Excerpt: I Ching Mathematics for the King Wen Version

The following is from Chapter Two of I Ching Mathematics for the King Wen Version.


Despite the efficacy and elegance of the traditional model of interpretation, much of the efforts of advanced diviners over the past few millennia have been spent on bringing more material into readings in order to increase the probability of analyzing the Oracle’s reply correctly and thereby making the most auspicious decisions possible (such other relevant material includes the nuclear and transitional hexagrams).  It is to this end that the divinatory map is devoted.

As the diagram below demonstrates, the distance number and origin number combine with the predictive hexagrams to create a comprehensive interpretive model of change—


Diagram 1:  The Divinatory Map


The hexagrams on the horizontal axis then, are the result of divination, in which the Divinatory Hexagram expresses the subject’s present situation and the Derived Hexagram expresses the subject’s developing situation.  The hexagrams on the vertical axis, on the other hand, are the result of mathematical calculations between those on the horizontal axis:  The one at the bottom of the vertical axis expresses the difference between the predictive hexagrams and the one at the top expresses their sum.

The difference expresses the influence of the future pulling the subject forward toward the Derived Hexagram.  It is the distance number and represents the momentum toward the desired future.  Just as one’s goals and plans for the future influence present actions, the distance number represents the influence of the Derived Hexagram upon the Divinatory Hexagram.

The sum expresses the influence of the past setting into motion the seeds of the present situation. It is the origin number and represents the momentum pushing the subject into the present.  Just as every person still carries the influence of their three-year old self into the present, the origin number represents the influence of the past upon the present.

In order to show how the divinatory map is applied to specific readings, we return to the example introduced at the end of the previous chapter, which explores the result of a divination using the coin method to cast Hexagram #56 The Wanderer changing into Hexagram #37 The Family—


Example 1:  Divinatory Map for Hexagram #56 changing to Hexagram #37

Interpretive models, of course, are not abstractions.  They are the underlying principles that allow us to build a comprehensive—and comprehensible—narrative of the divination.  They provide us with better analytical tools with which to balance our communion with the Oracle’s reply.

In the present case, we can see how the divinatory map helps build just such a divinatory narrative—


Example 2:  Building the Divinatory Narrative

—especially, when placed within the context of the subject’s question, which in this instance involved starting up an eco-tourism business centered around visiting the ruins of ancient civilizations.  Suddenly, the Oracle’s answer emerges effortlessly.

Influence of the Past:  #11 Peace, which speaks to a time of social harmony, cultural flowering and widespread prosperity—all key elements of the Toltec civilization that constructed the ruins in question.

Focus of the Present:  #56 The Wanderer, which speaks to welcoming the eco-tourists to the site and helping them adapt to the physical and cultural environment.  It also speaks to the culture who left behind the ruins, those peoples of the past who were themselves, wanderers.

Influence of the Future:  #27 The Corners of the Mouth, which speaks to the act of providing nourishment—an essential feature of the proposed business, since eco-tourists come to the project in order to be fulfilled by a more meaningful experience than just wandering from one tourist trap to another.  The means to providing folks with such meaningful experiences, according to this hexagram, lies in making sure they have times of stillness and tranquility, so that they might absorb the atmosphere and presence of the people who built the ruins.

Focus of the Future:  #37 The Family, which speaks to maintaining the continuity of past generations and integrating their lifeways into the present.  This implies that what participants will take away with their experience will add to the culture within which they live by enriching it with the closer bond between nature and spirit that inspires indigenous people.

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The Cycle of 6 – 7 – 8 – 9



compass bigrams6 copy

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12-Month Divination Method

Following is the method for conducting the traditional 12-Month Divination, as given to me by Master Khigh Alx Dhiegh.  As such, it uses the hexagram numbering system of the King Wen Arrangement.

This is a marvelous tool for personal Inner Work and Intentional Goal-Setting.

12-month divination

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Divination: How Can I Be Genuinely Happy?

The following is a reply to the question, “How can I be genuinely happy?” as interpreted via The Toltec I Ching.

Divinatory Hexagram:


Hexagram 4

34 Mirroring Wisdom

Image:  A male warrior faces an eagle and a jaguar, who are teaching him the lessons of nature so that he can successfully respond to every circumstance he encounters.  The speech glyphs are multi-colored to depict the different dimensions of nature’s lessons.

Interpretation:  The eagle is a symbol of the day, of the masculine force, and represents the direct approach to circumstances.  The jaguar is a symbol of the night, of the feminine force, and represents the indirect approach to circumstances.  Taken together, they symbolize a balanced and harmonious way of life, meaning that you are able to use both direct action to confront circumstances and indirect action to mature circumstances, tailoring your responses to the need of the time.  The male warrior is a symbol of the way of testing and training human nature that increases its versatility and fortitude.  The speech of the eagle and jaguar symbolize the lessons that can be learned from the primary forces of nature by those who listen respectfully.  Taken together, these symbols mean that you succeed in your fierce determination to train your emotions, thoughts, and will to act in concert to overcome every hardship.

Action:  The masculine half of the spirit warrior calls your feminine half to open her heart and feel herself part of a spiritual initiation as old as creation.  He calls her to awaken to her innate capacity to change things and to view as a bridge this lifetime across which she journeys.  He calls on her to reunite in a higher and more creative unity by complementing his purposeful nature with her own nurturing nature.  By combining your dual nature in the right proportions, you can acquire the wisdom of the old ones, who learned from nature both how to adapt to change, as well as how to anticipate it.  This is a time for studying the behavior of nature and its relationships in order to better understand the behavior and relationships of human nature and spirit:  now is a time when the voice of the great-great-great-grandfather is especially strong, so you can approach him as you would the sky spirit itself and receive the eternal meanings behind all of nature’s symbols.  By filling your heart now with the intent to travel the ancient path of wisdom, you can pursue your lifework knowing that you are helping build the road of perfect freedom.  Do not doubt that spirit dwells within nature nor that it speaks in a language understood by your heart nor that it leaves tracks in its passing that you may follow.

