Liber de Octo Mutationibus

The Book of the Eight Changes:
Universal Cycles and the Trigrams

(c) 1995, John Opsopaus


Whenever two opposed forces act upon a thing (unless that thing happens to be at the place where the forces are exactly balanced), the thing will oscillate between the extremes (as does a pendulum or weight on a spring). Such cycles between opposites are everywhere in the world, from the wheel of the year to the alchemical rotation of elements to processes of growth and decline. Chapter I explains the eight phases of any such cycle, including its shifting balances of state and energy. This eightfold structure is based on mathematical principles, though the presentation here is nonmathematical. Chapter 2 relates these eight phases of cyclic change to the trigrams of the I Ching in the sequence of the Earlier Heaven. As Heraclitus said,

Opposition is fitting, and from differences comes the most
beautiful harmony, and all things come to be through strife.

Caput I: De octo vicibus

Concerning the Eight Exchanges

i. We consider cyclic processes, which unite dualities by bringing each extreme to its polar opposite.

ij. We call the opposites High and Low, though they may be any distinguished pair: Firm-Yielding, Light-Dark, Active-Passive, Male-Female, etc.

iij. The extremes mark two distinguished points in the cycle, which we call H and L (for High and Low).

iv. There are two paths in the cycle, the Ascending path from Low to High, and the Descending path from High to Low.

v. We consider here only non-retrograde motions, i.e., once started in a direction, they go to the extreme in that direction before reversing. There is no Ascending in the Descending path, and no Descending in the Ascending path. (The motions are pure.)

vi. There is a point of Equilibrium between the High and the Low; we call it B = Balance (or E = Equilibrium).

vij. In each path there is a place of equilibrium where the balance shifts.

viij. The Ascending Equilibrium, called A, is where the balance shifts from Low to High.

ix. The Descending Equilibrium, called D, is where the balance shifts from High to Low.

x. High, Low and the Ascending and Descending equilibria mark four distinguished points in the cycle (L, A, H, D).

xi. In passing from Ascent to Descent, the process must pause, at least momentarily, at the High point, and in passing from Descent to Ascent, the process must pause, at least momentarily, at the Low point.

xij. The extremes are thus states, or points of stasis, between the opposed processes.

xiij. So also the Ascending and Descending points are pure process in equilibrium between the two extremes.

xiv. The extremes H and L are pure state; the equilibria A and D are pure process. These four points correspond to pure being and pure becoming, respectively; all other points in the cycle are mixtures of state and process (being and becoming).

xv. The possible mixtures are AL = Ascending from Low, AH = Ascending to High, DH = Descending from High, DL = Descending to Low.

xvi. Each cycle has at least one natural notion of "energy" (though it may be hidden and hard to discover), which is conserved (neither created nor destroyed).

xvij. This energy is of two kinds: energy of state (location) and energy of process (motion), which are converted into each other. (Energy is the medium of exchange between being and becoming.)

xviij. Energy of state has its origin in the tension inherent in the polarity between the extremes. (In physical systems, this is potential energy.)

xx. Energy of process measures the vehemence of the transformation between the extremes. (In physical systems, this is kinetic energy.)

xxi. Since there is no motion at the extremes, there is no process energy at H and L, and all the energy is invested in the state.

xxij. At the equilibrium points the extremes are in balance, so there is no energy of state at A and D. Therefore, all the system's energy is in the process, and thus the process energy is at its greatest at the equilibria.

xxiij. Since all the energy is in the state at the extremes and in the process at the equilibria, in each quarter of the cycle there must be at least one point where the process and state energies are in balance.

xxiv. We shall restrict our attention to processes that are non-retrograde in this transfer of energy, so that there is only one such balance point in each quadrant.

xxv. There are thus four points where the state and process energy are balanced, which are called L=A, A=H, H=D and D=L.

xxvi. Thus there are eight distinguished points in the cycle: L, L=A, A, A=H, H, H=D, D, D=L.

