Chaos Theory.

Chaos is the science of surprises, of the nonlinear and the unpredictable. It teaches us to expect the unexpected. While most traditional science deals with supposedly predictable phenomena like gravity, electricity, or chemical reactions, Chaos Theory deals with nonlinear things that are effectively impossible to predict or control, like turbulence, weather, the stock market, our brain states, and so on. These phenomena are often described by Fractal Mathematics, which captures the Infinite Complexity of Nature. Many natural objects exhibit Fractal Properties, including landscapes, clouds, trees, organs, rivers etc, and many of the systems in which we live exhibit Complex, Chaotic behavior. Recognizing the Chaotic, Fractal Nature of our world can give us new insight, power, and wisdom. 

Principles of Chaos

The Butterfly Effect: This effect grants the power to cause a hurricane in China to a butterfly flapping its wings in New Mexico. It may take a very long time, but the connection is real. If the butterfly had not flapped its wings at just the right point in space/time, the hurricane would not have happened. A more rigorous way to express this is that small changes in the initial conditions lead to drastic changes in the results. Our lives are an ongoing demonstration of this principle. 

Unpredictability: Because we can never know all the initial conditions of a complex system in sufficient (i.e. perfect) detail, we cannot hope to predict the ultimate fate of a complex system. Even slight errors in measuring the state of a system will be amplified dramatically, rendering any prediction useless. Since it is impossible to measure the effects of all the butterflies (etc) in the world, accurate long-range weather prediction will always remain impossible.

Order / Disorder: Chaos is not simply disorder. Chaos explores the transitions between order and disorder, which often occur in surprising ways.

Mixing: Turbulence ensures that two adjacent points in a complex system will eventually end up in very different positions after some time has elapsed. 

Fractals: A fractal is a never-ending pattern. Fractals are infinitely complex patterns that are self-similar across different scales. They are created by repeating a simple process over and over in an ongoing feedback loop. Driven by recursion, fractals are images of dynamic systems – the pictures of Chaos. Geometrically, they exist in between our familiar dimensions. Fractal patterns are extremely familiar, since nature is full of fractals. For instance: trees, rivers, coastlines, mountains, clouds, seashells, hurricanes, etc.



Metaphysics is the science of the universals;

it is the science of
essences, i.e. realities that are universal and unchanging,i.e. do not
depend on time or any particular degree of manifestation. Metaphysics is
not the same as speculative philosophy or theories of creation.
Metaphysics is and is true whether or not Big Bang Theory of the
Hypothesis of Evolution are true. The subject matter of metaphysics
proper is the Truth as perceived by the so-called Divine Mind.
Metaphysics is not a human knowledge but is the content of the Divine
Intellect or Pure Intellect. Metaphysics is not invented or learned; it
cannot really be taught; it is only discovered, i.e. remembered, by a
Seeing that is altogether other-worldly and absolute. This science,
contrary to all other human sciences, is not done by speculation or
experimentation but through intellection which is a transcendental, and
by no means mental, activity of the spirit.

Metaphysics is about Truth Itself and not what men and women, whether
saints or philosophers, have thought or said about the truth.
Metaphysics is about the architectonics of reality as a whole, i.e.
totality, as opposed to empirical science which consider reality only
insofar as it is sensible and measurable by minds and men. We cannot
say, for example, that metaphysics is other than physics though it is
also not identical with it. Metaphysics encompasses all other sciences
and is their very ground, but the nature of its relation to human
sciences is always misunderstood; this relation is best understood only
within the framework of an analogy, of course until the attainment of
metaphysical realization which is the same as the Liberation. So, we
offer the following analogy that we hope clarifies the nature of the
relationship between metaphysics and empirical reality or empirical

Consider a video game in which your avatar, i.e. your embodied
character inside the game-world, is put in a world similar to ours and
its mission is to explore this world and find its natural laws.
Basically, in this game you are a scientist that has to use the tools of
the game to find the most general regularities of that world, things
such as  gravity, electricity, etc. Now, if we want to transpose the
idea of metaphysical knowledge into the context of this game, what
element of the game should we choose? Let us begin by saying that
metaphysics is not anything of the nature of a fact or a piece of
knowledge within the game-world and can be sought and found in the same
manner that one seeks and finds the facts of a world. It is not
something that our scientist can find by means of exploring inside the world game.

