In speaking of “Taoist thought” I have often throughout this work used the term as a convenient shorthand for “primeval Chinese thought.” Strictly speaking, this usage is historically incorrect. Laozi is traditionally regarded as the founder of Taoism and is associated with “primordial” or “original” Taoism. Whether he actually existed is disputed. According to tradition the classic text attributed to him, the Tao Te Ching, was written around the 6th century BCE. The oldest extant text, however, dates to the late 4th century BCE. The earliest strata of the I Ching predate both these historical periods by many centuries, if not millennia. Taoism derived its cosmological notions from the philosophy of yin and yang, and from that of the Five Phases or Five Elements. Both these schools of thought were overwhelmingly influenced and shaped by exposure to the oldest known text of ancient Chinese classics, the I Ching.[1]
The actual symbolic logic of Taoism, although derived from the I Ching is extremely simplistic compared with that of the original upon which it is based. Whereas the philosophy of yinandyang as presented in the Tao Te Ching comprises little more than a two-dimensional cycle of two-valued elements, in the I Ching these two represent vectors in a six-dimensional combinatorial manifold of 64 hexagrams (1,2). Clearly, it is a difference like that between night and day. It is, in fact, a literal comparing of 22 with 26, the latter holding many more possibilities. The actual difference[2] in the logic and geometry emerging from the two is greater even than it appears at first. It eventuates not from just a simple geometric progression but from a mandalic intertwining and association of logical elements that give rise to different amplitudes of dimension as well as to a greater number of dimensions. This mandalic interweaving leads also to a richer catalogue of relationship types.[3]
Long viewed as mainly an ancient text of Chinese divination,theI Chingencompasses many more categories of thought - - - among them symbolic logic, geometry, and combinatorics. As a treatise which deals with combinatorics alone, it soars without equal, the first known compendium of combinatorial elements and still one of the finest. The logic and geometry that are embedded in the hexagram system of the I Ching are best understood in terms of dimensions and vectors akin to those in Cartesian systematics, and of logic gates analogous to the truth tables of Boolean algebra. And still the cognoscente will want to explore beyond the pertinency of these disciplines as also beyond Taoism to find the full meaning and intent of the I Ching.[4]
Having existed for millenia, and itself a treatise regarding change[5] in its many aspects, it would be inconceivable that the I Ching as we have it today is as it was in its beginnings. Popular at all societal levels through its entire existence, reinterpretations and reworkings have been myriad. Confucianism in particular interlaced its own brand of philosophical and “ethical-sociopolitical teachings” during and after the fifth century BCE. Other schools of thought added their unique perspectives to what became essentially a massive melting pot of schematization, one not always self-consistent by any means.
When one attempts to uncover the original face of the I Ching the difficulties encountered soon appear insurmountable. If involved in such a venture, it is imperative to bear in mind the bedrock strata of the work were in some ways more ingenuous, and in some more intricate, than the traditional version that has come down to us. The earliest layers arose in context of a preliterate oral tradition with all the many unique aspects of being that entails. In some ways the golden age of the I Ching ended with coming of the written word and literacy. The multidimensional logic that was readily accommodated by an oral tradition foundered and eventually was all but lost in the unrelenting techno-sociological onslaught of script with its associated inevitable linearity. Anyone who hopes to excavate the buried multidimensional logic of the primordial I Ching can expect to do a good deal of laborious digging.
[1] Two diagrams known as bagua (or pa kua) that figure prominently in the I Ching and its Commentaries predate their appearances in the I Ching. The Lo Shu Square is sometimes associated with the Later Heaven arrangement of the bagua or trigrams, and the Yellow River Map is sometimes associated with the Earlier Heaven arrangement of trigrams. Both are linked to astronomical events of the sixth millennium BCE. Although part of Chinese mythology, they played an important role in development of Chinese philosophy. The Lo Shu Square is intimately connected with the legacy of the most ancient Chinese mathematical and divinatory traditions. The Lo Shu is the unique normal magic square (1,2) of order three (every normal magic square of order three is derived from Lo Shu by rotation or reflection). [Wikipedia]
[2] Taking into account both changing lines and unchanging lines of hexagrams there are four possible variants for each line: unchanging yin, unchanging yang, changing yin, and changing yang. This results in a total of 46 or 4096 possible different line combinations for each six-line figure. This allows for an enormous number of logical / geometric configurations, all of which map to various points of the mandalic cube or, in terms of Cartesian coordinates, to discretized points of the three-dimensional cube bounded by the eight Cartesian triads which have coordinates of +1 and/or -1 in all possible combinations (corresponding to the eight trigrams.)
