every 3,600 years, so 43,200 years add twelve days. Taking half gives 45,360 years, used to calculate an increase of six days.

A day consists of daylight and darkness. The calendar also accounts for the moon’s varying speed, which creates differences in its reckoning. Together these make twelve days. One day is added every 3,600 years, so 43,200 years add twelve days. The remaining 2,160 years are used to calculate six fractional units in the remainder. Add another 2,160 years from the exchange number, and the total increase is twelve fractional units, which serve as the basis for inserting a leap month.

Thus, when the lesser cycle completes sixty changes, the total is 366 days. Six is the number of Heaven, and four is the number of Earth. Heaven governs form and relies on Earth to give form to things; Earth distributes functions and receives their effects from Heaven. Heaven and Earth depend on one another, just as form and function are mutually reliant.

Qian, the pure Yang hexagram, is one. Beginning with its fifth line, the Qian hexagram differentiates line by line to become the Great Possession hexagram, corresponding to the number 360. Differentiating from the fourth line, it becomes the Small Restraint hexagram, corresponding to 129,600. Differentiating from the third line, it becomes the Treading hexagram, corresponding to 16,796,160,000. Differentiating from the second line, it becomes the Fellowship with Others hexagram, corresponding to 282,119,990,745,600,000. When the first line of Qian differentiates, it forms the Coming to Meet hexagram, corresponding to 79,586,611,109,994,648,843,919,360,000,000,000. These are called “fractional numbers”: large numbers gradually divide into smaller ones. Since the process proceeds from top to bottom, it is associated with Yang numbers.

One gives rise to two, forming the Breakthrough hexagram, corresponding to the number 12. Two give rise to four, forming the Great Strength hexagram, corresponding to 4,320. Four give rise to eight, forming the Peace hexagram, corresponding to 559,872,000. Eight give rise to sixteen, forming the Approach hexagram, corresponding to 940,369,996,915,200,000. Sixteen give rise to thirty-two, forming the Return hexagram, corresponding to 2,652,887,036,648,800,294,797,312,000,000,000. Thirty-two give rise to sixty-four, forming the Kun hexagram, the pure Yin hexagram, corresponding to the number of the Limitless. These are called “growing numbers”: small numbers gradually increase. Since the process proceeds from bottom to top, it is associated with Yin numbers.

Heaven governs form, so the eight Kun hexagrams correspond to the number of the Limitless. This, too, is called a “growing number”: it grows gradually from small to large, proceeding from bottom to top, and is therefore associated with Yin numbers.

Heaven takes its own substance as its foundation. It therefore undergoes eight transformations and ultimately returns to sixteen. Earth takes function as its division. It therefore undergoes six transformations and ultimately returns to twelve. The number of Heaven begins with one and ultimately reaches seven ti, nine thousand five hundred eighty-six wan, six thousand one hundred ten gai, nine thousand nine hundred forty-six wan, four thousand eight hundred eight jing, eight thousand four hundred thirty-nine wan, one thousand nine hundred thirty-six zhao. The number of Earth begins with twelve and ultimately reaches two hundred gai, six thousand nine hundred eighty wan, seven thousand three hundred eighty-one jing, five thousand four hundred ninety-three wan, eight thousand four hundred ninety-nine zhao, seven hundred twenty wan yi.

Only when Earth exists does “two” come into being; only when there is “two” do day and night arise. The two forces of Yin and Yang interact and combine with other numbers, giving rise to the myriad things. Thus the Yi takes “two” as the number from which things arise and twelve as the basis of transformation. “One” itself is not counted as a number, yet numbers take shape from it. The celestial bodies move without rest and have no division into day and night in themselves. People live on Earth and so experience the alternation of day and night; therefore, the numbers used in the human world are based on those of Earth.

From the Heaven hexagram Lin upward, and from the Earth hexagram Shi upward, the subject is cyclical numbers. From the Heaven hexagram Tongren downward, and from the Earth hexagram Dun downward, the subject is numbers of years. Cyclical numbers belong to Heaven, and numbers of years to Earth. From the Heaven hexagram Bi upward and the Earth hexagram Gen upward, the subject is numbers of function. From the Heaven hexagram Mingyi downward and the Earth hexagram Pi downward, the subject is numbers of conjunction. From the Heaven hexagram Zhen upward and the Earth hexagram Jin upward, the subject is numbers of existence. From the Heaven hexagram Yi downward and the Earth hexagram Yu downward, the subject is numbers of nonexistence. These hexagram names come from the Yi and mark stages in the transformations of number and principle.

The numbers of Heaven that exist begin with the Qian hexagram and end with the Zhen hexagram. The rest belong to nonexistence, because the stars of Heaven cannot be seen. The number of Earth leaves out “one” and begins with twelve, because Earth’s fire always lies hidden beneath the ground. Thus Heaven takes substance as its foundation, yet often conceals that foundation; Earth takes function as its root, yet often keeps its function hidden from view.

A year counts only three months, and a month counts only thirty days; the hours represented by Zhen, the trigram symbolizing the movement of thunder, end there as well. The remainder belongs to the portion called “Nonbeing,” because the stars in the sky cannot be seen. The earth subtracts one count and gives rise to twelve because earthly fire is often hidden beneath the ground. Thus, Heaven is founded on its ti (substance, or fundamental form), yet often conceals its foundation; Earth takes its yong (function, or activity) as fundamental, yet often hides its functions from view.

A year takes only three months, and a month only thirty days; in both cases, the count of chen—the hours or units of time—is subtracted. The Eight Trigrams are therefore paired and doubled to form the sixty-four hexagrams. Of these, eight remain unchanged, while seven categories can change. Seven times eight equals fifty-six, which explains the meaning of this statement.

The solid Yang line represents the count of daylight, and the broken Yin line represents the count of nighttime. Heaven and Earth meet, and Yin and Yang join; day and night thus alternate, while firmness and yielding intermingle. In spring and summer, Yang energy is more abundant, so the count of daylight is greater and that of nighttime smaller. In autumn and winter, Yin energy is more abundant, so the count of daylight is smaller and that of nighttime greater.

The stalk count for the numbers of substance is 384. Subtracting the stalk counts of the four hexagrams Qian, Kun, Kan, and Li gives the numbers of function: 360.

The functional count of the numbers of substance is 270. Subtracting the stalk counts of Qian and of Kan and Li yields the numbers of function; hence the count of daylight is smaller and the count of nighttime greater.

The stalk count for the numbers of substance is 384. Subtracting the stalk counts of the four hexagrams Qian, Kun, Kan, and Li gives the numbers of function: 360.

The functional count of the numbers of substance is 270. Subtracting the stalk counts of Qian and of Kan and Li yields the functional count of the numbers of function: 252. Of the 270 functional counts of substance, 156 belong to Yang and 114 to Yin. After subtracting the stalk count of Li, the Yang count is 152 and the Yin count is 112; these are the counts used in practice. The general principle is that the Yang count subtracts Li and draws on Qian, while the Yin count subtracts Kun and draws on Kan. Thus, Heaven’s Yang stalk count is 112, and Earth’s Yin stalk count is also 112. The Yang stalk count has an additional 40, obtained by subtracting the Yang count associated with the north and south directions.

When the south reaches extreme heat and the north reaches extreme cold, nothing can grow. These two climatic extremes are therefore excluded. Could the forty within this total be the excess portion of the numbers of Heaven? Yang Qi encroaches on Yin Qi, and daylight overtakes night, so these changes are manifested on Earth. Taken together, they make one hundred cold numbers; since nothing can grow, these are excluded. Could the forty within this total be the excess portion of the numbers of Heaven? Yang Qi encroaches on Yin Qi, and daylight overtakes night, so these changes are manifested on Earth.

Together, there are 152 Yang numbers and 112 Yin numbers. Subtract the number of stalks assigned to the Qian hexagram from the Yang total—the stalk count used to calculate the values of hexagram lines—and the number assigned to the Kan hexagram from the Yin total. This leaves 146 Yang numbers and 108 Yin numbers. These are the “numbers put to use,” the portions of the numerical system actually applied. Thirty-six times three gives 108 for the Yang numbers, and thirty-six times three also gives 108 for the Yin numbers. There are three Yang units and three Yin units, with each side accounting for half. The Yang numbers have one additional remainder of thirty-six; together, this gives 146 Yang numbers and 108 Yin numbers. Thus, the “use of the fundamental numbers”—the portion drawn from the numerical system’s foundational numbers—is 270, while the number actually used is 364. The “numbers put to use” total 252.

There are sixty-four hexagrams, but only thirty-six are actually used; there are 384 lines, but only 216 are used. Divide sixty-four into four parts of sixty-four each, for a total of 256. Likewise, remove the first and top lines from each hexagram, and the result is also 256. This is the number by which the myriad things are generated. The Li and Kan hexagrams therefore govern the generation of the myriad things: Li has four Yang lines, and Kan has four Yin lines. For this reason, the number by which the myriad things are generated must be counted in units of four.

There are 112 Yang numbers and 112 Yin numbers. Remove the lines of the Li and Kan hexagrams, and the total is 216. There are forty of each, Yin and Yang, making 256 altogether.

Accordingly, the changes of the Eight Trigrams (Bagua) operate through six lines—the six positions in each trigram—and are governed by the Qian and Kun trigrams. The changes of the six lines, in turn, operate through four positions and are governed by the Li and Kan trigrams. Neither the dimness of the sky nor the break of day can bring things to growth; things grow only when the sun is at its zenith. Neither the northern nor the southern reaches of the earth can bring things to growth; only the central region can bring forth all things.

What are “structural numbers,” the numbers that represent the underlying structure of things? They explain how all things come into being. What are “operational numbers,” the numbers that represent change and movement? They explain how all things function. Functioning belongs to Heaven; bringing all things into being belongs to Earth. Heaven operates on its own, so its operational numbers are multiplied by themselves. The moment these operational numbers take effect is the moment all things come into being. Earth brings forth all things through the pairing of Yin and Yang, so it uses the mode of operation of structural numbers: Yang is multiplied by Yin to give the number by which all things are generated.

The number of Heaven is three. Thus, six multiplied by six and then by six gives 216, the total number of stalks for the Qian hexagram in divination using yarrow stalks. The number of Earth is two. Thus, twelve multiplied by twelve gives 144, the total number of stalks for the Kun hexagram. The Qian hexagram uses nine: three times eight is twenty-four, and multiplied by nine gives 216; two times eight is sixteen, and multiplied by nine gives 144. The Kun hexagram uses six: three times twelve is thirty-six, and multiplied by six gives 216; two times twelve is twenty-four, and multiplied by six gives 144.

For Kun, multiply twelve by three and sixteen by four, then include half of six as the portion remaining to Qian. This gives 252 for Qian and 108 for Kun.

The four Yang hexagrams have twelve lines in total: eight Yang lines and four Yin lines. Multiplying each Yang line by thirty-six and each Yin line by twenty-four gives a total of 384.

The text as a whole contains 384 lines, yet only 360 actually function in practice. Why? Because the four hexagrams Qian, Kun, Kan, and Li do not directly take part in the application of those 360 lines. Their not being applied directly is precisely what enables the remaining 360 lines to fulfill their function. Thus, although all things change without ceasing, the fundamental order represented by these four hexagrams does not change. Change is possible precisely because there is an unchanging foundation.

The number used in practice is normally fixed at 360, yet it can also be 366. Why? Because the count includes an excess; this additional portion embodies the full function of the Qian hexagram. Qian and Kun are not applied directly, while Kan and Li are each applied by half. Why is Qian used in full? Because Yang governs fullness. Why are Qian and Kun not applied directly? Because solitary Yang cannot generate growth, and solitary Yin cannot bring things to completion. Why are Kan and Li each applied by half? Li is in the east and Kan in the west. They occupy the midway points where Yin and Yang alternate, like the spring and autumn equinoxes and the gateways where day turns into night and night into day.

Why is Qian sometimes used to explain things, and Kan and Li at other times? When speaking from the perspective of Yang Qi’s dominance, Qian is used; when speaking of Yang Qi exceeding its bounds and gradually encroaching on Yin Qi, Kan and Li are used. Yang governs fullness, so the Qian hexagram functions in its entirety; Yin governs emptiness, so the Kun hexagram does not function directly. Yin and Yang wax and wane, encroaching on each other, so Kan and Li each function by half.

Thus, when viewed through the celestial phenomena, everything to the south is visible, everything to the north is hidden, and half of what lies to the east and west is visible. Li and Kan mark the boundary between Yin and Yang. Li therefore corresponds to the hour of Yin (about 3–5 a.m.), and Kan to the hour of Shen (about 3–5 p.m.). The actual count often exceeds this boundary because Yin and Yang Qi overflow. Even so, the number that functions in practice does not extend beyond the hour of Yin, and the number marking the boundary does not extend beyond the hour of Shen.

The Qian hexagram has forty-eight, divided into four parts, one of which is overcome by Yin Qi. The Kun hexagram also has forty-eight, divided into four parts, one of which is Yang Qi that has been overcome. Qian therefore receives thirty-six, and Kun twelve. Yang Qi governs advance, so its count is projected forward as 360 days; Yin Qi governs decline, so twelve days are subtracted from the twelve months.

In forward order, Qian is one, Dui is two, Li is three, Zhen is four, Xun is five, Kan is six, Gen is seven, and Kun is eight. In reverse order, Zhen is one; Li and Dui together are two; Qian is three; Xun is four; Kan and Gen together are five; and Kun is six.

Qian’s number is forty-eight, Dui’s is thirty, Li’s is twenty-four, Zhen’s is ten, Kun’s is twelve, Gen’s is twenty, Kan’s is thirty-six, and Xun’s is forty.

In another method of counting, Qian is thirty-six, Kun is twelve, Li, Dui, and Xun together are twenty-eight, and Kan, Gen, and Zhen together are twenty. The passage “Li above is upright” calls for further consideration.

