CRACKING PI – PART 1
by Marty Leeds
Greetings again World Mystery readers! My name is Marty Leeds and this is the sixth article in a series I am writing regarding the subjects of sacred geometry, sacred number and gematria. I am the author of three books, Pi – The Great Work and Pi & The English Alphabet Vol. 1 and Vol. 2, all available at amazon.com. I have an extensive youtube channel (youtube.com/martyleeds33) with a video series detailing a wide variety of subjects and their relationship to mathematics, numerology and gematria. I am also a teacher at the School of the Holy Science (www.schooloftheholyscience.org) along with some fantastic thinkers and researchers such as Santos Bonacci, Dr. Johan Oldenkamp, Bill Donahue, Jason Verbelli, J.S. Williams and a growing list of others. I also have for sale a gematria calculator for your android phone that will allow you to easily calculate words and phrases using the cipher for the English alphabet (something we will explore in this article). This app is an extremely handy tool to help aid you in your exploration of numbers and letters. It is available for purchase here:
I will also have available a full-length record of original songs entitled “Opus Medico Musica” for sale via amazon.com, via my site or directly from me within the next few weeks. Stay tuned for more webinars, videos and interviews at www.martyleeds33.com!
This will be a three part article in which we will be looking into the mathematical phenomenon of Cracking Pi. We will be utilizing the English cipher to perform this numerological, gematria-magical and geometric feat so please take the time to intuit this cipher, for it has many hidden treasures just waiting to be unveiled. This cipher was, without a doubt, constructed by highly intelligent, very mystical and spiritual people who had a direct, gnostic connection to nature and to the conscious intelligence at work within the universe. I urge you to write out this cipher and keep it handy as you read through the remainder of this text as it will help you calculate the value of the words as we unfold the mystical nature of pi. Below is a very abridged version of this cipher.
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“If you wish to make apple pie you first must invent the universe.” – Carl Sagan
Throughout the last few blogs, we have come to intimately know pi, one of the most fundamental ratios in mathematics. Pi is simply the ratio of a circle’s circumference to its diameter. If we make the diameter of a circle 1, its circumference will be 3.14159…
Pi is considered an infinite, irrational and transcendental number, or in other words, pi’s decimal places go on forever and never repeat. Throughout this blog series, we have found pi hiding within the mathematical structure of our alphabet and have explored some of the many other places where this ratio shows its face (the Great Pyramid of Giza being a prime example), securing the fact that pi must have been important to our ancient brethren. Whoever moved, carved, sanded and placed those enormous stones making up the Great Pyramid and whoever fabricated, channeled or constructed the English Alphabet, without any doubt whatsoever, did these things with pi in mind. What is so mysterious about this ratio? Why do pi’s decimal places unfurl boundlessly and never repeat? Why does such a simple geometric measure yield us this infinite set of digits? Does pi represent the chaotic nature of our existence in the randomness of its unfolding? In modern mathematical theory exists one of the greatest riddles of all and that is the feat of Cracking Pi. The modern interpretation of this great problem is aimed at finding a pattern or order within pi’s infinite digits. Is there possibly a rational sequence within these decimals that will allow us to peer inside the heart of this behemoth number that will once and for all allow us to make sense of pi’s infinitude? Though this modern explanation attributed to the “problem” of cracking pi is the one that is accepted in universities and institutions of higher learning, this will not be the explanation that we are to focus on today. This article will not be an attempt at explaining exactly how and why the numbers of pi unravel in the particular order that they do, for this is not what we are going to concern ourselves with. What we wish to do in this article is try to tackle pi using symbolism, language, philosophy and occult and esoteric methodologies. It is in the opinion of this author, that pi is actually a representation of the creation of our universe. Through personal experience, philosophical exploration and deep contemplation on the nature of this number, I have come to the position that Pi is a number that was given to us by a creator as something to focus on – a key, central vertex in the archetypal architecture of our cosmos. For somewhere within this grand ratio, this most puzzling of mathematical constants, is an answer to the mystery of our world.
