Appendices C and D are included as they are referenced in the chapters given in these web pages.



Geometry is a type of mathematics which deals with space. Because the qualities of the material world—the qualitative domain—interpenetrates with its spatial attributes—the spatial domain—geometry can be used to understand how the world is created. (The concepts concised here are discussed systematically and in depth in their relevant chapters.)

a. Space as Currently Defined: Most modern physicists begin and end their cosmologies with space. It is true that everything is said to be composed of light (electromagnetic vibrations), but these are said to be merely fluctuations in space. Space is said to connect everything and actually to be everything. At its ground state (lowest energy level) space is said to be a ‘vacuum,’ which means ‘void’ or ‘empty space.’ The vacuum of physics, however, is said to never be empty of fluctuations much less empty of space itself. Hence it cannot, in truth, be perceived of as pure Being—the infinite (∞)—nor as no-thing or zero space (0).

In the hermetic cosmology the infinite comes first and is totally non-spatial in nature. This is the so-called substrate, and it is a true vacuum. Although only infinite in potential relative to matter it is real in and of itself and is pure absolute Being.

In addition, there is a central point of pure Being—a personal spirit (the shekinah)—in every living system. This is a ‘part’ of the substrate. That shekinah produces light. Light in turn produces both energy as motion and energy as a substance or ‘extent’ (space). In this cosmology light as an electromagnetic ray is the energy of motion and is the energy of space, but space is only one of two attributes light possesses—and the substrate and personal spirit are prior even to light.

b. Space as the Extent of a System: The personal spirit is a zero point at the center of a system. That point gives life to the system. (All centered systems are living or have the potential to become living.) Light emerges (emanates) from the personal spirit and among other things is experienced as space. There is no energy which is not a part of a system—be it energy as a substance (space) or energy as motion (kinetic energy). ‘Soul’ is the qualitative and spatial extent of the work of the personal spirit at any one moment in time. ‘Space’ is the extent of the growth of a system—the size of its soul.

It is the nature of ‘soul-work’ to produce a spatial extent—but also to provide limits. The boundary condition a system experiences as ‘size’ entails its current actualized extent—the extent of its spatial growth (and qualitatively of its evolution). In terms of electrodynamics, the size of a particular system is a function of the real existence of one wave of an electromagnetic ray. In particle form this is the size of a single photon. (Every system is a photon but there are many different sizes of photons.)

c. Spatial Coordinate Systems: A Cartesian coordinate system is a graph with a zero point at the center. This type of graph can be utilized to map points making up a system composed of three spatial dimensions.

Usually the coordinates are called +x and -x (to-the-right and to-the-left), +y and –y (to-the-fore and to-the-back), and +z and –z (up and down). These coordinates represent parts—be it parts in the body of a person or in the external environment. (Places ‘in’ space are parts of a system because even an external world is a system—a whole-in-the-making.)

One of the most valuable things about this type of graph is that it shows these parts have zero (the shekinah) as their origin point. In the process it can be seen that a line is composed of polarities which progress outward from the central point. A second thing the graph does is make a case against the belief that negative directions are connected to negative things in the sense of being bad, or even to things which relate to non-being. The graph makes it clear that the negative directions are not negative in either sense and do not entail non-being, but rather ‘to-the-left-of’ (-x), ‘in-back-of’ (-y), and ‘below’ or down (-z). The material world is not a composite of non-being and Being. Matter is composed of polarities which are merely different perspectives on zero point (on spirit or pure Being). The left side of a person is not non-existent (or bad). When a person moves backwards instead of forward, they do not step into nothingness. [Light has positive and negative poles. There are places in a Fallen world where there is an absence of both polarities (an absence of light), but these entail lack of the correct level of light.]

d. Space and the Elements: Space is an attribute of light. It arises as soon as the polarities begin to interact. The in and out movements of the two poles of an electromagnetic ray produce four elements and in the process three domains—one of which is space and another of which is motion. In astrology these primary interactions are referred to as fire (+), earth (-/+), air (+/-), and water (-) elements. In addition to producing space and motion they produce the current directions which a system can move in space (in a three-dimensional world). In terms of the direction experienced as ‘in’ and ‘out’ the positive (electric) pole of light, when going out from center is purely positive (+). When it moves back towards center, it is still positive but manifesting a negative direction ‘inward’ (+/-). The negative (magnetic) pole of light when moving in towards the center is purely negative (-); however it too at some point in time moves out from the center. ‘Out’ is a positive direction, so again there is a combination of directions (-/+). Animated versions of electromagnetic rays can be accessed on the internet.1 (Note that an electromagnetic ray also moves overall at a 90o angle to these movements. It does not merely cycle between polarities.)

e. Value in Nature: A Cartesian coordinate system helps show there is ‘value’ in nature. Value refers to preference. Among other things value can mean there are beginnings but no endings. The coordinates have a beginning at zero point. Once begun they have no end. Numbers can be put on a Cartesian graph. There are a finite number of numbers from any number chosen to 0 point (e.g. 5, 4, 3, 2, 1, 0); but there are an infinite number of potential numbers from zero outward (0, 1, 2, 3, 4, 5, 6, 7, 8 . . . ). ‘Growth’ entails an extending of the outer limits. The outer limits of a coordinate system (and of a living system) can potentially reach to infinity.

In addition to the capacity for the limits of a three-dimensional system to potentially reach out to infinity, there is at all times a potential for the system to move up to a fourth dimension, and ever higher levels of space. The existence of the three actualized dimensions is evidence there are higher dimensions, and this is what the archetypes teach. [A three-dimensional system with four elements (3 x 4) is manifesting twelve archetypes. Two new coordinates or directions (four new elements) would presumably be added with each higher dimension which the system actualized.]