xxvij. These eight points define eight segments in the cyclic path, which are eight phases in any cycle.

xxviij. The octants adjacent to the extremes are dominated by state and are comparatively static.

xxix. The octants adjacent to the equilibria are dominated by process and are relatively dynamic.

xxx. The octants are named by their dominant character (Low, Ascending, High, Descending) and their subdominant character. In the cycle from Low to High and back, they are LA, AL, AH, HA, HD, DH, DL, LD.

xxxi. The High state dominates HA and HD; the Low state dominates LA and LD.

xxxij. The Ascending process dominates AH and AL; the Descending process dominates DH and DL.

xxxiij. Nevertheless, all the octants of the cycle comprise both state and process (being and becoming), though the quality and quantity of each varies.

finis capitis I

Caput II: Clavis illius libri vicis

The Key to The Book of Change

i. In the High quadrant, comprising octants HA and HD, the High state is dominant. This corresponds to pure yang, represented by a digram with two firm lines: || [drawn from left to right rather than from bottom to top]. This part of the cycle is called Complete (or Culminating or Climaxing) Yang.

ij. In the Low quadrant, comprising octants LA and LD, the Low state dominates. This corresponds to pure yin, represented by the digram with two yielding lines: ::. This is called Complete (or Culminating or Climaxing) Yin.

iij. In the Ascending quadrant, comprising the octants AL and AH, the Ascending process dominates. It is yang because ascending, but has an admixture of the yin, which gives it motion, so it is represented by the digram |:, which is called Incipient Yang (or Lesser Yin).

iv. In the Descending quadrant, comprising the octants DL and DH, the Descending process dominates. It is yin because descending, but has an admixture of yang, which gives it tension, and therefore motion, so it is represented by the digram :|, which is Incipient Yin (or Lesser Yang).

v. In octant AL the Ascending process (|:) dominates, but is tempered by, the Low state (::), so the Incipient Yang digram (|:) is modified by the upper line of the Complete Yin digram (::), to yield the trigram |::, called "Thunder."

vi. In octant AH, Ascending (|:) is tempered by the High State (||); thus |: is modified by the upper line of :: to yield |::, "Fire."

vij. In octant HA, High (||) is tempered by Ascending (|:) to yield ||:, "Lake."

viij. In octant HD, High (||) is tempered by Descending (:|) to yield |||, "Heaven."

ix. In octant DH, Descending (:|) is tempered by High (||) to yield :||, "Wind."

x. In octant DL, Descending (:|) is tempered by Low (::) to yield :|:, "Water."

xi. In octant LD, Low (::) is tempered by Descending (:|) to yield ::|, "Mountain."

xij. In octant LA, Low (::) is tempered by Ascending (|:) to yield :::, "Earth."

xiij. This is the sequence of trigrams attributed to Fu Hsi, and called the sequence of the Earlier Heaven or the Primal Order (literally, the Before-the-World Sequence).

xiv. The path of Ascent comprises the octants LA, AL, AH, HA, which correspond to the forward-moving trigrams :::, |::, |:|, ||:. The path of Descent comprises the octants HD, DH, DL, LD, which correspond to the backward-moving trigrams |||, :||, :|:, ::|. [TC I.A.2, 4]

xv. Octant LA is dominated by the Low state, but incorporates the beginning of the Ascending Process; it is the Low (::) beginning to Ascend (|:), so its trigram is :::, called "The Receptive" (K'un), with its image Earth. It is yielding and the nourishing, sheltering womb of rebirth [SK II.4-5, III.10]. This is the Mother, who seeks the male and gives birth to the Ascending Path, which seeks Heaven (|||). Its direction is North.

