Chapter 3: Theoretical Foundations

Although the principle-and-qi schools are mutually exclusive of one another, they draw on a shared "parts bin": yin-yang and the Five Phases, the River Chart and Luo Writing, the Earlier and Later Heaven trigrams, the stems and branches with na-yin and na-jia, the Twenty-Four Mountains, the Three Cycles and Nine Periods, and the Nine Stars. This chapter takes these shared components apart one by one. Readers already familiar with fate calculation or Yijing scholarship may read this chapter quickly, but should pay attention to the note at the end of each section on "how this component is used differently across the various schools"—the very same component, installed in a different machine, can serve an entirely different function, and this is precisely the technical root of the schools' disagreements.

3.1 The Discourse on Qi, and Yin-Yang and the Five Phases

Qi is the ontological premise of the entire body of fengshui doctrine. The "living qi" in the Zangshu's statement "in burial, one rides upon the living qi" refers to an energetic state of being that circulates between Heaven and Earth and is capable of nurturing and sheltering the ten thousand things. The principle-and-qi school's basic assumptions about qi are: qi is formless yet has attributes—it cannot be seen, yet it carries the properties of yin-yang and the Five Phases; qi has position—it is distributed unevenly across space according to direction; and qi has timing—its waxing and waning cycle with time. The goal of fengshui practice is to have a human dwelling (or burial site) take in qi of the correct nature, at the correct time, facing the correct direction.

Yin-yang is the most basic binary system for assigning attributes. Almost every symbol within the principle-and-qi school must first be sorted into yin or yang: the stems and branches have their yin-yang, the trigrams and their lines have their yin-yang, the Twenty-Four Mountains have their yin-yang—and, crucially, different schools assign yin and yang to the very same symbol differently. Take, for instance, the direction "zi": within the pure-yin-pure-yang system it belongs to yang (the Kan trigram takes in gui, shen, zi, and chen, and Kan occupies one of the four cardinal positions of the Earlier Heaven arrangement, hence yang); yet within the Three-Cycles-dragon system of Xuankong Flying Star it belongs to yin (the branches at the four cardinal points of the Heaven-Cycle dragons are yin). Whether the star-shifting method flies forward or backward, and which path the gua-flipping method takes as its starting point, both hinge entirely on this assignment of yin and yang—so differences in how yin-yang is assigned directly cause the various schools' star charts to differ. When reading a principle-and-qi text and encountering the characters for "yin" and "yang," one must always first ask: which system of yin-yang is this$10

The Five Phases (metal, wood, water, fire, earth) carry the work of characterizing properties and of reasoning about generation and overcoming. Generation: wood generates fire, fire generates earth, earth generates metal, metal generates water, water generates wood. Overcoming: wood overcomes earth, earth overcomes water, water overcomes fire, fire overcomes metal, metal overcomes wood. The principle-and-qi school uses the Five Phases for two purposes: first, to assign properties to directions (east is wood, south is fire, west is metal, north is water, with the four intercardinal directions and the center belonging to earth in the standard assignment—alongside several variant systems such as double-mountain Five Phases, Hongfan Five Phases, and lodge-degree Five Phases); second, to argue for the fortune or misfortune of a relationship through generation and overcoming (that which generates me is auspicious and that which overcomes me is inauspicious is the most common rule, as in the sand-adjusting method, though there are also finer refinements in which that which I overcome represents wealth and that which drains me is inauspicious—detailed in Chapters Four and Six). It likewise bears noting that there is more than one set of Five Phases. Laid out side by side on the compass are the standard Five Phases, the double-mountain Sanhe Five Phases, the trigram Five Phases, the Xuankong Five Phases, the lodge-degree Five Phases, and more, each with its own dedicated use; the Sanhe school uses the double-mountain Five Phases to derive the Stage of Birth, the sand-adjusting method uses the lodge-degree Five Phases, and the Eight Mansions school uses the trigram Five Phases to argue the overcoming relations of the Roaming-Year stars—use the wrong set, and the whole chart goes wrong. This situation of "multiple sets of Five Phases coexisting" is the direct reason the compass carries so many layers.