To this point changing lines have not been discussed to avoid overcomplicating already complicated matters too soon. Changing lines play an indispensable role in all changes of yin lines to yang lines and vice versa, and therefore, in changes of one hexagram to another. They are also essential elements in formation of the geometric line segment generated by the I Ching hexagrams which I have earlier referred to as the "Taoist line“ and which we have yet to broach fully. Mandalic line segments uniformly comprise sixteen interrelated elements, hexagrams with changing and/or unchanging lines. Though various mandalic line segments have different compositions in terms of six-dimensional hexagrams, these hexagrams can always be reduced in logical and geometrical terms to sixteen bigram forms containing changing and/or unchanging lines. These bigram sets are all identical. No other variants are possible, since 42 equals 16. In this sense there is a single species of mandalic line segment but one which takes on different characteristics in different dimensional contexts. Every hexagram has a commentary appended to each of its six lines, which annotation is intended to be reflected upon only if the line is a changing one at time of consulting the oracle. Justly put, this system is brilliant beyond belief.
[3] Understand here that ‘relationship types’ may variously refer to human relationships in a society, to particle relationships in context of the atom, or to any other species of relationship one might imagine.
[4] For an exhaustive listing of linkstoI Ching related materials on the Web see here.
[5] Indeed, an alternative name of the I Ching in English is Book of Changes. The ensconced multidimensional logic encoded in the original work purports to be a microcosm describing all possible pathways of change, and their incessant changing relationships in the greater macrocosm of the universe.
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Scroll to bottom for links to Previous / Next pages (if existent). This blog builds on what came before so the best way to follow it is chronologically. Tumblr doesn’t make that easy to do. Since the most recent page is reckoned as Page 1 the number of the actual Page 1 continually changes as new posts are added. To determine the number currently needed to locate Page 1 go to the most recent post which is here. The current total number of pages in the blog will be found at the bottom. The true Page 1 can be reached by changing the web address mandalicgeometry.tumblr.com to mandalicgeometry.tumblr.com/page/x, exchanging my current page number for x and entering. To find a different true page(p) subtract p from x+1 to get the number(n) to use. Place n in the URL instead of x (mandalicgeometry.tumblr.com/page/n) where n = x + 1 - p. :)
When people think of “the elements,” they’re probably thinking of the typical earth, air, water, and fire, but they don’t think of the fifth element, nor do they think about the stats of the elements or even the power behind them. This post is meant to go into detail about the five elements, and I hope that I (and my excessive reasearch, lol) are of use to you!
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Earth
The Earth element is the one most closely linked with our physical world, and the densest of all the elements. It is the foundation on which the other elements, and is a receptive energy, helping us to accept responsibility and bringing to our attention limitations in our makeup. It is represented in the forms of burying objects in the earth, herbalism, and making images out of wood or stone. Spells that benefit from the element are business-related spells, fertility-related spells, prosperity-related spells, and stability-related spells.
Represents: strength, abundance, stability, prosperity, wealth and femininity
Trees: Cypress, Honeysuckle, Jasmin, Lilac (some say Lilac is Water)
Animals: cow, bull, dog, horse, ant, bear, wolf
Instruments: drums and percussion
Type Of Magick: Gardening, magnet images, stone (jewel divination, work with crystals), knot, Binding, money spells, grounding, finding treasures, runes
Ritual Action: Burying, making clay effigies, planting trees or herbs
Chant to Invoke:
“Here and now
I invoke the elemental force of earth
I call to the swirling dust
And dawn lit mountains,
To the farmer’s field
and all the swaying trees
You that remains solid
You that teaches of quiet stability
You that holds us firm against your skin.