If you are not familiar with the work I have been involved in, my web series and books, and have no background in attributing mathematics to spirituality or an understanding of sacred geometry and sacred number, then that last sentence has probably stopped you dead in your tracks. Statements like these tend to weed out those who dare not illumine the right hemisphere of their brain and those who dare not take an imaginative and subjective look at something so “objective” as mathematics. Even the consideration of numbers and geometry as sacred, viewing them through the eyes of the esoteric as opposed to the exoteric, is blasphemy to those who only deal with mathematics in the mechanistic, reductionist and generally accepted methods pervading the current intellectual climate. Could numbers actually be the language of a creator being? Could the qualities and essences of numbers themselves reveal cosmological principles at work within the universe? Does the power of geometry and number elucidate the qualities of nature herself, expressing its harmony, intelligence and elegance within the ever-shifting, moving current of time? Is numerology a valid form of mathematics? Could pi actually represent much more than simply the ratio of a circle’s circumference to its diameter? It is questions like these that will not find their way into any sort of classroom setting in any academic university, and that is exactly why we are going to ask those questions here today. Abandoning the spirit and intensifying our focus on the matter, disregarding the ethereal within the material, choosing the exoteric over the esoteric and narrowly viewing our world in such a corporeal way has prevented us from unearthing the true magic and power within the study of mathematics. Simply put, this mindset has left us chasing our own tails and has left us at a complete loss when trying to wrap our head around the endless, infinite tail of pi.
“We’re captive on the carousel of time. We can’t return we can only look behind from where we came and go round and round and round in the circle game.” – Joni Mitchell (The Circle Game)
THE POWER OF THE WORLD WORKS IN CIRCLES
“The power of the world works in circles and everything tries to be round.” – Black Elk (Black Elk Speaks)
“Which came first, the phoenix or the flame?”
“Hmm . . . What do you think, Harry?” said Luna, looking thoughtful.”
“What? Isn’t there just a password?”
“Oh no, you’ve got to answer a question,” said Luna.
“What if you get it wrong?”
“Well, you have to wait for somebody who gets it right,” said Luna. “That way you learn, you see?” “Yeah . . . Trouble is, we can’t really afford to wait for anyone else, Luna.”
“No, I see what you mean,” said Luna seriously. “Well then, I think the answer is that a circle has no beginning.”
“Well reasoned,” said the voice, and the door swung open.” — J.K. Rowling ( Harry Potter and the Deathly Hallows)
Since we are going to approach the riddle of Cracking Pi not in its contemporary, literal mathematic sense and instead going to utilize philosophy on this mystery, let’s first define exactly what philosophy is. The subject of philosophy is defined as the study of general and fundamental problems, such as those connected with reality, existence, knowledge, values, reason, mind, and language. The term philosophy is informing us, within the etymological and syllabic breakdown of the word itself, of the importance of mathematics when contemplating the nature of reality. Both “Phi” and “Phee” are phonetically sounded when the word PHI – loso – PHEE is uttered. These two aspects of the ratio of Phi, or 1.618 (Phi is general noted as 1.618 whilst its counterpart Phee is known as .618), known as the Golden Mean or Golden Proportion, within the word philosophy is very clearly stating that if one wishes to ponder and ruminate on the universe and the meaning of existence, the study of math must be a prime focus. Thus, any philosophy that has any leg to stand on will ultimately be one founded upon the principles of mathematics. And the study of mathematics will inevitable and ultimately lead one to the power of the wholly circle. The circle can be defined, philosophically, as one of the most important geometric forms in creation. The properties of a circle tell us much about its inherent power. We may deduce meaning directly from its geometry by studying its qualities, quantities and form. This is, in fact, how the language of number speaks directly to you. The universe, the natural world, and we may even say God himself, does not speak to human beings directly using Greek, Latin, Coptic, English or Arabic languages, but instead speaks to us through the language and magic of number.