Within the context of our game, metaphysical knowledge can be
compared not to any natural law or any fact of the game-world but to the
programming code that is behind the very phenomenon called the
game-world and has made that world possible. Our scientist cannot find
this underlying code by exploring inside the game-world and
experimenting on its phenomena; he himself and all his explorations,
etc. are nothing but the manifestations of the programming code
underlying the game. To access metaphysical knowledge, i.e. the code in
this analogy, the avatar does not even have to look outside himself or
to move around, for this knowledge is, as it were, inside him, i.e.
known by realizing that “there is a game” and then trying to transcend
it. Now, how a game can be programmed so to make such our scenario
possible, and whether it is possible or not, is entirely irrelevant
here. The point of analogy was only to show the radical nature of this
science of metaphysics and its relation to all other empirical sciences
which can know only what is inside the game and not what is behind it.
Even the methods of inquiry are radically different: In empirical
science we explore and experiment, but metaphysical truths, i.e. that
programming code, is not susceptible to such methods of investigations;
the only way of accessing such knowledge is to somehow exit or transcend
the game, or more precisely, to wake up rather than to look out and

It is natural that the methods of inquiry inside the game, methods
designed to find empirical facts and natural laws, can in no way help
one even become aware of the possibility of a programming code behind
the game, let alone finding that code. All such methods, all empirical
sciences, are sciences of phenomena, but metaphysics, being the science
of essences, i.e. the science noumena as opposed to phenomena,
has nothing to do with phenomena but the meaning behind them. In other
words, metaphysics studies the metaphysical roots of phenomena.
Therefore, the failure of empirical methods in becoming conscious of the
possibility of metaphysical knowledge, let alone discovering it, is
only a failure and a shortcoming and doesn’t mean that there is no
metaphysical foundation, or code, behind the game, a code that is
different from the facts and natural laws inside the game simply because
these laws are themselves manifestations, or projections, of that very
code. One cannot use these methods to prove or deny the existence of a
program behind the game, and this indicates the futility of all attempts
at denying that there is a metaphysical foundation behind all things.
The ultimate proof of metaphysical truths and realities is metaphysical
realization, and this realization has been known and done and is not
something up for discussion or refutation. As we have said many times,
those trying to deny metaphysical knowledge, which by the way has
nothing to do with god or religion but encompasses them, are like blind
men trying to dispute the reality of a rainbow. A true metaphysician,
i.e. a Jivan Mukta, never bothers trying to prove to anyone the
possibility and reality of metaphysical truth; he can at best show the
way for the seeker of truth to see and realize for himself that which is
never a matter of opinion or speculation of any kind: The only proof of the Face is the face Itself.  

Now, what does all this have to do with geometry? Well, as we said
metaphysics is the science of universal and immutable truths, realities
that are unchanging, and hence do not depend on time or any becoming
whatsoever. Thus, all theories of creation, modern or traditional,
religious or secular, are only human theories and speculations and at
best have symbolic value, for they all presuppose a becoming of some
sort. In metaphysics, there is no becoming. Creation is a human fact;
from a metaphysical, i.e. transcendental, point of view, creation and
becoming are absurd and unreal concepts. But since we find ourselves as
humans in the midst of a world of becoming, our thinking is conditioned
by it and can understand things mostly in terms of being and becoming.
At the same time, because of the transcendental nature of metaphysics it
can only be understood through analogies until the point of
metaphysical realization in and through which all metaphysical truths
are grasped immediately and intuitively and with absolute certainty.

A proper and successful analogy is that which is based on a
fundamental but common feature present in both sides of the analogy.
Since immutability and the absence of time and becoming is the most
fundamental and definite characteristic of metaphysics, the most
appropriate analogical means for its expression should be another
science that is devoid of the concepts of time and becoming. We know
that all empirical sciences such as physics, biology, etc. are in fact
about change and becoming, so they cannot possibly provide enough ground
for a successful analogical method of communicating metaphysical
truths. Of all the sciences accessible to man, the only one that is
devoid of the concept of change and time is geometry, and in general
pure mathematics. There is a direct correspondence between most
propositions of geometry and abstract algebra, and this to the extent
that we can even say geometry and abstract algebra are only two
different ways of expressing same mathematical truths: In abstract
algebra we are dealing with abstract symbols and their relationships but
in geometry we are dealing with spatial relationships, so it is like
abstract algebra only with the advantage of visualization. For this
reason, geometry is a little more suitable for communicating
metaphysical truths because it allows some space for visualization which
is a great tool in all learning.

