Hexagram of the Day Tuesday, January 27, 2026: #1 The Creative (Heaven) (乾)

Qián (pronounced qu-yan). The six-line figure is the Gua drawn by Fuxi. A single unbroken line is an odd number, representing the number of Yang. Qián denotes vigor, representing the nature of Yang.

In the original commentary, the word 'Qián' refers to the name of the three-line trigram: the lower is the inner trigram, and the upper is the outer trigram. In the canon text, the word 'Qián' refers to the name of the six-line hexagram.

Fuxi looked upward to contemplate the heavens and looked downward to observe the earth; seeing that Yin and Yang possess the numbers of odd and even, he drew one unbroken line to symbolize Yang, and one broken line to symbolize Yin.

Seeing that each Yin and Yang further gives birth to another Yin and Yang, he doubled them repeatedly from bottom to top, forming the Ba Gua in three steps.

Seeing that the nature of Yang is vigorous and that its greatest manifestation in bodily form is Heaven, he named the Gua of three unbroken lines Qián and likened it to Heaven.

Once the three lines were complete and the Ba Gua established, he tripled the lines to form six lines, placing each of the Eight Trigrams atop one another to generate the sixty-four hexagrams.

In this Gua, all six lines are odd, and both upper and lower are Qián; thus it is pure Yang and the utmost of vigor. Therefore, the name Qián and the image of Heaven remain unalterable.

'Supreme success, beneficial through perseverance' (Yuan Heng Li Zhen) are the words appended by King Wen to determine the auspiciousness or inauspiciousness of the entire Gua, known as the Judgment (Tuan).

Yuan means great; Heng means penetrating; Li means appropriate; Zhen means correct and steadfast. King Wen held that the Dao of Qián possesses supreme penetration and utmost correctness.

Therefore, in divination, when this Gua is obtained and none of its six lines change, the prognosis is that one will attain supreme penetration, yet benefit is found solely in steadfast correctness; only then can one preserve its end.

Such is the profound intention of the Sage in creating the Changes to instruct humanity in divination, thereby unlocking potential and accomplishing undertakings. The remaining hexagrams follow this model.

Tuàn (pronounced tu-luan). The Tuàn consists of the words appended by King Wen; the Commentary (Zhuàn) represents Confucius's words elucidating the canon. All subsequent references to the Zhuàn follow this.

This section exclusively employs the Heavenly Dao to clarify the meaning of Qián, further dividing Yuan, Heng, Li, and Zhen into four virtues to elucidate them; this opening passage first explains the meaning of Yuan. 'Great indeed' is an exclamation of praise.

Yuan signifies greatness and beginning. The Yuan of Qián is the great commencement of Heavenly Virtue; hence the myriad things all rely on it for their origin.

It is also the head of the four virtues, running through Heavenly Virtue from beginning to end; hence it is said to 'command Heaven.' 'Bestowing' (shī, pronounced shǐ-chì, the same throughout the hexagram). This explains the Heng (penetration) of Qián.

Beginning refers to Yuan; the end refers to Zhen. Without an end, there is no beginning; without Zhen, there is nothing by which to constitute Yuan.

This signifies that the Sage thoroughly comprehends the beginning and end of the Dao of Qián, observing that the six positions of the hexagram are each completed according to their proper time; mounting these six Yang lines to enact the Heavenly Dao constitutes the Sage's supreme success (Yuan Heng).

Change (biàn) is the gradual unfolding of transformation; transformation (huà) is the culmination of change. What creatures receive from Heaven is their nature; what Heaven confers is destiny. Supreme Harmony is the tranquil, blended qi arising from the union of Yin and Yang.

'Each aligns' means that which is obtained at the onset of birth; 'preserving and uniting' means keeping it intact throughout life.

This explains that through the transformations of the Dao of Qián, nothing fails to benefit, and all creatures obtain their nature and destiny to preserve their wholeness, thus elucidating the meaning of 'beneficial through perseverance' (Li Zhen).

The Sage presiding above, exalted far beyond all things, mirrors the transformations of the Dao of Qián; the myriad realms each finding their place and enjoying universal peace mirrors the myriad things each rectifying nature and destiny and preserving Supreme Harmony.

This expresses the Sage's perseverance and benefit. Taken comprehensively, Yuan is the initial sprouting of things; Heng is their luxuriant growth; Li is their movement toward fruition; Zhen is the ripening of the fruit.

Once the fruit is ripe, its stems fall away, and it may be replanted to grow anew. This is why the four virtues circulate without end. Yet through them all, the vital breath flows ceaselessly without interruption; this is why Yuan encompasses the four virtues and commands Heaven.

Regarding the Sage, Confucius's intention was that this Gua serves as a divination of the Sage obtaining Heaven's throne, walking the Heavenly Dao, and bringing about Great Peace.

Although some textual interpretations differ from King Wen's original sense, if readers seek their meanings respectively, both interpretations may proceed side by side without conflict. The Receptive (Earth) hexagram follows this rule.

The Images (Xiang) are the two trigram images (upper and lower) and the six lines of those images, consisting of the words appended by the Duke of Zhou. Heaven is the image of the Qián Gua.

Generally, doubled hexagrams derive their meaning from repetition; this Gua alone does not, because Heaven is one and indivisible.

Yet speaking of the movement of Heaven reveals that it completes one circuit in a single day and another the next day, an image of continual recurrence which none but the supremely vigorous could achieve.