There are both numerous levels within a particular dimension and the levels experienced as dimensions. In terms of the former, a three dimensional body can be composed of atoms, molecules, cells, organs, etc., all of which are levels within a three dimensional system. (As with the dimensions, each level encompasses those below.)

f. Inner and Outer Worlds: Systems have ‘inner and outer worlds’ because of the existence of levels of being. The nature of reality is such that systems always have both an inner actualized self and an external world, the latter of which is a higher level whole-in-the-making for them, one which they themselves will one day encompass when they realize it is currently both an external world and a personal potential—a future kind of ‘self.’ When a system ascends to a higher dimension, in that higher world they then have a more extensive internal (actualized) world with an added dimensional layer, plus a new external world (a new whole-in-the-making).

g. Higher Dimensions: There are no spatial dimensions except in so far as they are embodied by a system. When trying to understand the concept of dimensions physicist David Bohm suggested looking at the atomic level of being and trying to visualize how it might be related to a higher level self as a higher dimensional reality.2

h. Space & the Infinite: Space derives from the infinite and continues to possess its own type of infinite nature. This can be seen in several ways including via the archetypes and their three domains—the energical, spatial and qualitative domains. The qualitative domain (that of Beinghood Per Se) is the most important. This helps show that all space is the space of a system (a whole or whole-in-the-making). The domain of Beinghood shows that space is ongoingly produced by the personal spirit of a system relating to the substrate. (Since matter is produced through a relationship between two types of spiritual substances it is actually harder to explain how matter can be finite than it is to explain how it can be infinite.)

Space and Finitude: Creation is the result of a system actualizing potentials via their personal spirit as it accesses the substrate. Spatially speaking, this begins with a point producing a line. The point is as a part to the whole. Wholes are over parts and this produces levels—spatially speaking dimensions. As dimensions are added, this process becomes one in which a lower dimension is relating to a higher dimension as part to whole. Because creation occurs in steps, each step can be complete-in-time. This level-like nature is why space is finite as well as infinite.

Space and Time: Time is the result of a system actualizing potentials via their personal spirit as it accesses the substrate. The famous physicist Hermann Minkowski claimed time was a fourth dimension of space, whereas from the hermetic perspective the current human-level experience of time is the process of a three-dimensional system relating to a fourth dimension (a whole-in-the-making).

Space, Time and Zero Point: The personal spirit is a zero point at the center of a system. Because time is a process of spatial levels interacting, what is zero in space is zero in time. Currently physicists do not recognize the reality of a true zero point in space or time (i.e., as no-thing but real). The shekinah is a true zero point, and it is real. That there is such a thing as zero space and time was the subject of the Einstein-Podolsky-Rosen (EPR) experiment.3 If two electrons which have once shared an atom are separated from one another they will continue to relate as parts even when they are theoretically on opposite sides of the universe, and the effect will be literally instantaneous. These parts which have been torn apart continue to act like parts in a whole, i.e., as if there is no space or time separating them. If for instance one has plus spin and the other minus spin, and the direction of the spin of one electron is changed, the other will immediately change its own spin. [This is also an illustration of how zero relates to the wholeness of a system, and how that which is eternal relates to that which is everlasting.]

Eternal vs. Everlasting: The personal spirit as a zero point (0) actualizes the infinite substrate (∞) by itself being infinitely small. It actually ‘reaches’ infinity. The infinite and zero are outside time. They are both eternal. Within a system the shekinah is a point of eternal being—the eternal now.

The body is an extended everlasting now. A ‘whole’ is something which combines a number of parts into one unit in space at the same time. That whole then also moves as a whole through time. All the many different parts working together as one in a system are sharing the same moment. [The substance of this idea is to be found in the paradox of ‘the arrow in flight’ put forth by the Eleatic philosopher Zeno (490 BC).4 This paradox illustrates that, when an arrow is in flight, the arrow moves as a whole. This is why all the parts in the arrow share each moment in time at the same time.] A whole is a material expression of a point-instant. This makes it possible for the body to be an expression of an infinite substance—an actual (material) infinity. What is materially infinite is ‘everlasting’ as opposed to ‘eternal.’

Space as a Whole & a Singularity: The above is related to the question of whether something manifesting ‘space,’ i.e., with an extended and presumably limited material body, can be infinite in space-time. As it turns out, the body expresses the infinite nature of spirit by being, as noted, an actual infinity. It was the mathematician Georg Cantor via his set theory who offered a proof of the real existence of ‘actual’ infinities. This is what a material body is when it is whole. People are a material infinity. They are also everlasting, and in a personal sense—their entire being as such, including their body—when and only when it is whole, with no unactualized potentials (in terms of light, no shadows).

All space is the space of a system and every system is a ‘world’. It is the existence of levels of being which makes it possible for a system (a world) to be a material infinity. Levels begin with the shekinah, which singles out a specific set of potentials and yet is always complete-in-time because, paradoxically, it is the substrate and Ein Sof is the all.

Space as a Whole-in-the-Making: Every time two or more systems relate they produce a little world so to speak—a whole-in-the-making. That world possessed the energy of substance as well as that of kinetic energy, and that substance is spatial in nature. (Space as noted is the extent of the personal spirit—in this case of a group personal spirit.) The space of a whole-in-the-making is of a type which cannot be seen because each system can see only the space within its own range and capacity to see. It sees all those to the left of its ‘event horizon’—those in the role of parts or potential parts for the system versus those of which the system is a part or a potential part.

i. Pure Math vs. Geometry: Geometry is about space. Number theory—so-called ‘pure’ mathematics—affirms the truths of geometry (and of the archetypes) relative to how the world and every system is composed and how it comes into being. In number theory the personal spirit is represented by zero (0), and the substrate by the symbol for the infinite (∞). ‘Soul-work’ (the production of a body and soul) is represented by the number one (1). The purpose of Chapter 6, was to explain what soul-work entails. What was referred to as the ‘external reference’ aspect of the soul produces limits and makes a system a singularity. The ‘internal reference’ aspect of the soul on the other hand makes it possible for a spatial continuum to exist so that a system can be whole internally. Both the terms ‘singularity’ and ‘whole’ have the sense of one (1).

In number theory the equation 0 x ∞ = 1 is a way to express the fact that a material system (as symbolized by the number 1) is created by the shekinah (0) via a relationship with the substrate (∞). One is the first real whole number and symbolizes an actual or real (material) infinity. Mathematicians agree this is a valid mathematical formula.5 Despite this, some still claim the equation 0 x ∞ = 1 is a lazy way to say ∞ × 0 = lim x→∞ (x × 1/x) = 1, in other words the process of producing any whole must be seen as approaching a limit but never reaching it. That is what Zeno thought too, but that is not what the formula says.

j. Matter as Composed of Spirit: As a spatial coordinate system helps show, zero is the origin of a material body. It is one thing to say matter derives from spirit, another to say it is composed of spirit. As the mathematician Claud Bragdon helped bring to light (cf. Chapter 6) when he encouraged people to understand how and why the very first dimension (a line) is continuous, geometry helps show that, like a line, three dimensional systems are composed of the substance of spirit, and specifically of zero (0) as it relates to the substrate (∞). Per Bragdon, it takes an infinite number (∞) of infinitely small points (0) to make a line whole (continuous). It takes an infinite number of infinitely small lines to make a surface whole, and it takes an infinite number of infinitely small surfaces to make a cube-being (a three-dimensional system) whole. Every line (surface, cube) is composed of spirit—of both spirit as zero (0) and spirit as the infinite (∞).