Intent:  When loving-kindness is not tempered with strength, people become dependent and resentful, trusting others too much and then growing disillusioned when their own good will is not reciprocated.  Become familiar with this pattern of imbalance and learn to recognize its signs of worsening—apathy, helplessness, and desperation—so that you can intervene at the right moment to break the fever, so to speak, by reintroducing the feminine half to its complementary masculine half.  Whether you find this imbalance in yourself or others, you can provide a counterbalance to the need arising from a growing sense of being unfulfilled by calling attention to the outer path, the route by which spirit warriors train to prove their immortality by overcoming every mortal obstacle.  Following this path toward the outermost horizon, you pass through every ordeal like an ancient tree passing through another season.

Summary:  No matter how well you see when things are as clear as day, the eagle sees better.  No matter how well you see when things are as obscure as night, the jaguar sees better.  Keep your heart filled with humility so you can keep learning from your spirit guides.  Wisdom cannot blossom among the weeds of opinion, arrogance, laziness, and self-satisfaction.  Eliminate nervousness, cultivate calm.  Work diligently to achieve goals that appear just beyond your reach:  the spirit within nature is the same spirit within you.


3rd:  The priorities can be changed but old habits of emotion cling like barnacles to the hull of a boat.  Just because they are under the surface does not mean they are not real.  Look where you feel righteous indignation and resentment—scrape these habits off and you will encounter no resistance.

6th:  When your new priorities are fully implemented, everything in the world is nourishing.  Everything teaches you about the invisible half of nature—and its invisible connections of cause-and-effect that underlie change.  You become a source of great comfort, advice, and nourishment to all you touch.


Derived Hexagram:


Hexagram 44


Refining Instinct

Image:  A male warrior places all his weapons and shields into a fire, the smoke from which takes the form of an ethereal butterfly.

Interpretation:  The male warrior symbolizes the testing and training that make people more adaptable, inventive, and courageous.  That he burns up all his weapons and shields means that you eliminate every tendency to attack others or defend yourself.  The fire symbolizes the inner work whereby old habits of thought, feeling, and behavior are converted into conscious acts of self-expression.  That the smoke takes the form of a butterfly means that your new habits of thought, feeling, and behavior reflect the spiritual metamorphosis you have undertaken.  Taken together, these symbols mean that you voluntarily subordinate your personal desires to a higher purpose.

Action:  The masculine half of the spirit warrior uses the energy of the meaningless to give form to the meaningful.  At the core of the spirit warrior’s intent is the whole-hearted effort to stop wasting energy.  Such an effort is futile so long as we succumb to the impulse to divide our experiences into opportunities and threats—opportunities to gain some advantage over others and threats of others taking advantage of us.  From the spirit warrior’s perspective, we waste energy until we stop obeying the base and brutish drives to exploit the vulnerabilities of others and block others from exploiting ours.  When we are devoid of any hope for gain or any fear of loss, on the other hand, all the energy of those baser impulses is available to be used for higher aims—when the goals of baser motives lose their meaning, in other words, their energy can be transferred to new goals whose nobler motives imbue them with a sense of genuine meaningfulness.  Harnessing base energy and directing it toward nobler goals is, in itself, the act of conserving energy:  voluntarily placing the baser instincts in the service of nobler goals is, in itself, the act of refining the instincts.  The emergence of our refined instincts is then embodied in the desire to express our vision in creative acts that bring benefit to people, nature, and spirit.  Because you voluntarily moderate the way in which you express your vision, you do not provoke an angry and oppressive backlash against your cause:  because you do not give others ammunition to use against your endeavor, it succeeds by moving past all resistance.  By not thinking in terms of personal gain and loss, you are able to act in accord with your highest ideals, make allies of those with similar values, and work together to realize your common goals.

Intent:  We spiritualize desire when we stop wasting energy on the pursuit of meaningless desires—those that either cannot be attained or, if attained, ultimately prove unfulfilling.  Likewise, we spiritualize the instincts when we stop wasting energy on the pursuit of base instincts—those that give rise to meaningless desires.  By spiritualizing the instincts, we follow in the footsteps of those who have created the most sublime monuments to the human spirit.  Because your spiritual instincts give rise to meaningful desires, you use the transformed energy of the meaningless to both give form to the meaningful and bring benefit to the people, nature, and spirit touching your life.

Summary:  Identify the goals you pursue out of fear, greed, or the need for approval—then make a conscious decision to no longer pursue those goals.  Create a new set of goals based on trust, generosity, and giving others the approval they deserve—then make a conscious decision to pursue those goals.  Be strict with yourself:  do not allow yourself to unconsciously slip back into pursuing your old goals.  You are your longings.


Note:  There is a mediating hexagram conjoining these two (see I Ching Mathematics: The Science of Change), which in this case is the hexagram comprised of—

Lower Trigram, Lake, Joy, and Upper Trigram, Lake, Joy

This seems an auspicious reply to the question about being genuinely happy—

Mediating Hexagram:  The Forces Constructing a Positive Future—


Hexagram 2

09 Sensing Creation

Image:  A female warrior is naked, immersed in water and surrounded by flowers.  A wellspring of water rises from between her hands.  The water drops are drawn as beads of jade in order to portray the precious nature of that which sustains life.

Interpretation:  This hexagram represents the great courage essential to creating a meaningful life.  The female warrior symbolizes the way of nurturing and encouraging human nature that increases its sensitivity and loving-kindness.  Being naked means that nothing stands between you and the world.  Being immersed in water means that you plunge whole-heartedly into the spirit of that which nurtures all.  Being surrounded by flowers means that you perceive the perfection of the world as it truly is:  each moment blossoms perfect and whole, then passes like a fading flower—each perfection born into the world must die.  The wellspring of water symbolizes the inexhaustible source of courage that allows you to use your awareness of mortality to more profoundly experience the joy and sorrow inherent within every encounter.  In this sense, the flowers and the water signify not only the wisdom attained through experience, but the aesthetic sensibilities to be moved by a beauty and truth not always apparent to others.  Taken together, these symbols mean that you open your spirit to the overwhelming perfection of the world and share your vision with all you touch.

Action:  The feminine half of the spirit warrior collects the movement and energy of the unseen forces, calming them and bringing them together in harmony, making a place for them to gather strength and then making that source of benefit open and available to all.  Where past injustices and resentments survive to poison the well of benefit, true need goes unmet and people suffer unnecessarily:  the spirit warrior fosters a climate of forgiveness and reconciliation, reuniting those whose hearts have become estranged and dissolving the tensions and insecurities that have prevented people from coexisting in harmony and mutual understanding.  Before action, the passions breeding distrust and discord appear too strong and too deeply entrenched to be overcome.  After action, the benefit you help cultivate results in a greater union of good will, hope, and creativity.  You succeed where others fail because you rely on the warrior’s refined sensibilities to guide you rather than past experiences.  You succeed where others fail because you reflect generosity in every thought, word, and deed rather than demanding that others first prove their worth.  You succeed where others fail because you cleanse yourself of all ill will rather than harboring any spiritual intent that might poison the well of benefit that you are become.