3.2 The River Chart and the Luo Writing

The River Chart and Luo Writing are the numerological wellspring of the principle-and-qi school. Legend holds that in the time of Fuxi a dragon-horse emerged from the Yellow River bearing the Chart, and a divine tortoise emerged from the Luo River bearing the Writing; in fact, these two numerical diagrams were only given their fixed canonical form in Song-dynasty Yijing scholarship (Zhu Xi places the diagrams at the head of his Zhouyi Benyi), though their numerical content (the numbers of Heaven and Earth, the numbers of the Nine Palaces) is already fully articulated in Han-dynasty sources.

The River Chart matches the numbers one through ten to the five directions: one and six occupy the north and belong to water; two and seven occupy the south and belong to fire; three and eight occupy the east and belong to wood; four and nine occupy the west and belong to metal; five and ten occupy the center and belong to earth. Its essential principle is "generation and completion": one is water's generating number and six is water's completing number, hence "one and six share the same ancestor"; likewise, two and seven follow the same path, three and eight are companions, four and nine are friends, and five and ten travel the same road. The principle-and-qi school draws on the River Chart mainly for this matched pairing of generation and completion: the Xuankong school, in discussing star combinations, treats one-six sharing a palace, two-seven sharing a palace, three-eight sharing a palace, and four-nine sharing a palace as all auspicious under the rubric of "matched generation and completion"; and the Xuankong Great Gua school treats the matched generation and completion of trigrams as especially central to its doctrine.

The Luo Writing distributes the numbers one through nine across the Nine Palaces: "nine crowns the head, one is underfoot; three on the left, seven on the right; two and four form the shoulders, six and eight form the feet, and five occupies the center." That is: north is one, south is nine, east is three, west is seven, northeast is eight, southwest is two, southeast is four, northwest is six, and the center is five. The sum of any row, column, or diagonal in the Luo Writing is fifteen—it is a third-order magic square. The importance of the Luo Writing can hardly be overstated: it constitutes the entire kinematics of Xuankong Flying Star. What is called "flying stars" is precisely the sequential placement of the nine numbers into the Nine Palaces along the Luo Writing's fixed trajectory (center → northwest → west → northeast → south → north → southwest → east → southeast); flying forward increases the numbers in sequence, flying backward decreases them. Matching the Luo Writing to the Later Heaven trigrams (Kan-one, Kun-two, Zhen-three, Xun-four, center-five, Qian-six, Dui-seven, Gen-eight, Li-nine) yields the "New Year's Chart" (yuandan pan)—the coordinate origin of the entire Xuankong system. In addition, pairs of numbers summing to ten—"he shi" (matched to ten): one-nine, two-eight, three-seven, four-six—are also an important criterion of auspiciousness within Xuankong doctrine.

The numerological application of the Luo Writing's Nine Palaces long predates the Song-dynasty canonization of the diagram-study tradition: the "Mingtang" chapter of the Han-dynasty Da Dai Liji already records the numbers "two-nine-four, seven-five-three, six-one-eight" for the nine chambers of the Bright Hall, and the path by which "Taiyi descends through the Nine Palaces" (proceeding in sequence from Palace One through Palace Nine), found in the apocryphal weft-texts and in the cosmic-board methods, is precisely the prototype for the later flying-star trajectory—what is called "flying stars" is, in fact, flying along the very route that the Han-dynasty deity Taiyi was said to patrol through the Nine Palaces. Recognizing this layer lets one understand why the Xuankong school claims its method "is rooted in the Luo Writing and transmitted from the pre-Qin era": as far as the numerical diagram itself is concerned, this claim is not wholly baseless, but taking a Han-dynasty theological patrol route and putting it to use as a Qing-dynasty algorithm for calculating a house's fortune involves a two-thousand-year semantic transposition—itself yet another instance of the accretive character of principle-and-qi knowledge.

3.3 The Earlier Heaven and Later Heaven Trigrams

The Eight Trigrams have two distinct spatial arrangements, serving sharply different functions.

The Earlier Heaven trigrams (the Fuxi trigrams) are arranged: Qian-south, Kun-north, Li-east, Kan-west, Zhen-northeast, Xun-southwest, Gen-northwest, Dui-southeast. This sequence derives from the "Explaining the Trigrams" commentary: "Heaven and Earth fix their positions; mountain and marsh interchange their qi; thunder and wind stir each other; water and fire do not shoot one another"—Qian and Kun, Gen and Dui, Zhen and Xun, Kan and Li are each paired as opposites, forming a highly symmetrical structural diagram. The principle-and-qi school treats the Earlier Heaven arrangement as "substance" (ti): the yin-yang assignment of the pure-yin-pure-yang system is fixed according to the Earlier Heaven trigram positions (Qian, Kun, Kan, and Li, occupying the four cardinal points, are yang; Zhen, Xun, Gen, and Dui, occupying the four intercardinal points, are yin); the sixty-four-hexagram circular diagram of Xuankong Great Gua is arranged according to the Earlier Heaven trigram sequence; and Qiankun Guobao's water methods based on "Earlier Heaven positions" take the Earlier Heaven trigram positions as their standard.