The gentleman models himself on this: he never allows human desire to impair the firmness of his heavenly virtue, thereby strengthening himself without ceasing.

Zhǎng (pronounced ding-wen, meaning elder/chief; the same in 'zhǎng rén'); gàn (pronounced gu-dan, meaning trunk/support).

This chapter expands on the meaning of the Tuàn and Xiang Commentaries to exhaust the deep reserves of The Creative (Heaven) and The Receptive (Earth), providing principles that can be applied to the remaining hexagrams.

Yuan is the beginning of the generation of things; of all the virtues of Heaven and Earth, none precedes it. In terms of seasons, it is Spring; in humankind, it is benevolence (ren), the head of all virtues.

Heng is the unobstructed flow of generated things; when things reach this stage, none are not beautiful and flourishing. In terms of seasons, it is Summer; in humankind, it is propriety (li), the meeting place of all beauties.

Li is the fulfillment of generated things, where each obtains its proper measure without mutual harm. In terms of seasons, it is Autumn; in humankind, it is righteousness (yi), attaining harmony within allotted shares.

Zhen is the completion of generated things, where true principles are fully embodied and self-sufficient everywhere. In terms of seasons, it is Winter; in humankind, it is wisdom (zhi), serving as the trunk of all affairs.

The trunk is the main body of a tree, upon which branches and leaves rely to stand. Taking benevolence as one's core substance, there is no being outside one's love; hence one is capable of leading people. When meetings are made auspicious, nothing fails to accord with propriety.

Allowing each thing to attain its proper benefit harmonizes righteousness. Those who are steadfastly correct recognize where correctness lies and firmly preserve it—the so-called knowing it and never departing from it; hence it suffices to serve as the trunk of affairs.

None but the gentleman of utmost vigor can practice this; hence it is said, 'Qián: supreme success, beneficial through perseverance.' This first section expands on the Commentary on the Judgment, not differing from the words of Mu Jiang recorded in the Zuo Zhuan.

It is suspected that these words already existed in antiquity; Mu Jiang quoted them, and the Master adopted them as well.

Thus, subsequent passages introduce Confucius's words with 'The Master said,' indicating that the commentators wished to clarify that the opening passage was an ancient saying. Yuè (sounded luò, or kǔ-xué). Dragon virtue is the virtue of the Sage. Being below, it is hidden.

'Change' means altering what one preserves. In general, the Wenyan Commentary elucidates all six lines of Qián through the Sage, demonstrating hiddenness and manifestation without difference in depth. Xíng (read in departing tone); xié (pronounced yi-jie).

Upright and central represents the time of neither remaining submerged nor yet leaping. Trustworthiness in ordinary speech and caution in ordinary action represent the culmination of abundant virtue.

Warding off depravity to preserve one's sincerity and acting without weariness also carry the sense of preservation. Saying 'this is the virtue of a ruler' explains why Nine in the Second Line is called a great man. Jī (sounded jī).

Loyalty and good faith reside in the heart, where not a single thought lacks sincerity. Cultivating words is seen in affairs, where not a single utterance lacks truthfulness.

Although one possesses a heart of loyalty and good faith, without cultivating speech and establishing sincerity, one has nothing whereby to dwell in them.

Knowing the ultimate and attaining it pertains to advancing virtue; knowing the end and ending it pertains to preserving one's vocation. This is why one strives vigorously all day long and remains apprehensive even at evening.

Capable of moving up or down without pride or anxiety—this is what is meant by 'no blame.' Nine in the Fourth Line says: 'Leaping hesitation at the abyss; no blame.' What does this mean?

The Master said: 'Rising or falling without permanence is not for the sake of wickedness; advancing or retreating without constancy is not to abandon the flock.

The gentleman advances his virtue and cultivates his vocation, seeking to act in accordance with the proper time; hence there is no blame.' Lí (departing tone). The inner trigram speaks of virtue and learning; the outer trigram speaks of time and position.

Advancing virtue and cultivating one's vocation are already complete in Nine in the Third Line; here, one desires to advance in a timely manner. Nine in the Fifth Line says: 'Flying dragon in the heavens; it is beneficial to see the great man.' What does this mean?

The Master said: 'Notes of the same tone resonate together; things of the same qi seek one another out. Water flows toward dampness, fire turns toward dryness, clouds follow the dragon, and wind follows the tiger. When the Sage arises, all things behold him.

What is rooted in Heaven cleaves to what is above; what is rooted in Earth cleaves to what is below. Thus each follows its own kind.' Yìng (departing tone). 'Arises' means springs forth; 'things' is like 'people.' 'Behold' explains the meaning of 'beneficial to see.'

What is rooted in Heaven refers to animals; what is rooted in Earth refers to plants. All things follow their kind; the Sage is the foremost of human kind, and when he rises above, all people behold him. Nine at the Top says: 'Arrogant dragon will have cause for regret.'

What does this mean? The Master said: 'Noble yet without position; exalted yet without people. Worthy men remain below without offering support. Hence, to act brings regret.' Worthy men remaining below means those from Nine in the Fifth Line downward.

'Without support' means that because Nine at the Top is excessively exalted and full of conceit, they do not come to assist him. This second section expands on the meaning of the Xiang Commentary. 'Hidden dragon, do not act'—it is below.