Again, pure mathematics supports geometry. A material line actually is made up of point-instants, and an infinite number of these. Both these conclusions are present in the other two ways of expressing the equation 0 x ∞ = 1. These are: (a) 1/∞ = 0, and (b) 1/0 = ∞. The first (a) says that, if you divide a line-being (1) infinitely (∞) what you will get down to is zero or a point-instant (∙). The other (b) says that, if you do not divide a line-being (1/0) the extent of the line is infinite in nature (∞). In order to be continuous internally, a line must be composed of an infinite number of point-instants. In order to be infinitely extended the line must be both infinite and complete. The existence of levels of being allows for a material (completed) infinity to exist. Both geometry and pure mathematics are a way to show that everything material is composed of the substance of spirit.

NOTE: It is important when visualizing a line as a system to remember it is composed of coordinates as illustrated via a spatial coordinate system. A line begins with zero, and zero is at the center of an evenly divided line. The same is true of a square and a cube. A three-dimensional coordinate system is like a cube which begins at the center. [Systems can also be visualized as globes with all potential coordinates out from center equal to every other. (Every line then also has ‘symmetry’ relative to the one opposite it.)]

k. Space and Motion: The equation 0 x ∞ = 1 not only explains how space is created but also motion. Creation is the act of producing motion as well as space. Motion is both finite and infinite because of the existence of levels of being. As with space, it takes an infinite number of points in a row to produce the inner wholeness of motion, and (externally) it takes the existence of levels so as to complete the motion. This is why motion as well as space is both finite and infinite. The crux of this idea is best represented by Zeno’s paradox of Achilles and the Tortoise.6 [Note: Every interaction between two or more systems has these characteristics.]

l. Infinity & Renormalization: There are many ways to see that the infinite is and remains an integral part of the material world. One of these is via the various mathematical formulas derived by physicists to explain the world. Quantum field theory for instance has infinities in it. This is not something which is acceptable today any more than the validity of the equation 0 x ∞ = 1 is acceptable to those who resist the reality of spirit. In order to get rid of the infinities, this popular way of explaining creation utilizes a process of subtracting infinities from infinities to get finite answers. Physicist Paul Dirac had a major role in formalizing quantum theory but himself felt this process of ‘renormalization’ was wrong. These uneasy feelings continue to this day, with many physicists asserting that renormalization is illegitimate and that quantum theory as it is formulated reflects human ignorance about the true nature of reality.7

m. Basic Math Operations: Mathematics supports the cosmological truths which geometry helps elucidate, and it does so in many ways. One is through the meaning of simple numbers like 0, 1 and 2. Another is through the basic underlying operations. A mathematical operation depicts a process of some type of relationship. These simple processes, when compared to the archetypes, illuminate the manner in which the world is created, from the way the shekinah relates to the substrate, to the fact that creation occurs in terms of levels of sets. (Cf. Chapter 6, Section III, Creation as a Process.)

Addition: Within the elements in light, the three fire signs Leo, Aries and Sagittarius govern addition. These three are immediate modes of the shekinah. The mathematical operation of addition reflects the process of spirit (via the shekinah) constantly adding substance to material creation by interacting with the substrate. Once a system is born it is ever-growing as well as everlasting.

Subtraction: The three water signs Pisces, Scorpio and Cancer govern subtraction and are immediate modes of the substrate. Subtraction entails taking something away; but while the shekinah grows in its relationship to Ein Sof, Ein Sof never becomes less. Subtraction in the material realm produces ‘change,’ a type of leaving behind. Because of levels of being (and because a system is a world), this is a process which occurs inside a system and does not entail loss for the system. The light from which a material body is created is everlasting. Once energy is created it cannot be destroyed (cf. the first law of thermodynamics which states that energy can change form and be used in different ways but cannot be destroyed).

Multiplication: This process illustrates and confirms the level-like nature of creation. In order for there to be a body there must be two or more separate things existing together at the same time and acting together as one. Multiplication adds numbers by sets. A set is a ‘whole’ and entails two or more parts united as one. The whole and the parts are two different levels. Wholeness is over partness. Multiplication illustrates the process of producing levels. (All sets, even the complex ones spoken of as ‘parts’ within human bodies, begin as polarities.) These parts are created via the archetypes which begin as polarities, which then produce elements, which then produce the archetypes.

The three air signs Aquarius, Gemini and Libra govern multiplication. [Libra governs the two polarities as the first interaction of the first set. Aquarius, the air sign in the domain of Form per se, expresses the concept more holistically (and qualitatively) via its key word ‘many-different-parts-acting-together-as-one.’]

Division: As was discussed in Chapter 6, the experience of qualitative differentiation and spatial division is due to the singularitiness aspect of the soul which in turn is due to the existence of levels of being (and completeness at each level). As systems evolve their bodies become composed of more and more layers of parts (cf. a human being vs. a microbe). If systems are to become more complex, there must be a principle of qualitative differentiation. In astrology the three earth signs, Virgo, Capricorn and Taurus, govern division. In division things are set apart from one another. Spatial division is to the domain of spatial extent what qualitative differentiation is to the domain of qualities and Form per se. The earth signs emphasize the apartness of parts (singularitiness) and the air signs the unity of parts (wholeness). [Although wholeness (the internal reference aspect of the soul) is more easily visualized as a form of Unity, singularitiness is just as much a way to express unity as is its twin.]

Exponentiation: Exponentiation is a special case of multiplication. It is related spatially to the concept of dimensions but more importantly to an ‘I Am’ (awareness) multiplication. Despite the ongoing and continuous nature of growth, including that of more and more levels in a particular dimension, at a certain moment in time a whole actually becomes a higher dimensional whole. It becomes a higher level self. In mathematics exponents or powers (e.g. X2) express the nature of this type of self-multiplication. (A ‘power’ is the product of multiplying something by itself.)