“If one places a stick in the ground and marks the position of the sun every day at the same time, after 365 days, the sun will naturally form a figure 8 onto the ground. This figure 8 is called an ‘analemma’ and is a Greek term which means ‘pedestal of a sundial.’ Our ancestors believed (or better stated, wholly recognized) that the sun is a conscious and intelligent being who was speaking directly to them. But the sun was not speaking to them in English or Aramaic or Latin or Greek, but instead, it was speaking the universal language of number and geometry. Most modern minds would probably consider our ancestral relatives to be downright crazy with such assertions…such thoughts are born from the minds of primitives and superstitious savages! Maybe. But guess how many minutes it takes for the sun’s rays to reach the Earth? 8.” – Claudia Pavonis
The French existentialist Jean Paul Sartre once said that “Nature is mute” and nothing could be further from the truth. Nature is only mute if you are not speaking its language. The French philosopher and writer Voltaire embodied a much more magical understanding of nature when he exclaimed, “If God didn’t exist it would be necessary to invent him. But all of nature cries aloud that He does exist.” The exact origin of human language remains a mystery and a mystery that we may never solve. But the language of nature is no mystery at all, for even the most intellectually arrested man may easily see that nature indeed cries aloud her works utilizing the principles, attributes, qualities and essences of number. The number of petals on a flower exemplifies this simple truth. Some of the greatest minds in recorded history have spoken of the profound glory of number and the beauty of geometry. Plato, Pythagoras, St.
Augustine, Galileo and Heraclitus all deemed number to be of a cosmic, godly origin. The study of this universal language, and communing with the numerical matrix that weaves together the archetypal world of forms into our living universe, is how one communicates with the divine. Familiarizing oneself with number allows one to familiarize oneself with God.
In the study of sacred geometry, the circle represented Heaven and the square represented Earth. This motif is seen within the Freemasonic Square and Compasses (the compass being Heaven and the square being Earth), within the ancient Chinese cosmographic concept known as Gai Tian (The square earth is a chariot, the round heaven its canopy) as well as one utilized by the Buddhists in the building of the sacred, mound-like or semi-hemispherical structure known as the Buddhist Stupa. It is important to note for our study that the place where God resides, or Heaven, is geometrically symbolized by the circle. If one takes a length of string and makes it a triangle, a square, a rectangle, or any other sort of polygon, the amount of space that string will create will always be smaller than if one makes it a circle. The circle encapsulates the most amount of space with the least amount of effort. Bringing the circle out into three dimensions to make it a sphere will encapsulate the most volume. This geometric fact is one of high symbolic value. The circle is expressing something about the nature of its own being. It is speaking to you. It is representing, within its own essence and qualities, the limit or sphere of creation. The furthest out we may go into space, whether that be the physical space of our universe or the internal infinite space of the imagination and mind (and according to the Hermetic text the Kybalion, they are one and the same, “The ALL is mind”) if we were to geometrically encapsulate or represent this limit or expanse, the circle would be, without question, the form we would utilize. The edge of our universe, the edge of our thoughts, the edge of our conscious apprehension of such magnitude, can be comprehended through the gnostic communication available to us through geometry. Gnosis is defined as a “divine mystical insight” into the universe and is where we derive the term “know.” To KNOW the EDGE of the expanse, of all thoughts, of all time and all space, and to encapsulate that breadth into one unifiedwhole,withthatwholenessbeingthewhollycircle,iswhatitmeanstohaveKNOW-L-EDGE. It’s what it means to be HOLY.
“To find yourself, cast your net out into the dark abyss of mind and when you find the edge, circle it round and bring it home again. Then you will see that the Holy See is right within you and right within me.” – Claudia Pavonis
“If you feel disordered, order the distance and whole you shall be.” – Claudia Pavonis
“God is a circle whose center is everywhere and whose circumference is nowhere.” – St. Augustine
The circle also leads us to the first number in existence, zero. If we were to attribute the zero to a geometric form, the most obvious form we could equate it to would be the circle. The number (or non- number) zero expresses the concept of nothing. But even considering the meaning of zero, or nothing, begets us an anomaly. How can there be nothing (or NO THING) when there is obviously SOMETHING (with that something being, of course, everything)? And how could there even be nothing without something or someone there to recognize this nothing? These paradoxical questions plague the rational mind, are ones that we cannot even begin to approach using the reductionist method and are inquiries that thrust us into the depths of epistemology. What can we know? The symbolism of the geometry lying within the heart and soul of the circle allows us to unify these conundrums and paradoxes and leads us right back to the first moments of our creation. The circle, by encapsulating the most space, and yet simultaneously being a representation of the zero, or NO THING, condenses all time and all space into one geometric form. It links us all the way back to the beginning of creation. Put simply, the circle represents the concept of all or nothing. As far out into the abyss we wish to go, and as close to nothingness as we may conceive, the circle represents both. Both the finite and the infinite may be understood philosophically by simply piercing a sheet of graph paper with the point of a compass and sweeping the arm around 360 degrees.