The Later Heaven trigrams (the King Wen trigrams) are arranged: Kan-north, Li-south, Zhen-east, Dui-west, Qian-northwest, Kun-southwest, Gen-northeast, Xun-southeast. This sequence derives from the "Explaining the Trigrams" commentary's passage "the Sovereign issues forth from Zhen, is made uniform in Xun, comes into mutual view in Li..." which describes the sequence in which the four seasons circulate. The principle-and-qi school treats the Later Heaven arrangement as "function" (yong): the compass's eight-palace division, the palace assignment of the Twenty-Four Mountains, the trigram positions of the Luo Writing's Nine Palaces, the Eight Mansions school's calculation of the Roaming Years, and Jinsuo Yuguan's eight-directional sand and water—all of these are built upon the Later Heaven trigram positions.

"Earlier Heaven as substance, Later Heaven as function" is a standing principle across the principle-and-qi school, but the conversion and intermixing of the two sets of trigram positions has also generated a great deal of both genuine subtlety and outright confusion—the very same northwest direction is Qian in the Later Heaven arrangement but Gen in the Earlier Heaven arrangement; one school takes the one, another school takes the other, and their conclusions naturally end up pointing in opposite directions. Whenever one reads any principle-and-qi text and encounters the name of a trigram, the first thing to confirm is: is this referring to the Earlier Heaven position or the Later Heaven position$1

3.4 The Heavenly Stems and Earthly Branches, Na-Yin, and Na-Jia

The Ten Heavenly Stems (jia, yi, bing, ding, wu, ji, geng, xin, ren, gui) and the Twelve Earthly Branches (zi, chou, yin, mao, chen, si, wu, wei, shen, you, xu, hai) form the common code shared across Chinese numerological arts. Their assignment to the Five Phases: jia, yi, yin, and mao belong to wood; bing, ding, si, and wu belong to fire; wu, ji, chen, xu, chou, and wei belong to earth; geng, xin, shen, and you belong to metal; ren, gui, hai, and zi belong to water; odd positions are yang and even positions are yin. Within the principle-and-qi school, the stems and branches carry three functions: first, marking direction—the eight stems, the twelve branches, and the four intercardinal trigrams together make up the Twenty-Four Mountains (detailed in the next section); second, marking time—the sixty-term ganzhi cycle is the basis for calculating the cyclical periods; third, linking to the individual's fate—both the immortal's fate (the stem-and-branch of the deceased's birth year) matched to the burial mountain, and the life-gua derived from the birth year, use the stems and branches as their bridge.

Na-yin is another system for assigning the Five Phases to the sixty-term ganzhi cycle (jiazi and yichou are "gold within the sea," bingyin and dingmao are "fire within the furnace," and so on), grouping every two stem-branch pairs into a set of thirty tones in all. Within the principle-and-qi school, na-yin is used mainly for fen jin ("parting the gold," where each of the one hundred twenty subdivisions has its own na-yin Five Phase, chosen so as to harmonize favorably with the burial mountain and the immortal's fate) and for date selection—it is a tool belonging to the finer-grained, refinement stage of the work.

Na-jia is the system that assigns the ten heavenly stems to the eight trigrams, originating in the Han-dynasty Yijing scholarship of Jing Fang: Qian takes in jia and ren, Kun takes in yi and gui, Zhen takes in geng, Xun takes in xin, Kan takes in wu, Li takes in ji, Gen takes in bing, and Dui takes in ding (the "moon-phase na-jia" theory explains this assignment by matching the trigram images to the phases of the moon). On this basis, the kanyu masters further sorted the twelve branches into the trigrams by the sanhe (three-harmony) groupings: Kan takes in gui together with shen, zi, and chen; Li takes in ren together with yin, wu, and xu; Zhen takes in geng together with hai, mao, and wei; Dui takes in ding together with si, you, and chou. In this way all twenty-four mountains can be assigned to the eight trigrams—this system of "kanyu na-jia" is the cornerstone of the pure-yin-pure-yang method and of the auxiliary-star gua-flipping water method (detailed in Chapter Nine). Note that it diverges slightly from Jing Fang's original version (ren is assigned to Li, gui to Kan)—this is a specialized adaptation made by the kanyu masters themselves.