'Dragon appearing in the field'—it is set aside by time. Shě (pronounced shě). This means it is not yet employed by the times. 'All day long active and vigilant'—he conducts his affairs. 'Leaping hesitation at the abyss'—he tests himself.

Not rushing into action, he tentatively tests what is feasible. 'Flying dragon in the heavens'—governing from above. Zhì (level tone). Occupying the heights to govern those below. 'Arrogant dragon will have cause for regret'—the disaster of reaching the extremity.

'The Qián Yuan uses nines'—the world is governed. Zhì (departing tone). This expresses that the Qián Yuan's use of nines is seen to differ from other hexagrams: when the ruler's path is firm yet capable of gentleness, nothing in the world fails to be governed.

This third section further expands on the preceding meaning. 'Hidden dragon, do not act'—the Yang qi is concealed and submerged. 'Dragon appearing in the field'—the whole world is bright and cultured.

Though not in high position, the entire world has already received his transformative influence. 'All day long active and vigilant'—moving together with the times. Because the time demands it. 'Leaping hesitation at the abyss'—the Dao of Qián undergoes a transformation.

Departing from below to rise above, a time of fundamental change. 'Flying dragon in the heavens'—he assumes the position of Heavenly Virtue. Heavenly Virtue is the Heavenly Throne. Only one with this virtue is suited to occupy this seat; hence it is named so.

'Arrogant dragon will have cause for regret'—reaching the extremity alongside time. 'The Qián Yuan uses nines'—here one sees the law of Heaven. Being firm yet capable of yielding is the law of Heaven. This fourth section further expands on the preceding meaning.

The Qián Yuan is that which begins and penetrates. Where there is beginning, there must be penetration; such is the natural momentum of principle. Beneficial perseverance is nature and disposition.

Gathering inward and returning to concealment reveals the true substance of nature and disposition. Qián begins and can benefit the whole world with wonderful advantages, yet it speaks not of what it benefits. Great indeed!

Beginning refers to Yuan and Heng; benefiting the world refers to Li; not speaking of what it benefits refers to Zhen. Some say that The Receptive (Earth) mentions 'the benefit of the mare,' thereby naming what it benefits. Great indeed is Qián!

Firm, vigorous, central, correct, pure, unmixed, and refined. Firmness refers to its substance; vigor encompasses its function. Central means its actions neither exceed nor fall short; correct means its stance is upright and unswerving. These four are the virtues of Qián.

Pure means unmixed with Yin weakness; unadulterated means unblemished by depravity. It is the utmost limit of firmness, vigor, centrality, and correctness, while refined represents the utmost limit of purity.

Some doubt that Qián, being purely firm without softness, cannot be termed central and correct; this is not so. Between Heaven and Earth, there is originally only the flow of a single qi possessing movement and stillness.

Regarding the unified body of this flow, it is simply termed Qián, encompassing everything. Only when divided by movement and stillness do distinctions between Yin and Yang, firmness and yielding arise. The six lines express and comprehensively penetrate the inner dispositions.

'Comprehensively penetrate' means exhausting every nuance. Riding the six dragons in timely fashion to drive across the heavens; clouds fly and rain falls, bringing peace to the world.

This says that when the Sage rides the six dragons in timely fashion to govern Heaven, it is like Heaven causing clouds to move and rain to fall, bringing peace to all under heaven. This fifth section again expands on the meaning of the opening chapter.

The gentleman takes perfected virtue as his practice, a practice visible day by day. 'Hidden' means concealed and not yet appearing, acting without yet completing; hence the gentleman does not act. Xíng (both in departing tone); jiàn (read as xiàn, appearing).

Perfected virtue is virtue already achieved. Nine at the Beginning indeed possesses perfected virtue, but his actions are not yet visible. The gentleman learns in order to gather, inquires in order to discern, is magnanimous in dwelling, and acts with benevolence.

The Book of Changes says: 'Dragon appearing in the field; it is beneficial to see the great man.' This is the virtue of a ruler. Through these four, the virtue of the great man is fulfilled.

Restating 'the virtue of a ruler' clearly emphasizes that Nine in the Second Line is indeed a great man. Nine in the Third Line possesses doubled firmness and is not central. Above, it is not in heaven; below, it is not in the field.

Hence, he is active and vigilant according to the times; though in peril, there is no blame. Chóng (level tone, same below). Doubled firmness refers to a Yang line in a Yang position. Nine in the Fourth Line possesses doubled firmness and is not central.

Above, it is not in heaven; below, it is not in the field; in the middle, it is not among men. Hence it says 'or/leaping.' 'Or' signifies hesitation and doubt; hence there is no blame.

Nine in the Fourth Line is not doubled firmness; the word 'doubled' is suspected to be a textual error. 'Among men' refers to the third line. 'Or' indicates adapting to the time without fixed certainty.

The great man accords with Heaven and Earth in virtue, with the sun and moon in brightness, with the four seasons in order, and with the gods and spirits in good and bad fortune.

When he acts ahead of Heaven, Heaven does not contradict him; when he follows Heaven, he complies with the heavenly seasons. If Heaven does not contradict him, how much less will men! How much less will the gods and spirits! Fú (sounded fú); xiān and hòu both in departing tone.

'Great man' explains the great man who is beneficial to see in the line texts. Only one possessing such virtue and occupying such a position can measure up to this.

Humanity, Heaven, Earth, and spiritual beings originally share a single principle; it is only because men are blinded by selfish desires of the ego that they become fettered by bodily form and cannot communicate.