Thus, we believe and we can show that metaphysical truths, which are
entirely independent of the concepts of god, creation, divine, etc. but
are at the same time the very source and ground of all these concepts
and realities, is best conveyed through geometry. And it is no surprise
that geometry has always been considered a sacred science and present
almost in all esoteric schools such as Pythagoreanism, Platonism,
Neoplatonism, Eastern and Western religious esoterisms, and also in
Freemasonry. For example, the letter G at the center of
the symbol for Freemasonry consisting of square and a compass,
traditional tools of architecture, stands both for God and Geometry, in
which God is viewed as the Great Architect of the Universe who creates
by means of immutable and intelligible relationships, i.e. geometrical
forms. We only add that geometry is not to be seen as identical with
metaphysics, and we should not think that in reality there are points
and circles; but geometry and its concepts are used as the best symbolic
means of expressing intelligible realities that are beyond any spatial
relationships. In other words, geometry is the reflection of
intelligible truths in the plane of human mind which can understand
things only in terms of the conditions of time and space. The reflection
of the sun in the pond is not the sun but can tell much about the sun,
at least about its form. Metaphysics too exposes the universal forms by
which truth can manifest Itself, the Truth Itself and in Itself
remaining always unmanifest and only known by being it, a mode of
knowledge accessed upon metaphysical realization, i.e. Supreme Identity.

It is outside the scope of this article to delve into geometry and
show the metaphysical truths that are reflected in it. Our goal was only
to show, firstly, the radical nature of the science of metaphysics and
its relationship to all other spheres of human knowledge, and secondly,
to suggest the best way of approaching this science, which is done
through geometry. We hope that in the future we can devote a few
articles to some aspects of metaphysics using geometrical truths. The
main problem that makes metaphysics difficult to understand for the
average mind is that metaphysics is not a science for everyone and
requires a very refined and objective intelligence not deformed by the
assaults made against the mind by the universal compulsory education.
One needs to know some abstract algebra and be very well familiar with
geometry, particularly the theory of functions, power series, Taylor
Expansions, etc. in order to perceive the subtle metaphysical truth
reflected in these forms. However, metaphysical truths, which is a way
toward liberation and Supreme Identity,
is not the only way. Religion and spiritual disciplines have the same
end in view. While metaphysics is the way to Truth for the born
philosopher, religion is a way for everyone, even the last man. The
spiritual man if he succeeds may come to see the Face of Truth, but the
metaphysician if he succeeds comes to see the Whole of Truth. 

Image above: A Hermetic Temple:  an integration of the Seventh Book of Hermes
Trismegistos (12 Penalties, 10 Potencies and the Secret Song of
Regeneration) with the Tree of Life, pillars of Solomon and Zodiac signs
with their Elements


The outer edge of the universe
Is where the spirits of creation reside
And from the deep corners of the mind
The space of consciousness

They are astral and physical beings
Pieces of us and separate from us
They show us all types of illumination: Light, wisdom, sacred flames, halos Geometric formation, colors
Pychedelia, even visions of the galaxy.

Often it is through birds
Where receive such illumination:
From our dreams and gnosis
And sources such as Ra, Horus and Thoth An owl, perhaps of Minerva for example With energy of the light bringer
Carries a light above their head
Symbolic of enlightenment, of the third eye And of crown chakra
And he comes to this plane
Entering through a green glow
His illuminating aura points to center: Freedom, nirvana, moksha, enlightenment Which we strive to consciously
And subconsciously reach
Primarily through our own will

Focus on your center
Travel through the path of green light
To heal your heart


The Geometry of Three [7/7/16]

Since 3 and 7 have a sum of 10 [Unity], they are complementary to one another.