Why is it that we do not find perfect geometry in the natural world? Everything in the universe, from stones, to flowers, to tree trunks, to planets has a tendency towards the round, though the perfect circle is never to be found within the experiential world. Perfect geometry: circles, straight lines, squares, etc. are elusive within the physicality of the material world. Why is this so? How can it be that nature herself cannot make perfect geometry but the hand of man can? How can it be that man can perform an act that nature can’t? What does this say about human intelligence? What does this say about the elevated nature of our consciousness? Further, why is it that even with our current 2D and 3D graphing technology of CAD programs (Computer Aided Design), when we draw a “perfect” circle and “perfect” line, and find the relationship between the two, they still yield us the infinite, irrational and transcendental number of pi (The acronym CAD, not-coincidentally, using the English Cipher yields us the numbers 314!). What is going on here? Is this, once again, proof, that there is no intelligence or rationality in the creation of our world? Or is it possible, that the creator wishes us to look at the problem in a different light? Can we find rationality in irrationality? Can we find, through the study of mathematics and geometry, using every faculty of our reason and creativity to penetrate into the very depths of this subject, the existence of a higher order? Is the proof of God available to us in a mathematical proof?
“I live my life in growing orbits which move out over this wondrous world, I am circling around God, around ancient towers and I have been circling for a thousand years. And I still don’t know if I am an eagle or a storm or a great song.” – Rainer Maria Rilke (Rilke’s Book of Hours: Love Poems to God)
The reason that we do not see perfect circles and perfect squares and straight lines within the geometry of the living world is because of the gift of this present we are given called time.
“Time is the moving image of eternity.” – Plato
Time is defined as the indefinite continued progress of existence and events in the past, present, and future regarded as a whole. The Latin word tempus means time and is where we derived the words tempo, meaning “time, rate and rhythm,” and temporal, defined as “related to life and or this world.” Thus, the Biblical word temptation, pertaining to a coaxing or inducing of a regrettable action, has a direct etymological root in the measurement of the movement of objects through space. May we presume that from this definition, temptation is referring to the temporal human experience and our immersion into the dimension of being? Temptation and time go hand in hand. Time is akin to a river, in constant motion, constantly flowing, and never seeing stasis. The great Greek philosopher Heraclitus said, “All flows.” The Moon spins round the Earth, shifting its tides and celestially harmonizing the bio- rhythms of all Earthly species, the Earth spins on its axis whilst chasing our light-bringer the Sun and the Sun itself spins and courses round the central sun of our Milky Way galaxy. Nothing in the universe ever ceases. Everything spins and turns and moves and sails on the oceanic tides of time. If number is the language of the universe itself, we must assume, due to the nature of time that we exist within a matrix of moving geometry. This geometry’s seeming imperfection only appears to us as such, for we have been tempted into the ever-flowing, never-static, fluctuating current of time.
“The NILE River is an anagram of LINE. A river is nothing more than a perfectly straight line, put into time that became a sine wave.” – Claudia Pavonis
Through the creation of time, the archetypal geometric forms pervading existence have been given the platform to live, to breathe, to grow, to expand and to explore themselves – to become “imperfect.” If there is intelligence force, a creative nature power, a God behind the construction of our universe, what kind of rationale would there be in creating time? If God is infinitely intelligent, what kind of gain would there be in creating the duality of past and future, up and down, left and right, and the unification of opposites that we find within the dimension of time? What is the point of creating pain and suffering, joy and elation, good and evil and positive and negative? Why go through the trouble of creating such polarities?