[As exponentiation is related to multiplication, so square roots are related to division. The square root is the converse of the exponent called a square: (22 = 4) and (-22 = 4); and (2 = √4) and (-2 = √4).]

Although exponentiation is expressed spatially via dimensional changes, it is primary to the qualitative domain. That is because this is the domain of Beinghood and as noted exponentiation has to do with self-multiplication.

n. Value in Nature Revisited: Just as a Cartesian coordinate system (section c) shows there is value in nature (section e), so also do the basic math operations, especially when they are examined in the light of the astrological archetypes. These show that movement, growth and evolution are implicit within material creation, be it expressed through addition, multiplication, or the monumental steps involved in exponentiation. Spatially speaking, systems grow. They do not shrink. Qualitatively speaking they evolve. They do not devolve. [It was not through subtraction or division, but through the operations of addition and multiplication by means of which Cantor provided a proof that the relationship called ‘greater than’ must be applied if one is to understand the reality of and the role of the infinite in number theory (and in creation).8]

Material creation is a process of the personal spirit relating to the substrate and multiplying that relationship, 0 x ∞ = 1. The ‘x’ sign which links the primary participants is a symbol for this, and specifically for a process which includes levels of being (groups or sets of things added together). [The equal sign (=) means that the soul-to-body process (1) is just what is meant by the shekinah-to-substrate process: (0 x ∞). In other words, that which people call ‘reality’ (the first real whole number) is produced from no-thing.]

As for why there is value in nature, the personal spirit is only a part of the whole (of the substrate), and seeks constantly to be the whole. This produces processes with preferences. The bodily part-to-whole relationship is a material expression of the part-to-whole nature of the personal spirit as it relates to the substrate.

The entire hermetic cosmology is based upon part-whole duality—the idea that a person (Hermes) is both a part (of Solomon) and a whole in his own right. It is based, not just on part-whole duality, but also on their interchangeability. Whether a person is a part of something or a whole in their own right depends upon the level under consideration. That part-whole duality-unity is a body-soul duality-unity. Body and soul are and are not different. What is ‘body’ or ‘soul’ depends upon the level being experienced. (At base of life the shekinah is the substrate.)

o. Spatial Shapes & Qualitative Correlatives: The laws of nature (the archetypes) are the qualities of experience. The Hermetic Category System (Appendix D) shows that space and qualities are at the same level. They arise concurrently and are simply different (and interpenetrating) ways to experience light. Because of this correlation there is a direct relationship between the basic laws and principles articulated through physics and certain geometrical shapes. Chapter 9 discusses the work of Nassim Haramein. Physicists like Haramein who have learned the value of the overlap between the domains of space and qualities utilize simple shapes to understand complex physics problems and, in a more general sense, the ‘shape’ of the world. This interest in geometrical structures goes all the way back in history to Pythagoras, and to Plato as well with his famous ‘Platonic solids’ as these relate to the four elements (Timaeus 53b-55e).

Points: A point represents the personal spirit. It resides at the center of both an inner (actualized) world, and an external world. [As for how the center of any system relates to its external world, every point in the universe depicts a place in space where all the conditions for that spot emerge and converge. When all the laws are considered together relative to a particular moment and point in space-time, it is possible to understand the nature of a system whose center occupies that point. This is what an astrological chart configures (cf. Ch. 11).]

Circles: A circle represents the soul. The extent of the power of the personal spirit produces the soul which is both an extent and a limitation or boundary condition for the material parts within a world.

While the soul is the primary limitation or bounding condition for the body, all of the archetypes produce their own types of boundary conditions. In physics the term ‘boundary condition’ refers to the material qualities which make a system what it is—the laws of nature.

Squares: Squares and cubes represent actualized matter and specifically (since these arise from a central point) the symmetry required of the poles in order for the four elements to arise and for matter to come into being.

[The difference between a circle (soul) and a square (matter) is that soul is the potential for every and all future coordinates as they can be manifested from any and every point outward from the center.]

Triangles: Triangles represent the fact that in the material world there are three domains, those of space, qualities and motion. (Within space itself there are three dimensions.)

All the various shapes above illustrate some of the ways in which the shape of the world can be represented. A good example of body, soul and spirit is Solomon’s Seal, sometimes called the Star of David. The point at the center represents the personal spirit, the circle represents the soul, and the two inverted triangles represent two (up and down, positive and negative) material polarities and their presence in a world with three domains (spatially, three dimensions).

Nassim Haramein’s specialty is what physicists refer to as ‘black-holes.’ These are points at the center of systems which put out and take in light. Harmaein believes all systems possess these types of centers and that it is possible through the above spatial shape to better understand how any system is constructed, be it a photon, a person, the solar system, the earth or the world as a whole. Haramein became interested in how the black-hole process of energy going into and out of a center plays out in a three-dimensional space where the flat star of David becomes a globe with two three-dimensional triangles or ‘tetrahedrons’ inserted inside that ball. He illustrates how these two tetrahedrons (with one inverted), when placed inside a globe, can help explain the nature of a three-dimensional system such as the earth, and not just the shape of the earth but also its behaviors—from polarity, to spin, to Coriolis (equatorial) effects. The picture he paints of the earth is that of an ‘energy body’ in other words a description of the energy constantly flowing into and out of the shekinah of the earth.9

p. Photons (Energy Bodies): As biophysicist Mae-Wan Ho (Ch. 7) helps point out, the form of a system is not just created through electromagnetic vibrations at the quantum level, but continues to be created directly by electromagnetic vibrations, no matter how advanced its state of evolution or how many material levels its body encompasses. In addition, many-layered complex systems as a whole apparently vibrate in accordance with a certain over-riding ruling frequency.

Light comes in both wave and particle form. ‘Matter’ has to do with the wave-form of light, ‘wholeness’ with the particle-form. Every complex material system is composed of many material layers of being. Since wholeness is manifested via the particle form of light while partness entails waves, systems are evidently composed of many layers of waves encompassed by a particle form, the latter of which is generally referred to as a photon (cf. Ch. 8 A Person as a Photon.)

When Haramein describes the energy body of the earth and how it relates to the ‘black-hole’ it apparently possesses at the center of its body, he describes what is going on as a process of light going into and out of a central point. That process (which has an extent) produces a world. (Black holes produce limits as well as energy processes.) Via what he calls a scaling law he is able to show that this energy activity is present in both a microcosmic photon and a macrocosmic system like the solar system. He is in this way able to formulate a TOE (Theory of Everything) which covers both the large and the small—atomic level physics and astrophysics. Furthermore, by seeing this energy body as present in a macrocosmic system like the earth (which can be studied easily), it is to be predicted that his work will some day help scientists visualize what a photon looks like.

