Surprised by this title? Did you think the next step in the Magical Arts might be to learn Hebrew or Greek or Egyptian heiroglyphs, or perhaps to study Tarot? Those are worthy arts and useful to a mage, but not yet. After the considerable task of mastering and becoming aware of your own feelings and thoughts, of mastering the deportment of body and mind, of cultivating awareness, the next step is math.
The entire edifice of modern material science was erected on numbers and the understanding of how numbers can be used to describe quantities. Indeed, when it comes to matter, most of what we call “qualities” are also quantitative. A particle has so much mass, so much positive energy, so much electrical charge, and so forth. Everything is defined in terms of quantities. Or put another way, every thing that we identify as a separate thing is defined (at bottom) by quantities of these identifiable factors. Even a leaf of a tree must be measured to discover to which species it belongs.
Not so in magery. Quantities of ingredients are important in recipes, but each separate herb is not valued for its inclusion in the binomial nomenclature. Magery affects molecular and subatomic interactions certainly, but not directly, and not physically. Magery speaks in terms of qualities; both qualities inate and qualities of affect upon things externally to a particular herb, stone, crystal, or metal. The stars, in astrology, for example, are valued according to their influences on the human soul or upon events, not according to their quantities of mass, gravitational pull, orbit, and internal make up.
This is an aspect of magic that is seldom understood by those educated only in modern science. When what we call today “science” divorced itself from qualitative affects and married itself to quantities, what we call today “metaphysical arts” or “magic” carried on in the old way of natural philosophy. The goal of science is deeper and more detailed understanding of the physical makeup of things. It is also a deeper understanding of how one thing effects another,how they may interact to produce a medical effect or molecular changes, even atomic changes. Today, the cutting edge of biology and medicine are molecular and the chemical manipulation of molecules (including the DNA molecule) is the primary modality of treatment and experimentation.
Magery is quite different but not the opposite of modern science. They are the same in their use of experimentation to determine cause and effect relationships. They both utilize numbers and, as we shall see, geometry. The difference is that magery uses numbers to express qualitative relationships, not quantitative ones. Now, the mathematician may object that he does compare and contract qualities but that those qualities are always capable of subtler quantitative differences. On of the broadest examples of trying to transform qualities into quantities is the attempt to define the terms “masculine” and “feminine” in terms of quantities of hormones.
Perhaps I am being unfair and oversimplifying scientific biology, and I do not mean to imply that the approach of science, the quantitative approach, is wrong. We have seen that it leads to many truths. However, we have also seen its affect on human minds and cultures when its claim to have a monopoly on truth turns every person and every nation, even the land we love as our motherland, into mere mechanisms composed of so many interacting parts that are (assumed to be) predictable by virtue of measurements.
By focusing on “qualities” defined as “quantities,” we lose sight of something very important — the human mind and spirit and its ability to sense qualities intuitively. Without counting, weighing, and experimentation, the human soul can perceive the qualities of a rose or the blossom of hyssop. The scientific mindset might say that intuition is nothing more than unconscious and very swift weighing and measuring in the mind. Recognizing the names or species of flowers, plants, trees, or the names of gems, stones, or crystals is no doubt a process of observation. The eye recognizes the physical geometry of a plant, its colors, and so on to identifying it scientifically.
The mage’s eye, however, is an inner eye, an intuition of the imagination, which sees into qualities which are not physical. Such are called “spiritual” qualities or “metaphysical properties.” These are rooted in the broad classifications invented by the ancient astrologers — the twelve signs of the zodiac, the seven visible planets. The twelve signs of the zodiac are fundamental because the planets pass among them. Other constellations undoubtedly have power too, but unless a visible body in space passes through them, they form no direct temporal relationship with the Earth. They do, however, form varying angular relationships relative to any particular point on the Earth’s surface.
For example, take a constellation such as Ursa Major, Latin for the Great Bear, or the Big Dipper as it is known in English. No planet passes through this constellation of stars, yet it is a constant influence upon the Earth. If you think about it, all constellations are defined from the viewpoint of Earth, so they do not even have any existence apart from the humans looking up at them from this particular place in space.