In order to understand the nature of the intelligence of the creator and the ways in which this great being goes about doing its business, we must first define the creator. Since the universe is infinite and we may not simultaneously consciously comprehend the entirety of the universe, such a definition is impossible to obtain. But we may use our KNOWLEDGE to firmly grasp its essence. Panentheism is the cosmological and philosophical understanding that everything in existence is God and that God interpenetrates every part of nature and timelessly extends beyond it. All time and all space are encompassed within the whole of deity and the divine. This understanding has been passed down to us through the concepts of the omnipotent, omniscient and omnipresent. God is omnipotent or all powerful, omniscient or knowing everything and omnipotent or everywhere at the same time. God is, henceforth, the entire thing and the entire thing is God.
“What is God? God is length, width, depth and height.” – Saint Bernard of Clairvaux
Speaking on the nature of God, the Hindu text The Upanishads claim that “No mind has touched it, no tongue has soiled it.” Since the greatness of such a being cannot be truly grasped or defined by a mere name or sound, we must declare that any reference to it, albeit God, Allah, Amma, Amen, Ra, Jah, Jehovah or any derivation of must fall remarkably and ridiculously short in identifying, defining or describing such a being.
Although every word that we utter from our mouths fails to characterize such grandeur, we must also, due to the ever-presence of the divine, assume that every word we utter speaks of its glory. This indivisibility in our language, this impossibility in separating God from itself, leads us directly into the study of symbolism. Through geometry and number, we can come to understand the symbolic nature of our world. Symbols are created using geometry and geometry and number stem from the same intelligent source. Even the words you are reading on this page were syntactically created using letters, which are, by very definition, symbols. Symbols represent archetypal principles at work within the continual construction of our world. Even the word archetype is interesting in this regard for arch is a reference to mathematics and geometry and type is of course a reference to letters and henceforth an archetype is a direct reference to mathematical letters. But before we can come to understand and intuit our own language, we must first understand the language of mathematics and how that language creates the symbolic world in which we are embedded in. The circle is the perfect symbol and archetype in which our ancestors used to embody the divine. As we have defined, the circle, through its own inherent qualities, gives us the perfect geometric metaphor to encapsulate the nature of the divine – it is all that shall be, was and will be. It is simultaneously all and nothing. Yet, as we know, this “perfect” circle is ever-elusive in nature. Even when we attempt to draw that “perfect” circle, utilizing the best software and technology available to us, we still see the movement, fluidity and expanding, unfolding nature of time within the infinite digits of pi. The outer sphere of the universe is expanding, and so is pi. The circumference of creation may never be fully measured for creation is constantly being created, its limits forever being pushed, its space expanding in all directions. In order to measure this edge or limit of our creation, we would have to leave the material realm, and step outside the universe itself. And not one being within the creation may exist outside of the realms of the creator, for the creator as we have established is omnipotent, omniscient and omnipresent. Trying to view the creation from outside the sphere of its encapsulation would dissolve us into the undifferentiated light of the creator. If we could truly gaze upon the face of the creator, we would be engulfed and absorbed into its higher state.
“Who, if I cried out would hear me amongst the angelic hierarchies? And even if one of them suddenly pressed me against his heart, I would merely be consumed by its stronger existence. For beauty is nothing but the beginning of terror of which we are a still able to bare and we revere it so for it calmly disdains to destroy us.” – Rainer Marie Rilke
This entire idea, though not in reference to pi, was understood by the 20th century mathematician Kurt Goedel. Goedel conceived of an idea called the Incompleteness Theorem, which stated that “A system cannot define its own axioms.” Or, to put it in simpler terms and to use pi as an example, if we wished to measure the ratio between the line and the circle, or the diameter and circumference, we would need to be inside a larger circle to have a space or plane to do that measuring. If we wished to measure the circumference of the circle that encapsulates us, we would need to step outside of that circle and therefore be within the boundaries of another larger circle. Again and again, if we wished to find the expanse of our creation, another larger circle would need to be created in order to give us the platform in order to measure our world. This philosophical idea leads one right out to the edge, or KNOW-LEDGE of the sphere of our creation. This is what was known as the Sacred Hoop revered and touted by many native cultures. It is the grand sphere of creation of which we may never step out of. It is the hands of the creator embracing all of its creation.