The number of the circle begins with one, while the number of the square begins with two, reflecting the distinction between odd and even numbers. Six can be grouped as one, and twelve as two. Heaven is circular, and Earth is square. The circular number begins with one and accumulates to six; the square number begins with one and accumulates to eight. In transformation, it begins with four and accumulates to twelve. This is because six regularly changes according to six, eight according to eight, and twelve according to eight. This is the natural order.

Eight is the number of Heaven and Earth’s substance; six is the number of their operation; twelve is the number of Earth’s operation. Heaven transforms the square into the circle while always preserving one. Earth divides a whole into four parts and remains square throughout. Heaven changes the form of substance without changing its function; Earth changes the operation without changing its form.

Six plus one makes seven, while twelve plus four makes sixteen. Yang advances, so Heaven adds one to the number six, making seven. Yin withdraws and holds back, so Earth subtracts four and stops at twelve. Thus Yang always preserves one, while Yin always conceals one from view. The number of Heaven and Earth’s substance therefore ends at eight; the number of Heaven’s operation reaches its limit at seven, and the number of Earth’s operation ends at twelve.

The circle functions by cutting away the corners of the square: one becomes four, and when one is removed from four, three remain. Three then transforms into nine; subtracting three from nine leaves six. The square, by contrast, takes shape by drawing in the circle: one becomes three, and together they make four. Four becomes twelve, and adding four more makes sixteen.

Thus the number of operation arises from three and reaches its limit at six; the number of form arises from four and reaches its limit at sixteen. A circle has a diameter of one and a circumference of three; starting from one, the calculation can accumulate to six. The square divides one into four, then divides four into sixteen. All of this follows the natural Dao (the Way).

One branch paired with two branches produces three branches; remove one branch from the three, and two remain. Derive nine branches from three, then remove one to leave eight; remove three, and six remain. Thus, one branch can be paired to form three, and three can in turn be paired to form two; three can produce nine, and nine can be arranged into eight and six. From this, two branches produce four, eight produce sixteen, and six produce twelve. Three branches plus one make four; nine plus three make twelve; and twelve plus four make sixteen. Thus, four has one as its root and three as its function; twelve has three as its root and nine as its function; and sixteen has four as its root and twelve as its function.

Through derivation, six becomes thirty-six, eight becomes sixty-four, and twelve becomes one hundred and fourteen. Six multiplied by six, through transformation, becomes three hundred and eighty-four; eight multiplied by eight, through transformation, also becomes three hundred and eighty-four. Eight times eight is sixty-four, and six times eight is forty-eight; through the corresponding derivations, these numbers combine to make three hundred and eighty-four.

For circular numbers, six is the basic unit of transformation. Repeatedly deriving six from six leads to sixty, and then to three hundred and sixty. For square numbers, eight is the unit of transformation, so eight times eight gives sixty-four. Yang Qi governs increase, so the numbers are derived forward to sixty.

When divining with yarrow stalks, why count by sevens rather than simply by sixes? Because the remainder is included in the count. Once the remainder is removed, the count is still by six, which is why the number of yarrow stalks is thirty-six. The number fifty corresponds to the sixty-four hexagrams and symbolizes the calendrical count added for leap years; the forty-nine stalks actually used in divination correspond to the year’s calendrical count of sixty hexagrams. In divination, gathering the remainder and setting aside one stalk is like inserting a leap month into the year.

Why are four subtracted from the number of the hexagram? Because Heaven undergoes change, and Earth gives expression to that change. Thus, when one is subtracted from the number of yarrow stalks, four are subtracted from the number of the hexagram.

The diameter of a circle is one and its circumference is three; counting it twice gives six. The side of a square is one and its perimeter is four; counting it twice gives eight. The Yi begins with three lines, corresponding to the function of the circle: its diameter is one and its circumference is three, and when counted twice these become the six lines. It also begins with the Four Images—the four basic forms produced by changes between Yin and Yang—corresponding to the form of the square: its side is one and its perimeter is four, and when counted twice these become the Eight Trigrams. The forms of all things between Heaven and Earth are composed of four directions, while their functions undergo three kinds of change. When the sages composed the Yi, they simply revealed to people the principles of nature.

Cutting a square into a circle is the way Heaven moves; dividing the large into the small is the way Earth brings forth and transforms the myriad things. Thus Heaven’s function undergoes six changes, while Earth’s function undergoes four.

One and eight together make nine. Through division, eight becomes seven; eight divided becomes six; sixteen becomes twelve; twenty-four becomes eighteen; thirty-two becomes twenty-four; forty becomes thirty; forty-eight becomes thirty-six; fifty-six becomes forty-two; and sixty-four becomes forty-eight. Divide one into four, eight into thirty-two, and sixteen into sixty-four; continuing in this way, ninety-six becomes three hundred and eighty-four.

One produces six; six in turn produces twelve; twelve produces eighteen; eighteen produces twenty-four; twenty-four produces thirty; and thirty produces thirty-six. This process of continual derivation and expansion, after sixty changes, produces three hundred and sixty. This is the numerical pattern governing the operation and transformation of things.

Four produces twelve; twelve produces twenty; twenty produces twenty-eight; and twenty-eight produces thirty-six. This is the numerical pattern by which the myriad things come into being. Thus, the number of yang counting rods for the Qian trigram, which symbolizes Heaven and Yang, is thirty-six; for the Li trigram, which symbolizes Fire, and the Xun trigram, which symbolizes Wind, it is twenty-eight; for the Kan trigram, which symbolizes Water, and the Gen trigram, which symbolizes Mountain, it is twenty; and for the Kun trigram, which symbolizes Earth and Yin, it is twelve.

Each change in the circular number produces six; subtract the initial one, and five remain. Two changes produce twelve; subtract two, and ten remain. Three changes produce eighteen; subtract three, and fifteen remain. Four changes produce twenty-four; subtract four, and twenty remain. Five changes produce thirty; subtract five, and twenty-five remain. Six changes produce thirty-six; subtract six, and thirty remain. Thus, when nothing is subtracted, the numbers are multiples of six; after subtraction, they are multiples of five.

Five is formed by adding one to four; four by adding one to three; three by adding one to two; and two by adding one to one. Therefore, one produces two, and subtracting one leaves one; two produces three, and subtracting one leaves two; three produces four, and subtracting one leaves three; and four produces five, and subtracting one leaves four. Thus, two takes one as its root, three takes two as its root, four takes three as its root, five takes four as its root, and six takes five as its root. These principles should be considered more carefully.

One “square” number gradually changes into four; four then gives rise to eight, and four plus eight makes twelve. Eight then gives rise to twelve, and eight plus twelve makes twenty; twelve gives rise to sixteen, and twelve plus sixteen makes twenty-eight; sixteen gives rise to twenty, and sixteen plus twenty makes thirty-six. Another method of calculation says: one gives rise to three, which together make four; twelve gives rise to twenty, which together make thirty-two; twenty-eight gives rise to thirty-six, which together make sixty-four.

Which number is the “Great Expansion” (Dayan)—the number used to derive the hexagrams—in the Yijing? It is the basis the sages used to establish the numbers of the hexagrams. The numbers of Heaven total twenty-five; doubled, they make fifty. The numbers of Earth total thirty; doubled, they make sixty. Hence the saying: “The five positions correspond with one another, and each has its own corresponding number.” Fifty is the number used in divination with yarrow stalks; sixty is the number of the hexagrams. Five is the smaller range of numerical derivation used with the yarrow stalks, so fifty is called the “Great Expansion.” The Eight Trigrams are the initial system through which hexagram images take shape, so the sixty-four hexagrams are called the “Great Completion.”

The principle of divination with yarrow stalks takes roundness to symbolize the numbers of Heaven; therefore, seven multiplied by seven gives forty-nine. The number fifty includes the one left over beyond the forty-nine. The principle of hexagram images takes squareness to symbolize the numbers of Earth; therefore, eight multiplied by eight gives sixty-four. The number sixty is obtained by subtracting four from sixty-four. The number of the yarrow stalks is the “functional number” used in derivation; the number of the hexagrams is the “structural number” that forms the underlying framework. Derivation is based on the hexagram structure, so one is retained; the hexagram structure, in turn, takes derivation as its foundation, so four are subtracted. The circle takes one as its foundation, while the square takes four as its foundation. Thus one is retained in the yarrow-stalk number, and four are subtracted from the hexagram number. The use of seven in yarrow-stalk divination, and the practice of retaining one among the remainder, both express this principle. Suspending one yarrow stalk during divination likewise signifies retaining one.

In divination, yarrow stalks—the stems used for divination—are used to calculate the hexagram numbers. First, one stalk is set aside to symbolize the Three Powers of Heaven, Earth, and Humanity. The remaining forty-eight stalks are the tally count used for a hexagram. Four times twelve is exactly forty-eight.

Subtract three from twelve, leaving nine. Four times three is twelve: this is the number of tallies removed. Four times nine is thirty-six: this is the number of tallies actually used, corresponding to the thirty-six yang lines of the Qian hexagram. Subtract five from twelve, leaving seven. Four times five is twenty: this is the number of tallies removed. Four times seven is twenty-eight: this is the number used, corresponding to the twenty-eight yang lines of the Dui and Li hexagrams.

Subtract six from twelve, leaving six. Four times six is twenty-four, which is both the number of tallies removed and the number used, corresponding to the twenty-four yin lines of the Kun hexagram. Subtract four from twelve, leaving eight. Four times four is sixteen: this is the number of tallies removed. Four times eight is thirty-two: this is the number used, corresponding to the twenty-four yin lines of the Kan and Gen hexagrams, together with the eight yin lines of the upper trigrams, for a total of thirty-two lines.

Thus, seven and nine are yang, while six and eight are yin. Nine is the culmination of yang numbers, and six is the culmination of yin numbers. When a number reaches its limit, it changes; these numbers therefore form the basis for changes in the hexagram images.

Zhen and Xun have no corresponding tally counts because they correspond to numbers that are not used. Heaven takes strength and vigor as its De (Virtue/Power), so its yielding aspect does not appear; Earth takes yielding compliance as its substance, so its strong aspect does not arise. For this reason, Zhen and Xun have no tally counts. The Qian hexagram uses nine, so its tally count is nine; multiplying by four corresponds to the four seasons, each of which lasts about ninety days. The Kun hexagram uses six, so its tally count is also six.

There are four odd numbers: one, two, three, and four. There are also four stalk-count numbers: six, seven, eight, and nine. Together, the two groups make eight numbers, corresponding to the eight variations of the square numbers, which symbolize squares and directions. The numbers for combining the remainder with the hexagram have six forms: five with four, nine with eight, five with eight, nine with four, five with eight, and nine with four. The numbers for combining the hexagram also have six forms: five with four, nine with eight, five with eight, nine with four, five with eight, and nine with four. These correspond to the six variations of the circular numbers, which symbolize circles and cycles.

The range of odd numbers ends at four; five is not used. The range of stalk-count numbers ends at nine; ten is not used. Five is equivalent to one “one,” and ten to two “ones,” so five and ten are set aside in favor of four and nine. The omission of five from the odd numbers and ten from the stalk-count numbers embodies the utmost of presence and absence, and serves as an analogy for the natural order of numbers.

There are sixty-four hexagrams. Why, then, are only sixty used in practice? Because the sixty hexagrams contain three hundred and sixty lines. The sexagenary cycle used to reckon days therefore ends at sixty, with the cycle beginning at Jiazi. Once the six Jiazi cycles have completed one full rotation, the cycle of Heaven’s Dao has also run its course. The stalk-count numbers correspond accordingly: thirty-six plus twenty-four equals sixty, and thirty-two plus twenty-eight also equals sixty.

The Qian hexagram has forty-eight, and the Kun hexagram twelve; the Zhen hexagram twenty, and the Xun hexagram forty; the Li and Dui hexagrams have thirty-two, and the Kan and Gen hexagrams twenty-eight. The numbers in each pairing add up to sixty.

The yarrow-stalk numbers—the numbers used in divination with yarrow stalks—are complete, so the yang stalk counts of thirty-six and twenty-eight add up to sixty-four. The hexagram numbers have four subtracted from them, so the yin stalk counts of twenty-four and thirty-two add up to fifty-six.

Advancing through the unfolding of nine yields thirty-six; adding the twenty-eight of the Gen hexagram gives a total of sixty.

The yarrow-stalk numbers are complete, so the yang stalk counts of thirty-six and twenty-eight add up to sixty-four. The hexagram numbers have four subtracted from them, so the yin stalk counts of twenty-four and thirty-two add up to fifty-six.

Nine, by successive progression, yields thirty-six. Since only yang numbers are used, this is called “yang within yang.” Seven, by successive progression, yields twenty-eight. Since yang numbers are taken first and yin numbers afterward, this is called “yin within yang.” Six, by successive progression, yields twenty-four. Since only yin numbers are used, this is called “yin within yin.” Eight, by successive progression, yields thirty-two. Since yin numbers are taken first and yang numbers afterward, this is called “yang within yin.”

After four successive progressions, the yarrow stalks—the stems used for divination—number one hundred; the hexagrams, after four successive progressions, number one hundred and twenty. Here, “one hundred” represents ten, and “one hundred and twenty” represents twelve.

After the yarrow stalks are separated and their remainders counted, then combined with the hexagram numbers, the total number of stalks is forty-nine when the result is “five and two fours”; it is forty-six when the result is “nine and two eights”; it is forty-seven when the result is either “five and two eights” or “nine and a four and an eight”; and it is forty-eight when the result is either “nine and two fours” or “five, a four, and an eight.” After one change, nine corresponds to the Qian hexagram; after one change, six corresponds to the Kun hexagram. After two changes, seven corresponds to the Dui and Li hexagrams; after two changes, eight corresponds to the Gen and Kan hexagrams.

Removing the number of the single stalk set aside—the one placed apart during divination—leaves thirty-two when the result is “five and two fours”; twenty-four when it is “nine and two eights”; twenty when the result is either “five and two eights” or “nine and a four and an eight”; and sixteen when it is either “nine and two fours” or “five, a four, and an eight.” Thus, by removing the numbers three, four, five, and six, the yarrow-stalk numbers nine, eight, seven, and six are formed.