3.5 The Composition of the Twenty-Four Mountains and Their Assignment to Yin and Yang

The Twenty-Four Mountains form the principle-and-qi school's standard directional coordinate system: the compass's three hundred sixty degrees are divided equally into twenty-four sectors of fifteen degrees each. Their composition is "twelve branches plus eight stems plus the four intercardinal trigrams": the twelve earthly branches occupy twelve sectors; of the ten heavenly stems, wu and ji belong to the central earth and are not used to mark direction, so the remaining eight stems occupy eight sectors; and the four intercardinal points are filled out with the four trigram names Qian, Kun, Gen, and Xun, bringing the total to twenty-four. The arrangement is as follows (organized by the eight palaces of the Later Heaven arrangement, each palace governing three mountains, with the middle mountain sitting at the palace's exact center):

(Degrees are measured clockwise from due north at 0°; the center of the Zi mountain is exactly 0°, and the center of the Wu mountain is exactly 180°.)

The assignment of yin and yang to the Twenty-Four Mountains is the focal point of disagreement among the schools; there are two main parallel systems in use:

Pure yin and pure yang (used by the Sanhe and gua-flipping systems): assigned according to na-jia matched to the Earlier Heaven trigram positions. Qian, Kun, Kan, and Li, occupying the four cardinal points of the Earlier Heaven arrangement, are yang, and the mountains they take in are pure yang—the twelve mountains Qian, Jia, Kun, Yi, Zi, Gui, Shen, Chen, Wu, Ren, Yin, and Xu. Zhen, Xun, Gen, and Dui, occupying the four intercardinal points of the Earlier Heaven arrangement, are yin, and the mountains they take in are pure yin—the twelve mountains Mao, Geng, Hai, Wei, You, Ding, Si, Chou, Gen, Bing, Xun, and Xin. The operative principle of pure yin and pure yang is "yin and yang must not be mixed": a yin dragon should be set to a yin facing and take in yin water, while a yang dragon should be set to a yang facing and take in yang water.

The Three-Cycles dragons (used by the Xuankong Flying Star system): each palace's three mountains are divided into the Heaven, Earth, and Human cycles. The middle mountain—together with the branches at the four cardinal points and the trigrams at the four intercardinal points—forms the Heaven-Cycle dragons (zi, wu, mao, you; qian, kun, gen, xun); the mountain to the counterclockwise side forms the Earth-Cycle dragons (jia, geng, bing, ren; chen, xu, chou, wei); and the mountain to the clockwise side forms the Human-Cycle dragons (yi, xin, ding, gui; yin, shen, si, hai). Their yin-yang: within the Heaven-Cycle dragons, the four cardinal branches (zi, wu, mao, you) are yin and the four intercardinal trigrams (qian, kun, gen, xun) are yang; within the Earth-Cycle dragons, the four stems (jia, geng, bing, ren) are yang and the four "tomb" branches (chen, xu, chou, wei) are yin; within the Human-Cycle dragons, the four stems (yi, xin, ding, gui) are yin and the four "birth" branches (yin, shen, si, hai) are yang. It is from this assignment that the forward or backward direction of the Xuankong chart's star-flying is determined (detailed in Chapter Seven).

The two systems of yin-yang share the same names but not the same substance, and are mutually incompatible. A considerable part of the chaos of "each school insists it alone is right" within the principle-and-qi tradition stems from the coexistence of these two systems of yin-yang assignment (and further systems besides).

3.6 The Three Cycles and Nine Periods: The Principle-and-Qi School's Temporal Coordinate System

The Three Cycles and Nine Periods (sanyuan jiuyun) is the standard framework by which the principle-and-qi school—chiefly the Three-Cycles Xuankong lineage—handles time. A great cycle of one hundred eighty years is called "the Three Cycles": the Upper, Middle, and Lower Cycles each span sixty years (one full ganzhi cycle); each Cycle is divided into three Periods of twenty years apiece, matched to the nine numbers of the Luo Writing—Periods One, Two, and Three belong to the Upper Cycle; Periods Four, Five, and Six to the Middle Cycle; and Periods Seven, Eight, and Nine to the Lower Cycle. In each Period, the star currently on duty is the "commanding star" (the qi presently in power); a Period that has already passed is in decline and moribund, while a Period yet to come is nascent and advancing.