Intent:  Whether the struggle is internal or external, work to increase your sensitivity to the realms of nature, human nature, and spirit.  Because people differ only in the degree of their sensitivity to the One Spirit, continue to open your perceptions to more and more sublime thoughts, feelings, memories, and sensations.  By recognizing that you are filled with the source of nurturance, you can calmly let all your adaptations arise from it.  By giving form to the source of nurturance, you can respond to things with dignity, patience, joy, and appreciation.  Because your sensitivity to the world is your strength, you can find the way to restore harmony and progress where others find only opposition and antagonism.  Make the well-being of others your goal right now and you can build a coalition of allies to undertake even greater endeavors in the future.  Avoid taking sides, work to bring them together.  Cultivate trust in the early stages of discord, rely on your lack of self-interest in its later stages.  You succeed because you bring future benefit to those separated by the past.

Summary:  The beauty and loving-kindness you seek are within your reach.  Let go of obsolete opinions and dogma handed down to you from others.  Find that which allows you to share happiness with others and you will achieve greater freedom and creativity.  Focus on the healing of old wounds, promote the forgiving of old wrongs.  Set aside personal ambition, act for the common good.





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Nine Emanations of the Oracle

The diagram below is from I Ching Mathematics:  The Science of Change.

It illustrates the eight pairs of hexagrams that derive from the initial “Predictive” pair  obtained by divination via coins or yarrow stalks or random number generators.

Each of the rectangles in this diagram, therefore, represents a pair of hexagrams to be analyzed according to its interpretive function (Constructive, Metamorphic, etc.).

The mathematical calculations—all of which derive from the divinatory hexagram and its line changes—are detailed below their respective functions.

9 Emanations + v3 300

 © 2014 William Douglas Horden


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Addendum II: I Ching Mathematics


Binary Sequence and King Wen Sequence



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Embodied Ecstasy


To be a diviner, one must live like water.



The path of wisdom has a single fixed destination:  The Ecstatic Life.  All other attainments are merely way stations on the Great Sojourn, for wisdom is not complete wisdom until I arrive at the place where there is no longer a path and I wander the world of worlds with the holy fools of all times, finding myself at last embodying the one standing outside myself.  Each station along the way marks a higher order of increasing subjectification by which the bounds of identity give way to ever expanding dimensions of communion.  Likewise, the destination itself is marked by the un-self-conscious rapture of at-one-ment with Omnipresence.  Love is answered with love:  As personal identification voluntarily relinquishes its stranglehold on pure awareness, the open heart of awe and adoration is met, tear of bliss for tear of bliss, by the grandeur and loving-kindness of the Creative Forces.

The Sphere of Universal Communion stands at the omnipresent Center, home to the initiated and the uninitiated alike.  It does not matter, in other words, whether we are presently aware of the unifying realm beyond the five senses nor whether we are presently aware of the ancient lineage working to bring this realm of the five senses into closer accord with that underlying harmony nor whether we are presently aware of our own place in that lineage—every being in this realm dwells simultaneously in the sacred space of the One Light, which is also called the One Mind, and, among initiates, We Are I Am.  Love answers love:  As every being awakens to its already-perfect state, its outpouring of joy, gratitude, awe and devotion is met, tear of bliss for tear of bliss, by the intimacy and harmony among all beings in all times.

The Ecstatic Life unfolds naturally from our immersion in oceanic benefit—from our conscious experience of simultaneously receiving and giving good fortune within the shared being of divine at-one-ment.  Making this experience of universal benefit conscious is what is meant by initiated:  Being presently aware of the magnanimous qi pouring through us into this realm of the five senses is the singular act awakening us to the Great Work of manifesting the unifying realm in this lifetime. Since time immemorial, the Great Work has advanced against the shadow of hate, fear, greed and force through the conscious implementation of the inspired action of the Universal Civilizing Spirit.

The Ethics of Inspired Action

Divination is knowing the mind of the spirit world.  It is the oldest of all forms of magic.  What the uninitiated call magic the initiated know to be the inflowing of the unifying realm into this realm of the five senses.  The ability to marshal that inflowing is first and foremost a matter of right intent:  Paradoxically an emptying and filling, it is a practice of emptying oneself of self-interest while filling the void of need in this realm wherein the land, water, air, plants, animals, people and spirits have been so depleted of their original good fortune.

Acting for the sake of the Whole, initiates entrust their wellbeing and good fortune to the underlying harmony of order and chance:  All boats are lifted together on the rising tide.  The practice of the Great Work culminates in standing watch at the Gate of Coming and Going, for this is the passageway through which the inflowing of the unifying realm arrives.  This inflowing is the mind of the spirit world, which arrives as shen, or spiritual intent, which then becomes more concentrated as qi, or generative energy, before it crystalizes as jing, or animate substance—and it is from this animate substance that all new manifestations take form within the realm of the five senses.  Opening the Gate of Coming and Going is granted to those who have brought their personal elemental forces into harmonious equilibrium with the universal elemental forces, for these are the people who have attained the complete wisdom of the Ecstatic Life and so embody the principle of universal benefit.

What is the daily practice of the Great Work?  Making use of the constant flux of personal change provoked by the interaction between inner and outer experience, we abide by the ethics of inspired action to bring our personal elemental forces into harmonious equilibrium with the universal elemental forces.

What is Inspired Action?  The inner and outer actions we consciously take as sacred beings toward every sacred being within our awareness.

What is the Universal Civilizing Spirit?  The omnipresent perfecting intent of the World Soul, which reveals the sacredness of form and formless through their infinite interchanges spanning the single moment of eternity.

The sacredness of everything is not an empty or abstract phrase.  It is an accurate description of reality and has profound ramifications in its mirroring of All This.  By All This, we mean all the subatomic particles and the space between, we mean all the stars and the space between, and we mean all other beings and the space between:  All This is Alive and Aware.  To consciously act as a sacred being among this universe of sacred beings—such is the first principle upon which the ethics of the initiated is built.