The numbers of Heaven are one, three, five, seven, and nine; the numbers of Earth are two, four, six, eight, and ten. Interweaving and combining the numbers of Heaven and Earth gives rise to change and produces different numerical patterns. They link Heaven and Earth, as day and night alternate in their course.

“One” is the beginning of number, yet it cannot be counted as a specific number. Thus, two times two is four, three times three is nine, four times four is sixteen, five times five is twenty-five, six times six is thirty-six, seven times seven is forty-nine, eight times eight is sixty-four, and nine times nine is eighty-one. “One” itself cannot undergo further change. A hundred reduces to ten, and ten in turn reduces to one; this reduction, too, cannot be altered. Thus, when deriving numerical principles, if the fundamental “one” is set aside, the changing numbers reach their limit at nine. Five times five is twenty-five, the number of Heaven; six times six is thirty-six, the stalk count of the Qian hexagram (the yarrow stalk count used to derive the hexagrams of the Yi); seven times seven is forty-nine, the number used in the Great Expansion; eight times eight is sixty-four, the number of hexagrams; and nine times nine is eighty-one, the number of the Xuan and Fan.

The number of the Great Expansion may be the source of all methods of calculation. Calculation begins with no more than shapes and relations such as square, circle, curve, and straightness. Multiplication increases numbers; division reduces them. Though there are many methods of calculation, in the end they all depend on these two kinds of change.

Among yin numbers there is no “one”; among yang numbers there is no “ten.”

When yang joins with yin, change arises; when yin joins with yang, results take shape. Thus, the yarrow stalk count is grouped in fours and uses nine, while the hexagram count is grouped in sixes and uses ten. This is like the interweaving of the Heavenly Stems and Earthly Branches: the Stems complete their cycle after six rounds, and the Branches after five.

Three times four equals twelve, and two times six also equals twelve. The yarrow stalk count pairs fours with nines, while the hexagram count pairs sixes with tens, just as the Heavenly Stems and Earthly Branches move in interwoven cycles: the Stems complete their cycle after six rounds, and the Branches after five.

Three times four equals twelve, and two times six also equals twelve. Twice twelve is twenty-four; three times eight and four times six also equal twenty-four. Three times twelve is thirty-six; four times nine and six times six also equal thirty-six. Four times twelve is forty-eight; three times sixteen and six times eight also equal forty-eight. Five times twelve is sixty; three times twenty and six times ten also equal sixty. These numbers correspond with one another through relationships that arise naturally.

Four times nine is thirty-six, and six times six is also thirty-six. The Yang number takes six, then adds half of the Yin number six, making nine. Thus, when expressed through two hexagrams—the figures in the Book of Changes composed of Yin and Yang lines—Yin and Yang each have three lines. In a six-line hexagram, Heaven, Earth, and Humanity each have two lines. These correspondences arise naturally.

Four times nine is thirty-six, and six times six is also thirty-six. The Yang number takes six, then adds half of the Yin number six, making nine. Thus, in two hexagrams, Yin and Yang each have three lines; in a six-line hexagram, Heaven, Earth, and Humanity each have two lines. Yin and Yang each contain Heaven, Earth, and Humanity, while Heaven, Earth, and Humanity each contain Yin and Yang. Hence the phrase, “Take three for Heaven and two for Earth as the basis for deriving numbers”: the numbers three for Heaven and two for Earth are used as the basis for working out the numbers.

The Yang number is one, which expands to ten, as exemplified by the Ten Heavenly Stems. The Yin number is two, which expands to twelve, as exemplified by the Twelve Earthly Branches and the twelve months.

In the first change, the number divides into two; in the second change, into four; in the third change, into eight, and the Eight Trigrams—the basic figures made up of three lines—are formed. The fourth change produces sixteen, the fifth thirty-two, and the sixth sixty-four, completing the sixty-four hexagrams.

The Book of Changes is founded on only three basic numbers. “Three for Heaven” means three multiplied by three, yielding nine; “two for Earth” means doubling three, yielding six. The phrase “Take three for Heaven and two for Earth as the basis for deriving numbers” does not refer to the actual numbers of Heaven and Earth themselves. “Take as a basis” means to model or compare: these numbers are derived by taking the actual numbers of Heaven and Earth as a point of comparison.

The numbers derived by the Book of Changes for the process of generation total 129,600, equivalent altogether to 4,320 generations. This describes the great number governing waxing and waning: it derives figures from the calendrical numbers associated with a period of thirty years, and then uses them as a basis for comparison. These are not the actual numbers of Heaven and Earth themselves. “Take as a basis” means to model or compare—that is, to derive numbers by reference to the actual numbers of Heaven and Earth.

The “generative numbers” mentioned in the Book of Changes total 129,600, or 4,320 “ages.” This is the great number governing the waxing and waning of Heaven and Earth. It is derived by calculating the number of periods over thirty years: a year has 360 days, and a day has twelve double-hours, making 4,320 periods in all. Multiply this by thirty, and the result is 129,600. Here, Jiazi and Jiawu mark the beginning of an “age.” This system of calculation belongs to the Huangji Jingshi; it begins with “the day at Jia, the month at Zi, the stars at Jia, and the periods at Zi.” In other words, the numerical sequences of the month, stars, and periods all follow the number of the day at Jia.

One, ten, a hundred, a thousand, ten thousand, and a hundred million are numbers that progress in accordance with the numbers of Heaven. Twelve, 120, 1,200, 12,000, and 20,000 are numbers that correspond to the numbers of Earth.

Divide fifty evenly, and the result is ten. Multiply according to the method of taking three from the numbers of Heaven and two from the numbers of Earth, and the result is six. Taking two from the numbers of Earth and multiplying gives four. These numerical principles explain how Heaven and Earth divide from the Taiji (Supreme Ultimate).

From the Return hexagram to the Qian hexagram, there are 112 yang lines; from the Gou hexagram to the Kun hexagram, there are 80 yang lines. From the Gou hexagram to the Kun hexagram, there are 112 yin lines; from the Return hexagram to the Qian hexagram, there are 80 yin lines.

The yang count increases from the base number of 360, while the yin count decreases from that same base.

Human beings are the most perceptive among the myriad things and, by category, belong to the walking creatures. Walking creatures belong to yin, so the number assigned to human beings is 120.

Each thing has its corresponding lifespan and number. Some exist for a day, others for a month, a season, or a year; some last ten years, or even a hundred, a thousand, or ten thousand years. Heaven and Earth themselves are also a kind of “thing” and likewise have their own number.

Each pair of opposite hexagrams consists of six yin lines and six yang lines. In the Book of Changes, there are twelve pairs of hexagrams in which six yang lines are set against six yin lines. After the four pure hexagrams are excluded, there are six pairs of hexagrams with eight yang lines and four yin lines, and six pairs with eight yin lines and four yang lines. There are three pairs with ten yang lines and two yin lines, and three pairs with ten yin lines and two yang lines.

The circle corresponds to the movement of the celestial bodies; the method of calculating the calendar likely originated from it. The square corresponds to the earth; the division of regions and the planning of well-field plots probably also followed this shape.

The circle embodies the numerical principles of the Hetu, while the square embodies the patterned writing of the Luoshu. Accordingly, Fuxi and King Wen drew on them to create the Yijing, while Yu the Great and Jizi organized their principles and numbers to establish the Hongfan.

After the Taiji (Supreme Ultimate), the undifferentiated source of the cosmos, divided, the two forms of Yin and Yang were established. Yang Qi descends and meets Yin Qi; Yin Qi rises and meets Yang Qi. From this, the Four Images arise. When Yang meets Yin and Yin meets Yang, the four images of Heaven take shape; when firmness meets yielding and yielding meets firmness, the four images of Earth take shape. Thus the Eight Trigrams come into being. When the Eight Trigrams interweave, all things arise.

Things therefore divide from one into two, then from two into four and from four into eight, proceeding in turn to sixteen, thirty-two, and finally sixty-four. This is what the Yijing means when it says: “Distinguishing Yin and Yang and applying yielding and firm in alternation, the six positions of the Yijing form the pattern of the hexagram.” Continue this progression, and ten becomes a hundred, a hundred becomes a thousand, and a thousand becomes ten thousand. It is like a tree: the trunk grows from the root, branches from the trunk, and leaves from the branches. The larger the whole becomes, the finer its constituent parts; as it is divided further, its kinds become more numerous. Gather them together, and they make one; unfold them, and they become ten thousand. Thus the Qian trigram represents division, and the Kun trigram represents convergence; the Zhen trigram represents growth, and the Xun trigram represents decline. Growth brings division, division brings decline, and after decline comes a return to convergence.

Qian and Kun establish the positions of Heaven and Earth. Zhen and Xun take shape after one joining of Yin and Yang; Dui, Li, Kan, and Gen take shape after a second joining. In Zhen, Yang is scant while Yin remains abundant; in Xun, Yin is scant while Yang remains abundant. In Dui and Li, Yang Qi gradually increases; in Kan and Gen, Yin Qi gradually increases. Therefore, Chen and Fire do not appear.

After the One Qi (the primordial vital energy before the myriad things were differentiated) divides, Yin and Yang appear separately. Where Yang Qi is more abundant, Heaven takes shape; where Yin Qi is more abundant, Earth takes shape. When Yin and Yang are in equal measure, form and substance come into being; when one outweighs the other, temperaments become distinct. Further differences in form and substance appear as firmness where Yang Qi predominates and softness where Yin Qi predominates. Further differences in temperament arise when Yang Qi reaches its utmost limit, becoming the extreme of Yang, or Yin Qi reaches its utmost limit, becoming the extreme of Yin.

The Dui, Li, and Xun trigrams receive more Yang Qi, while the Gen, Kan, and Zhen trigrams receive more Yin Qi. They can therefore take part in the workings of Heaven and Earth. Qian is the extreme of Yang and Kun the extreme of Yin, so they do not take part in these workings.

Qian and Kun each take one quarter and give it to the other: Qian divides off one share for Kun, and Kun divides off one share and offers it to Qian. Their union gives rise to six children: the three male trigrams, Zhen, Kan, and Gen, and the three female trigrams, Xun, Li, and Dui. The three male trigrams all belong to Yang, and the three female trigrams all belong to Yin. Dui gives one share of Yang Qi to Gen, Kan gives one share of Yin Qi to Li, and Zhen and Xun each take two shares and exchange them. Taken together, Yin and Yang are thus in equal measure. Water and Fire both nourish and restrain each other, and from this the myriad things are generated.

The names and positions of the Qian and Kun trigrams cannot be exchanged. The names of the Kan and Li trigrams can be exchanged, but their positions cannot. The positions of the Zhen and Xun trigrams can be exchanged, but their names cannot. Both the names and positions of the Dui and Gen trigrams can be exchanged.

The Li trigram resembles Qian, and Kan resembles Kun. The Zhongfu hexagram resembles Qian, the Yi hexagram resembles Li, the Xiaoguo hexagram resembles Kun, and the Daguo hexagram resembles Kan. Therefore, Qian, Kun, Kan, Li, Zhongfu, Yi, Xiaoguo, and Daguo cannot be exchanged.

Li, representing fire and the sun, occupies the position of Heaven and corresponds to night; thus Yin is contained within Yang. Kan, representing water and the moon, occupies the position of Earth and corresponds to daytime; thus Yang is contained within Yin. Zhen, representing thunder, gives rise to Yang where Yin begins to mingle; Xun, representing wind, gives rise to Yin where Yang begins to wane. Dui, representing the marsh, signifies the growth of Yang, while Gen, representing the mountain, signifies the growth of Yin.

Zhen and Dui are Yin images within the way of Heaven, while Xun and Gen are Yang images within the way of Earth. Thus, in the hexagrams of Zhen and Dui, the upper part is Yin and the lower part is Yang; in Xun and Gen, the upper part is Yang and the lower part is Yin. To speak of the way of Heaven is to begin with the first emergence of the myriad things: Yin above and Yang below, the two energies mingling and flowing freely. This is what “intermingling harmony” means. To speak of the way of Earth is to begin after the myriad things have taken shape: Yang above and Yin below, each in its proper place of precedence.

Qian and Kun, representing Heaven and Earth respectively, establish the positions of above and below; Li and Kan stand at the left and right gates. The opening and closing transformations of Heaven and Earth, and the rising and setting of the sun and moon, all arise from this. The succession of spring, summer, autumn, and winter; the moon’s dark phase, new moon, first and last quarters, and full moon; changes in the length of day and night; and the varying speeds and waxing and waning of the sun and moon’s courses are all connected with these transformations.

Movement from below upward is called “rising,” and movement from above downward is called “descending.” Rising represents growth; descending represents decline. Thus Yang rises from below, while Yin rises from above. The transformations of the myriad things proceed in cycles: Yang arises within Yin, Yin arises within Yang; Yin gives rise to Yang again, and Yang gives rise to Yin again, in an endless cycle.

Yin-Yang gives rise to and divides into the Two Forms: two basic, contrasting forms such as Heaven and Earth. The Two Forms combine to produce the Four Images, the four forms created by further combinations of Yin and Yang. The Four Images combine to produce the Eight Trigrams, and the Eight Trigrams combine to produce the myriad things. Thus, the Two Forms generate things such as Heaven and Earth, while the Four Images determine their forms. The Four Images generate things such as the sun and moon, while the Eight Trigrams determine their forms. The Eight Trigrams generate the myriad things, while doubled trigrams—formed by placing one trigram above another—determine the distinct forms of those things. “Category” refers to the sequence in which things come into being; “form” refers to the concrete shape produced when images of Yin and Yang combine. To determine the category to which something belongs, one must begin with the process by which it came into being. To observe its form, one must look at how images of Yin and Yang are combined. When the sequence of generation has yet to become apparent, it can be inferred in reverse; once a form has taken shape, it should be observed by following its outward expression. Thus the sun and moon belong to the same category: although they move in different positions, they display the same images of Yin and Yang. Extending this reasoning further, what could not be inferred?