The Gregorian start and end dates of the recent and current Periods (following the commonly accepted reckoning, tracing back to the jiazi year of 1864 as the start of Period One of the Upper Cycle):

It should be noted that the calculation of the start of a Period is not entirely free of controversy: schools differ on whether the year of the change of Period is bounded by the first day of the lunar new year, by the Beginning of Spring solar term, or by the winter solstice; a few individual schools also hold differing views on the starting point of the Three-Cycles ganzhi count itself. In practical use, one must always first check which convention a given lineage follows. This article, throughout, follows the commonly accepted convention: at present (2026), we are in Period Nine of the Lower Cycle.

Beyond the Three Cycles and Nine Periods, schools such as Xuankong Great Gua and Xuankong Liu Fa adopt the Two Cycles and Eight Periods (eryuan bayun) system instead: the one hundred eighty years are divided into an Upper and a Lower Cycle, with each of the eight trigrams governing one Period; the number of years in each Period is calculated from the lines of its trigram—a yang line counting nine years and a yin line counting six years—for a combined total across the eight trigrams of one hundred eighty years. The two systems of Periods disagree on the determination of "which Period we are currently in" (for instance, under the Two Cycles and Eight Periods system, the starting year reckoned for "Period Nine" differs from that of the Three Cycles and Nine Periods system)—and this is yet another technical source of the divergence in conclusions among the schools.

The philosophical underpinning of the doctrine of cyclical periods is a cyclical view of history built on "the fortune of the Three Cycles' qi": there is no principle by which qi remains unchanged for a hundred years, and no configuration of land that is permanently auspicious. It brings two distinctive corollaries to the principle-and-qi school: first, fengshui requires "renovation"—a house's fortune shifts along with the cyclical periods, hence there are methods for "changing the heavenly heart" or altering a gate's facing in order to catch a new Period's favor; second, the fengshui master's business is never in danger of running dry—a remark half in jest, and half a genuine sociological fact.

The doctrine of cyclical periods has also given rise to a layer of popular discourse visible everywhere today: each Period "sets the tone" for its full twenty years according to the trigram and Five-Phase attributes of its commanding star. The commanding star of Period Eight (2004–2023), Eight White, belongs to Gen-earth, which practitioners dubbed the "earth period," associated by extension with the boom in real estate; the commanding star of Period Nine (2024–2043), Nine Purple, belongs to Li-fire, and so "the Li-fire period" has become a buzzword on the Chinese internet in recent years, with energy, culture, "middle-aged women" (a category derived from the Li trigram's human associations), and much else besides all swept up in the association. This kind of "fortune narrative" does have a legitimate place within the traditional literature (the Shenshi Xuankong Xue itself discusses the worldly conditions associated with each Period), but contemporary media has stripped it out of its original house-siting context and amplified it into a general-purpose divination of the era at large—readers would do well to know both its origin and its original, limited place within the system it came from.

Another practical concept derived from the doctrine of cyclical periods is the calculation and renewal of a house's Period. Which Period does a given house belong to$2 The common convention takes the Period in force at the time the house was completed (or underwent a major renovation with "changing the heavenly heart," or was moved into) as the standard, but three positions coexist: those who hold to "completion" take the topping-out of construction as the boundary; those who hold to "changing the heavenly heart" take the re-tiling and renovation exposing the central palace to the sky as the boundary; and those who hold to "moving in" take the arrival of human qi into the house as the boundary. The very same building, topped out in 2023 and occupied in 2024, yields two different star charts under these three positions. Around the boundary of a Period (such as the turn from 2023 to 2024), the professional trade has traditionally seen brisk activity: breaking ground or moving in right around the change of Period, so as to "seize the Period," is a genuinely observed pattern of behavior in Xuankong practice. In this way, the model's own temporal markers end up, in reverse, shaping the rhythm of human behavior—this is perhaps the most sociologically interesting scene produced by the principle-and-qi school's "temporal dimension."