The ethics of the initiated is not defined, in other words, as an inventory of given intentions and actions appropriate to given situations and circumstances.

It is defined, rather, as the conscious behavior of an angel toward all the other angels in the universe.

The Angelology of Form

By angel we do not refer to any modern concepts that anthropomorphize the elemental creative forces of this world of worlds—forces that are essentially inhuman, cold as crystal, clear as fire, immortal as death, the archetypal substance of every form.  Inhuman, yes, in the sense of transcending the mortal awareness of mortality.  Yet more human than human, in the sense of having lived so many mortal lifetimes that the poignancy of each moment of life is a perfect diamond of memory carved into space.  By angel, therefore we revert to the ancient worldview of the emanations between the original Act of Creation and all its subsequent manifestations of form—the shen, or spiritual intent, of pre-manifestation substance that takes form.

Angels are, literally, the Messengers of the Divine.  They carry the full import of the sacred in their own Being, heralding the immediate presence of the Divine.  Each is an eternal Archetype, a perfected Idea, of the One Mind.  Each is, in other words, an individual Aspect, a unique Face, of the Divine.  To meet an Angel, therefore, is to gaze into the Face of the Divine.  To recognize oneself as an Angel is to gaze into the image and reflection of the Divine. Because everything is the Divine, every thing is an Angel.  It does not matter how big, small, dense, subtle, near, far, clear, or obscure:  Each thing, every being, from the subatomic to the galactic, is one of the unique Faces of the Divine.

It is in this sense that it is said that Every Form is an Angel. And it is in this sense that it is said of the totality of all things that The universe itself is the eternal Convocation of Angels.  It is not just the burning bush that is speaking—every thing, every Angel, is always speaking its message to all the other Messengers everywhere.  In the same way that an infinite number of individual fires grow together into a single bonfire that emits a single vital light, all the speakings of all the Angels—the speakings of all the rocks and trees and mountains and rivers and clouds and wind and the sun and moon and stars and children and women and men and animals and flowers and soil and rain—grow together into a single great song of joyous communion.

Herein lies the culmination of complete wisdom, which has little to do with intellectual, theoretical, or scholarly rationale, for following the Inner Path along its natural course into the Inner Landscape of the World Soul leads in the opposite direction, retracing the mystics’ path of return to the Ecstatic Life.  This step back into The Imaginal realm—the realm of pure Being, the realm of the angelic doubles manifesting all forms—is the singular act of self-recognition that evaporates the mirages of separateness on the soul’s return to the Sphere of Universal Communion.  To recognize one’s own deathless angelic nature is to immerse oneself in the universal at-one-ment of the deathless angelic nature of All.  To recognize one’s own perfected Idea at the root of all one’s lifetimes is to hear one’s own speaking amidst the universal choir of Messengers.

The Imaginal is also called the Crossroads of the Diviners, the place where all the Ancients of all the cultures and traditions have always met to hear the Messengers of the One.  As such, it is the omnipresent site of divining, wherein reading the mind of the spirit realm is coincident with listening to other Angels.

Question:  What is it that Messengers herald?

Answer:  Change.

The Inner Path

The personality cannot think its way into The Imaginal.  Entrance into the realm of subtle bodies is gained instead by stepping out of Thinking and back into Being.  This is called Remembering your original face before your mother and father ever met.

Thinking is the function of the body’s conscious awareness, which is called the personality, as it signifies the person born to certain parents in a certain culture in a certain historical time.  The body’s personality is also called the mortal soul, as distinct from the immortal soul of the spirit.  The two souls are traditionally conceived as the lower soul, which is conditioned by the circumstances into which the body is born, and the higher soul, whose unconditioned nature coincides with the timeless spatiality of the unchanging unifying realm.  This is the realm of Being, which is the substance of the higher soul that precedes the names, words, and internal narrative of Thinking.  It is the realm, too, of the inner master, the personal guide, that is the personality’s Angel.

Because the immortal soul is already always awakened to its true angelic nature, it has traditionally been said that It is the mortal soul that awakens.

It is, then, the process of awakening the personality to its angelic nature that constitutes the Inner Path.  And it is the purpose of the higher soul to guide the lower soul to that awakening.

The awakened angelic nature, however, is unconditioned by any circumstance or state.  This means that no part or aspect of its nature is caused by any event or condition—and because it is not the effect of any cause, the awakened nature cannot be brought about by any effort, whether external or internal.  The higher soul may guide forever but never toward a specific result—all it can do is lead the lower soul to create an opening in the Intentional Field where the spirit of transmutation can enter when it is convinced the time is ripe.  The overarching goal of the Inner Path is the cultivation of the mortal soul:  It depends utterly on the personality voluntarily taking up the practice of the intentional body in order to radiate the most beneficial intent in every possible dimension.  It is this intent, stabilized over a period of time, that creates the opening in the Intentional Field known as the site of soul-making.

Question:  What is intent?

Answer:  Purposive imagination.

Intent, in other words, is comprised of the same substance as The Imaginal itself:  Like can only be known by like.  What the personality learns on the Inner Path is how to focus imagination in an ever more single-pointed questioning of the universe of Angels.

Purposive Imagination

Passive imagination is unfocused, seeking outlets in idle daydreaming, fantasizing, and escapism.  Its lack of purpose, other than keeping the imagination vigorous, can be seen in the absence of positive transformation it evokes in the personality.  Yet its very efforts to exert itself into the realm of conscious life demonstrates both its life-affirming vitality and refusal to be denied expression.  Our unconscious life is even more its purview, as dreams are nearly pure imagination, cut off as they are from the primary senses and conscious perception.  But clearly, passive imagination is of the same substance from which focused purposive imagination is formed.

The intentional body, then, is purposive imagination—which is why it is also called the dream body, being a focused marshaling of the same pure substance of dreams.  The dream body is activated, in this sense, by directing the full brunt of one’s waking attention onto an Idea.  Just as dreams are the personal entryway into the collective unconscious via archetypal images laden with memories, associations, emotions, and multi-layered meanings, purposive imagination is the personal entryway into The Imaginal via single-minded concentration on an archetypal Idea and its self-revelatory relationships to other Ideas.