When the seasons of Heaven change, things on Earth respond accordingly. In the seasonal cycle, Yin Qi changes and Yang Qi responds; among things, Yang Qi changes and Yin Qi responds. Thus, the seasons can be understood by reasoning backward from their effects, whereas things necessarily take shape gradually as change unfolds. Yang Qi therefore goes ahead to meet what is coming, and Yin Qi follows after. When speaking of Yin Qi, the direction of change is inverse; when speaking of Yang Qi, it is forward.

In terms of form, Heaven divides into Earth, and Earth further divides into the myriad things, but the Dao cannot be divided. At the end, the myriad things return to Earth, Earth returns to Heaven, and Heaven returns to the Dao. Therefore, the noble person honors the Dao.

Wherever there is change, there must be a corresponding response. A change within therefore produces a response without, while a change without also brings about a response within. A change below draws a response from above, and a change above draws a response from below. When the celestial signs change, the sun responds; thus change takes Heaven as its guide, while response follows the sun. The sun’s course is regulated by the stars, and the moon meets them in the regions where they appear. Water arises from earth, while fire lies hidden in stone; birds dwell in trees, and beasts depend on plants; the heart and lungs are joined to one another, and the liver and gallbladder belong together. These phenomena have no other cause: they all follow the same pattern of change and response.

When Yang Qi and Yin Qi unite, they produce animals such as those with hooves and horns. When firmness and softness meet, they produce plants such as roots and grasses. When Yin Qi and Yang Qi unite, they produce creatures with feathers and wings. When softness and firmness meet, they produce plants such as branches and trunks. When Heaven and Earth unite, their Qi responds to and resonates with each other. Thus there are creatures with feathers that walk on the ground, and creatures with feet that can leap and soar through the air. Woody plants grow among grasses, and herbaceous plants grow among trees. By reasoning from one kind to another, the forms of living things broadly fall within these patterns. Creatures adept at walking are suited to the ground, while those adept at flying are suited to the air: each follows the qualities of its own kind.

For some creatures found on land, corresponding kinds can also be found in water, just as a shadow corresponds to its form. Land creatures are generally adept at walking, while water creatures are generally adept at swimming. This results from the interaction and transformation of different kinds of beings. Thus, creatures that are large on land are often small in water, while creatures that are large in water are often small on land.

The fur of tigers and leopards resembles grass, while the feathers of eagles and hawks resemble trees.

Trees are the descendants of the stars, so their fruits correspond in appearance to the stars.

Leaves belong to Yin, while flowers and fruit belong to Yang. Branches and leaves are soft; roots and trunks are hard.

Humans have large bones and a complex bodily structure. Tree trunks are thick and their branches dense. All these things correspond to the patterns of Heaven and Earth.

Animals that move extend horizontally, while plants grow vertically. Humans are naturally suited to horizontal extension, yet instead grow upright.

Flying creatures have wings, while walking creatures have toes. A person’s two hands correspond to wings, and the two feet correspond to toes.

Flying creatures eat food from trees, while walking creatures eat grass. Humans eat both kinds of food, as well as birds and beasts, and are therefore the most honored among all things.

All things must join with one another in form in order to come into being. Thus, Yang joined with firmness gives rise to the heart and lungs; Yang joined with softness gives rise to the liver and gallbladder; softness joined with Yin gives rise to the kidneys and urinary bladder; firmness joined with Yin gives rise to the spleen and stomach. The heart is linked to the eyes, the gallbladder to the ears, the spleen to the mouth, the lungs to the bones, the liver to the flesh, the stomach to the marrow, and the urinary bladder to the blood. Accordingly, the trigrams of the Book of Changes correspond to parts of the human body: Qian corresponds to the heart, Dui to the spleen, Li to the gallbladder, Zhen to the kidneys, Kun to the blood, Gen to the son, Kan to the marrow, and Xun to the bones. The Tai hexagram corresponds to the eyes, Zhongfu to the nose, Jiji to the ears, Yi to the mouth, Daguo to the lungs, Weiji to the stomach, Xiaoguo to the liver, and Pi to the urinary bladder.

Heaven and Earth have eight trigrams, while human beings have sixteen. Why? Humans are formed from the Qi of Heaven and Earth and come into being through the union of their parents; therefore, the human body contains sixteen trigrams.

Why are the heart within the lungs and the gallbladder within the liver? To speak of human nature and life is to trace them back to Heaven; to speak of the human body is to trace it back to Earth. Heaven is hidden within Earth, just as fire can arise from stone. The heart and gallbladder symbolize this relationship. Why do the heart and gallbladder resemble things hanging upside down? Plants and trees are forms of life on Earth, yet the growth patterns of both humans and plants run contrary to the usual direction, and so they appear inverted.

Why do the mouth and eyes grow horizontally, while the nose and ears grow vertically? Because bodily forms must join with one another. Thus, organs that move and should be vertical are horizontal, while organs that grow upright and should be horizontal are vertical. This is how they interlace with one another.

Heaven has four seasons, Earth has four directions, and humans have four limbs. The joints of the fingers can therefore be used to observe the seasons, and the lines of the palm to discern the geography of Earth. The principles of Heaven and Earth are all present between the fingers and in the palms. How could one fail to value them?

Shen is governed by the heart, Qi by the kidneys, and the body by the head. Form and Qi interact, while Shen resides at the center and presides over them. This is the principle of the Three Powers: Heaven, Earth, and humanity.

Each of the four limbs has its own network of channels. Each channel is divided into three sections, and each section into three indicators, corresponding to the numerical patterns of Heaven.

Each of the body’s four limbs has a pulse corresponding to one of the four seasons. Each pulse is divided into three positions, corresponding to the three months of a season; each position is further divided into three periods, corresponding to the early, middle, and late ten-day periods of a month. Four times nine makes thirty-six: this is the number of counting rods for the Qian trigram, and the ultimate number of Heaven. The Suwen says, “The twelve joints are all connected with the Qi of Heaven.” The “twelve joints” here refers to the correspondence between the body’s twelve meridians and the Qi of nature: there are three Yin meridians and three Yang meridians in each of the hands and feet. The three periods can also refer to the pulse qualities of deep, floating, and intermediate, used to determine whether Yin and Yang Qi are excessive or deficient.

The heart stores Shen (spirit), the kidneys store Jing (essence), the spleen stores Hun (ethereal soul), and the gallbladder stores Po (corporeal soul). This account pairs the Five Viscera with Shen, Jing, Hun, and Po.

The stomach receives food and digests it, then sends Qi to the lungs and blood to the liver; water and food residue are conveyed to the bladder and intestines.

Heaven is round and Earth is square. Heaven is higher in the south and lower in the north, so from the ground it appears like a sloping canopy. The land, meanwhile, is lower in the southeast and higher in the northwest; hence the southeast has many waters, while the northwest has many mountains. Heaven covers Earth, and Earth supports Heaven. Since Heaven and Earth contain one another, Earth is within Heaven, and Heaven is also within Earth.

Heaven moves above us, deep and difficult to fathom, so people observe the movement of the Northern Dipper to infer celestial patterns. The direction in which the Dipper points reflects the patterns of the celestial movements. The Dipper’s bowl—the four leading stars—points toward the Zi position, while its handle—the three trailing stars—points toward the Yin position. In the arrangement of the stars, the Yin hour marks the beginning of daytime. Since the Northern Dipper has seven stars, the movement through day and night is also said to have seven stages, with daylight lasting no more than one-seventh of the cycle. This account merits further examination.

The movement of the celestial bodies produces day and night; the Sun’s movement brings cold and heat. In summer, the Sun’s path is shallower; in winter, it is deeper. This is a change arising from the meeting of Heaven and Earth. The celestial bodies revolve to the left while the Sun travels to the right: this is how the movements of Heaven and the Sun intersect.

The Sun is in the east in the morning and in the west at dusk, following the movement of the celestial bodies. In summer, it lies farther north; in winter, farther south, following seasonal changes in the position where Heaven and the Sun meet. During one complete revolution of the celestial bodies, they pass one lunar mansion, corresponding to the Sun’s movement. The central time of spring is the You hour, of summer the Wu hour, of autumn the Mao hour, and of winter the Zi hour. This reflects how the position where the Sun and the celestial bodies meet changes with the seasons.

The sun moves slowly, appearing to advance; the moon moves quickly, appearing to retreat. When the sun and moon meet, half a day is gained or lost, giving rise to leap days. Over one great cycle, the sun advances by six days while the moon retreats by six days, giving rise to a leap discrepancy.

When the sun moves through the degrees of Yang, it appears full; when it moves through the degrees of Yin, it appears to wane. This reflects the relationship between guest and host. As the moon moves away from the sun, its face gradually brightens and changes slowly; as it approaches the sun, its shadow gradually appears and changes quickly. This reflects the relationship between ruler and minister.

When Yang Qi (vital energy) declines, Yin Qi grows, giving rise to a leap discrepancy.

When the sun moves through the degrees of Yang, it appears full; when it moves through the degrees of Yin, it appears to wane. This reflects the relationship between guest and host. As the moon moves away from the sun, its face gradually brightens and changes slowly; as it approaches the sun, its shadow gradually appears and changes quickly. This reflects the relationship between ruler and minister.

When Yang Qi declines, Yin Qi grows. Thus, when the sun sets, the moon rises in the west. When Yin is strong, it contends with Yang; thus, on the night of the full moon, the moon rises in the east. Heaven is the father and the sun is the son, so the celestial sphere turns to the left while the sun travels to the right. The sun is the husband and the moon is the wife, so the sun rises in the east while the moon appears in the west.

Lunar and solar eclipses are celestial phenomena that occur when the sun and moon cross paths. A lunar eclipse occurs when the moon faces the sun; a solar eclipse occurs when the moon obscures the sun. This is like water and fire overcoming one another. Thus, the noble person acts through wisdom, while the petty person acts through force.

The sun turns with the celestial sphere, the moon follows the sun, and the stars appear in accordance with the moon. Thus, the stars take their model from the moon, the moon from the sun, and the sun from Heaven. The sky is always half bright and half dark; the sun is always half waxing and half waning; the moon is always half full and half incomplete; and the stars are always half in motion and half at rest. These are all expressions of Yin-Yang transformation.

Heaven is present both day and night: the sun appears by day, and the moon by night. The moon waxes and wanes, while the stars appear and disappear. These are all expressions of Yin-Yang transformation.

Heaven is present both day and night: the sun appears by day and the moon by night, though at times half of the moon cannot be seen. At night, only half the stars are visible as well. This reflects distinctions in rank between the honored and the humble.

The moon can also be seen by day, so it is Yin within Yang. The stars can be seen at night, so they are Yang within Yin.

The numbers of Heaven are odd, and the numbers of Earth are even. Therefore, to observe the heavens, one need only observe the stars; to examine the earth, one need only observe its mountains, rivers, and waters. By observing the stars, one can discern the form of the celestial sphere; by observing mountains, rivers, and waters, one can discern the form of the earth. The celestial sphere contains all things, and the earth bears all things. Thus, form in some measure approaches the Dao (the Way).

When summer heat in the south reaches its extreme and winter cold in the north reaches its extreme, the south melts and the north congeals. Both are places where living things struggle to survive. In summer, the sun moves northward, following the positions of the Northern Dipper; in winter, it moves southward along those positions. Thus the Qi of Heaven and Earth joins, and cold and heat are brought into balance. Only when they are balanced can the myriad things grow.

Heaven takes strength and vigor as its nature, so pliant things are not seen in the sky. Earth takes yielding and receptivity as its substance, so hard things cannot grow underground. Thus, Zhen, one of the Eight Trigrams (Bagua) and a symbol of thunder, is Yin within Heaven, while Xun, another trigram and a symbol of wind, is Yang within Earth. Earth is Yin by nature, yet it contains Yang Qi. As Yang Qi moves southward with the sun, Yin and Yang join and cold and heat are brought into balance. Only then can the myriad things grow.

Heaven takes strength and vigor as its nature, so pliant things are not seen in the sky. Earth takes yielding and receptivity as its substance, so hard things cannot grow underground. Thus, Zhen is Yin within Heaven, while Xun is Yang within Earth. Earth is Yin, yet contains Yang Qi; Yin, in turn, imitates Yang. The most Yin are the stars, and the most Yang is the sun, yet both are in the sky. On Earth there are only water and fire. For this reason, things on Earth all have form. When Yang Qi is hidden within Yin Qi, form takes shape; when Yin Qi is hidden within Yang Qi, nature and disposition arise. Thus Yang can give rise to Yin, and Yin can also give rise to Yang; Yang can restrain Yin, and Yin can also restrain Yang. The part of Yang Qi that cannot be suppressed does not appear on Earth; the part of Yin Qi that cannot be restrained does not appear in Heaven. Things that contain less Yang Qi must have pliant forms, so they fear Yang Qi and are driven by it. Things that contain more Yang Qi must have firm forms, so they can withstand Yang Qi and are instead driven by Yin Qi. Water and fire therefore move actively, following Yang Qi, while earth and stone remain still, following Yin Qi.

Yang gives rise to Yin, so water forms first; Yin gives rise to Yang, so fire forms later. Yin and Yang give rise to one another, and form and nature likewise depend on each other. Thus, when Yang Qi disappears, Yin Qi withers; when Yin Qi is exhausted, Yang Qi also perishes.

When Metal and fire meet and contend, the Metal melts into liquid. When water and fire meet, the fire blazes. This is because each follows its own kind.

When water becomes cold to the extreme, it congeals; when it encounters fire, it dries up. This is because water is affected by what it restrains.

When Yang Qi meets Yin Qi, rain forms; when Yin Qi meets Yang Qi, wind forms. Firmness meeting gentleness gives rise to clouds; gentleness meeting firmness gives rise to thunder. Without Yin Qi, rain cannot fall; without Yang Qi, thunder cannot sound. Rain is gentle in nature and belongs to Yin, but Yin Qi cannot act on its own, so it must await the aid of Yang Qi before it rises. Though thunder is fierce and forceful, it depends on a physical form; form cannot act on its own, so thunder must await the impetus of Yang Qi before it strikes.