“The life of man is a self-evolving circle, which, from a ring imperceptibly small, rushes on all sides outwards to new and larger circles, and that without end. The extent to which this generation of circles, wheel without wheel, will go, depends on the force or truth of the individual soul.” ? Ralph Waldo Emerson
Philosophically, attributing pi to the birth of our creation actually makes sense out of pi’s irrationality and infinite nature. Currently there have been over 10 trillion digits of pi calculated and still, no rational sequence has been found within these digits. The current model pervading physics explaining the birth of creation is what is known as the Big Bang. In this model, science supposes the idea that there were four main forces of creation (gravity, electro-magnetism and the strong weak nuclear forces) and all of this potential energy that would be unleashed at the moment of this big bang was compacted into something smaller than the head of a pin, known as a primordial atom. With this model, supposedly no intelligence, blueprints, architecture or supernatural force is needed to understand the creation of our universe. Just a few forces and random chaotic chemical reactions may explain the entirety of our cosmos. The Hindu’s postulated a very similar scenario for the birth of our world, though their conclusions differed wildly from modern science. In the beginning, according to Hindu mythology, the entire potential of the universe was encased inside a primordial egg known as the Brahmanda (Brahm meaning expanding cosmos and Anda meaning egg). Upon the cracking of this cosmic egg, made by an all-pervasive sound of God (known as the vibratory essence of AUM, also akin to the Biblical story of creation where “God SAID let there be light!”) came forth every living thing; every galaxy, solar system, mote of star dust and inanimate and animate being emerged from the darkness and emptiness of this first moment. This motif is not just exclusive to the Hindu’s though, for we see egg references in Egyptian cosmogony with the Cosmic Egg, in Grecian cosmogony with the Orphic or World Egg, in the study of alchemy with the Philosopher’s Egg, in the Taoist myth of Pangu, and we even have hints of this universal archetype in the nursery rhyme of Humpty Dumpty.
“Humpty Dumpty sat on a wall. Humpty Dumpty had a great fall. Threescore men and three score more can place Humpty Dumpty as he was before.” – Traditional Verse published in 1810
The word religion means “bond between humans and gods.” Though its etymology is widely disputed, religion also seems to reference linking oneself back to the first moments of creation. Religion comes to us from the Sanskrit and Latin word religio and most likely was derived from ligare, meaning to “bind, connect or link” and re meaning to “do again,” or put simply, to relink. Yoga is the mental and physical discipline practiced by peoples the world over and the term yoga means “union, yoking or linking.” Interestingly enough, a yoke is a link of chain and phonetically the yolk of an egg and the yoke or unifying link of yoga, are identical. It would seem that the etymology of the word religion is therefore referencing a spiritual process in which one links oneself back to the first moments of creation. And according to both modern science and religion, from this one thing sprang all things. From the singularity bloomed the multiplicity, which, paradoxically, though separate, has somehow remained unified. If it had not, we would not be here to experience and wonder at its glory.
“Within a single seed lies the potentiality
of a sprouting blooming madness of beauty
catching dark and light onto a pair of single eyes
and within its rise and eventual demise
lies the circumgyration of life,
spinning back again a new spring at winters end
rendering new to a form so long ago sent
through the archetypal shadows of time.” – Claudia Pavonis
“What came first, the chicken or the egg? The answer to this question lies in philosophy. How many species lay eggs? Birds, fish and snakes all lay eggs. The egg is a fundamental archetype of nature whilst the chicken is merely one of the myriad forms crafted by the hands of time. Therefore, we may say, with all certainty, that the egg came first. For even you first started out as an embryonic egg.” – Claudia Pavonis
“Geometry will draw the soul towards truth, and create the spirit of philosophy.” – Plato
If this tremendous, universe-manifesting event had such an epic beginning, with the fundamental forces being unleashed, millions of chemical reactions, explosions, etc. as modern science claims, then the amount of activity in our universe’s inception must have been staggeringly numerous. According to modern theory, within the first fractions of a second, the universe grew with enormous rapidity. If such a model has any foundation of truth, we must assume that within this brief moment of time, a numeric representation of this event would have digits ranging into the trillions. If we are to theorize that pi is indeed a numeric representation of the creation of our universe, and its unfurling decimals represent the numerical matrix that underlies the continued expansion of our universe, then in the first split seconds of creation, the universe could easily have created trillions and trillions of the digits of pi. This would be rather a rational supposition.