Ideas cannot be described.  They can be named but that says little about the actual mechanism of searching for them, questioning them, and understanding their reply.  This process has nothing to do with Thinking.  It is neither linear nor word-based.  It is spatial and feeling-based, requiring a kind of journeying into the depths of living imagination in pursuit of one of its figures that appear as emotion-laden, memory-laden, and meaning-laden images.  It bears repeating that each of the archetypal Ideas is an Angel:  Each is a living facet of the One Mind, no different than each of us.

Following are the names of a few Ideas upon which the dream body can easily concentrate.  Mountain.  Ocean.  Atom.  Sun.  Moon.  Child.  Love.  Peace.  World.  Human.  Approach an Idea as another Idea, with genuine curiosity, wonder, and sincerity:  This establishes the basis of communion and the free flow of understanding between responsive Angels and the questing mortal soul.  It can help at the beginning of this method to address an Idea as if it were a symbol occurring in one of your dreams—say, a Mountain, for instance, which does not unpack all its contents to the thinking mind but does open to inquiry by purposive imagination.  It goes without saying, perhaps, that there exist an infinitude of Ideas, many of which are much more complex than the examples above:  These more subtle bodies cannot be named easily, as they comprise parts of highly complex webs of ascending orders of meaning.  This interrelatedness of eternal Ideas is what inevitably stirs the still surface of unchanging Being, giving rise to the timebound linearity of Thinking:  It is the necessity of thinking words rather than perceiving images that distinguishes our standing in the realm of Thinking from that of Being.

The attentive diviner will have noticed how similar this mechanism is to that of addressing the Oracle, whose reply is activated by asking a question.  In the process of divination, too, the question is not posed by the thinking mind in the form of words or sentences but, rather, in a kind of cloud of associations, memories, emotions, and multiple points of view:  In this manner, one’s purposive imagination is trained on a web of relationships constellated around the primary Idea of the divinatory inquiry. It is worth noting in this regard that the Oracle often appears to the diviner as the Archangel of Change.

The Life of Water

From a particular standpoint in The Imaginal, everything in the universe is water and the universe is its flowing.  Trees are slow moving water.  Mountains are water standing nearly still.  Fire is inside-out water.  People are conscious water.

From the perspective of the realm of the five senses, on the other hand,  the life of water forms a cycle that begins in the ocean, where each of its drops tastes of salt.  Water evaporates from the sea, leaving its saltiness behind and forming clouds that float over land to collect along mountains, where they rain down as freshwater.  Collecting in rivulets, streams, tributaries, and eventually rivers, freshwater follows the line of least resistance to return back to the ocean, no sooner reentering the sea than its saltiness is immediately restored.

Within The Imaginal, this life cycle of water is a literal and physical symbology of the soul’s journey through the realm of the five senses.  The ocean is the eternal reservoir of souls, the Sphere of Universal Communion.  The saltiness of each drop of the sea is the immediate sense of communion with all other souls—the knowing of being a vital part of the at-one-ment of all beings.  The evaporation of the drops of water into clouds is the voluntary decision to visit the realm of the five senses again.  The loss of saltiness via evaporation is the voluntary relinquishment of the memory of the oceanic reservoir of souls.  Falling as freshwater in the mountains is birth into a physical body.  Flowing over the land as freshwater, nurturing everything touched is the necessity of making one’s way through this world on faith, as actions taken without a real sense of mortality lack genuine magnanimous benevolence.   Each drop recovering its saltiness upon returning to the sea is the full complete spontaneous recovery of the immediate sense of communion with all other souls—as well as the full complete spontaneous recovery of the memory of all the individual’s lifetimes.

Through the eyes of the dream body, moreover,  water is the shape-shifter.  As water, it takes on the form of its vessel, whether an ocean, a river, a lake, a puddle, a channel, a bowl, or a cup.  Cooled, water takes the form of ice, a solid which, if heated, melts back into its liquid state of water.  Heated, water takes the form of vapor, a gas which, if collected and distilled, returns to its liquid state of water.

From within The Imaginal, this shape-shifting character of water is viewed as demonstrating both the threefold nature of reality and the inherent ability of all form to change states.  From this perspective, the gaseous state of vapor symbolizes the spiritual intent of shen, the liquid state of water symbolizes the generative energy of qi, and the solid state of ice symbolizes the animate substance of jing.

Trigram Lines Names Life-Forces Life-Forces Pre-Manifestation Names States
Top Heaven Spirit Conscious Spiritual Intent Shen Vapor
Middle Mankind Human Nature Psyche Generative Energy Qi Water
Bottom Earth Nature Unconscious Animate Substance Jing Ice

Figure 1:  Correlations within the Threefold Nature of Reality


In this sense, the life of water symbolizes imagination, the shape-shifting essence that maintains its integral identity by eternally conforming to its current vessel.  As such, imagination is neither the conscious nor the unconscious—it is pure psyche itself, the qi, or generative energy, from which the conscious (shen) and the unconscious (jing) derive. Question:  Why is life subjected to suffering and death? Answer:  This is how we make souls.

The Site of Transformation

The soul is not in the body,

The body is in the soul.

The mortal soul awakens when the bubble of its memory is pierced by the arrow of the immortal soul’s understanding.  Until that moment, the personality is driven to act and react by past experience—by the mortal soul’s conditioned sense of self, which is the sum of all the body’s experiences.  This conditioned self is artificial in the sense that it is the product of fate:  Born to certain parents in a certain culture within a certain historical era, the body’s experiences are reinforced through familiar repetition until they fossilize into habitual thoughts, feelings, and associations.  This habit-mind is bounded on all sides by the horizon of birth-and-death:  There is no direct knowledge of anything prior to the birth of the body nor subsequent to its death.  The mortal soul has no first-hand knowledge of anything but its own five senses, so its beliefs, values, and ethics are guided by self-interest—to the extent it acts otherwise is a matter of the faith it places in second-hand knowledge obtained from others.  Moving through life thus, the mortal soul proceeds toward death and the dissolution of its bond with the body.