A pyramid is defined as a polyhedron created by connecting a polygonal base with a point, known as the apex. This quality of evolving upward toward a single point of unity reflects the strong association of the Pyramid with the Solar number 10. The same is true of its 2D counterpart, the upward-pointing triangle. This shape traditionally represents the element of Fire, which is a property of the numbers 3 and 7. The unifying quality of 3 is reflected in words like Sun and Unity [both 21], which relate closely to 10 words such as Solar [19+0] and Nucleus [37].

Although a pyramid can be based on any kind of polygon, there are two major types which are most commonly encountered. These are the Tetrahedron [a Platonic solid with a triangular base] and the square-based pyramid seen in the monuments at Giza. This dual emphasis on 3 and 4 as alternate types of foundations is reflected in the first two letters of the word Pyramid [P = 4, Y = 3], which correspond to the values of the Mayan calendar signs of Kan [Seed – Foundation] and B’en [Pillars – Support]. The third aspect is Lamat [Star – Apex], which is connected to B’en through a relationship of complementarity, expressed by the sum of 20 which results when their numerical values are are paired in a crosswise manner. Three multiplied by four is twelve, which reduces back to three. The sum of three and four is seven.

I used a simple method for reducing each polyhedron to a single number which conveys its essence. First, each face is converted to a number corresponding to its number of sides [e.g., each triangle becomes a 3]. All of these numbers are then added together and reduced to a single digit. By following this procedure, the tetrahedron comes out to 12 or 3, while the square-based pyramid is 16 or 7 [the same value as the word Giza].

In this way, the relationship between 3 and 7 is modeled by the two primary manifestations of the pyramid form. But it is also contained within the form of the square-based pyramid alone. This pattern is expressed through a process of building up by threes. The 3-6-9 triad seen in the structure of the triangular prism results from starting at zero and repeatedly adding 3. Three iterations of this process yield a final value of 9. Zero and nine, respectively, symbolize the primordial and mature aspects of the Divine Feminine. However, there is another way to do this which produces differing yet parallel results. Starting the process at one yields a pattern of 1-4-7-10, with 1 and 10 representing the primordial and mature aspects of the Divine Masculine. The square-based pyramid follows this pattern, beginning with a single square from which arise 4 triangular sides, creating a form with a combined value of 7 which naturally points toward a single apex, representing 10.

When I was organizing this chart, I decided to include a section on the relationship between frequency, wavelength and energy in various types of electromagnetic radiation. This is mainly because it expresses a very similar numerical pattern to that of the pyramid, with the frequency of every type of radiation coming out to some form of 3, while the corresponding wavelength reduces to 1. The energy of each of these kinds of radiation is expressed through a variation of the sequence 124, which adds up to 7. The four triangular faces of the tetrahedron are quantified as the number 12, to which the square pyramid adds a square base with a value of 4. Although I only had room to include three entries, this pattern holds true across a much longer list incorporating all forms of electromagnetic radiation. The pyramid form does appear to have some unique properties which affect the flow of electromagnetic energy in certain contexts, as indicated by a 2014 [=7] experiment involving pyramid-shaped nanoscale antennas.

While the 1-4-7 triad is characteristic of the pyramid, the 3-6-9 triad is more apparent in the triangular prism. The primary qualitative difference between the Pyramid and the Prism is one of Fire vs. Water, which results from the pairing of the shared element of 3 with either 7 or 6. The Water aspect of the Prism is reflected in its similarity to the biological eye. Whereas the Pyramid channels diverse elements toward a homogeneous state, the Prism does the opposite, beginning with a homogeneous input and eliciting diversity.

‘Conceptual Association – Basis of Unicity’


In the definition of Conceptual Association, Unicity is the primordial concept of Unity; Circularity is a transposition of this Unity after the event of duality due to its ability to contradict itself (a derivative of Linearity’s duality)

Unicity, geometrically, is as the 0th Dimension, or in CA (Conceptual Association), the First Instance; it has no determinate otherness because all is within the singularity. This means that infinite possibility lies within the infinite singular notion of this concept, however, the potential resonates dormant. It is, regardless of conceptual intricacy and application, both the protrusion and envelopment

Unicity is different from the attribute of unity within Circularity, as well as the concept of everything; the singularity cannot, in turn, imply nothing, but instead the implication of coming from nothing. There is also no magnitude of change, no measurement to describe or confine it. 