A photon apparently has similar attributes to the wave form, such as cycling, but manifests cyclic motions through rotating on an axis (referred to as spin). The earth does this when it rotates on its axis. The spin has polarity. As for the energy coming into and going out of the center of the earth, the upper half of that process evidently spins one way and the lower half the other way. Per Haramein this produces what is called Coriolis effect. On the earth Coriolis effect makes hurricanes rotate in opposite ways south of the equator as opposed to north of the equator. (It also makes water drain the opposite way down the drain).

[Just as an electromagnetic ray both cycles and moves forward, the earth not only spins on its axis, it also moves forward as it goes around the sun. It even moves forward with the solar system as that higher level system moves through the galaxy. What the astrological archetypes indicate is that these movements create different types of time (e.g., a day, a year, and a great year).]

When Haramein describes the energy processes connected to the center of the earth, it is as though there is a cubed figure eight, in other words, something shaped like two donuts with energy coming in and going out of both the equator and the poles and with opposite spin. This shape is called a double torus. As noted, the upper and lower halves spin in opposite ways (left vs. right). Each of these energy flows also goes up and down alternately, as well as going in and out towards the center in opposite ways.

A ray of light in wave-form produces the elements. The elements were depicted in Chapter 6 as a type of moving figure 8. Haramein shows how this becomes a cubed figure 8 in a double torus.

The outer edge of the energy body of the earth corresponds to its equator—a meeting point between its inner and outer worlds. The archetypes indicate that interactions between inner and outer worlds occur at a crossing point between two singularities. One is at the equator of a three-dimensional system—a 0o Aries type of point for the wave form (cf. Chapter 8). The other singularity is at the center of the system. To understand how particles and waves interact is to understand what physicists speak of as electromagnetic coupling. (This is also how levels interact, since at each level whether something is a whole or a part, a particle or a wave, depends upon the level under consideration at that moment.)

q. Coupling: When one system (or level) is in particle-form and another in wave-form, the two have the capacity to interrelate. If they did not, there would be no connections in the world. A particle has a singularity manifesting through its shekinah or center. The wave form has a point which is another type of singularity, although ‘crossing point’ would be a better term so as not to confuse this with ‘one’ (1) as a material singularity. The crossing point is at the beginning of one wave of an electromagnetic ray, and although material is a zero point in matter. In astrology as noted this is 0o of the first sign (Aries). The wave-form generates the elements.

The wave and the particle form evidently relate to one another as per the graph below. This is apparently how a particle relates to its internal parts, and how inner and outer worlds interact. Note that point ‘a’ below is both the center of the larger circle and a 0o Aries type of crossing point for the smaller circle (a lower level wave actually in wave-form). Note too that the type of singularity depends upon the level under consideration. In the graph on the right any one of the circles has a center—but the circle (the particle) can itself be a wave in a higher level situation. [Since in astrology the sun represents the center type of singularity, there is a joining of two types of singularities when (in astrological terms) the sun is in 0o of Aries.]

Note via the diagram on the right that, for the two singularities to be in the same spot the circles below must be equal in size. Note also that, even if a very large photon or wave related to a very small one, some variant of the mathematical notation of pi would be involved. This graph shows the role of symmetry in coupling (cf. Ch. 8).

r. Symmetry and Harmony: The material parts of the world relate in two basic ways—via symmetry and via harmony. Symmetry entails equality and is expressed by a circle or cycling, with every radius out from the center at an equal point from the circumference. It can also be expressed by an equally divided line which begins at the center and has equal and opposite sides which are the same but divided into two sides facing one another. Symmetry of motion is to be found in lawfulness, i.e., ‘for every action there is an equal reaction.’

Harmony is related to symmetry but is to be found in what mathematicians call the phi relationship (the golden ratio). It has to do with freedom and growth—an input of newness. An electromagnetic ray not only cycles but also moves at a 90o angle into the future. [Cf. also ‘Pi’ and ‘Phi’ in Sections w and x, and in particular x which shows how phi is expressed geometrically via a divided line which is not equal and is referred to as the ‘phi ratio.’

In kabbalah the symmetry of equality is said to be like silver, and that of harmony like gold. Both are considered to be highly valuable, but the golden ratio more so. In the stories of Hermes and Solomon (cf. Chapter 4 and the Song of Solomon), silver is said to represent the two pillars which are at base of creation—the equality of the two (positive and negative) polarities. These continually seek to be more (a higher sense of oneness) and that produces the process of creation—including value in nature—moving outward, onward and upward.

s. Pi-Phi in Beauty & Truth: ‘Beauty’ consists of both symmetry and harmony—both pi and phi. The Greeks were especially fascinated by the golden mean and historically related beauty to the phi ratio. Plato himself referenced the golden mean when discussing both beauty and truth. (Beauty is an expression of Unity, of the coherence criterion for truth—many different parts working together as one.)

For the Greeks Truth was also real Being (cf. the correspondence criterion for truth). Being-Unity (pure Spirit) is also the Good. Hence in Greece, beauty was said to be related to the Good as well as to Being-Unity (cf. Philebus 64d-65a). [The judgement seat spoken of in Chapter 7 (the shekinah as pure Being-Unity) judges beauty, truth and goodness.]

t. Pi-Phi & the Way: Unlike parts in an evenly divided line, a line divided in the phi relationship has two parts which are like non-identical twins, but still twins (this time of a higher and lower type). The masters taught humanity about both types of twinhood. What all this meant was important, not just in regards to theory but also practice—the right way to live. Mean means median or middle value. Over the millenniums many Middle Way groups arose. Some became like religions in the sense of having standardized doctrines, e.g., Buddhism, Daoism, and Confucianism. ‘Dao’ literally means ‘Way’ and even Christians originally called themselves the people of the Way (cf. Ch. 14, Innovations in Religion).

What is taught by the masters and how commentators interpret the teachings are two different things. Over the years there were several philosophical issues which came up for those interested in following the Middle Way.