At the same time, the Great Bear and other “fixed stars” do move apparently in the Earth’s sky from the point of view of the Northern and Southern hemispheres. As the world upon its tilted axis revolves around the Sun, the fixed stars move northward or southward as the Sun does (apparently). Scientific astronomy has made a big point out of the measurable fact that the Earth is not the center of the universe and that it revolves around the Sun and not vice versa, as the ancients observed. However useful this information may be, the physical truth of astrology lies in what appears to happen, not in what actually happens.
For example, the human mind experiences the Sun moving across the sky. It does not experience the Earth’s rotation. Our senses are incapable of feeling the Earth’s rotation and only if we get off the Earth can be actually observe the physical reality of a solar system in which Earth appears to be but a tiny, almost insignificant, part. For us, down on the ground, the Sun moves, the starry dome moves, the planets move, in relation to us. Magical qualities are based upon this point of view. That does not make them wrong or “false”; it just makes them true in a subjective, Earthbound way. Objectivity is always dependent upon where you stand to make your observations. What the twentieth century has taught us, is that it is very hard to find a place to stand where one can observe objects without interfering with them. The human mind interferes in some way, no matter where it stands. The human mind trained by modern science is full of assumptions and “truths” which it has accepted without direct experience. Magery is much the same, in that it requires training of the mind to interpret what the eye sees and the hand feels into reasonable sense. And the outcome is not the same. This does not mean magery’s way of seeing the world is more true than that of science. It means it is just as true, but in a different way.
Let us take Light for example. Science has become slightly stuck on the problem of light. Is it a wave or is it a particle? Scientific observation finds that it appears to be both and is the only example of anything that behaves that way. Considering that most kinds of observation depend on light, one would think that to be more of a problem than physicists make it. For the mage, it doesn’t matter in the least. The mage’s experience of light is simply that it permits vision. It is bright or dim and may be given many qualities based upon the source of light and the environment in which it exists. Light may cause joy; the lack of it fear. These are strong emotions that are useful in creating magical effects. Whether light is particle or wave matters not at all to the mage. Whether light is joyous or disturbing, uncanny, or weird matters very little to the physicist.
Light is one of the fundamental principles or ideas in magery. In the system of the Taoist sages of China, Light and Shadow are expressed as Yang and Yin. They are often treated as a “polarity” or as “oppositions,” but this is an error. True, within human psychology in particular cultures, these concepts may be conceived of as “opposites” but the concept of opposition is itself merely a human idea, not part of nature itself. Light and Shadow simply are, they exist. In one sense they are part of one thing, for shadow is cause by the blocking of light coming from a source. In magery, Light is a symbol of knowledge and understanding — seeing — while shadow or darkness is a symbol of ignorance and lack of understanding — what is hidden from the eye.
The dynamic relationship between what is seen and what is unseen may be applied to everything that is. The old Latin word for that which is unseen is “occultus” from which we derived the word “occult” in English. While some religious sects have re-defined the word to include connotations of “evil, forbidden, devilish,” this is not the original meaning of the word. Such connotations derive from the use of darkness in some religions as a symbol for evil, and the assignment of all that is evil to a single evil being called variously Satan, the Devil, etc. Magery itself has no real use for such religious concepts. That which is unseen is not necessarily evil. Electricity is for the most part unseen and therefore an “occult” force in the universe. Whether it is used for good or evil, is up to humans and other intelligent entities. I do not dismiss “Satan” for every mythos in the world contains such a figure: the mischief-maker, the trickster, a being who delights in fear and mahem and upsetting the plans of the other gods. For mages, however, taking these mythic personifications literally can seriously interfere with understanding magery and the structure of the cosmos. Personifications are useful for the purposes of prayer and evocation. The fact that they are “personifications” does not mean they are unreal. Things that are “made up” in the eyes of modern material science are quite real and very important to study.
The natural division of life into day and night, waking and sleeping, need have no connotations of good and evil. The notion that night or darkness had something to do with evil probably goes back a long time to the simple fact that for homo sapiens, who do not see well in the dark and are not by nature nocturnal, night was simply dangerous.
In magery, as an art, good and evil are not magical categories; they are moral categories. The seepage of the idea of polar opposites from religion into magery has caused a good deal of confusion. Those things that religion defines as “opposites” are better thought of as different phases of being, states of existence. These transform and transmute into each other; they are complementary, but not two poles of an either-or scenario. Take for example, two signs of the Zodiac that are opposite each other in the circle of the sky — say, Gemini and Sagittarius. These signs are very different from each other, but they are not “opposites” in an absolute sense. In astrology if there is a planet in Gemini and another in Sagittarius at the same degree of each sign, those planets are said to be “in opposition.” That does not mean that they are “opposites” in the sense of the word which implies polarity. One is not positive and the other negative, as we say (arbitrarily) with regard to electrical charge or magnetic poles.
