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.
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.
The following is a reply to the question, “How can I be genuinely happy?” as interpreted via The Toltec I Ching.
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.
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—
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.
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.
© 2014 William Douglas Horden
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.
It is necessary to actually work through these examples—and others of your own design—to see how elegantly the calculations proceed.