There are two poles to experience—two sides. The Middle Way entails respect for the essential sameness of the two poles. They are two sides of one whole. Unfortunately, some philosophers decided the Middle Way idea referred to badness and goodness. (Was not the negative pole ‘bad?’) During the Piscean Age, when matter was still being seen as something undesirable, desirelessness for all material things (even good things) was said to be the Middle Way. If the Fall is not taken into account, and if it is believed that pain and evil are always going to be present in the world because they are a natural part of material creation, then it is best to find a way out of material manifestation. In many Middle Way philosophies it was believed that desire led one to move towards things. If the bad is the necessary converse to and accompaniment of the good, then to desire neither that which is good in the world nor that which is bad is the best way to live.

Despite what people do with them, the hermetic truths shine through. It is not known for instance where the symbol for Daoism came from—perhaps from the Master who knew it would eventually get a message across. Below is that symbol on the left (herein tilted). The symbol on the right is a segment from the above diagram in section ‘q’ on coupling. This is how light is created, and how electromagnetic waves couple. The negative pole in light is not that which is bad, and it is not darkness.

[Since light, when it divides, does so in terms of colors, these two poles might be better represented by red and blue when referring to an actualized world. When referring to the horizon involved with an actualized (visible) world verses a higher (or lower) form of light (which cannot be seen), then it would be best to make some notation to the effect that what a person experiences as lack of light is still light—but at a different level.]

There is much to learn from this symbol. It shows that the two polarities in light both arise from spirit, from the center of each of the small circles, i.e., from Being-Unity-Goodness. (Just as the negative pole of light is light, Being is not non-being.) The symbol also shows that the two become one at a higher level of being. It is at their collective heart or crossing point that they reach upward to a higher level of expression. The symbol also shows the polarities must be equal if they are to move upward. These poles are at base of both matter (as law), and of the polarities in their role as individuals as opposed to that of the poles in electromagnetic radiation. As individuals they are together in a higher level whole-in-the-making. The Middle Way is about lawfulness and about equality in regards to husbands and wives. Ultimately that means recognizing the essential equality of all living systems.

The ‘Way’ of life entails manifesting both harmony and symmetry. These two types of unity are interrelated and interdependent. Relative to harmony the Way includes passion for growth and betterment in all areas. To be passionless (desireless) in regards to the material world is not the answer to the problems which currently exist. The material world is created from the Good. Passion for the Good increases the rate of a system’s growth and evolution, and (relative to the Fall) the rate of its resurrection back to wholeness. Thus it can be harmful to believe the bad has to exist as a polarity to the good.

Even in paradise—the best of all possible worlds—there still is growth. As was discussed in Chapter 7, the purpose of life is to materially manifest the substrate and to do so in an ever increasing way. As was also discussed in Chapter 7, the best of all possible worlds involves a world of both spirit and matter. (Pure Love would be incomplete without objects to love.)

u. Squares as the Base: Squares show the need for meeting the requirements for law (and for equality) when moving up. The diagram below on the left helps show how the bodily dimensions arise—that they do so in terms of steps. Spatially speaking, a point produces a line, which produces a surface, which produces a square. (Because these encompass one another, the fourth dimension can be symbolized as a hyper-cube—the diagram on the right.) A square has sides which are equal. Squares are like a base, and in that respect act as a foundation.

v. Perfect Squares: Motion exists because there is a constant straddling of dimensions. Like motion, space is also a factor of dimension-straddling. As systems move ‘through’ space they produce space. In the process there is constant spatial growth and qualitative evolution just as there is constant motion.

Although systems move, grow and evolve every moment ‘in’ time, they also at some point in time become a higher level whole, and what was a part becomes a whole. The diagram above looks like a set of ascending steps in the form of squares. When wholes multiply themselves (as wholes), that is when a new dimension arises, as symbolized by the square sign (2). What is called a power or an exponent is directly connected to multiplication and entails a self multiplying itself as a whole. This represents a point in time wherein a perfected system can rise to a higher dimension as can be seen via the square root of a perfect square.

w. Pi: Circles represent the soul but they also represent cycling. Both the soul and cycling are represented by a numerical relationship. In a circle pi (π) represents the ratio of the circumference of a circle to its diameter (and more specifically to its center via the radius). No matter what the size of a circle there is always a particular ratio between the radius and the circumference. Numerically speaking pi is approximately 3.14159 . . .

x. Phi: Pi depicts symmetry and phi (φ) depicts harmony. The phi ratio (the ‘golden’ ratio) is approximately 0.6180.10 The phi ratio can be represented by a line which is not evenly divided:


1 .618 . . . .

It can also be represented by a surface. A surface helps show how squares are involved, and consequently how law must be fulfilled if the way up is to take place. Both Phi (1.6180 . . .) and phi (0.6180 . . .) are based upon the so-called Fibonacci numbers. These are: 0, 1, 2, 3, 5, 8, ,13, 21, 34, 55, 89 . . . (Note the number of squares below.)

If one number (e.g., 13) is divided by the number which follows it (in this case 13 divided by 21) it equals phi or approximately 0.6180 . . . If that same number (13) is divided by the preceding number (8) it equals Phi or approximately 1.6180. (The larger the numbers the closer the approximation comes to either 0.6180 . . . or to 1.6180 . . . )

There is value implicit within creation. The shekinah, because it is only a part, constantly seeks to be the substrate, and a material part seeks ever higher levels of material wholeness. This is the added input behind ‘motion’ (in the domain of process), behind ‘growth’ (in the spatial domain), and behind ‘evolution’ (in the qualitative domain).

Systems produce time. Time is an ongoing relationship between one dimension and another. Systems move and, due to poles, they cycle. A cycle is a circle, but systems do not merely circle. They both cycle and move forward, creating the next dimension in the process. The next dimension is larger. In the diagram above the circles are not perfect circles. Growth is factored in. The degree of the difference between a perfect circle and the phi circling is a factor of the growth implicit in creation. As a system grows the expansion produces a spiral—the phi spiral in the diagram above.

y. Pi and Phi: If systems did not couple and resonate in terms of phi as well as pi there would, not only be no wave-particle (or level) interaction, there would be no such thing as music. Connections between octaves (between the same note at a different level) is expressed through pi (cf. Ch. 11). A each level there are twelve basic notes. These are the ‘sets’ at each level or octave. Each note is a manifestation of phi. [Life is (supposed to be) a symphony.]