How profound was King Wen’s creation of the Classic of Changes! He understood how Heaven and Earth function: the Qian hexagram, symbolizing Heaven and firmness, and the Kun hexagram, symbolizing Earth and gentleness, join to form the Tai hexagram, symbolizing free flow; the Kan hexagram, symbolizing water, and the Li hexagram, symbolizing fire, join to form the Ji Ji hexagram, symbolizing the completion of affairs.

The Qian hexagram begins to arise at the hour of Zi, around midnight, while the Kun hexagram begins to arise at the hour of Wu, around noon. The Kan hexagram reaches its end at the hour of Yin, in the early morning, and the Li hexagram at the hour of Shen, in the afternoon. This corresponds to the timing of Heaven. Qian is placed in the northwest, while Kun withdraws to the southwest; the eldest son, represented by the Zhen hexagram, takes charge, and the eldest daughter, represented by the Xun hexagram, takes the mother’s place. Kan and Li each occupy their proper positions, while the Dui and Zhen hexagrams are paired. This corresponds to the directions of Earth. A ruler’s governance of the realm takes Heaven and Earth as its model; its principles can largely be understood through these patterns.

Qian and Kun are the foundation of Heaven and Earth; Li and Kan are the keys to their functioning. Thus, the Classic of Changes begins its Upper Canon with Qian and Kun, discusses Li and Kan in the middle, and concludes with the Ji Ji and Wei Ji hexagrams. The Pi hexagram, signifying obstruction, and the Tai hexagram, signifying free flow, stand midway through the Upper Canon; the Xian hexagram, signifying resonance, and the Heng hexagram, signifying constancy, begin the Lower Canon. All of these explain how Heaven and Earth function.

Kun governs the three female hexagrams in the southwest, while Qian governs the three male hexagrams in the northeast. The Upper Canon begins with the third hexagram, and the Lower Canon ends with the fourth; both carry the meaning of Yin and Yang joining in harmonious flow. Thus, the essential meaning of the Changes lies in its application: Qian applies nine, and Kun applies six; divination by the number of the Great Expansion uses forty-nine yarrow stalks, while “The hidden dragon: do not act” teaches that one should not exert oneself while in concealment. The way of application is truly vast! In this, I see the intent of the sages.

Qian and Kun join to form the Tai hexagram; through further changes and combinations, they become the hexagram images presented in the Miscellaneous Hexagrams.

Qian, Kun, Kan, and Li are placed in the Upper Section. The way of application is truly vast! In this, I see the intent of the sages.

Qian and Kun join to form the Tai hexagram; through further changes and combinations, they become the hexagram images presented in the Miscellaneous Hexagrams.

Qian, Kun, Kan, and Li are the hexagrams at work in the first part; Dui, Gen, Zhen, and Xun are those at work in the second. Yi, Zhongfu, Daguo, and Xiaoguo are the central hexagrams of the two parts.

The Changes describes the alternation of Yin and Yang. Zhen and Dui symbolize the beginning of their interaction, corresponding to morning and evening. Li and Kan symbolize the point at which their interaction reaches its height, corresponding to midnight and noon. Although Xun and Gen do not fully unite, Yin and Yang remain mixed within them, so they correspond to intermediate positions in the process of interaction. Qian and Kun represent pure Yang and pure Yin, respectively, and thus correspond to positions where Yin and Yang do not interact.

Qian and Kun are arranged vertically, while the six child hexagrams—the Zhen, Xun, Kan, Li, Gen, and Dui generated by Qian and Kun—are arranged horizontally. This is the fundamental structure of the Changes. Zhen and Dui are arranged horizontally, while the other six hexagrams are arranged vertically. This is how the Changes is applied.

The Yang Qi of Heaven is in the south, and its Yin Qi is in the north. The Yin Qi of Earth is in the south, and its Yang Qi is in the north. In human beings, Yang Qi is above and Yin Qi below. When Yin and Yang unite, Yang Qi turns downward and Yin Qi rises.

The twelve temporal markers refer to the positions in time represented by the twelve Earthly Branches. The time when the sun and moon meet is called a “chen.” Chen is the framework within which the heavenly bodies move, while their underlying substance is formless Qi.

The Yang Qi of Heaven is in the south, so the sun travels toward the south. The firm Qi of Earth is in the north, so mountains are mostly found in the north. This gives rise to a configuration in which the terrain is higher in the northwest and the celestial aspect higher in the southeast.

The celestial spirit is lodged in the sun; in human beings, the functioning of Shen is expressed through the eyes. When a person is awake, Shen resides in the heart; during sleep, it resides in the kidneys. This correspondence between the human body and celestial phenomena explains the pattern of day and night.

Cloud Qi moves and produces rain; flashes of lightning appear and thunder rumbles. These, too, follow the principle that things of the same kind respond to one another.

Blowing, spitting, sighing, exhaling, and calling out are sounds produced by human breath. Wind, rain, clouds, fog, and thunder are celestial phenomena. The two belong to corresponding categories of phenomena.

All things follow their own sequence of development through Taiji, the Two Modes, the Four Images, and the Eight Trigrams. They also have images that correspond to changes from ancient times to the present.

Within clouds, water, fire, earth, and stone have different qualities; things in other categories likewise each have their own differences.

Between the winter and summer solstices, the two points are separated by 180 degrees east to west and by 60 degrees north to south.

In the month of the winter solstice, the moon’s path resembles the sun’s path at the summer solstice. In the month of the summer solstice, the moon’s path resembles the sun’s path at the winter solstice.

The Four Correct Trigrams are Qian, Kun, Kan, and Li, symbolizing Heaven, Earth, Water, and Fire respectively. Looking at their trigram forms, we see that they do not undergo repeated changes; hence they are called “correct.”

When Yang is within Yin, Yang Qi moves in reverse; when Yin is within Yang, Yin Qi also moves in reverse. When Yang is within Yang, and Yin within Yin, both move forward. This is a profound principle of things, which can be seen in the diagram.

Small grasses belong to Kun, which symbolizes Earth.

Wood among the Five Phases can represent a whole class of things; Metal among the Five Phases originates in stone. Water, Fire, Earth, and stone are all inferior to Metal and Wood, within which they grow.

Things that receive the Qi of Heaven move; things that receive the Qi of Earth remain still.

Yang things are naturally round, but take on a square form when they assume concrete shape; Yin things are naturally square, but take on a round form when they assume concrete shape.

The branches and trunks of trees, as well as the solidifying of earth and stone, are formed by Earth Qi, so they are not easily changed. Leaves and flowers are formed by the Qi of Water and Fire, so they change more quickly.

East is red, south is white, west is yellow, and north is black: these are the primary colors. This can be seen by observing at dawn, noon, dusk, and night.

The winter solstice falls at the midpoint of the Zi hour, when Yin Qi is at its strongest. The spring equinox falls at the midpoint of the Mao hour, when Yang Qi reaches balance. The summer solstice falls at the midpoint of the Wu hour, when Yang Qi is at its strongest. The autumn equinox falls at the midpoint of the You hour, when Yin Qi reaches balance. Divide the year into 360 degrees, then split it in half to make 180 degrees. These are the degree intervals between the winter and summer solstices and the spring and autumn equinoxes.

There is Yin within Yang and Yang within Yin: this is the Way of Heaven. The Yang within Yang is the sun, embodying the Way of heat. The Yin within Yang is the moon; because it belongs to the Yang category, it can also be seen by day. The Yang within Yin is the stars, which appear at night. The Yin within Yin is “chen,” meaning the celestial lodgings and regions of the heavens.

“Chen” stands to Heaven as the substance of Heaven and Earth does. The same applies to Earth. The moon is the Yin within Yang; because it belongs to the Yang category, it can also be seen by day. The stars are the Yang within Yin, and therefore appear at night. The Yin within Yin is “chen,” meaning the regions of the heavens.

The terrestrial branches (the twelve Earthly Branches that mark the passage of time) stand in relation to Heaven as the forms of Heaven and Earth do. Earth has the Five Phases; Heaven has five celestial markers—the planets Wood, Fire, Earth, Metal, and Water. On Earth there are only water and fire, while in Heaven there are also the sun and moon. The moon is true water, and the sun is true fire. From them, the essential energies of Yin and Yang give rise to the Five Phases. Thus, the numbers of Heaven and Earth are both founded on five. The Yang number extends on its own to seven, so beyond the five organs there are also the pericardium and the Gate of Life, making seven altogether. The true heart belongs to Li Fire, and the Gate of Life to Kan Water; from these the five organs arise. They govern the spirit and are the root of nature and life.

The Heavenly Stems take their meaning from a main trunk and belong to Yang; the Earthly Branches take their meaning from branches and belong to Yin. There are ten Heavenly Stems and twelve Earthly Branches, showing that Yin is contained within the number of Yang, and Yang within the number of Yin.

Fish belong to the aquatic kind, while insects belong to the wind kind.

The eyes take their meaning from the stems and belong to Yang; the branches take their meaning from the branches and belong to Yin. There are ten Heavenly Stems and twelve Earthly Branches, showing that Yin is contained within the number of Yang, and Yang within the number of Yin.

Fish belong to the aquatic kind, while insects belong to the wind kind.

The eyes and mouth project outward, while the ears and nose have openings. These openings are used to hear sounds and smell scents, and some things cannot close them. The eyes and mouth can distinguish colors and tastes, yet external objects can cover them. Though these four differ in form, each has all four functions.

Water is the foundation on which fire depends for its existence; fire is the energy manifested by wood. Black is the basis on which white appears, just as cold is the basis on which heat appears.

A beast crouching among the grass has a form like a grass stem; a bird dwelling in the woods has feathers like leaves. This is how environments shared by creatures of the same kind shape their forms.

The patterns in stone resemble phenomena such as the crystallization of salt.

Creatures in water and creatures on land do not differ in essence; each kind has its own qualities of cold and heat. Broadly speaking, land belongs to Yin within Yang, while water belongs to Yang within Yin.

The sun, moon, stars, and celestial markers together form Heaven; water, fire, earth, and stone together form Earth. Ears, eyes, nose, and mouth together form the head; marrow, blood, bones, and flesh together form the body. These are all numbers in which five kinds of things are formed from four components.

Fire arises from nonbeing; water arises from being.

When a celestial marker moves to the sun’s position, this is “generation”; when the sun moves to the marker’s position, this is “function.” In general, movement along the course is called generation, while movement against it is called function.

The Yi contains three hundred and eighty-four lines; this is the true principle of astronomy.

Birds such as eagles and pengs eat living creatures; chickens and mallards (wild ducks), by contrast, arise from nonbeing, while water arises from being.

When the hour of Chen arrives, the sun begins to rise; this is called “generation.” After the sun reaches its height at noon, it enters the stage of acting and bringing things into effect; this is called “function.” In general, following the sequence of time is generation, while going against it is function.

The Classic of Changes contains 384 lines—the symbols within the hexagrams that represent changes between Yin and Yang. They reveal the patterns by which Heaven and Earth operate.

Birds such as eagles and great roc-like birds eat living creatures, while chickens and wild ducks do not. Tigers and leopards eat living creatures; cats and dogs eat both living creatures and grain. From these categories, other cases can be understood by analogy.

Horses and oxen both belong to the Yin category. If the categories are further divided, horses belong to Yang and oxen to Yin.

Flying animals are drawn to the wind and are adept at rising upward; walking animals are drawn to the earth and suited to running along the ground. This is caused by the Qi of Yin and Yang.

The eggs of birds and insects resemble fruits and grains. Grains usually contain many seeds, and insects likewise often lay many eggs.

Creatures such as silkworms are produced in a yearly cycle: moths lay eggs one year, and the eggs hatch into silkworms the next. Plants such as turnips follow the same pattern: they first grow roots and then shoots one year, and the shoots produce seeds the next. These are all organisms with a one-year cycle.

When the Qi of Heaven and Earth moves from north to south, it tends toward order; when it moves from south to north, it tends toward disorder. After disorder persists for a long time, the movement turns southward from the north once again. This is true of both the Way of Heaven and human affairs. By examining changes across successive dynasties, one can see the principles governing rise and decline.

Animals that live in water do not close their eyes; animals that live in the wind do. When walking animals close their eyes, the upper eyelid moves downward; when flying animals close theirs, the lower eyelid moves upward. This results from the category to which each belongs.

Animals that live in water and have scales and a mane belong to the flying category, while creatures such as turtles and otters belong to the walking category.

The Four Images—the four basic qualities, such as Yin and Yang, firmness and yielding—can be understood through the following correspondences: the sun and moon are the Yin and Yang of Heaven; water and fire are the Yin and Yang of Earth. The stars and celestial bodies are the firm and yielding of Heaven; soil and stone are the firm and yielding of Earth.

Among creatures that change from flying to walking are chickens and wild ducks; among those that change from walking to flying are dragons and horses.

Yang Qi governs expansion and growth, while Yin Qi governs contraction and urgency. When the sun’s course exceeds its usual measure, Yin follows Yang; when the sun’s course falls short of its usual measure, Yang follows Yin.

Shen is the ruler of the human being. As one is about to fall asleep, Shen is in the spleen; in deep sleep, Shen is in the kidneys. As one is waking, Shen is in the liver, though some say it is in the gallbladder. Once fully awake, Shen is in the heart.

The greatest awakening among all things between Heaven and Earth takes place in summer; the human spirit resides in the heart.

Creatures in water are governed mainly by Yin, with Yang as a secondary force; creatures on land are governed mainly by Yang, with Yin as a secondary force. Thus, aquatic animals die when they leave the water, while creatures that live in the air die when they enter the water. Yet some animals can move between water and land, such as turtles, crabs, geese, and wild ducks.

The proportion in which Heaven and Earth intersect is three-tenths.

Heavenly fire has no fixed form, while earthly fire has a fixed form. Formless fire takes on visible form only by attaching itself to things. Fire from burning metal and stone is more intense than fire from burning plants and trees because fire behaves differently depending on the material to which it attaches.