This concept can be described (in post-dimensional manifestation) as the centripetal point to any complexity. It can be described as the center of any situation or the source of any event. 

Unicity does not bare polarity, so instead, it is the expression of (in) totality, or even perhaps the existence of (pre-) duality as one instance.


Julius Reichelt – Astrological Sigils, 1673.

According to Weill-Parot, the concept of having astrological images on sigils is exclusive to the Christian Latin West. Albertus Magnus proposed the creation of a type of talisman whose power rested completely in natural causes, excluding illicit forms of necromantic magic. This ‘natural magic’ included the use of sigils with astrological images that would contain the astral power of the planets. 

Principles of sympathy and antipathy governed the preparation of astrological sigils made of metal. The Sun was astrologically and alchemically associated with gold, so a gold sigil would be struck with a picture of the Sun (usually when it was at its strongest influence, during the vernal equinox) or an astrological sign ruled by the Sun, such as Leo, so the wearer was protected from the malignant influence of the heavens.

Several of Reichelt’s sigils were designed to work by sympathetic principles. Sigils 1–4 and 6–8 were sigils of the Sun in astrological house of Leo. The obverse of sigils 2, 4 and 6 also displays the sign of the ‘heart of the lion’ cor leonis, which is Regulus, the brightest star in the constellation of Leo, as well one of the brightest stars in the night sky. The cabalistic symbol for Regulus is engraved on the obverse of sigils 1, 2 and 7. 

The sigils’ astral power could be further enhanced by incorporating scriptural quotations and the names of Biblical prophets. Inscribed on sigils 1, 2, 4 and 6 is the common apotropaic formula “Vincit Leo de tribu Iuda, radix David” from Revelation 5: 5, a reference to the biblical David and to astrological Leo. Similarly, some of Reichert’s sigils were inscribed with words from the Gospel of John: “Verbum caro factum est”, causing demons to flee before the power of ‘the Word made Flesh’.

Inscribing the names of angels on sigils was also thought to be efficacious, a tradition begun in the thirteenth century by the increasing influence of Jewish cabalistic texts such as the Sefer Yezirah and the Sefer Razi’el. The texts claimed that the ‘secret names of the God and the angels provided the means by which the powers were called down into the sublunar levels of the cosmos’, and hence used an intricate and often bewildering angelology in ritualistic magic. In sigils 1 and 7, ‘Verchiel’ is inscribed. Verchiel was invoked as the angel of the month of July, ruler of the sign of Leo. Verchiel (here called Zerachiel) is also governor of the Sun and grants powers of the intellect, language, learning and mathematics.

Several of Reichelt’s sigils also bear geometrical characters of triangles, circles and lines, which he realized represented the ‘intelligences and demons’ of the planets based on numerical associations made with the heavenly bodies derived from the rules of cabala. There is also a magic square or grid of numbers engraved on sigil 10, devoted to the planet Mercury. For early modern philosophers, mathematics and magic were intimately connected. From his doctrine that the elements of the body were mingled in geometrical proportions, and that the soul’s elements combined numerically, Agrippa determined that the derived geometrical and numerical figures had peculiar corporeal and spiritual powers.




This report began as a simple re-examination of the design features of Stonehenge beginning seriously in 2002. It is a book of questions and perhaps, the reader will eventually decide, a few answers. The author wondered whether any relationships existed between Stonehenge features and whether such relationships could help confirm or reject the many claims of links to astronomical phenomena, namely the cycles and movements of the Moon, Earth and Sun.

Either we have coincidences of ‘astronomical’ or indeed ‘monumental’ improbability linking monument features to the geometries of regular polygons and Pythagorean triangles , the Golden Section, phi and numerous lunar/solar/terran parameters and cycles, or something is very wrong with our assumptions about the knowledge and sophistication of the megalith builders. However

© Prof D.P. Gregg, 2010


The Self is an archetype that represents the Unification of the Unconsciousness and Consciousness of an individual. The Creation of the Self occurs through a process known as Individuation, in which the various aspects of personality are integrated. Jung often represented the Self as a Circle, Square or Mandala.” – Kendra Cherry