Even though pi is different from phi there is an integral relationship between them. Each note (the twelve basic types of electromagnetic rays) is not itself round in terms of height versus length, and each has a different length (in space-time); however, they all cycle, and cycling is a circle. This is what pi is all about. (Two mathematicians by the name of Ed Oberg and Jay Johnson have discovered a mathematical relationship between these two constants of nature.11)

z. The Pythagorean Theorem: A material body, when it moves upward to a higher dimension, will add a new 90o angle to its coordinates. This can be illustrated through triangles.

According to the Pythagorean theorem a2 + b2 = c2. The exponents in this theorem (self-multiplication via ‘squares’) offers a clue that this is a way to understand a dimensional rise, including the fact that any higher dimension will manifest a 90o difference in direction.

What is interesting about the triangle above is that it incorporates the golden mean. Phi is the part-to-whole relationship which is responsible for the levels in creation, including the existence of different dimensions. It is the idea of levels which is behind the entire hermetic cosmology, and it is the existence of levels which makes it possible for a person to be both infinite and finite—an everlasting, immortal being.

People know these truths in their heart, albeit unconsciously. They preserve them in their symbols, such as Solomon’s Seal and the symbol for Daoism. They even preserve them in their monuments. The Great Pyramid of Giza was built in accordance with the triangle depicted above. Its base is a square. Its rise is in accordance with the golden ratio. (For those in a Fallen world, this is the Way home.)

– – – – –

Geometry, even though only spatially oriented, is a simple way to understand creation, especially when illuminated through the astrological archetypes. An important lesson to be learned is that the Way upward depends upon recognizing the equality of all systems. Another closely related lesson is that matter is composed of the substance of spirit. The negative pole of light is not ‘bad.’ Nor is the negative pole of light darkness. Darkness entails a lack of light at the correct level of being—a potential at that level which is not being actualized as it should be. Another lesson to be learned is that it is ‘good’ to work for betterment. This is especially important in a fallen world. If matter is naturally both good and bad, who would want to work to perpetuate such a state of affairs? On the other hand, if it can be shown that matter is naturally good and can be returned to a state of pure goodness, people will work unceasingly to achieve what they know can be achieved. This is not just about a world ‘out there.’ It is about people being naturally good. People are capable of being all good, and not half good and half bad. The stakes are high. The purpose of The Essential Wisdom has been to collect proofs which attest to the true nature of creation, and the true nature of every person. The Secret of Secrets is that people are divine beings. They are immortals in body, soul and spirit. This is the truth, and one which can be known indubitably—beyond doubt.


The Hermetic Category System

The Essential Wisdom represents the culmination of a lifetime of research into a set of ontological categories of being. In philosophy ‘ontology’ refers to the knowledge of (‘-ology’) being (‘ont’). An ontological category system is an effort to explain the nature of reality via a few basic principles. Scientists do this when they use the known laws of nature to create an intelligent cosmology. In addition to scientists many philosophers have constructed category systems, including Aristotle, Plotinus, Kant, Hegel, Peirce, and others. Plato called whatever produced the categories ‘Forms’ and saw them as responsible for shaping everything in the material world.

The word ‘category’ is used because there is an attempt to organize the individual items into some type of order, including levels of encompassment. The idea is first of all to ascertain the highest category and then show how the lower categories are subsets of the highest. For example, if there is a category ‘shoes,’ then sub-categories include ‘dress shoes’ and ‘casual shoes.’ Under the sub-category ‘casual shoes’ there are sub-sub-categories of ‘sneakers’ and ‘loafers.’ In a category system the highest subsumes the lower ones. (Both the sub-categories and sub-sub categories are still ‘shoes.’) An example of a scientific category system would be an attempt to understand for instance the two categories of space and motion, i.e., what kind of substance underlies and produces these two things. Then as a sub-category motion would be considered individually, while a sub-sub category under that of motion would be the various laws of motion, e.g., the 1st, 2nd and 3rd laws as science now describes them.

There are two types of category systems—those which are purely material, and those which incorporate both spiritual and material substances. For Plato the highest Form was that of pure Being. It was not a material substance but it encompassed and gave ‘being’ to all the material types of being. A number of metaphysically oriented philosophers (and theologians) have dubbed this highest substance Spirit, an appropriate term since it is metaphysical, i.e., ‘above and beyond’ (‘meta’) physical matter. At the same time, the basic idea of a category system is that the lower levels are sub-sets of the higher. Thus pure Being would be above matter but not beyond it. The category system explored in this book links material categories with spiritual ones. In this system pure Being is on the top rung of the ladder while at the very bottom there are twelve basic types of being. These twelve are each a different way to actualize and express pure Being. Everything in the material world is produced by (sometimes said to be ‘ruled’ by) one of the twelve, each of which can be spoken of as an archetype as well as a basic type of being. The character of both the physical world and the mental world of understanding and knowledge is produced through these twelve.

I did not invent this category system. It can be found in many places, including in a partial form within science. The twelve basic types of being at the bottom of the ladder are the fundamental principles and laws of physics, including for instance the various laws of motion.

In addition to science this explanatory system also exists within the religions of the world—both current and old. In the current religions the character of the twelve archetypes is to be found in the twelve patriarchs of Jacob and in the great archangels of the throne.

The older religions were especially explicit about the twelve archetypes. In the old nature-astral religions there were twelve minister gods who helped the world-god with his creation. They bore names (in Rome) of Venus, Mercury, Jupiter, and so forth. Each god ruled over a particular area of life. Venus for instance (goddess of love) is connected to the sign Libra. Venus ruled over male-female polarization and union. (The scope of her jurisdiction widens in this category system to include the positive and negative polarities in light as they alternate and through these activities produce the third law of motion, ‘For every action there is an equal and opposite reaction.’)

Although I am not the inventor of this category system, what I did was to bring together all the various components, clarifying both their nature and their place within the system and its levels. I did my master’s thesis in philosophy on this subject. I have never seen a more powerful explanatory system, not even among those produced by the best physicists or philosophers.

The ontological order of the series is: pure spirit → a personal spirit → light (with its positive and negative polarities) → the domains → the elements → the twelve basic types of being (the archetypes).

The topmost principle is in a way the base—that which has been called pure Being, the substrate, or just pure Spirit. It contains the potential for anything that can ever be. Pure Spirit produces a ‘personal’ spirit whenever a system arises from it. This begins the process of creation. The myths speak of this process as the ‘Deep’ (pure Spirit) compressing a part of itself into a ‘dot.’