When the body and breath are strong, the hun and po souls are strong as well; when the body and breath weaken, the souls weaken too.

The hun changes with the breath, while the po depends on the body and remains with it. As long as the body exists, the po exists; when the body perishes, the po disperses.

Stars are the Sun’s residual Qi; chen—the stars and constellations—are the Moon’s residual Qi.

When stars as tiny as grains of dust and sand fall, they accumulate into mounds of earth.

The zang is the movement of Heaven, and the fu is the movement of Earth. Heaven and Earth move together, and their coordination gives rise to the Eight Trigrams (Bagua).

The Eight Trigrams intersect and combine with one another to form the sixty-four hexagrams.

The foundation of the Yi lies in the Qian and Kun hexagrams, and its unfolding begins with Fu and Gou. When firm Yang Qi meets yielding Yin Qi, the Fu hexagram is formed; when yielding Yin Qi meets firm Yang Qi, the Gou hexagram is formed. From there, change continues without end.

The dragon corresponds to the Eight Trigrams.

The Eight Trigrams intersect and combine with one another to form the sixty-four hexagrams.

The foundation of the Yi lies in the Qian and Kun hexagrams, and its unfolding begins with Fu and Gou: when firm Yang meets yielding Yin, the Fu hexagram is formed; when yielding Yin meets firm Yang, the Gou hexagram is formed. From then on, change is endless.

The dragon can grow large or become small, but it is also constrained and influenced by Yin and Yang Qi. It can transform only when the time is right; once its changes are exhausted, it can change no further.

In a year with a leap day, the extra days are counted as six for Yin and six for Yang. This makes thirty-six days over three years, so one leap month is added every three years; over five years it makes sixty days, so two leap months are added every five years.

The Pre-Heaven Diagram, arranged according to the Pre-Heaven Eight Trigrams, is like the center of a ring.

The moon is dark in itself. Only when it receives light from the sun does it appear bright.

In the human body, water corresponds to blood, and earth corresponds to flesh.

The gallbladder and kidneys both belong to Yin; the heart and spleen both belong to Yang. The heart corresponds to the eyes, and the spleen corresponds to the nose.

Yang within Yang is the sun; Yin within Yang is the moon. Yang within Yin is the stars; Yin within Yin is chen (stars and constellations). The softest of the soft is water; the soft that contains hardness is fire. The hard that contains softness is earth; the hardest of the hard is stone.

The Qi in the nose corresponds to the moon. Yang within Yin corresponds to the stars; Yin within Yin corresponds to chen (stars and constellations). The softest of the soft corresponds to water; the soft that contains hardness corresponds to fire. The hard that contains softness corresponds to earth; the hardest of the hard corresponds to stone.

The Qi in the nose can be seen through the eyes; words spoken by the mouth can be heard through the ears. This is the principle by which things of the same kind respond to one another.

The Canopy-Leaning theory holds that Kunlun, the legendary high mountain, slopes on all sides, thereby forming the seas. On closer examination, this account does not hold up. The earth is flat, square, still, and unmoving. How could it be like the rounded, revolving heavenly bodies?

Animals begin growing from the head, while plants begin growing from the roots. Animals begin their life activity from the head, while for plants the root is the seat of life.

The tides are the earth’s breathing. They rise and fall with the moon because the two belong to corresponding categories.

The Yi uses the Zhen trigram to symbolize the dragon. Its image is one Yang line beneath two Yin lines, signifying Yang Qi stirring beneath Yin Qi. When creatures move at the bottom of an abyss, could that not be the dragon?

Wind and water belong to the same category, though they are opposites in scale.

The Yang Qi of Heaven lies in the southeast, where the sun and moon travel, forming the image of the Zhen trigram. When creatures move at the bottom of an abyss, could that not be the dragon?

Wind and water belong to the same category, though they are opposites in scale.

The Yang Qi of Heaven lies in the southeast, where the sun and moon travel. The Yin Qi of Earth lies in the northwest, where fire and stone are found.

The section “Beginning with Zhen and ending with Gen” explains King Wen’s Eight Trigrams; the section “Heaven and Earth take their places” explains Fuxi’s Eight Trigrams. “The Eight Trigrams interweave” means that they cross and combine with one another to form the sixty-four hexagrams.

“To count what has gone by is to move with the current” means rotating to the left, like following the movement of the Way of Heaven. It refers to hexagrams that have already taken shape, and so is called “counting what has gone by.” “To know what is coming is to move against the current” means rotating to the right, against the movement of the Way of Heaven. It refers to hexagrams not yet formed, and so is called “knowing what is coming.” The numbers of the Changes’ hexagrams are derived through backward inference. This section directly explains the meaning of the hexagram diagram; the “moving against the current” described here is like reasoning backward to foresee the changes of the four seasons.

The “Canon of Yao” says that a year has 366 days. The count of days has an excess of about six, while the count of months falls short by about six. If the twelve days arising from these two differences are subtracted from 366, 354 days remain. This is the number of days in the solar cycle; divided among twelve months, it gives twenty-nine days per month.

The “Plain Questions” says that the lungs correspond to the skin and body hair, the heart to the vessels, the spleen to the flesh, the liver to the sinews, and the kidneys to the bones. This arrangement proceeds from above to below and from the exterior to the interior. The correspondence between the heart and blood, and between the kidneys and bones, involves interaction; “interaction” means that they exert an effect.

Examples such as “Qian is Heaven” are primary images; examples such as “Qian is Metal” are derived images.

When Heaven and Earth operate in parallel, the zang organs and fu organs form four corresponding pairs: the zang belong to Heaven, and the four fu organs belong to Earth.

The Qian hexagram (symbolizing Heaven, Yang, and strength) is composed of odd-numbered lines and belongs to Yang. Its nature is strong and vigorous, so nothing under Heaven is stronger than Heaven. The Kun hexagram (symbolizing Earth, Yin, and yieldingness) is composed of even-numbered lines and belongs to Yin. Its nature is yielding and receptive, so nothing under Heaven is more yielding than Earth; Earth follows Heaven.

The Zhen hexagram symbolizes arousal and begins with a Yang line. To be aroused is to set things in motion, so nothing under Heaven sets things in motion more forcefully than thunder. The Kan hexagram symbolizes sinking: one Yang line is trapped between two Yin lines. Sinking also means moving downward, so nothing under Heaven is lower than water. The Gen hexagram symbolizes stillness: its Yang line reaches this point and stops, so nothing under Heaven brings things to rest more than a mountain. The Xun hexagram symbolizes entering: one Yin line enters beneath two Yang lines, so nothing under Heaven penetrates more than wind. The Li hexagram symbolizes attachment: one Yin line is attached between two Yang lines. The interwoven image forms a pattern and appears beautiful, so nothing under Heaven is more radiant and splendid than fire. “Li” also means to cling to or depend on something. The Dui hexagram symbolizes joy: one Yin line is exposed on the outside, and so it faces all things with delight. Nothing under Heaven brings people more joy than a marsh.

Fire is dark within and bright without, so the Yang line of the Li hexagram is on the outside; fire’s action manifests outwardly. Water is dark without and bright within, so the Yang line of the Kan hexagram is on the inside; water’s action proceeds from within.

Why do people entrust their bodies to the “walking kind” (animals that move by walking)? Because the walking kind is the eldest son born of Earth.

Between the Tai hexagram (Heaven and Earth in communication) and the Pi hexagram (Heaven and Earth no longer communicating), the Gu hexagram (symbolizing accumulated troubles that need to be put right) appears. Between the Pi hexagram and the Tai hexagram, the Sui hexagram (symbolizing following and compliance) appears.

Heaven has five celestial bodies: the sun, the moon, the stars, the constellations, and Heaven itself, making five in all. Earth has the Five Phases: Metal, Wood, Water, Fire, and Earth, also making five.

There are hot springs, but no cold fire. This is because Yin can follow Yang, while Yang cannot follow Yin.

Where there is thunder, there is lightning; where there is lightning, there is wind. Rain forms from water, dew condenses from the Qi of the earth, thunder issues from stone, and lightning arises from fire. Lightning and wind are both phenomena that occur when Yang Qi reaches its utmost flourishing, so the appearance of lightning necessarily brings wind.

Only thunder can shake hard wood; only dew can nourish tender grass.

Yang is exalted and mysterious. Because it is exalted, it can command the myriad things; because it is mysterious, its workings remain concealed. Thus the Dao gives rise to Heaven, Earth, and the myriad things without revealing itself. Heaven, Earth, and the myriad things all take the Dao as their model.

Yang is the Dao’s function, while Yin is the Dao’s substance. Yang makes use of Yin, and Yin makes use of Yang. If Yang is treated as the function, then Yin is held in honor; if Yin is treated as the function, then Yang is held in honor.

Yin is close to the Dao, so Yin is used as a metaphor for the Dao. In the numerical system of the Yi Jing, after six transformations one can arrive at thirty-six; after eight, sixty-four; and after twelve, three hundred and eighty-four. Repeated derivation from six as the base yields thirty-six through six-by-six transformations, sixty-four through eight-by-eight, and ultimately three hundred and eighty-four. Deriving from eight as the base yields forty-eight through six-by-eight transformations, sixty-four through eight-by-eight, and three hundred and eighty-four through twelve transformations. These transformations are listed repeatedly in the text to show how the Yin-Yang trigrams and hexagrams can be derived through successive layers.

Before the Non-Polar (the source that has not yet taken visible form), Yang is contained within Yin; once form appears, Yang differentiates Yin. Yin is the mother of Yang, and Yang is the father of Yin. Thus the mother conceives the eldest son, forming the Returning hexagram; the father begets the eldest daughter, forming the Coupling hexagram. Yang therefore begins to sprout with the Returning hexagram, while Yin begins to sprout with the Coupling hexagram.

Nature cannot take shape without substance, and substance cannot give rise to life without nature. Yang takes Yin as its substance, and Yin likewise takes Yang as its substance. Movement is nature; stillness is substance. In Heaven, Yang governs movement and Yin governs stillness; on Earth, Yang governs stillness and Yin governs movement. Nature depends on substance to become still, while substance moves in response to nature. Thus Yang unfolds gradually, while Yin moves swiftly.

Yang cannot establish itself alone; it must have Yin in order to take shape, so Yang takes Yin as its foundation. Yin cannot manifest itself alone; it must await Yang to set it in motion, so Yin takes Yang as its guide. Yang knows the beginnings of things and enjoys the fruits once they are complete; Yin follows the principles established by Yang and, in the end, bears the toil of bringing things to completion.

Yang belongs to the side that can perceive and see; Yin belongs to the side that cannot perceive or see. What can be perceived and seen is being. Thus Yang is characterized by “being,” while Yin is characterized by “nonbeing.” Yang has aspects that it does not favor, whereas Yin has no aspects it does not favor. Yang departs, while Yin often remains. After Yang departs, Yin can perceive; Yang can see, while Yin cannot. What can be perceived and seen is being. Thus Yang is characterized by “being,” while Yin is characterized by “nonbeing.” Yang has aspects that it does not favor, whereas Yin has no aspects it does not favor. What favors nothing and yet often remains is substantial. Thus Yang’s form is empty, while Yin’s form is substantial.

Does the foundation of Heaven and Earth arise from the center? Thus Qian and Kun, symbols of the Yin-Yang of Heaven and Earth, undergo repeated transformations yet never depart from the center.

Human beings dwell between Heaven and Earth, and the heart occupies the center of the human body. The sun is at its strongest when it reaches its midpoint, and the moon is at its fullest when it is round. Therefore, the exemplary person values the center: a state of being centered and unbiased.

All things originally come from a single Qi (vital energy). As Qi arises, it becomes Yang; as it recedes, it becomes Yin. Thus, in the end, Yin and Yang are one. The Four Symbols, the four states formed through further changes of Yin and Yang, return to two; the six lines of a hexagram return to three; and the Eight Trigrams return to four. For this reason, when speaking of Heaven, one does not speak of Earth separately; when speaking of a ruler, one does not speak of ministers separately; when speaking of a father, one does not speak of children separately; and when speaking of a husband, one does not speak of a wife separately. Yet Heaven and Earth must come together for the myriad things to grow; a ruler needs ministers to assist him for decrees to be carried out; and fathers with children, and husbands with wives, are needed for family relations to be established. Thus, where there is one, there is two; where there are two, there are four; where there are three, there are six; and where there are four, there are eight.

Where there is an idea, there must be words to express it. Where there are words, an image must take shape. Where there is an image, numbers can be derived. Once the numbers are determined, the image appears; once the image appears, the words become clear; and once the words are clear, the idea becomes evident. Images and numbers are like the fish basket used to catch fish and the snare used to catch rabbits; words and ideas are like the fish and rabbits themselves. After catching the fish or rabbit, one may forget the basket or snare. But to set them aside while hoping to catch the fish or rabbit is difficult.

The transformations of Heaven are mirrored by human beings, so the Yi speaks of transformation through “Origin, Flourishing, Advantage, and Constancy.” Human conduct responds to Heaven, so “Good Fortune, Misfortune, Regret, and Distress” speak of outcomes. If “Origin” and “Flourishing” are the transformations, then “Advantage” and “Constancy” are the responses. If “Good Fortune” and “Misfortune” are the responses, then “Regret” and “Distress” are human reactions to transformation. Thus, “Origin, Flourishing, Advantage, and Constancy” describe the transformations of the Yi, while “Good Fortune, Misfortune, Regret, and Distress” describe their outcomes. “Origin” and “Flourishing” are transformations, with “Advantage” and “Constancy” as responses; “Good Fortune” and “Misfortune” are outcomes, with “Regret” and “Distress” as transformations.

At the beginning (Origin), there is good fortune, and good fortune brings advantage. But when the outcome is flourishing, it may instead turn to danger. Responding to danger by holding to what is right can turn it into good fortune. Regret can lead toward good fortune, while reluctance and obstruction can bring misfortune. Thus, response is contained within transformation, and transformation within response. The responses within transformation belong to the Way of Heaven: when “Origin” is the transformation, “Flourishing” is the response; when “Advantage” is the transformation, “Constancy” is the response. The transformations within response concern human conduct: an improper transformation brings misfortune, while a fitting response brings good fortune; transformation can give rise to distress, while response can give rise to regret. Regret is a sign of good fortune to come; reluctance and obstruction are the roots of danger. Therefore, the noble person follows the Way of Heaven rather than simply yielding to human feelings.