Rather, the opposition of planets is a geometric relationship. It means that they are connected by a straight line or an angle of 180°. Astrology is built up upon symbolic meanings for the constellations and planets, but it is also built upon geometry. The aspects and transits in a horoscope form angles and shapes. Planets (and this of course includes the Sun and Moon in astrological terms) are located at certain angular relationships. A “square” is an angle of 90°. A “trine” is an angle of 60°. A “sextile” is an angle of 30°, a semi-square an angle of 45° and so on. Geometrically, a trine alludes to an equilateral triangle, and a square to a geometric square, or equally well, a right triangle. Oppositions and conjunctions allude to lines and points, the conjunction, if perfect, meaning that the two planets occupy the same degree of the same sign, and so, geometrically speaking, the same point. Naturally, this is not the case in the scientific solar system. It is a reality that exists within the symbolic universe of the horoscope, which is drawn from the viewpoint of a particular spot on the Earth’s surface.
Pythagoras, one of the first great geometricians, found meaning in the relationships between angles and shapes. Mathematics may be said to be based in geometry, as are all the arts of building, and our whole understanding of the physical world. What magery adds to this is a spiritual or imaginal significance to numbers and proportions, angles and shapes. The symbolic system of Free Masonry is based upon such meanings. The right angle signifies moral rightness, correctness, and truth. If we consider the right angle of 90°, it is the fourth part of a circle. The circle signifies wholeness, the universe, and the limits of one’s knowledge, or of one’s behavior within a moral system.
The significance of the fourth part of a circle (a quarter circle) is brought forth in the horoscope in which each quarter of the circle of the sky represents a phase of life, and particular aspects of life. That is, the development of the psyche inwardly and in relationships as the cycle of life progresses. The astrological aspect called a “square” is an angle of 90° between two planets. Squares are sometimes considered troublesome, indicating areas of confliction, but this is a negative interpretation of something which is simply part of life — two aspects of life that demand our attention at the same time. The Masonic meaning of the square (the builder’s tool of that name) holds a more exact significance of this aspect; it suggests that the right angle brings together the horizontal and vertical dimensions of human existence. The horizontal is our relationships with others; the vertical, our relationship with God. Or, if you prefer a different term, our aspirations towards the sublime, the universal, the infinite. It is these two dimensions that make up the life of a human being and the correct relationship between the two (the angle of 90°) signifies a perfect balance in which these different impulses act upon each other to create a whole.
Why believe that the positions and relative angles of planets in signs of the Zodiac affect human life? Because it has been found useful. It is a symbolic system based upon the observation of the sky, which was developed long ago as a way to understand human behavior and the events of life. Do these geometries in the sky affect us from a modern scientific perspective? Of course not. Not in the “reality” defined by materialism.
Besides the 19 fundamental categories of astrology (signs and planets) magery has other elements. Yet these are not the 118 “elements” defined by atomic physics. These are the four elements defined by essential physics, the science of created essences. Philosophers long have argued over the “reality” of essences. Does a thing have an essence? Or is it created in the human mind? As in most things of magery, the answer is both. Earth, Air, Fire and Water are the four classical and alchemical elements — or to avoid confusion, let us say “elemental essences.” We may call the study of essences and their interactions, “essential physics” to distinguish it from material physics. Once, essential physics was all we had — it was not distinguished from material physics. Only in the 19th an 20th centuries do we find a strict distinction being made. Materialism, as a cultural ideology, absorbed the imaginations of the Western cultures. For reasons that were partly political, men decided to cast off all the ideas created by “the Church” (meaning Catholicism usually) and along with them, practically all the ideas of the Middle Ages because the only scholars and “scientists” in the Middle Ages were monks and clerics. For the new materialist worldview, things do not have essences; they have protons and electrons and certain physical properties. Again, this is fine, fascinating, and a wonderful field of study. Essential physics looks at things in a different way. It is concerned not with defining and explaining thisngs in terms of “matter” (a concept that is breaking down in the field of physics) as reality but with imaginal reality. The fact that the one field and the other have been separated is a good thing, in one way, because it was causing problems when people did not realize what was verifiable fact and what was imagination. In effect the “birth of modern science” was the birth of a narrower and easier field of enquiry: those things perceptible by physical senses and capable of easy repetition. Repeating alchemical experiments is much harder, because the work is subjective as well as objective. It depends upon the awareness of the experimenter.