The great man has no self and takes the Dao as his body; how could there be any distinction of self and other, before and after? 'Preceding Heaven without contradiction' means what his will undertakes aligns silently with the Dao.

'Following Heaven and complying with its seasons' means knowing principle to be thus and reverently enacting it. The Uyghurs said to Guo Ziyi: 'The diviner said that on this expedition we would behold a great man and then return.' Their divination coincided with this text.

Though Ziyi may not have reached the heights discussed by the Master, his supreme impartiality and selflessness certainly earned him the title of great man of his era.

'Arrogant' means knowing how to advance but not how to retreat, knowing preservation but not extinction, knowing gain but not loss. Sàng (departing tone). Hence acting brings regret. Is it not only the Sage?

Knowing how to advance and retreat, preserve and let perish, without losing his correctness—is it not only the Sage? Knowing principle and momentum to be thus, and handling them according to the Dao, one avoids reaching regret.

This is certainly not calculating personal gain to evade harm. Repeating 'is it not only the Sage?' begins as a rhetorical inquiry and concludes as a resolute affirmation. This sixth section again expands on the meaning of sections two, three, and four.

When the ancient sages first drew the Ba Gua, the ways of the Three Realms were complete. Thereupon they doubled them to exhaust all changes under Heaven; hence six lines formed a hexagram. The doubled Qián constitutes The Creative (Heaven).

Qián is Heaven: 'Heaven' refers to its bodily form, while 'Qián' refers to its nature and inner disposition. Qián means vigor; vigor without ceaseless interruption is called Qián. Taken comprehensively, Heaven is the Dao—as in 'Heaven itself does not contradict him.'

Divided, its bodily form is called Heaven, its governing power is called the Sovereign Ruler, its functional efficacy is called the spiritual beings, its wondrous operation is called the spirit, and its nature and disposition are called Qián.

Qián is the origin of all things; hence it is Heaven, Yang, father, and ruler. Yuan, Heng, Li, and Zhen are termed the four virtues. Yuan is the beginning of all things; Heng is their growth; Li is their fulfillment; Zhen is their completion.

Only The Creative (Heaven) and The Receptive (Earth) fully possess these four virtues; in other hexagrams, they alter according to the circumstances of affairs.

Thus Yuan specifically denotes great goodness, Li centers on steadfast correctness, while the embodiments of Heng and Zhen correspond to their respective affairs. The meaning of the four virtues is broad and vast indeed!

The statement beneath a hexagram is the Tuàn (Judgment); the Master followed and elucidated it, generally referring to it as the Tuàn.

The Tuàn expresses the essential meaning of a whole hexagram; hence the wise observer, upon examining its text, has grasped more than half of its ideas. 'Great indeed is Qián!' praises the vastness of the Dao of the Qián Yuan in originating all things.

The Yuan of the four virtues is like the benevolence (ren) of the Five Constant Virtues: spoken of separately, it is one matter; spoken of comprehensively, it encompasses all four.

'The myriad things rely on it for their beginning; thus it commands Heaven' speaks of Yuan: the Qián Yuan comprehensively expresses the Heavenly Dao. The Heavenly Dao originates all things, and all things rely on Heaven for their beginning.

'Clouds move and rain falls, and diverse things flow into bodily forms' speaks of Heng: the Heavenly Dao operates and nurtures all things.

'Thoroughly comprehending the end and the beginning of the Heavenly Dao' means seeing that the six positions of the Gua are each completed according to their proper time.

The beginning and end of a hexagram represent the beginning and end of the Heavenly Dao; riding the times of these six lines reflects the movement of Heaven. 'To drive Heaven' means to align with the heavenly movement.

Through the transformations of the Dao of Qián, all things are generated: large and small, high and low, each according to its kind rectifies its nature and destiny. What Heaven confers is destiny; what things receive is nature.

'Preserving and uniting Supreme Harmony, it is beneficial through perseverance': 'preserving' means constantly existing; 'uniting' means constantly harmonizing. By preserving and uniting Supreme Harmony, it is beneficial and steadfast.

That the Dao of Heaven and Earth endures ceaselessly is because it preserves and unites Supreme Harmony. Heaven is the ancestor of all things; the king is the leader of myriad realms.

The Dao of Qián emerges foremost among all creatures, and myriad species flourish; the ruler's path exalted upon the Heavenly Throne commands the allegiance of the Four Seas. When the king embodies the Heavenly Dao, the myriad nations all enjoy tranquility.

The Commentary on the Image below a hexagram explains the image of the whole hexagram; the Commentary on the Image below a line explains the image of a single line. All hexagrams take images as models to emulate.

The image of the Dao of Qián covering and nourishing is vast beyond measure; none but a sage can fully embody it. Wishing for all people to be able to model themselves upon it, the text takes only its vigorous movement as the standard.

Utmost vigor is indeed sufficient to manifest the Heavenly Dao. 'The gentleman strengthens himself without ceasing' models itself upon the vigorous movement of Heaven.

Other hexagrams contain only the Judgment and Image commentaries; Qián and Kūn alone are additionally provided with the Wenyan Commentary to illuminate their deep meanings, extending the Dao of Qián into human affairs.

Yuan, Heng, Li, and Zhen are the four virtues of Qián; in human terms, Yuan is the head of all virtues, Heng is the gathering of beauties, Li is the harmony of righteousness, and Zhen is the foundation of management.