Since trillions and trillions of digits could have been created in those first moments, it is only reasonable to assume that trillions upon trillions upon trillions more have unfurled since that first moment. Modern scientific theory claims that the universe is roughly 14 billion years old, which means that if the universe bequeathed to us a singular number to represent this great span of time, this number could have more digits than any modern super-computer could even possibly calculate. Even if a machine or computer could calculate the rate of expansion of the universe as an unfolding numeric sequence, theoretically it could never reach the present moment, for this moment is always expanding and is unobtainable since the sphere of creation may never be exceeded.
What we are going to explore in the following pages is the concept of this first moment of creation being the wholly / holy circle and how everything in our glorious universe sprang from no thing. It is in the opinion of this author that Pi represents the continual creation of our universe by a Grand Architect, an all-encompassing, conscious, intelligent source and hence why we may never see the tail of our great pi. Though this is just one man’s opinion, it must be noted that, as any good architect knows, an opinion without pi is just an onion.
“All we have to do is to peel the shrines like an onion, and we will be with the king himself.” – Howard Carter
This entire philosophical concept, if it has any merit whatsoever, begs the question; “If pi is a representation of the creation of our universe, then what was encased inside the all-encompassing circle? What lie beneath the inner shell of our primordial egg? Since the tail end of pi is elusive, the only thing we are left to do is go back to the beginning. We need to link ourselves back to the first digit of Pi to see what was going on with the first moments of creation. And this religious process leads us to that holiest of holy numbers, three.
“Geometry existed before the creation. It is co-eternal with the mind of God. Geometry provided God with a model for creation.” – Johannes Kepler
“Geometry is the only science that it hath pleased God hitherto to bestow on mankind” – Thomas Hobbes
THREE BECOMING ONE – HEAVEN IS WHENEVER
“Heaven is whenever we can get together.” – Craig Finn
“Three, oh three! It’s the magic number!” – Schoolhouse Rock
“Measure twice, cut once.” – Carpenter’s credo
“There is a story about two Hungarian aristocrats who decided to play a game in which the one who calls the largest number wins. “Well,” said one of them, “you name your number first.” After a few minutes of deep contemplation, the aristocrat finally named the largest number he could think of. “Three,” he said. Now it was the turn of the first one to do the thinking, but after a quarter of an hour, he finally gave up. “You’ve won.” He agreed.” – Hungarian Proverb
Since we are considering Pi to be a representation of the creation of our universe, and since we have looked briefly at the nature, power and qualities of the all-encompassing circle, let us turn to the digit before the decimal place in Pi, the all-powerful, holy number three. We expressed earlier that Freemasonic, Chinese and Buddhist lexicons all considered the circle to be a representation of heaven and further, the circle was represented by the number three. The number three has long been considered a number related directly to deity. Most of us know of the Father, Son and Holy Spirit within the Christian mythos, but this is not the lone case where the power of three makes its way into religious mythology. Hinduism celebrates the three gods Shiva, Brahman and Vishnu and within the Egyptian lore exists Isis, Osiris and their child, Horus. In all three of these traditions, these three gods were considered different aspects of one unified god. The term trinity, or tri-unity, is a combinatory word that is derived from the words tri, meaning three and unitas meaning unity. Further, the Holy Trinity seems to reiterate the idea that the three is unified or whole / holy. In order to create a polygon, three points must be joined. One point is merely a point, which can be infinitely large or infinitely small, two points may be connected to form a line but still, no space or plane is created. It is only with three points that one may make the first geometric form in creation, the triangle, securing that three is, indeed, something of a distinguished number (further elucidated with the transcendental ratio of Pi – 3.141…. transcendental meaning “beyond that of other objects”). Three becoming one now leads us to the number one. The number one is easily understood to be a unifying principle. Oneness and monotheism is the unifying principle within the three major Abrahamic religions of the world. Though Judaism, Islam and Christianity seem to be at odds with one another over the particularities of scriptural interpretations, these three all glorify the existence of one supernal god. In our number line, the number one has only one number that exists before it, which is considered a non-number, and that being the zero which we equated to the circle. Acting much like the octave on a musical scale, the zero represents the placeholder and order of magnitude in which we experience the scale of numbers. The difference between 18, 180, 1,800, and 18,000 is merely how many zeroes we add to the number 18. The question must be asked: How is it that the nothingness of zero, when added to the end of a number, makes it a more abundant and larger number? This phenomenon within the heart of mathematics more than confirms that equating the circle to the zero, whose geometry and properties speak of to us of the all or nothing, is more than just fanciful guesswork by the author. Alone, the no thing of the zero is NONE, but with others, it is a magnifier of the ALL ONE. Even as NONE the zero and / or circle are ALL ONE.