I call your body here to infuse my intention
With your boundless gifts.
I call you here to fashion the spirit cavern,
Root my will in your soil,
and ground my purpose in the stones
Boulder and gravel
Redwood and rose
Earth, I call to thee.“
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Air
Air governs the realm of the mind and all mental activity, it is the most ethereal of the elements. As it is the element of the wind, it governs all movement. Air is represented in the forms of tossing objects into the wind, aromatherapy, songs, and hiding things in high places. It rules spells involving travels, instruction, freedom, knowledge, discovering lost items, and can also be used to develop psychic faculties. Air also rules the visualization.
Represents: the mind and intelligence, communication, telepathy, psychic powers, inspiration, imagination, ideas, knowledge, dreams and wishes
Trees: Acacia, Almond, Aspen, Hazel, Linden, Maple, Pine
Animals: Eagle, raven, spider
Instruments: flute, wind instruments
Type Of Magick: Divination, concentration, wind magick, prophecy, Karma work
Ritual Actions: Playing a flute, tossing objects in the air (over the shoulder), burning incense, hanging objects in trees
Chant To Invoke:
“Here and now
I evoke the elemental force of air.
The winds of intellect and imagination,
Satisfying source of flight, breath, and life.
I seek the open sky within myself
That I might breathe deep of freedom, ideas, sounds, and space.
I call you forth to sweep away
All that accumulates in the unseen places and to sing beauty into the world.
Wing and Feather,
Storm and Leaf,
Air, I call thee hence”
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Fire
Fire cleanses and purifies, but it is also creative and destructive. It can consume everything in it’s path and it is the only one of the elements that cannot exist without feeding on something else. It offers warmth and cooks food, but can get out of control. It has the power to transform everything it touches. It is positive and lifting, but can be frightening if not controlled. It is the most physical and spiritual of the elements and represents magick itself. Fire is represented in the forms of burning objects, love spells (always preferably self-love spells), baking, and lighting candles and fires.
It is the element of love and emotions, constantly active beneath the surface, influencing our moods and emotional responses. It purifies, heals, offers emotional release, and removes all that is stagnant. It is represented in the forms of pouring water over objects, brew making, healing spells, ritual bathing, and tossing objects into of water. Spells that benefit from this element are friendship spells, fertility spells, happiness spells, and relationship spells.
Represents: emotions, absorption, subconscious, purification, eternal movement, wisdom, the soul, emotional aspects of love and femininity
Gender: Feminine
Direction: West
Energy: Receptive
Symbols: Ocean, river, shell, spring, lake, well, rain, fog, cup
Spirit (also known as Ether/Aether) is, by far, the most complex and complicated element to explain. It is what unites all things, anywhere and everywhere, and is our connection to the otherworld in rituals. The spirit element transports us beyond any narrow confines and allows us to open up to something much bigger, it is present in all aspects of life, and goes beyond thought and emotion. Unlike the other four elements it has no defined place or location, even though we cannot specifically place it, we know it is there. It provides the space, connection, and balance for the other elements to exist. All spells benefit from this element.
✨Represents: the sense of joy and union
Gender: none
✨Direction: everywhere
Energy: universal
✨Symbols: cord, rope
Pentagram Placement: upper
✨Goddesses: The Lady
Gods: The Horner God
✨Spirits: —
Time: always
✨Cycle Of Life: eternity
Season: year cycle (all seasons)
✨Zodiac: —
Colors: white
✨Sense: higher receptions
Stones and Jewels: —
✨Magick Tools: —
Metals: —
✨Herbal: —
Trees: —
✨Animals: dove
Instruments: —
✨Type Of Magick: —
Ritual Action: —
✨Chant To Invoke:
“Here and now,
I reach deep within myself.
Here and now,
I invoke spirit.
I call on the force connecting me
To the whole of existence
The thread running back through my blood,
And the ripples spreading over from my actions
I call on the visions that have inspired me, the kindness that has lifted me,