“Origin” corresponds to spring and to the virtue of benevolence. Spring begins the cycle of the four seasons, and benevolence is the foremost of the virtues. At this time, the seasonal force has not yet reached its height, but benevolence is enough to guide the people. For this reason, the discussion here concerns virtue, not the season’s circumstances. “Flourishing” corresponds to summer and to ritual propriety. Summer is the season of greatest abundance, and ritual propriety is the outward form of virtue. After abundance must come decline, and the refinements of ritual cannot save what is falling into ruin. For this reason, the discussion here concerns the season’s circumstances, not virtue. Thus, the text says, “Great indeed is Qian’s Origin,” yet the top nine line of the Qian hexagram still contains regret.

“Advantage” corresponds to autumn and to righteousness. Autumn is when all things mature, and righteousness is the standard of conduct. As things approach maturity, they gain advantage; yet the principles emphasized by righteousness must not be confused with the pursuit of profit. For this reason, the discussion here concerns the season’s circumstances, not virtue. “Constancy” corresponds to winter and to wisdom. Winter is the close of the year, and wisdom is the inward expression of virtue. Holding to what is right brings good fortune; failing to do so brings misfortune. For this reason, the discussion here concerns virtue, not the season’s circumstances. Thus, the text says: “Advantage through constancy is the nature and condition of things.”

The Dao gives birth to Heaven, and Heaven gives birth to Earth.

After completing his achievements, he yielded the throne. Thus his son inherited the imperial position that his father had ceded. This is what it means for the Qian trigram to withdraw to the subordinate position.

Images—the forms things present—arise from physical form; numbers—the quantities and patterns of things—arise from their underlying nature. Names arise from speech, and meanings from function. All the numbers under Heaven originate in principle. To depart from principle is to fall into the techniques of numerology. People rely on numerical techniques and become caught up in the art of numerology, thereby losing the fundamental principle.

In all matters under Heaven, if one acts in accordance with the Dao (the Way), neither fortune nor misfortune, worry nor joy can disturb one.

The workings of the Way of Heaven can be fully investigated through principle, but they cannot be completely depicted in concrete forms. The theory of the encompassing Heaven, which seeks to explain celestial phenomena through the shapes and movements of heavenly bodies, attempts to exhaust the Way of Heaven through form. Is this possible?

Only by studying principle in depth and reaching a state of spiritual insight and understanding can one put what one has learned into practice. If one has not grasped principle thoroughly, one cannot attain spiritual understanding and insight, and so cannot put it to practical use.

The art of governance must understand change; it cannot remain fixed, like glue binding a tuning peg in place. Just as one cannot impose the ordinances of winter in spring.

What arises naturally and cannot be altered belongs to the inner images and numbers; everything else belongs to the outer images and numbers.

The transformations of the Way of Heaven are precisely the principles on which the expedient measures of kingly governance—adapting to circumstances as they change—are based.

Each trigram has its own character and structure, yet none lies beyond the gateway of Qian and Kun. In the same way, all things receive their nature from Heaven and then develop their own distinct dispositions: human beings have a human nature, birds and beasts have their natures, and plants have theirs.

Heaven takes Qi (vital energy) as primary and physical form as secondary; Earth takes physical form as primary and Qi as secondary. Things between Heaven and Earth are generally similar.

Qi can nourish nature, and nature also contains Qi. Thus, where Qi exists, nature exists; when nature changes, Qi moves along with it.

The images and numerical patterns of Heaven can be derived. But the wondrous workings of the Way of Heaven cannot be measured.

That which unfolds naturally and follows its own nature is the Way of Heaven. Only sages can investigate and grasp it. Human beings model themselves on the Way of Heaven; if they can respond to the moment and know when to act and when to stop, then even their human endeavors accord with the Way of Heaven.

The impulse of life is nature and belongs to Heaven; taking shape is physical form and belongs to Earth.

The sun passing below the horizon is an image of Yin-Yang joining and the essences of Qi mingling.

The body has four basic states in its original condition; through transformation, it presents six states, which also involve the workings of spirit and Qi. The changes of Qi must take on six states, which is why the number “three” is spoken of. Though humans belong to the human realm, they too receive the Dao of Heaven. This “three,” stated more fully, is the number three hundred and sixty.

What sprouts and possesses life is nature, belonging to Heaven; what takes shape as a physical body is form, belonging to Earth.

The sun setting into the Earth symbolizes the union of the essence and Qi of Yin and Yang.

In any undertaking, when you approach the limit, it is enough to stop at about seven tenths of completion. For example, on the day of the summer solstice, daylight lasts about sixty ke. If dawn and dusk are counted as well, the sky’s light can already be discerned. This is roughly seven tenths of the whole.

Though the diagram has no written explanation, the principles I speak of throughout the day have never strayed from it. The principles of all things between Heaven and Earth are contained within it.

Qi has a single root, governed by Qian, the hexagram in the Classic of Changes that symbolizes the Way of Heaven. Spirit, too, has a single root. It rides upon Qi and transforms, moving between being and nonbeing. It has no fixed location, and its transformations cannot be measured.

Without understanding Qian, one cannot grasp the principles of nature and life.

To speak only when the moment is right is to speak in accord with change; one’s words do not arise from personal intent. When speech is like this, Qian governs its transformations. Spirit, too, has a single root. It rides upon Qi and transforms, moving between being and nonbeing. It has no fixed location, and its transformations cannot be measured.

Without understanding Qian, one cannot grasp the principles of nature and life.

To speak only when the moment is right is to speak in accord with change; what is said is not controlled by my subjective will.

Only when humaneness and virtue accord with Heaven and Earth can someone be called a “human being.” Only the humane can truly be called human.

Life arises from this, takes shape through transformation, and continues to sprout after taking shape. This is the principle of the Classic of Changes.

Qi is where spirit resides; the body is where Qi resides.

Heaven accounts for six parts, Earth for four. Heaven takes Qi as its foundation and spirit as its wondrous working; Earth takes physical form and substance as its foundation and Qi as its wondrous working. Humans alone receive the endowments of all things, and so become the most numinous among them. Animals each produce only the sounds of their own kind; humans, by contrast, can produce every kind of sound. The same is largely true when this principle is extended to other matters. Only humans can make use of the effects brought about by the conjunction of Heaven and Earth, and the sun and moon; other living beings cannot. Human life is truly precious. When people fail to cherish themselves despite receiving this precious endowment from Heaven and Earth, they go against the principles of Heaven and Earth. This is the greatest ill omen.

The changing brightness and dimness of lamplight symbolizes the appearances of the sun and moon.

The moon is the sun’s shadow; emotion is the shadow of one’s nature. The heart takes nature as its guide and emotion as its support. Nature belongs to the spirits; emotion belongs to ghosts and demons.

Mind and nature are like the Taiji (Supreme Ultimate): they are the fundamental principle of Heaven and Earth. No calamity is more serious than the loss of rightness in mind and nature.

The changing brightness and dimness of lamplight is like the movement of the sun and moon.

The moon is the sun’s shadow; emotion is the shadow of one’s nature. The heart takes nature as its guide and emotion as its support. Nature belongs to the spirits; emotion belongs to ghosts and demons.

The heart is the Taiji. Some also say that the Dao is the Taiji.

The physical form can be divided, but the spirit cannot.

Yin’s influence is generally greater than Yang’s, perhaps because Yang is one while Yin is two.

After the winter solstice, the Qi of Heaven and Earth begins to exhale; after the summer solstice, it begins to inhale. This is Heaven and Earth’s breathing over the course of a year.

To feel joy in response to external things, and sorrow in response to them as well, is fitting when such emotions arise in due measure.

If you do not take yourself as the standard for measuring all things, you can understand and use them rightly.

Indulging the self gives rise to emotional fixation. Fixation clouds the mind and makes a person confused. By following the nature of things, one can reveal one’s own nature. When nature is revealed, the spirits become clear and the mind is lucid. The spirits can dwell unseen between Heaven and Earth, reach their destination without moving, and remain beyond the sway of Yin-Yang’s changes.

Of calamities sent by Heaven, one in ten can still be avoided; of calamities caused by people, nine in ten are difficult to escape.

The study of what is innate lies in the heart; the study of what is acquired lies in the traces of things. That which can enter and leave existence and nonexistence, life and death, is the Dao.

Of calamities sent by Heaven, one in ten can still be avoided; of calamities caused by people, nine in ten are difficult to escape.

The study of what is innate lies in the heart; the study of what is acquired lies in the traces of things. That which can enter and leave existence and nonexistence, life and death, is the Dao.

The spirits are everywhere and have no fixed dwelling. A Perfected Person—a person whose cultivation has reached a profound level—can commune with the minds of others because their roots are originally one.

“Dao” and “One” are both names used to speak of the spirits, though any name is inadequate. To explain the spirits through the spirits themselves is the most fitting way to speak of them.

The human body is like the earth, and nature is rooted in stillness. The body’s movement comes from the driving force of blood and Qi.

Heaven and Earth bring forth life and multiply the kinds of things; this is their work. The sages distinguish things into different kinds; this is the function they fulfill.

To regard all things from their own standpoint reflects nature; to regard all things from the self-centered standpoint reflects emotion. Nature is impartial and clear; emotion is partial and obscured.

Yang’s function is to open and extend outward; Yin’s is to gather and contract inward.

When the sun reaches the Zi position, the direction of Water, it begins to grow; when it reaches the Li position, the direction of Fire, it begins to wane. This refers to whether the Qi of Yin and Yang mingle or remain apart.

Yin and Yang seem to be two opposing forces. Yet when Yang Qi arrives, all things grow; when Yang Qi departs, all things decline. The life and death of the myriad things between Heaven and Earth depend chiefly on Yang, so at the root, everything still returns to the One.

Shen has no fixed form or direction, while the nature of each thing has its own particular form and substance.

When nature manifests, it appears as emotion; when emotion manifests, it appears as outward form. Things respond to one another according to the kinds they share.

Heaven and Earth give birth to the myriad things and regard them as the myriad things. The Dao gives birth to Heaven and Earth, so Heaven and Earth, too, are among the myriad things.

What makes human beings precious is that they embody the natures of all things. Only when people cherish themselves do they reveal their own worth, and thus become able to make use of all kinds of things.

The good and evil of ordinary people are revealed in their words and actions, and only then can others know them. But as soon as a thought arises in the heart, or deliberation begins, the spirits and gods already know. This is why the noble person is careful with words, actions, and thoughts when alone.

When Qi changes, the body changes with it.

Human beings, as a kind, possess the various natures of all things.

The Shen within human beings is connected with the Shen of Heaven and Earth. If people deceive themselves, they are also deceiving Heaven and Earth. How could they fail to be vigilant?

People fear ghosts, just as ghosts fear people. When someone accumulates good deeds, Yang Qi flourishes, and even ghosts respect and fear them. When someone accumulates evil deeds, Yin Qi flourishes, and ghosts no longer fear them. Those of lofty De are in accord with the spirits and gods in matters of good and ill fortune. What, then, is there to fear?

The study of ultimate principles cannot be attained without utmost sincerity. When investigating the principles of things, one may sometimes encounter what cannot yet be understood; one must not force an explanation. To explain by force is to introduce subjective preconceptions. Once preconceptions take hold, one departs from principle and falls into unorthodox techniques and arts.

When the mind is unified and undistracted,

The study of ultimate principles cannot be attained without utmost sincerity. When investigating the principles of things, one may sometimes encounter what cannot yet be understood; one must not force an explanation. To explain by force is to introduce subjective preconceptions. Once preconceptions take hold, one departs from principle and falls into unorthodox techniques and arts.

When the mind is unified and undistracted, it can respond to all things. This is why the noble person keeps the mind empty and still, and is not easily disturbed by external things.

The sage brings benefit to all things without any sense of self.

In the bright realm are the sun and moon; in the hidden realm are the spirits and gods.

The six classics of the sages form a seamless whole, without any trace of deliberate arrangement, just like the Way of Heaven. The Spring and Autumn Annals records events that truly took place, and good and evil become evident in those records.

There are two ways to speak of the Mean: what arises from within and accords with the Mean is one’s nature; what is sought from outside and follows external standards is artificial.

In composing rhymes, the changes between open and closed mouth correspond to the rhythms of the Way of Heaven, while clear and muddy sounds correspond to the distinctions in the Qi of Earth. A sound that begins with the mouth closed and then opens is a spring sound; one made entirely with the mouth open is a summer sound; one that begins with the mouth open and then closes is an autumn sound; a winter sound is made with the mouth closed and no sound. The East belongs to spring, so it corresponds to spring sounds. Yang Qi is abundant, so it corresponds to summer sounds. This shows that those who compose rhymes can also grasp the patterns by which things operate. “Xian” belongs to the winter sounds.

To be still and unmoving, return to the root, and restore quietude is the season of the Kun hexagram, which symbolizes Earth and yielding. Once stimulated into response, one can understand the principles of all things under Heaven. This describes Yang Qi stirring within, with almost no gap or delay; it is the meaning of the Fu hexagram, which symbolizes the first emergence of Yang Qi.

To act rashly without noticing a change is reckless action, like trying to act when one is in the time of the Pi hexagram, which symbolizes obstruction and disconnection. To notice a change and then act is Wuwang, responding to what is real without acting recklessly. But if this brings disaster, it is because Yang Qi is weak and receives no response. Acting in response to something, by contrast, can bring increase.

“Jing Qi forms things” refers to the formation of physical bodies; “wandering souls bring about change” refers to transformations of the spirit. It can also be said that “Jing Qi forms things” refers to physical form, while “wandering souls bring about change” refers to wondrous efficacy.