Embodying the benevolence of Qián provides the way of leadership, sufficient to preside over people. Embodying benevolence means embodying Yuan; to align with and model oneself on it is called embodying. Attaining the auspiciousness of harmonious assembly accords with propriety.

If one does not accord with propriety, it is contrary to principle; how could it be deemed beautiful? Without principle, how could there be penetration? Harmonizing with righteousness enables one to benefit things.

How could anyone fail to attain appropriateness yet still benefit things? Steadfast correctness is that by which one manages affairs. Practicing these four virtues aligns one with Qián. 'Hidden dragon.'

From here downward speaks of the application of Qián, the path of 'using nines.' Nine at the Beginning is the subtle inception of Yang, the hidden dragon virtue—the sage or worthy living in obscurity.

He maintains his path without shifting with the world, cloaks his conduct without seeking recognition from his era, remains confident and joyful in himself, acts only when seeing it appropriate, and retreats when perceiving difficulty.

His steadfastness is resolute and unshakeable; this is the virtue of the hidden dragon. 'Virtue of a ruler.'

One possessing dragon virtue who abides in correct centrality: dwelling in the correct center of the hexagram signifies attaining the meaning of centrality and correctness. In ordinary speech truthful, in ordinary deeds cautious, he never departs from this even in haste.

Having occupied a position free from excess, his only task is to ward off depravity; once depravity is warded off, sincerity is preserved.

He does good to the world without boasting, taking no credit for his merit; his virtue is broad and transforms others, rectifying himself so that all things are rectified.

These are all deeds of a great man; though not yet occupying the ruler's throne, he possesses the virtue of a ruler. '...with whom one can examine the seeds of things. Knowing the end and ending it, with whom one can preserve righteousness.

Therefore, he occupies a superior position without pride, and dwells in a lowly position without anxiety. Hence he is active and vigilant according to the times; though in peril, there is no blame.'

The third line occupies the top of the lower trigram, and ruler-like virtue is already evident. What should he do? Only advance his virtue and cultivate his vocation.

Accumulating inner loyalty and good faith is how one advances virtue; choosing words carefully and solidifying resolve is how one dwells in one's vocation.

Knowing the ultimate and attaining it is the extension of knowledge: seeking to know where the ultimate lies and subsequently reaching it. Knowledge comes first, and thus one can examine the subtle seeds; this is the so-called 'initiating order is the work of knowledge.'

Knowing the end and concluding it is vigorous practice: having known where to conclude, one exerts effort to reach the end and preserves it afterward; thus one can maintain righteousness. This is the so-called 'concluding order is the work of the sage.'

Such is the beginning and end of learning. When the gentleman's learning is like this, he understands the way of abiding in high or low positions without pride or worry, staying untiring and cautious; thus, though in a perilous place, he incurs no blame.

'Heaven' is the name of bodily form; 'vigorous' is that which actuates the bodily form.

Form is a burden to things; yet possessing the form of Heaven while perpetually enduring without deficiency, standing at the head of all creatures—could what commands it be anything other than the utmost vigor?

By clearly understanding the way of the end and beginning, the six positions are completed without missing their proper time.

Ascending and descending without constancy, adapting to the times: when resting, one mounts the hidden dragon; when emerging, one mounts the flying dragon; hence it is said, 'He mounts the six dragons in timely fashion.'

Riding change to command the Great Vessel, resting with singleness of purpose and moving with directness, never losing Supreme Harmony—could this be anything other than rectifying the nature and disposition of destiny? Lacking harmony results in harsh violence.

The myriad states are peaceful because each possesses a ruler.

From 'The Tuàn says: Great indeed is the Qián Yuan' to 'each rectifies nature and destiny.' Sub-commentary: The Tuàn commentary composed by the Master discusses the overall meaning of a hexagram, explaining its virtues, significance, or name.

Thus the General Outline states: 'What is the Tuàn? It comprehensively discusses the body of a hexagram and clarifies the principal ruler from which it arises.' Master Chu and Master Zhuang both say: 'Tuàn means judgment; it determines the meaning of a hexagram, hence its name.'

This Tuàn explains the virtues of Qián alongside Yuan, Heng, Li, and Zhen. Various scholars divide the four virtues differently. We find Master Zhuang's exposition closer in principle and follow it here.

'Great indeed is the Qián Yuan, which all things rely on for their beginning; thus it commands Heaven'—these three sentences interpret Qián and Yuan together. 'Qián' is the hexagram name; 'Yuan' is the head of the virtues of Qián; hence Yuan is paired with Qián.

'Great indeed is the Qián Yuan': the Yang qi is vast and Qián's substance extensive; moreover, through Yuan, it gives birth to all things, hence the praise.

'All things rely on it for their beginning' explains why the Qián Yuan is called 'great': all things draw upon it to begin their lives without losing their proper measure.

'Thus it commands Heaven': being of utmost vigor and the origin of things, it commands Heaven; Heaven is a corporeal entity, and through its utmost vigor, Qián governs all corporeal form—this is the virtue of the Qián Yuan.

'Clouds move and rain falls, and diverse things flow into bodily forms'—these two sentences explain the virtue of Heng (penetration): Qián employs Heaven's virtue to circulate clouds and spread rain, allowing all categories of things to take shape and attain unhindered penetration.

'Thoroughly comprehending the end and the beginning, the six positions are completed according to their time'—these two sentences summarize the virtue of Qián.