The spirit, or immortal soul, dwells in the eternal present of the unifying realm and so has nothing that can strictly be called memory.  Its awareness is unbounded, being coincident with the unifying realm itself—and, thereby, coincident with the awarenesses of all other immortal souls, as well.  This is the state of at-one-ment that forms the gravitational coherence of the Sphere of Universal Communion, an horizonless state of shared understanding forged in the fires of uncountable mortal lifetimes.  For it is immortal spirit that gives form and lives through every manifestation in Creation, from the infinitesimal to the infinite.  As the unconditioned self, the higher soul is the true self guiding the personality through the labyrinth of self-interest back to the omnipresent Center, the secret garden, of the World Soul.   Just as the higher soul does not possess memory, it likewise does not possess knowledge in the way the mortal soul does.  This is because such knowledge is the product of the body’s experiences, which is relative to time and place and form.  After all, the higher soul has been part of uncountable forms across the eons and the particulars of such knowledge, as well as all such memories, have been distilled into pure understanding.

By understanding we mean the essential relationships between things.  The moment the mortal soul first follows the higher self back into the omnipresent Center has long been described as a single lightningbolt illuminating the entire landscape on a dark moonless night:  Suddenly the entire web of eternal relationships making up the essential nature of the underlying harmony of the world appears with crystal clarity.  It is The Vision of the Secret Allies, which is also called the first-hand experience of the interdependence of all things.

Most people go through life sensing they have some untapped potential, a part of themselves that they cannot reach, a purpose they cannot define, a destiny they worry is slipping away from them.  Despite their best efforts, they grow increasingly frustrated by their inability to change in any long-standing and meaningful way.  As civilization becomes increasingly complex, there seems less time and energy to dedicate to internal metamorphosis.  It is with an eye to future generations that the ancients codified and safeguarded the sacred technologies of transformation.

The mortal soul is born into a culture of competition.  From its earliest years, it learns to fear that there will not be enough.  Enough food, enough money, enough security, enough clothes, enough love, enough attention:  From its earliest years, it learns that the only way to ensure there will be enough is to win it.  Even at the expense of others, if need be.  Because others are competing to ensure they have enough even if it means taking it from others.  This is the path of self-interest, the way of the uninitiated.

For the uninitiated, winning means having enough, which they call good fortune—losing, on the other hand, means not having enough and is called misfortune.  The initiated, however, do not allow the self-interest of conventional thinking to misguide them into seeking good fortune or avoiding misfortune.  Rather, they maintain their focus on ennobling the mortal soul.   This, indeed, is seen as the overarching purpose of the higher soul—to inspire the personality to accept its own sacred angelic nature.

Such acceptance is reached by stabilizing one’s focused concentration on spirit, not manifestation.  This means holding in mind pre-manifestation, most particularly one’s spiritual intent, instead of one’s past, present, or possible circumstances.  Seeing with the intentional body’s eyes, working with the dream body’s hands—such is the path of true good fortune.  Rather than following the lead of the uninitiated, who attempt to manipulate their circumstances to gratify their self-interest, the initiated increasingly sensitize themselves to both their own spiritual intent as well as others’ within the Intentional Field.  This is the natural fruit of the seed of divination:  To read the mind of the spirit realm.

Explore The Imaginal by feel, sense the intents of others.  Recognize that not all of them are currently incarnated within a human body or, if they are, their physical presence may be very distant from your own.  Do not avoid contact but, rather, seek out allies with everyone, exuding your own well-disciplined and constant intent:  Let Us Share Plenitude!  There is no limit of magnanimous qi in the realm of pre-manifestation:  Here!  Come to My Table!  There is Plenty For All!  By becoming a wellspring of benevolence in the pre-manifestation realm, you pave the way for the corresponding animate substance to take form in the realm of manifestation.  This is called The wisdom of the heart.

Question:  How do we embody ecstasy?

Answer:  We become the site of transformation.



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Addendum to I Ching Mathematics

The material below details the mechanism by which binary calculations are made using only the hexagram figures.

This information supplements the other mechanisms illustrated in I Ching Mathematics, which was published earlier this year.

addendum math

It is necessary to actually work through these examples—and others of your own design—to see how elegantly the calculations proceed.


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Sacred Geometry


pi hex 2a




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The Mandate of Heaven II

The Toltec I Ching is the first completely new version of the I Ching in modern times.

Such was not my intention when I stepped onto this path some 45 years ago.  As dedicated to the classic King Wen version as any other student, it never occurred to me that I might make the changes to that text that I have.  In retrospect, however, it seems inevitable.

Every field of study has its fundamentalists.  This is especially so among studies of religious and spiritual texts and traditions.  Those who have made a concentrated study of their specialization come to identify with the positions and interpretations they have accepted and to which they have contributed.  This is compounded by the fact that religious and spiritual texts and traditions carry with them a sense of the sacred, which is too often perceived as an unchanging—and unchangeable—manifestation of eternal truth.

The field of I Ching studies is rife with such fundamentalists.  For personal reasons, both intellectual and emotional that reflect what they have come to identify with, these are students who have mistaken a closed mind for dedication to the Way of Change.  One of the first lessons that the I Ching demands of us is the ability to adopt multiple points of view.  Until we abandon our strictly personal viewpoints for the greater capacity to shift between many points of view, we cannot be said to have learned even the most rudimentary of the Oracle’s lessons.

Not all I Ching researchers and enthusiasts fall into the category of fundamentalist, of course.  Most are open-minded and concerned with carrying the oracular tradition forward into the coming generations.  It is to such honest investigators that the remainder of this article is dedicated.


Why A New I Ching?

There are two principal aspects of The Toltec I Ching with which I Ching fundamentalists take exception.  The first is the fact that the text no longer follows that handed down in the received version, particularly the names and judgments of the hexagrams.  The second is the fact that the order in which the hexagrams appear is not that in the received version.

There is another basic lesson that the I Ching teaches:  Change should never be made merely for the sake of change.  So what is it that necessitates changing this venerable text at this time?

First of all, the ancients never thought of the I Ching as an unchanging monolithic artifact.  It was a living Oracle that allowed them to communicate with the world of spirit.  The oracular tradition was part and parcel of life long before the Chou dynasty produced the received, King Wen, version we know today.  The Shang dynasty emperor was himself an accomplished diviner and there are many records of the divinations conducted by palace diviners on behalf of the state.  Indeed, it is no exaggeration to say that the I Ching was a tool of statecraft:  the received version we know today was actually produced by the founder of the Chou dynasty, King Wen, and his son, the Duke of Chou—and the historical epoch they initiated is celebrated as a golden age of enlightened rulers, humaneness and justice.