A gentleman should make self-cultivation the foundation of learning. Governing others and responding to things are further matters that follow from it.

The ability to act decisively and settle matters depends on talent and strength; the ability to see clearly and distinguish principles depends on wisdom and insight; breadth of heart and a generous bearing depend on virtue and capacity. None of these three can be lacking.

Those without virtue are quick to blame and resent others, and quick to become complacent. Once complacent, they cease to make progress.

Those who act in accordance with the principles of Heaven can take part in the development and transformation of things.

If learning cannot bring together the Way of Heaven and human affairs, it cannot be called genuine learning.

Even when one asks about things above the world, it is as though nothing exists.

Those who grasp the principles of Heaven can cultivate not only the body but also the heart and mind; and beyond cultivating the heart and mind, they can even nurture and strengthen their nature and life.

The calculation of the calendar cannot be entirely free of error. Those who study calendrical science today know only its specific methods of calculation, but not the principles behind it. Luo Xiahong excelled at laying out calendrical calculations, while Gan De and Shi Shen excelled at working out the movements of celestial bodies. Luo Xiahong understood only the calendar, whereas Yang Xiong understood both the calendar and its underlying principles.

Yan Hui managed not to take his anger out on others and not to repeat the same mistake. Taking anger out on others and repeating mistakes both arise from emotions and ingrained habits; they are not part of human nature. Without understanding the principles of nature and life, one cannot be called a true lover of learning.

Yang Xiong wrote the Tai Xuan (or simply the Xuan), a philosophical work modeled on the Yi, beginning from the principles underlying the calendar.

Yan Hui managed not to take his anger out on others and not to repeat the same mistake. Taking anger out on others and repeating mistakes both arise from emotions and ingrained habits; they are not part of human nature. Without understanding the principles of nature and life, one cannot be called a true lover of learning.

Yang Xiong’s writing of the Tai Xuan can be said to have grasped the fundamental intent behind Heaven and Earth’s ceaseless generation of life.

The Yi has no fixed form. Some say it has enduring principles; that makes it sound as though it has a fixed form. To keep people from therefore treating the Yi as rigid and immutable, it is said that it “cannot be made into a fixed standard.” Its principles endure: this is constancy. Yet it cannot be treated as a fixed standard: this is change.

In eloquence, Zhuang Zhou may have had no equal in thousands of years. For example, in the Zhuangzi, when Ding the Butcher carves an ox, he is described as “hesitating” and “looking all around.” And when Confucius watches the waterfall at Lüliang, he speaks of following the current without acting from private intent. Both passages express profound truths.

The Yi is a tool by which sages support the noble person and weaken the petty person. When the way of the noble person is flourishing, it must be guarded against the petty person’s power before that power takes shape. When the way of the petty person is in decline, it must likewise be checked before disorder arises. Flourishing and decline, opening and closing, unfold with such natural harmony that their traces are barely visible. Who could accomplish this without the most wondrous principles under Heaven?

The Great Exceeding hexagram symbolizes weakness at both the roots and the tips. To rescue such a situation requires both lofty virtue and high position. By ordinary principles, some circumstances can be saved; but to go beyond the norm and shoulder a great responsibility requires lofty virtue and high position. Yi Yin and the Duke of Zhou were such people: they were fit to bear the burden and had no need to fear. Others may have noble virtue without a prominent position; they cannot act beyond their station. Confucius and Mencius were such people and could not overstep their place. Does this mean their positions were insufficient to support their virtue?

How great is the power of position! It is the place from which one awaits the right moment and puts one’s abilities to work.

The Return hexagram follows the Stripping hexagram, showing light returning. Does this mean good government arises from disorder? The Coming to Meet hexagram follows the Resoluteness hexagram, showing that Yin will rise again. From this we can see that some people, though they have noble virtue, cannot act beyond their station because they lack high position. Confucius and Mencius were such people and could not overstep their place. Does this mean their positions were insufficient to support their virtue?

How important are position and timing! They are what enable one to await the right moment and put it to use.

Consider that the Hexagram of Stripping is followed by the Hexagram of Return. Does this mean that good governance emerges from times of disorder? The Hexagram of Coming to Meet is followed by the Hexagram of Resolving. Does this mean that disorder emerges from good governance? The key is timing. Nothing that has been stripped away and declined fails to move toward renewal, and no decisive resolution is followed by an end to encounters. One must guard against calamity before it occurs; only then can the state endure and its descendants flourish. Thus the sage gives importance to preventing trouble before it arises. This is the central teaching of the Changes.

The learning of the Earlier Heaven—an account of how all things between Heaven and Earth come into being and change—is a method of the mind. Its diagrams therefore all begin at the center. The myriad changes and affairs arise from within the mind.

In how one lives and acts, the path one follows must be broad. A broad path brings fewer obstacles.

Those who truly understand the Changes need not cite its passages in order to explain it. Mencius never spoke of the Changes, yet his words contain its principles, though few people recognize them. To understand the Changes is to apply its principles in practice; Mencius can be said to have been skilled in putting them to use.

The terms Sovereign, Emperor, King, and Hegemon refer not only to the ancient rulers known as the Three Sovereigns, Five Emperors, Three Kings, and Five Hegemons. They also describe different ways of governing: ruling through Wuwei (non-action) is the Way of the Sovereign; ruling through benevolence and trustworthiness is the Way of the Emperor; ruling through impartial justice is the Way of the King; and ruling through strategy and force is the Way of the Hegemon.

Ghosts and spirits have no form, yet they can exert an influence; their nature can be understood through their effects. The ears, eyes, nose, and mouth, the hands and feet, and the branches, leaves, blossoms, fruits, and colors of plants are all brought forth by ghosts and spirits. Who governs the bestowal of blessings on the good and calamities on the wicked? Who gives all things such qualities as intelligence and uprightness? And what governs the power by which events come swiftly without prompting, and things arrive without traveling? These are the workings of ghosts and spirits.

The Yi Jing contains images that express meaning. Images are established to explain the trigrams. Broadly speaking, its images fall into three kinds: verbal images, which explain principles directly in words without using concrete things; figurative images, which use particular things as metaphors to convey meaning; and numerical images, which represent meaning through numbers, such as seven days, eight months, three years, or ten years.

The numbers in the Yi Jing can be used to trace the changes of Heaven and Earth from their beginning to their end. Someone asked, “Do Heaven and Earth also have a beginning and an end?” Since they undergo waxing and waning, how could they have neither beginning nor end? Though vast, Heaven and Earth are still things with form and substance. Thus Heaven and Earth are two distinct existences.

The Yi Jing has inner images, meaning the principles it contains, and outer images, meaning images that point to definite things and do not change.

In human beings, the Way of Qian, the firm and active principle, forms men, while the Way of Kun, the yielding and receptive principle, forms women. In the myriad things, the Way of Qian forms Yang, while the Way of Kun forms Yin.

“Spirit has no fixed direction, and the Yi has no fixed form.” If something is confined to one direction, it cannot change; it is then not spirit. If something has a fixed, unchanging form, it cannot adapt to change; it is then not the Yi. Though the Yi does have a “substance,” this substance refers to its images. It manifests its substance through images, yet has no fixed form of its own.

In every matter, whether great or small, there is the Dao. To keep to one’s proper place is to be in accord with the Dao; to fail to do so is to be out of accord with it.

When correcting pitches and numbers, the count stops at seven because on the day of the summer solstice the sun rises during the Yin hour and sets during the Xu hour. During the Hai, Zi, and Chou hours, the sun has already set below the earth and cannot be seen by the human eye. The numbers for these three hours are therefore not visible. This does not mean they do not exist: the numbers are present, though unseen. The numerical principles governing the growth of the myriad things are the same.

The “Six Emptinesses” refers to the six line positions in a hexagram. These positions seem empty so that they can accommodate the changes of things.

Where there is form, there is substance; where there is nature, there are feelings.

Heaven governs function, and Earth governs form; sages govern function, and the people receive its form. Thus the Yi says that people use its principles every day, yet often do not know it.

The standards and laws began with Fuxi and took shape in the time of Yao. Through the changes made by the Three Kings of Xia, Shang, and Zhou, they reached their culmination, and feelings then arose.

Heaven governs the workings of all things, while Earth bears their physical forms. Sages place importance on carrying out instruction, and the people are shaped by its influence. Thus, although people put these principles to use every day, they often do so without realizing it.

Institutions and laws began with Fuxi and reached a measure of completion in the time of Yao. They were transformed under the Three Kings of the Xia, Shang, and Zhou dynasties, flourished in the era of the Five Hegemons of the Spring and Autumn period, and finally came to an end under the Qin. The signs of order and disorder in every age all follow this pattern of change.

Shen (spirit) governs the Yi (Classic of Changes), and therefore has no fixed direction or form. The Yi, in turn, is the way Shen’s workings become manifest, and therefore has no fixed substance.

To follow the principles inherent in things is ordinary reason; what goes beyond ordinary reason is extraordinary.

Fire takes its nature as primary and its form as secondary; water takes its form as primary and its nature as secondary.

Yang belongs to nature, Yin to feeling; nature belongs to spiritual clarity, feeling to ghostly Qi.

The Yi begins with the Qian and Kun hexagrams, passes through Kan and Li, and concludes with the union or separation of water and fire. All of these embody the highest principle.

Taiji (the undivided fundamental state of the cosmos) is unified and still. From it arise the Two Modes; as they change and move, they become Shen. Shen gives rise to number, number to hexagram images, and hexagram images to concrete things.

Taiji in its stillness is nature. When nature stirs, it appears as Shen; Shen appears as number, number as image, and image as form (concrete things). As concrete things change, they ultimately return to Shen.

If the changes of the hexagrams do not directly unite through Qian and Kun, they arise through the relation between the Tai and Pi hexagrams. Tai and Pi are expressions of the union of Qian and Kun. Qian and Kun are composed of the two types of line, solid and broken, which in turn originate in Taiji.

What Heaven endows me with is called destiny; destiny as it manifests within me is called nature; when nature takes shape in the myriad things, it is called principle.

In the cyclical changes of Yin and Yang Qi known as Shuoyi, Yang Qi begins to arise in the north and, after completing one cycle, is extinguished there again. This is called the cycle of transformation and change.

In spring, Yang Qi predominates, so drought is common; in autumn, Yin Qi predominates, so rain is common.

“Origin” is the source from which all things begin. Heaven and Earth began to form through Taiji; the beginning of each individual thing, in turn, is the root from which it grows.

The heart of Heaven and Earth is the root from which all things are brought forth. The nature of Heaven and Earth refers to the forms they display, which are the same as the forms displayed by ghosts and spirits.

Zhuangzi and Huizi were strolling on a bridge over the Hao River. Zhuangzi said, “The white fish swim to and fro at ease. This is the happiness of fish.” When one has fully realized one’s own nature, one can also understand the nature of all things. The fish are like this, and so are all things under heaven. A person like Zhuangzi can be said to be exceptionally skilled at understanding all things.

Laozi understood the fundamental principles of the Yijing (Classic of Changes).

To be free of thought and action is a state in which the mysterious spirit returns to unity. The sage uses this to cleanse the mind and spirit, withdrawing to dwell in seclusion.

Taiji (Supreme Ultimate) is the utmost point of the Dao (the Way); Taixuan is the Dao’s original source; Taisu is the origin of color; Taiyi is the beginning of number; Taichu is the beginning of things. What they ultimately bring about is, at root, one and the same.

The great broth, seasoned with nothing, can be harmonized; the dark wine, used in sacrifice to symbolize water, can be clarified. So too, the workings of creation can be harmonized and clarified.

When one looks from the other person’s circumstances, one is free of self-centered preconceptions.

Sincerity is the fundamental means by which one’s nature is governed; it has no beginning and no fixed place.

How wondrous is wisdom! The Marquis of Liu, Zhang Liang, was skilled at concealing his abilities and leaving them unused.

Texts such as the Suwen and Miyu can be said to have explored the principles of divination and calculation with great depth.

When Gusou, Shun’s father, tried to kill him, Shun regarded giving up the realm as no more than tossing aside a worn-out shoe. He fled with his father on his back and lived by the sea for the rest of his life, still content and joyful, forgetting all affairs of the realm. Even possession of the realm could not change a sage’s natural affection for family.

Someone asked what the Yijing means by “making benevolence manifest and keeping its workings hidden.” The reply was: “The sun and moon shine on all things, and the four seasons cycle to complete the year: this is making benevolence manifest. The patterns and numbers within these processes operate as they do, yet people do not know why: this is keeping the workings hidden.”

When a gentleman studies the Yijing, he should examine closely its hexagram images, numbers, statements, and underlying meanings.

“Dui” signifies joy. Other things may bring hindrance, but friends learning and discussing together do not impede this joy. That is why the Yijing speaks of it as reaching the utmost.

The Doctrine of the Mean is not some thing that descends from Heaven or springs up from the earth. It means weighing how things stand, understanding the feelings and circumstances of people, and acting in a way they can accept with peace of mind. Only then is one acting appropriately.

“Origin, success, benefit, and steadfastness”—the four virtues named in the Book of Changes—each contain different possibilities, including good fortune, misfortune, regret, and difficulty. Even when an action accords with virtue, it may bring danger if it runs counter to the times.

When Tang of Shang exiled Jie of Xia, or King Wu of Zhou attacked Zhou of Shang, they were not considered regicides. As Mencius said, it is proper for men and women not to pass things directly from hand to hand; but if one’s sister-in-law falls into the water, reaching out to save her is an exercise of expediency, adapting one’s conduct to a special circumstance. Thus Confucius revered both Boyi and Shuqi, and also approved of Tang and King Wu. Boyi and Shuqi embodied benevolence; Tang and King Wu embodied righteousness. But only people like Tang and King Wu, who possessed their virtue, could act in this way. For anyone lacking their virtue, it would be usurpation.

Yin is the shadow of Yang; ghosts are the shadows of people.

Duke Mu of Qin had once rendered service to the royal house of Zhou and was able to correct his mistakes and improve himself. He therefore became a hegemon among the feudal lords.