3.7 The Origins of the Nine-Star System: One Set of Star Names, Many Different Faces

The Nine Stars refers to the system of star names comprising the seven stars of the Northern Dipper (Greedy Wolf, Giant Gate, Salary Preserver, Literary Fortune, Chastity Fault, Military Fortune, and Poison Army), plus the two stars Assistant and Forerunner. This set of star names is among the most frequently used—and most easily confused—symbols in the principle-and-qi school, because at least four mutually distinct systems all share these same nine names:

1. The Form School's Nine-Star landforms: the nine star names are used to describe the shapes of mountain peaks (Greedy Wolf, straight and tapering like a bamboo shoot; Giant Gate, square and upright like a screen; Poison Army, broken and jagged like a tattered banner...), as seen in the Canglong Jing. This has nothing to do with principle-and-qi, but shares the same origin for its star names.
2. The Eight Mansions school's Roaming-Year stars: the eight stars Life Qi (Greedy Wolf), Heavenly Physician (Giant Gate), Prolonged Life (Military Fortune), Reclining Position (Assistant/Forerunner), Death Cutoff (Poison Army), Five Ghosts (Chastity Fault), Six Killings (Literary Fortune), and Calamity Harm (Salary Preserver), distributed across the eight palaces according to the Great Roaming Years formula (detailed in Chapter Five).
3. Xuankong Flying Star: One White Greedy Wolf (Kan-water), Two Black Giant Gate (Kun-earth), Three Green Salary Preserver (Zhen-wood), Four Emerald Literary Fortune (Xun-wood), Five Yellow Chastity Fault (center-earth), Six White Military Fortune (Qian-metal), Seven Red Poison Army (Dui-metal), Eight White Left Assistant (Gen-earth), and Nine Purple Right Forerunner (Li-fire)—here the numbers form the substance, the stars provide the names, and the trigrams supply the properties, flying through the Nine Palaces according to the cyclical Period (detailed in Chapter Seven). The annual and monthly Nine Stars used in Purple-White date selection share this same origin.
4. The gua-flipping Nine-Star water method: Assistant-Forerunner, Military Fortune, Poison Army, Chastity Fault, Greedy Wolf, Giant Gate, Salary Preserver, and Literary Fortune are distributed across the eight directions according to the gua-flipping palm-method, and the auspiciousness of taking in water is judged by na-jia pure-yin-pure-yang doctrine (detailed in Chapter Nine).

Across these four systems, the broad pattern that Greedy Wolf, Giant Gate, Military Fortune, and Assistant/Forerunner are (in most systems) auspicious while Poison Army, Chastity Fault, Salary Preserver, and Literary Fortune are inauspicious holds roughly true, but the logic by which they are distributed is entirely different in each case. Whenever one reads a principle-and-qi text and encounters "Greedy Wolf" or "Giant Gate," one must first determine which of these faces is meant—this is the single most important key to avoiding confusion as a beginner.

The origin of the Nine Stars' names lies in the worship of the Northern Dipper. The notion that the seven stars of the Northern Dipper govern life, death, and fortune is already prominent in pre-Qin and Han-dynasty sources (the Dipper as the Sovereign's chariot, turning at the center and overseeing the four directions); Daoism inherited this notion, incorporating the seven stars together with the Assistant and Forerunner stars into its belief in star-lords and its rites of exorcism and appeal, and the names Greedy Wolf, Giant Gate, Salary Preserver, and the rest took their fixed form in Daoist astro-fate literature of the Tang-Song period (the Beidou Jing system), spreading from there, via fate-calculation arts (the same set of star names is also used, for instance, by the later system of Zi Wei Dou Shu), into a shared public resource of the numerological arts. What the principle-and-qi school valued in borrowing this set of star names was precisely the inherent sanctity and the ready-made character of fortune or misfortune that came attached to them—once a star's name is spoken, its fortune or misfortune is self-evident, requiring no further argument. Viewed from the standpoint of a knowledge-archaeology, the Nine Stars are the component of the principle-and-qi school in which its religious genetic material is most plainly visible: every "flying of the stars" on the compass traces back, in its distant origin, to that very dipper in the heavens that people of the Han dynasty once looked up to see.

With this, the inventory of the parts bin is complete. The next chapter will first examine the physical vessel that carries these components—the compass—before we move on into the inner workings of the individual schools.