That tiny dot then produces light. As light comes forth it includes within its nature a division into two ‘symmetrical’ (equal but opposing) sides—the two polarities referred to as electric and magnetic poles.

As the polarities in light interact, they produce (concurrently) three basic attributes which light possesses. First of all, the interaction itself produces motion. Secondly, the extent of the radius of the motion produces space. Space is the most primal form of extent or quantification. A single bi-polar wave of an electromagnetic ray is just what is meant by ‘space.’ Thirdly, as this interaction between the polarities produces motion and space, it concurrently produces all the qualities of experience via the phases and frequencies in light. These three together—motion, space and qualities are three ‘domains.’

Each of the three domains has four elements [‘fire’ (+),‘earth’ (-/+), ‘air’ (+/-), and ‘water’ (-)], altogether producing twelve basic types of being. The categories take place in steps, and each step depends upon the ones preceding. Thus the elements show in their own nature how they arise from the polarities. In the domain of motion for instance, motion itself is governed by Aries, a positive (+) fire sign, while its correlative Scorpio, a negative (-) water sign, governs change. From these ‘parent’ principles two ‘children’ arise—two laws connected to motion/change.1 These are Libra and Taurus. The air (+/-) sign Libra governs the 3rd law of motion “For every action there is an equal and opposite reaction.” This has to do with energy exchanges and (alternating) back and forth motions. Libra is a child of Aries and Scorpio, with Scorpio ruling change, the ‘back’ side of motion, and Aries ruling ‘to-the-fore’ and going forth, that which is overt motion. As with Libra, the earth (-/+) sign Taurus is also a child of Aries and Scorpio and rules non-change of motion. It governs the 1st law of motion which produces inertial mass.

The four elements in the domain of motion show how motion arises, the four elements in the spatial domain show how space arises, and the four elements in the qualitative domain show how the qualitative aspects of experience arise. Each of the fire signs is a material expression of or ‘mode’ of the personal spirit, showing its role in a particular domain. Each of the water signs is a mode of the substrate, showing its role in a particular domain.

The twelve basic types of being on the bottom row correlate to the signs of the zodiac, each of which is ruled by a planet or luminary. Cosmology, mythology and astrology were all connected in antiquity. In the old religions the solar system was a world (specifically a world-god), and the planetary deities were his helpers. The planets to this day have the same names as the gods, i.e., Venus, Mercury, Jupiter . . . .

A number of historical philosophers have tried to create category systems. Aristotle claimed there were ten basic categories. The highest was Substance (pure Being), while other lower categories included quantity, quality, and relation.2 In the second century Plotinus reduced Aristotle’s ten to five with the lowest being ‘quality, quantity, and motion.’ The other two categories were ‘substance’ and ‘relation.’ The highest category (‘substance’) appears to have been viewed by Plotinus in a manner similar to Aristotle, i.e., as pure Being, a type of substrate. Where the category of ‘relation’ fit into the scheme of Plotinus is difficult to say, but when light is configured into the system, all twelve of the basic principles underlying creation can be said to entail types of relationships, and these begin with the primal relationship of the polarities (+ and – charge) within light.

This category system is superior to any devised to date. What makes the system so compelling is that it is also possible to construct the rows from the bottom up. In other words, it is possible to study the twelve signs of the zodiac and see how the universe is created, and specifically that it is composed of the substance of spirit. The qualitative domain is the most enlightening. This domain shows how all the basic qualities (all the types of being) arise. It shows how the entire process of creation takes place. There are two elements in the qualitative domain which attest to the existence of the top two components in this category system. The Leo/sun principle is an immediate mode of the personal spirit and the Neptune/Pisces principle is an immediate mode of the substrate. The other two elements (Aquarius and Virgo) attest to the results of the process of the ongoing relationship between the personal spirit and substrate—the creation of a body and soul. The twelve principles as ‘soul’ are ‘archetypes’—a set of potentials. The twelve principles as ‘body’ are actualized ‘types of being.’

The reason the upper echelon of this category system can be correctly reconstructed is because light reflects its origin. This is the sepher-seraph concept mentioned in Chapter Four which makes a study of light so insightful. This is also a way in which the material world (via light) can offer a proof that this category system is real and true.

Footnotes, Appendix C

1. Cf. Wikipedia: The Free Encyclopedia, ‘electromagnetic radiation.’

2. Bohm, Wholeness and the Implicate Order, pp. 236-240. Cf. also Talbot, p. 44.

3. Einstein, Podolsky, Rosen.

4. Edwards, Vol. 3-4, p. 189, ‘Zeno’s paradox,’ ‘the arrow.’

5. To follow all the current discourse over this equation try for instance or or

6. For another overview of the paradoxes of Zeno see Wikipedia: The Free Encyclopedia, ‘Zeno’s Paradoxes.’

7. Cf. Lewis, Quantum Field Theory, p. 390. For a general overview try Wikipedia: The Free Encyclopedia, ‘renormalization.’ See also, ‘how infinity is ruining physics, or, ‘The Infinite’ in the Internet Encyclopedia of Philosophy, available on-line at

8. Edwards, Vol. 3-4, p. 185 “Cantor’s Theory of Transfinite Numbers.”

9. Haramein and Rauscher, The Origin of Spin, cf. also Haramein, Black Whole. (Cf. also, Wikipedia ‘coriolis effect,’ and ‘coriolis force.’

10. Mathematicians sometimes look at phi from two different directions and so they differentiate between 1.6180 . . . and 0.6180 . . . Phi (Φ) is spelled with a large ‘P’ and is approximately 1.6180 . . . while phi (φ) has a small ‘p’ and is approximately 0.6180 . . .

11. Oberg and Johnson. Their formula and complete paper, The Pi-Phi Product 7 April 2000, is available on line: or for a brief overview see

Footnotes, Appendix D

1. 1st and 3rd laws infer a 2nd. There are actually four laws of motion—Aries, Scorpio, Libra and Taurus. Motion (Aries) entails a change (Scorpio) in place within the space-time continuum. Scorpio supports the motion from behind. Scorpio also governs (material) power, a manifestation of ‘force.’ The 2nd law of motion (as formulated by Newton) states that the acceleration (change in motion) of an object is dependent upon two variables, the net force acting upon the object and the mass of the object. It is the degree to which the velocity of an object changes when it is subjected to an external force.

2. Aristotle’s concept of Substance correlated to what Plato referred to variously as the Receptacle or pure Being.

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