With its virtue, Qián clearly grasps the Dao of beginning and end: beginning as submerged, ending as soaring; hiding when appropriate, flying when appropriate. Thus the six line positions are realized according to time.

If one did not understand this, one would fly when one should hide, or spawn when one should destroy, failing to complete the positions timely.

'Mounting the six dragons in timely fashion to drive across the heavens'—these two lines clarify how Qián Yuan 'commands Heaven': Qián rides the Yang qi of the six lines to govern the celestial sphere. The six dragons are the dragons of the six positions.

In terms of position, they are six places; in terms of ascending and descending Yang qi, they are six dragons.

'Thus it commands Heaven' spoke generally of Qián's virtue through utmost vigor; here, riding the six dragons assigns specific operations, hence 'to drive across the heavens.'

'The Dao of Qián transforms, and each rectifies nature and destiny'—these two lines further expand on all things relying on Qián Yuan. The body of the Dao is formless, naturally enabling all things to unfold; hence it is called 'Dao.'

The virtue of Qián naturally penetrates things; hence 'the Dao of Qián.' 'Change' (biàn) refers to the subsequent replacing the former through gradual transition; 'transformation' (huà) refers to sudden shift between being and non-being.

The Dao of Qián causes things to gradually change or suddenly transform, each correctly establishing its nature and destiny.

Nature is the innate quality endowed by Heaven, such as firm or soft, slow or swift; destiny is what man receives, such as noble or base, short-lived or long-lived.

On the note from 'Heaven is the name of bodily form' to 'could this be anything other than rectifying the nature and disposition of destiny?': Sub-commentary: Bodily form is a burden to creatures; corporeal things are burdened by form, and living beings fret over nature and destiny.

Yet Heaven and Earth, though corporeal, endure perpetually without defect and lead all things—is this not because what governs them possesses the utmost vigor?

'Riding change to command the Great Vessel': riding change means mounting the hidden or flying dragons; 'the Great Vessel' refers to Heaven. Riding these dragons to steer Heaven's body keeps its motion unceasing.

'Resting with singleness of purpose and moving with directness, never losing Supreme Harmony': when Qián is at rest, it is concentrated and unwavering; when in motion, it is upright and unswerving.

Thus the Great Treatise says: 'Qián in stillness is concentrated, and in motion is direct; therefore it produces greatness.' 'Never losing Supreme Harmony' corresponds to 'preserving and uniting Supreme Harmony' below.

'Could this be anything other than rectifying the nature and disposition of destiny?': since Qián rectifies the nature and destiny of things, this refers to things having their own dispositions, not that Heaven has human feelings.

Heaven is without emotional bias, yet things have feelings. What is received at birth is called nature; thoughts that arise with time are called feelings. Speaking here of sentient beings, the term 'disposition' is used.

The Master's format for the Tuàn determines the meaning of a hexagram through various stylistic forms. Master Zhuang identified twelve forms, but we summarize the main outlines without excessive detail.

Zhuang states that some Tuàn begin with exclamations of praise, such as 'Great indeed is the Qián Yuan' or 'Utmost indeed is the Kūn Yuan.' Because the virtues of Qián and Kūn are vast, they are praised first before their meanings are detailed.

Some repeat texts and explain meanings before praising, as in Enthusiasm (Yù): 'Great indeed is the time and meaning of Yù!'

Some first explain the hexagram name before concluding with it, as in Fellowship with Men: 'The yielding attains position, attains the center, and responds to Qián, hence it is called Fellowship with Men'; and Possession in Great Measure: 'The yielding attains the honored position, the great center, and upper and lower respond to it, hence it is called Possession in Great Measure.'

Some explicitly repeat the hexagram name, as in Fellowship with Men: 'Fellowship with Men says: Fellowship with men in the open: success.' The remaining hexagrams vary in detail, order, and structure.

Comparing them with overly rigid categories contradicts the Sage's original intent; hence we address their nuances under each individual hexagram. Sub-commentary: These two sentences explain 'beneficial through perseverance' (Li Zhen).

Pure Yang is hard and fierce; without harmony and compliance, things would find no benefit and lose correctness. By preserving and uniting the great way of benefit, it benefits and rectifies all things.

Sub-commentary: From above, all has discussed Qián's natural way of nurturing things.

These two sentences discuss the Sage modeling himself on Qián to nurture all beings: the Sage as ruler stands exalted above all creatures, appointing rulers to govern the myriad realms, bringing universal peace.

The sovereign's position is exalted, hence 'emerging foremost among all creatures.' Yet his mind must remain humble, matching 'no head: auspicious.'

The earlier text detailed Qián employing Heavenly Virtue, so this text concisely portrays the Sage mirroring Qián through human affairs.

From 'The Image says: The movement of heaven is full of vigor' to 'strengthens himself without ceasing.' Sub-commentary: This is the Great Image (Dà Xiàng), the third wing of the Ten Wings, summarizing the image of an entire hexagram.

All things naturally possess forms and images; the Sages devised hexagrams to portray these images. Here the Master explains what this hexagram symbolizes, hence 'The Image says.' Heaven possesses pure firmness and thus acts with vigor.

Drawing a hexagram of pure Yang to mirror it is called an Image. The Image follows the Tuàn because the Tuàn is detailed while the Image is concise.

'The movement of heaven is full of vigor': 'movement' refers to motion; 'vigor' denotes strength; 'Qián' is interpreted as encompassing all vigor.