So, elemental essences are not simply “early science” that was “proved wrong.” Fire, in the alchemical sense, encompasses all things that give off heat and light. It is the essence of those properties. Moreover, alchemical Fire is the process of transformation, which causes material things to dissolve and disintegrate and be reformed into something else. It is the element of purification as well. Transformation and purification have meaning for chemistry too, but in alchemy they go further, as symbolic of the psyche and its relationship to its own supra-material existence. Modern science has proven that many things which it believes to exist contradict the ordinary model of material existence. The whole concept of matter and energy being different things is itself dissolving and transforming into new ideas. No doubt, in time, the idea that matter was composed of energetic particles will seem quaint and laughable.
The concepts of magery are, however, neither quaint nor laughable. They describe the psyche’s relationship to this existence we call material, and it is a fundamental relationship, not a superficial one. Mages have long said that Mind is the basis of all existences. That does not mean that what science calls the human mind is the basis of existence; it means that Mind is what we call the basis of existence. Not a thing somehow inside the brain’s chemistry, but the very matrix of existence itself, of which the human brain is merely a kind of receiver. I like the analogy of the radio, which receives many channels broadcast in that invisible medium of radio waves through the surrounding air (or more broadly space). Invisible, unseen, occult. Matter, and consequently material events, exist as expressions of this invisible medium we may call Mind. Or, if it is any less confusing, call it Essence with a capital E.
The alchemists called it Aether. That term has been used for a number of theoretical substances over the history of the development of chemistry. The alchemical use of the term Aether, refers to that matrix from which all qualities are born: Air, Earth, Fire, Water. The four elements describe the totality of qualities in the material reality experienced directly by our bodies and the limited physical senses of those bodies. Aether is therefore that which generates all bodies and bodies, from particles to stars, are motion. For energy is motion. A particle without motion is an impossibility (or at any rate unknown) for without motion it simply has no existence in what we call the material world. In fact things of the higher planes are also always in motion and defined by their motion.
And motion is understood within the concepts of Geometry. Space is often spoken of as if it were a “thing” but in reality it is the geometric matrix of motion. Time is not a “thing” either, despite the wishes of science and science fiction. Time is merely an invention of men to measure motion and transformation. It is geometry that fundamentally describes all reality on all planes of existence. And it is in the Aetherial matrix of All that magery is performed. It is possible because Mind is Aetherial and our brains and thoughts can tune in to Mind. If scientists believe mages to be “out of their minds” that is a reasonably accurate assessment, for doing magery requires one to realize that the brain is not the extent of one’s mind in a personal sense, nor is the “personal” mind actually separate from that Universal Mind.
Having arrived at that realization, we then need to begin understanding that the cosmos and everything in it is geometry. Geometry defines things and magical geometry (as distinct from what you probably learned in school) gives essences and qualities to angles and polygons. They are not just useful for calculating areas and volumes in the material plane of existence. They also allow us to calculate essential qualities and relationships in the higher planes of existence. The square, for example, represents the four elements, a totality. The square (or the cube) is used as a symbol of cosmos. The square in one plane (geometrical plane) symbolizes the Earth or the material plane of existence. Similarly, the circle squared, which is a circle with two perpendicular lines through it, is a symbol used by astrology for elemental Earth. Different signs of the Zodiac are defined in terms of each of the four elements. So, for example, Gemini is an Air sign, while Saggitarius is a Fire sign. Cancer is Water, Taurus is Earth, and so on. There are three signs for each essential element, and these express three different aspects of the essence. Gemini, Libra, and Aquarius each express an aspect of elemental Air, but each is also quite different from the other two. Yet, this network of qualities can be expressed in terms of a triangle, a triad or grouping of three in one.
This article merely introduces the significance of geometry, mainly from the standpoint of astrology. Aspiring mages who neglect the study of astrology will be missing the fundamentals of magical cosmology. Those who study astrology only as a mode of divination may still miss its broader significance in giving meaning to the angles and shapes of geometry.