xvi. In octant AL the Ascending Process comes into dominance and the state is moved swiftly toward Equilibrium. It is the process of Ascending (|:) from the Low state (::), so its trigram is |::, called "The Arousing" (Chen), with its image Thunder. Its character is to incite movement; it awakens the seeds; it is decisive and vehement. It is the creative force stirring in Nature's womb. The Mother brings forth the Eldest Son. Its direction is Northeast. [SK II.4-5, III.10, 11; TC I.A.3]

xvij. In octant AH the Ascending Process passes through Equilibrium and moves rapidly toward the High State. It is the Ascending Process (|:) striving to the High State (||), so its trigram is |:|, called "The Clinging" (Li), with the image Fire. It is the Lightning presaged by the rumbling Thunder, and it brings warmth and light (attributes of the High state). It is the trigram of the Sun; its season is Spring and its direction is East. It is the time of rapid growth. Fire is the Middle Son sought by the Mother. [SK II.4-5, III.10-11]

xviij. In octant HA the Ascent slows as it approaches its culmination in the High State. Here the High State (||) achieved by the final Ascent (|:), so its trigram is ||:, called "The Joyous" (Tui), with the image Lake. This is the phase of joy and pleasure, for as the High State is reached, relaxation can begin and the fruits if the Ascent can be enjoyed. Its direction is Southeast. Lake is the Youngest Son brought forth by the Mother. [SK II.4-5]

xix. In octant HD the the cycle, having reached its extreme in the High State (||), slowly begins its Descent (:|), so its trigram is |||, called "The Creative" (Ch'ien), with the image Heaven. It is strong, governing and creative. Its season is Summer and it stands in the South, for in both the Sun is strongest. This trigram is the Father, who seeks the female, and sires the Descending Path, which seeks the Earth (:::). This path corresponds to the four elements in order of increasing density: Fire (Heaven), Air (Wind), Water and Earth. Of necessity, the seeds of the Descent are hidden in the High State, as the Ascent was hidden in the womb of the Low State. [SK II.4-5, III.10; TC I.A.3]

xx. In octant DH the Descent from the High state accelerates as it returns to Equilibrium. Since it is a Descent (:|) from the High State (||), its trigram is :||, called "The Gentle" (Sun), with the images Wind and Wood. The character of the Wind is penetration and dispersion, so it is the active process that brings the rapid dissolution of the High State. Like the Thunder (|::), which awakens in the Earth (:::), the Wind (:||) dissolves the icy rigidity of Heaven (|||); it is the creative force stirring in the Heavens. In seeking the female the Father sires the Eldest Daughter. Its direction is Southwest. [SK II.4, III.10-11; TC I.A.3-4]

xxi. In octant DL the Descent passes through Equilibrium and approaches the Low State. Since it is a Descent (:|) to the Low State (::), its trigram is :|:, called "The Abysmal" (K'an), with the image Water. This water moves rapidly, sometimes flowing straight, other times turning, ever seeking to descend to the depths. The Wind (:||) descends to become Rain (:|:), which then descends to the Mountain (::|), and soaks into the Earth (:::) to engender new birth. As a rapid plunge into the depths, this phase is dangerous, but it provides necessary moisture (fluidity). Water (:|:) corresponds to the Moon, as Fire (|:|) does to the Sun. Water is the Middle Daughter Sought by the Father. Its direction is West, where the heavenly lights sink into the water. [SK ii.4-5, III.10-11; TC I.A.3-4]

xxij. In octant LD the Descent slows as it nears the Low State. Here the Low State (::) is achieved by the Descent (:|), so its trigram is ::|, called "Keeping Still" (Ken), with the Mountain its image. Here the process stops, and the movement rests before starting a new Ascent (and so it balances the Joyous Lake, ||:). All things are brought to perfection by Keeping Still; here the seed is planted for a new beginning. It is the Gatekeeper to the Earth, where rebirth takes place. [SK II.4-5, III.10-11; TC I.A.3-4]

xxiij. And so we return to octant LA; the depths of the Low State (::) hold the seeds for a new process of Ascent (|:), which occurs in the Earth (:::), the receptive Mother, who is in the North.

finis capitis II

& finis libri de octo mutationibus