The Great Image singles out 'Heaven' rather than other vigorous things because, while all strong things eventually decline, Heaven's movement advances by one degree each day, rotating ceaselessly without rest; hence 'the movement of heaven is full of vigor.'

'Vigor' defines Qián, just as 'yielding' defines The Receptive (Earth). The Receptive says 'the capacity of the earth is Kūn.' Here it does not say 'the movement of heaven is Qián' but 'is vigorous'; as Liu Biao observed, this clarifies its quality.

Heaven is the name of substance, Qián is the name of function, and vigor is its definition; presenting all three provides the fullest clarity, honoring Qián above other hexagrams.

The sixty-four hexagrams articulate images in varied ways: some present the origin of the image without naming physical bodies or distinguishing upper and lower trigrams, as in Qián and Kūn.

Others directly name both trigrams: 'Clouds and thunder: Difficulty at the Beginning (Zhūn)'; 'Heaven and Earth intersect: Peace (Tài)'; 'Heaven and Earth do not intersect: Standstill (Pǐ)'; 'Thunder and lightning: Biting Through (Shì Hé)'; 'Thunder and wind: Duration (Héng)'; 'Thunder and rain arise: Deliverance'; 'Wind and thunder: Increase'; 'Thunder and lightning both arrive: Abundance'; 'Repeated thunder: The Arousing'; 'Wind following wind: The Gentle'; 'Repeated water: The Abysmal (Water)'; 'Doubled brightness: The Clinging'; 'Doubled mountains: Keeping Still'; 'Attached lakes: The Joyous.'

These fourteen hexagrams mention both trigrams to establish meaning.

Some present trigrams in contrast: 'Heaven and water move in opposite directions: Conflict'; 'Heaven above and the lake below: Treading (Lǚ)'; 'Heaven and fire together: Fellowship with Men'; 'Fire above, lake below: Opposition.'

These four express divergence, union, or hierarchical succession.

Others specify the upper trigram first: 'Clouds ascend to heaven: Waiting'; 'Wind moves over heaven: Small Taming'; 'Fire in heaven: Possession in Great Measure'; 'Thunder emerges from the earth: Enthusiasm (Yù)'; 'Wind moves over the earth: Contemplation'; 'Mountain attaches to earth: Splitting Apart'; 'Lake submerges wood: Preponderance of the Great'; 'Thunder in heaven: Great Power'; 'Brightness emerges over the earth: Progress'; 'Wind issues from fire: The Family (Jiā Rén)'; 'Lake rises above heaven: Breakthrough'; 'Lake rises above the earth: Gathering'; 'Wind moves over water: Dispersion'; 'Water over fire: After Completion'; 'Fire over water: Before Completion.'

These fifteen name the upper image first.

Twelve others name the lower image first: 'Water on the earth: Holding Together'; 'Earth above the lake: Approach'; 'Lake on the mountain: Influence (Xián)'; 'Fire on the mountain: The Wanderer'; 'Water on wood: The Well'; 'Fire on wood: The Cauldron'; 'Wood on the mountain: Development'; 'Thunder over the lake: The Marrying Maiden'; 'Water on the mountain: Obstacle'; 'Water over the lake: Limitation'; 'Wind over the lake: Inner Truth'; 'Thunder on the mountain: Preponderance of the Small.'

Thirteen mention the upper body first to derive the lower: 'A spring issues beneath the mountain: Youthful Folly'; 'Water within the earth: The Army'; 'Wind beneath the mountain: Decay'; 'Fire beneath the mountain: Grace'; 'Thunder moves under heaven: Innocence'; 'Thunder beneath the mountain: Nourishment'; 'Mountain beneath heaven: Retreat (Dùn)'; 'Lake beneath the mountain: Decrease'; 'Wind beneath heaven: Coming to Meet'; 'Mountain within the earth: Modesty'; 'Thunder within the lake: Following'; 'Wood grows from the earth: Pushing Upward'; 'Fire within the lake: Revolution.'

In these, when heaven or mountain is the upper body, it says 'beneath'; when earth or lake is upper, it says 'within.'

Four hexagrams name the lower image as being beneath the upper: 'Thunder in the earth: Return'; 'Heaven within the mountain: The Taming Power of the Great (Dà Xù)'; 'Brightness enters the earth: Darkening of the Light (Míng Yí)'; 'A lake without water: Oppression.'

These categories outline general rules, whose specifics are discussed under each hexagram.

Earlier scholars noted that image texts contain real images and figurative images: real images, such as 'water on the earth' or 'wood growing from the earth,' describe actual phenomena; figurative images, such as 'heaven within the mountain' or 'wind issuing from fire,' have no literal reality but represent ideas.

Both convey meaning and are called 'Images.' 'The movement of heaven is full of vigor' reflects heaven's natural image. 'The gentleman strengthens himself without ceasing' applies this to human affairs: the gentleman utilizes this hexagram's image to exert himself untiringly.

'Gentleman' denotes one who presides over others and cherishes the common people, encompassing the Son of Heaven, feudal lords, and nobles with estates. Those of higher rank emulate more of the hexagram's scope; those of lower rank emulate less, each acting according to ability.

Where the meaning applies strictly to the sovereign, the text says 'the former kings,' as in Holding Together, Enthusiasm, Contemplation, Biting Through, Return, Innocence, and Dispersion.