The version handed down to us was never conceived as the only possible version.  The official records of the Chou dynasty, dating back more than 3,000 years, state that three different versions of the I Ching then existed—one for each of the historical dynasties.  The most ancient of the dynasties, the Xia, it was said, possessed the Oracle but the order of the hexagrams was different:  it began with the hexagram Mountain over Mountain.  The succeeding dynasty, the Shang, reportedly possessed the Oracle but, again, the order of its hexagrams differed in that its sequence began with the hexagram Earth over Earth.  As he was contemplating the overthrow of the Shang dynasty, King Wen discovered in the re-ordering of the hexagrams the mandate of heaven authorizing him to initiate a new dynasty:  it was, then, with the Chou dynasty that the order of the received version came about, an arrangement that begins with the hexagram Heaven over Heaven.

Whether the hexagrams existed as long ago as the Xia and Shang dynasties is a matter of historical question.  That the Shang used oracle bones to consult the oracle on matter of statecraft is an historical certainty.  That the Chou dynasty used the ordering of the hexagrams to re-form the Oracle as a means of legitimizing the founding of the new dynasty is a matter of their own record.  Likewise, they justified this reading of the mandate of heaven by pointing backwards in time to say that the ordering of the hexagrams was instrumental in the legitimization of the preceding dynasties.

A thousand years later, people were still experimenting with variations, as the Mawangdui Silk Texts of the Second Century B.C. demonstrate.  In what is the oldest extant copy of the I Ching, the order of the hexagrams is again changed and the names of many of the hexagrams differ from the received version.  Another 1,200 years later, the great Neo-Confucian philosopher and I Ching scholar, Shao Yung, made public the natural number order of the hexagrams, which he attributed to the ancient culture hero, Fu Xi.  It was this order that the missionary Bouvet sent to Gottfried Leibniz in the 17th Century and which Leibniz recognized as the very binary code he was in the process of discovering in the West.

So the I Ching fundamentalists, citing their dedication to the past by clinging to a single version of the text while ignoring the greater context within which it was created and evolved, are mistaken.  The ordering of the hexagrams was, within Chinese culture, a complex question responding to political and philosophical purposes.

The same is true of the naming and interpreting of the hexagrams.  Over time, and again within Chinese culture, various interpretations of the Confucian text emerged in order to illuminate the fuller potential of the I Ching’s relevance to other spheres of study.  Lui I-Ming produced a version expressing the Taoist alchemical perspective. Chih-hsu Ou-i produced another version reflecting the Tianti Buddhist worldview.  And the 11th Century scholar Cheng Yi produced a version reflecting the philosophy of his school of inner design.

Given the facts, why then does a new version of the I Ching meet with resistance from the very people one might expect to welcome it with, at the least, open-minded curiosity?  The answer, I suspect, is not precisely what one might expect.

Resistance comes from those who are dedicated to their idea of the I Ching and not to the I Ching itself.  Theirs is an intellectual pursuit far removed from the oracular tradition—they are not, in a word, animists.  They do not adhere to the principle that all of matter is invested with spirit and they certainly have no first-hand experience of sensing the spirit animating stone, water, wind and plants.  They treat the I Ching as an object of study rather than actively engaging the spirit of the Oracle.  They forget that an oracle is essentially a speaking and they ignore the question of who or what it is that speaks.  They are not, in another word, diviners.

This is why The Toltec I Ching is the first new version of the ancient classic in modern times.  It is a book for diviners.  It embodies the animistic lifeway of treating all of nature, all of matter, as spiritual entities deserving recognition and respect for the part they play in the whole of Creation.  Its emphasis consistently falls on the ethics of inspired action within the emerging world culture seeking peace and prospering for all.  It recognizes that just as human beings have a visible body and an invisible spirit, so does every other part of nature—a recognition that extends to the whole of nature itself, whose invisible half is the living World Soul.  It does not simply pay lip service to the yin-yang worldview that originated with the ancient I Ching—it illuminates the mechanics of restoring a harmonious balance to life by identifying the intent of the masculine and feminine halves of spirit in each of the 64 hexagrams.

It is an Oracle in the old sense of the word:  the agency or medium of a divine spirit.  This Oracle has an historical relationship with human beings that extends back at least 3,500 years.  It uses the hexagrams and their line changes as its means of expression.  It speaks in symbols that give voice to the archetypal essences of the changing relationships between things.  The Toltec I Ching releases the Oracle from the cage of intellectualism, loosing its magic back into the world of magic.  And this is just what the Oracle does for us, for to encounter the Oracle with our question is to approach the Great Mystery with a sense of the magic of potential transformation at hand—and to receive the Oracle’s answer is to have our own souls released from their cell of intellect and loosed back into the magic of the World Soul’s embodiment.

Beyond these essentially philosophical reasons for a new version, there are the political ones.  The first is related to class and the second to gender.  As mentioned above, the I Ching was an instrument of statecraft, not only consulted by but also produced by the very rulership of the dynasty.  This was not necessarily an ignoble enterprise initially, forming as it did part of the ancient experiment in governing, whereby great emphasis was placed on creating an enlightened rulership that would then create a peaceful and prosperous commonwealth.  Reading the received version of the I Ching, we can see how much of the commentary is written to the ruler, giving advice on how to govern those below.  Moreover, because the received version was produced by the victorious rulers of the Chou dynasty, much of the commentary is based on the military and political machinations involved in establishing their new dynasty.  This focus is amplified by the fact that the received commentary to the hexagrams essentially reflects a bias toward Confucian philosophy, which emphasized adherence to hierarchical relationships.

As to gender, the difficulty with the received version is well-known.  Hand-in-hand with its patriarchal classism, its patriarchal sexism of three and a half millennia ago is so obsolete as to be laughable at the very least and actually offensive in some cases.


The Toltec Connection

Such, in short, are the factors necessitating a new version of the I Ching in our time.

Now, a legitimate question can be raised:  Why introduce the ancient Toltec worldview of native Mesoamerica into the ancient Taoist worldview of native China?  The answer to this question is more straightforward than one might expect.

First, we need to start with the fact that the indigenous Native Americans and the indigenous Chinese share a common Mother Culture.  Linked by migrations across the Bering Straight ice bridge over the course of the Ice Ages, the peoples who eventually settled in ancient China and the ancient Americas shared an animistic, or shamanic, lifeway with numerous basic symbolic correlations.  Not the least of these is the oracular tradition, so foundational to their civilizations, that their respective writing systems begin with their divinatory systems—the Shang oracle bones in ancient China and the sacred calendar of the Olmec-Zapotec in ancient Mesoamerica.

Second, we need to accept that the I Ching is no longer merely a “Chinese text”.  For some time now, it has reached across borders to become a “World text”, even as its study has, simultaneously, been suppressed during modern times in China.

Third, we need to remember that even within ancient China, there were versions of the I Ching that shifted its focus onto another worldview, such as the Taoist and Tiantai Buddhist perspectives mentioned above.  The concept of reinterpreting the I Ching through another perspective is similar to looking through different facets of the same gem:  not only was this an accepted practice in ancient China, but it was considered proof of the universality of the I Ching’s applicability to all of human life.  Moreover, even the received King Wen version is an interpretation:  it is essential to keep in mind that King Wen composed the texts for each of the hexagrams while his son composed the texts for each of the line changes.  The founders of the Chou dynasty did not just re-order the sequence of the hexagrams—they wrote the texts.  That this is made explicit by the Chou dynasty’s own records accentuating the fact that the real I Ching, the core I Ching, is comprised of the 64 hexagrams and nothing more—just the 64 possible combinations of six solid and broken lines making up the hexagrams, without any accompanying text, commentary or interpretation.  It is the work of diviners to read the interaction between the upper and lower trigrams making up each hexagram and interpret it in light of the question.  What is called the King Wen version is as arbitrary a reading of the I Ching as any other interpretation.

As for the Toltec lifeway, specifically, it is because they are a people at the edge of mythological and historical times that are held up as the pinnacle of civilization by all those in the central plateau of ancient Mexico.  Their king, the universally-esteemed Quetzalcoatl, or Plumed Serpent, fostered the birth of the sacred calendar, writing, mathematics, art, architecture, and medicine, all while forbidding practices such as sacrifice.  It was a time of peace, in which the crops were never more bounteous, the production of goods was never more beautiful, and the people were never more happy.  The Toltec were great traders, as well, and their influence extended all the way down to the Maya in what is now Sothern Mexico and all the way up into what is now the South-Western United States.  They were part of the great Tolteca-Chichimeca migration that is marked by the peoples of the high desert plateau of the Inter-Mountain region of North America and Mexico—a people united by their common linguistic roots in the Uto-Aztecan language group.

It is with the descendants of those ancients, the contemporary Rarámuri of the Barranca del Cobre in Mexico, that my wife, daughter, and I were honored to live for two years in the late 1970s.  It was among those semi-nomadic indigenes that I found the family of the village shamans, the head of whom adopted me and initiated me into both the Rarámuri lifeway and the most secret of their rituals.  And it was from my exposure to their traditional life, relatively unchanged for thousands of years, that I was changed into an animist:  I was not any longer separated from nature by my humanity but was united with it by the commonality of spirit shared by all material—and immaterial—form.

It is no coincidence, then, that my collaborator in The Toltec I Ching, Martha Ramirez-Oropeza, is a direct descendant of the Rarámuri people.  An accomplished muralist in Mexico, Martha was co-founder of the Universidad Nahuatl in Ocotepec, Mexico—an institution that taught the traditional arts and sciences of the ancient Toltec lifeway.  She was especially successful in bringing contemporary Nahuatl-speaking elders from indigenous communities to teach, from whom she inherited a vast treasure house of knowledge and wisdom.

That knowledge and wisdom is immediately apparent in the Illustrations that epitomize each of the 64 hexagrams of The Toltec I Ching.  Derived primarily from the symbols found in the pre-Columbian codices and monumental architecture, the Illustrations mark a revival of the ancient Mesoamerican writing system and stand as an important accomplishment in their own right.

In this matter, The Toltec I Ching is not just the first new version of the I Ching in modern times—it is also the first version ever to interpret the Oracle through both visual imagery and the written word.   In modern parlance, we would say it constitutes a single language speaking simultaneously to the right and left hemispheres of the brain.  Conceived and executed as translations of equal weight, the images of the Illustrations and the words of the text form a single interpretation that shifts the focus of the I Ching from the Old World and onto the New World—it shifts the focus away from the cultural intimacy of the ancient Chinese to their land and history and spirituality and towards the cultural intimacy of the ancient Mesoamericans to their land and history and spirituality.

But it is also a shift in a metaphorical sense, as well—away from the Old World lifeway of top-down patriarchal classism and sexism doing violence to people and nature, and toward the New World lifeway of bottom-up self-governance revering all the people, animals, plants, land, water and climate making up this living world that is our common home.  It is a shift away from the Old World of justifying a civilization of war and hatred based on a history of unforgiveable wrongs on all sides, and towards the New World of building a new civilization of peace and prospering for all that is based on universal amnesty and reconciliation.  It is a shift, in other words, towards the future that everyone wants, not just for themselves but for their children and their children’s children and all their relations in the coming generations.

It is a shift away from the Old Dynasty of the few overruling the many and desecrating nature, in other words, and toward the New Dynasty of the many ruling themselves in order to live in perpetual harmony with nature.

It is the founding of this emerging world culture that The Toltec I Ching commemorates.


Legitimizing A New Dynasty

The Spirit of the Age has reversed course again and we have entered a new Dynasty.  Unlike the dynasties of old that ruled one nation or one people, this time it is an egalitarian Dynasty, a global shift of awareness, setting free the potential of all nations and all people—and their collective relationship with the environment—for the next 5,000 years.

The old Dynasty of nationalism, aggression and self-interest is overturned now by time.  In its place, like billions of seeds fallen on the fertile plain of history, the first signs of the new age of enlightened peers reveal the emerging change to all.  Like the light from a distant nova that takes years to reach us, the effects of this spiritual revolution are already on their way.


As outlined above, The Toltec I Ching follows the ages-old tradition of legitimizing the new Dynasty by introducing a new version of the I Ching that more accurately reflects the vision and ethics of our age while still maintaining the shamanically-charged power of the Oracle.  Keeping to the path laid down by the ancients, we continue the practice of periodically re-ordering the sequence of the 64 hexagrams in order to renew cyclic time and restore humaneness to the social order.

This, then, is the ultimate reason for the appearance of a completely new version of the I Ching at this time:  The Toltec I Ching is an intrinsic part of the theurgic process of legitimizing the New Dynasty of Universal Benefit that diviners of many different traditions have foretold.

It is a part of the evolving Mandate of Heaven.

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