In Peace and Coming to Meet, it says 'the ruler' (hòu), encompassing both sovereign and lords. Otherwise, all hexagrams refer to 'the gentleman.'

From 'The Wenyan says' to 'Qián: supreme success, beneficial through perseverance.' Sub-commentary: The Wenyan is the Master's seventh wing.

Because Qián and Kūn are the gateway to the Changes, and all other hexagrams and lines issue from them, their principles are profound; hence the Wenyan was composed to explain them.

Master Zhuang said: 'Wen means ornamentation; because the virtues of Qián and Kūn are vast, they are specially adorned, hence called Wenyan.'

We hold that the Master was clarifying the Dao of the Changes and elaborating its principles rather than producing flowery ornament; it explains the canon text (jīngwén) of the two hexagrams, hence 'Wenyan.'

From here to 'supreme success, beneficial through perseverance' explains the four virtues of Qián as the first section; from 'Nine at the Beginning says: hidden dragon, do not act' to 'action brings regret' explains the six lines as the second section; from 'hidden dragon, do not act' to 'the world is governed' discusses human affairs in the six lines as the third section; from 'hidden dragon, do not act: the Yang qi is concealed and submerged' to 'here one sees the law of Heaven' discusses natural qi as the fourth section; from 'The Qián Yuan is that which begins and penetrates' to 'bringing peace to the world' re-examines the four virtues of Qián Yuan as the fifth section; from 'The gentleman takes perfected virtue as his practice' to 'is it not only the Sage?'

broadens the meaning of the six lines as the sixth section. We explain each according to the text. This first section discusses the four virtues of Qián. 'Yuan is the head of all virtues': Qián is the function of Heaven.

The cyclical changes of Heaven and Earth occur naturally, arising from non-being into being, acting spontaneously without conscious effort. Heaven has no mind to invent the virtues or names of 'Yuan, Heng, Li, Zhen.'

The Sage matched them with human affairs, designating this natural work as Heaven's four virtues to provide a model for subsequent sages.

Master Zhuang says: 'Yuan is the head of all virtues because Heaven's nature generates and nourishes all things; of all goods, giving life is greatest, and Yuan is the source of giving life.

Heng is the gathering of beauties: Heaven brings unhindered growth to all things, gathering all that is fine. Li is the harmony of righteousness: Heaven benefits all things so that each attains its fitting place in harmony.

Zhen is the trunk of affairs: Heaven uses central, correct qi to bring all things to fulfillment.'

Zhuang correlates these four virtues with the four seasons: Yuan corresponds to Spring and benevolence; Heng corresponds to Summer and propriety; Li corresponds to Autumn and righteousness; Zhen corresponds to Winter and wisdom/faith.

Among the Five Elements, Earth is omitted because Earth governs all four seasons equally, and without Earth the four seasonal qi cannot be sustained.

'The gentleman embodies benevolence, which suffices to preside over people': from here on, humanity models itself on these four virtues. Embodying benevolence models Heaven's Yuan. 'Auspicious assembly suffices to accord with propriety' models Heaven's Heng.

'Benefiting things suffices to harmonize righteousness' models Heaven's Li. 'Steadfast correctness suffices to manage affairs' models Heaven's Zhen. In state affairs, Yuan is benevolence, Heng is propriety, Li is righteousness, and Zhen is good faith.

Wisdom is omitted because practicing these four inherently relies on knowledge. 'The gentleman practices these four virtues; hence it is said: Qián: supreme success, beneficial through perseverance.'

Sages realize these virtues to the utmost, while gentlemen practice them according to their capacities. Because the Qián Gua symbolizes Heaven, these four virtues are all heavenly virtues.

When Yin and Yang unite, both images interact and possess virtues; thus other hexagrams also possess these four virtues, though none match Qián in completeness. Qián simply states the four virtues without qualification, showing that it encompasses everything.

Other hexagrams add specific conditions due to their narrower scope, as in The Receptive (Earth) or Revolution (where 'On the day of oneself there is belief; supreme success, beneficial through perseverance; regret vanishes').

Seven hexagrams possess all four virtues: The Creative (Heaven), The Receptive (Earth), Difficulty at the Beginning, Approach, Following, Innocence, and Revolution.

Six hexagrams possess three virtues: The Clinging, Influence, Gathering, The Joyous, Dispersion, and Preponderance of the Small.

Seven hexagrams possess two virtues: Possession in Great Measure, Decay, Development, The Taming Power of the Great, Pushing Upward, Oppression, and Inner Truth.

Fifteen hexagrams possess one virtue (Heng): Youthful Folly, The Army, Small Taming, Treading, Peace, Modesty, Biting Through, Grace, Return, Preponderance of the Great, The Arousing, Abundance, Limitation, After Completion, and Before Completion.

Eleven hexagrams mention no virtues: Enthusiasm, Contemplation, Splitting Apart, Progress, Obstacle, Deliverance, Breakthrough, Coming to Meet, The Well, Keeping Still, and The Marrying Maiden.

In general, inauspicious hexagrams like Splitting Apart, Obstacle, Breakthrough, and Coming to Meet lack virtues, while some auspicious ones like Progress and Deliverance also lack stated virtues.

In the four virtues, Heng and Zhen often stand independently, whereas Yuan and Li are frequently paired with specific affairs (such as 'beneficial to cross the great stream' or 'beneficial to see the great man').

These virtues appear not only under hexagrams but also under line statements.