It is well known by Egyptologists that the Egyptians did not have a symbol for the zero and this has led many Egyptologists and mathematicians to falsely assume that the Egyptians had no concept of zero. The Egyptians, passed onto us through the study of Hermetics and Alchemy, embraced the philosophy of “As above, so below.” This concept embodied the idea that the far and away, the finite and the infinite, the within and the without, and the Heavens and the Earth, were two aspects of one unified whole. We see this same idea expressed mathematically in the Mobius strip. A Mobius strip can be easily created by taking a paper strip and giving it a half-twist, and then joining the ends of the strip together to form a loop. If one were to travel along the length of this strip, one would return to its starting point having traversed the entire length of the strip (on both sides of the original paper) without ever crossing an edge. The number 8 is a two-dimensional representation of this idea and the number 8, as represented in our numeric characters, is an infinity symbol that is perched upright. Placing one’s pen on a sheet of paper, the figure eight gives us this exact idea of the so within and so without being two aspects of one universal motion. By traveling outward the figure eight then loops back around to travel inward only to then travel back out again. In and out are two unified aspects of one singular movement. Not coincidentally, using the English cipher, PI, or P3 and I5 sums to 8. The numerical equivalent of Pi not only gives the 8 of infinity but also is an infinite number and further, by the measurement of its circumference, tells us of the expanse and nothingness of the mighty circle or zero.
The Quadrivium (The Four Classical Liberal Arts of number, Geometry, Music & Cosmology – Walker & Company Press, 2010) has this to say about the zero: “The circular form that ‘nothing’ assumed under the Indians reflected the indentation left in the sand when a pebble used for counting is removed. Thus our modern zero, inherited from the Indians, began as the visible trace of something no longer there. Like one, the zero probes the borderline between absence and presence. In early Indian mathematical treatises it is referred to as Sunya, meaning ‘void,’ calling to mind the abyss, the ultimate knowable, the pregnant ground of all being.” This polarity of absence and presence, of Heaven and Earth, is recognized in the Mayan glyph for zero, a conch shell. A conch shell is a living representation of the exact same principles at work within the Mobius Strip. The interior of the shell becomes the exterior and vice versa, merging together to become one unified shell. It is also extremely interesting, and highly symbolic, that when one blows into a conch shell the sound emitted reminds one of the eternal vibratory essence made by the creator in Indian cosmology, known as the AUM. In the Egyptian and Greek cosmology, though they did not have a symbol for the zero, they did have a glyph that carried with it the meanings of wholeness and divinity, often used to denote a pharaoh or god, known as the Monad. The Monad is created by piercing a piece of paper with the tip of one’s compass and swinging the arm around 360 degrees. Using the English cipher on the word compass, we can derive a whole number approximation of PI. COMPASS yields us the numbers C3 O2 M1 P3 A1 S6 S6, summing to 22, and dividing this 22 by the 7 letters making up the word compass, we get 3.142. We can view the two aspects of one universal motion within this glyph as well. The central point in the Monad becomes the finite and the outer circle becomes the infinite – two aspects of reality created by one instrument. Both the circular Monad and the Mayan Conch Shell, or zero, symbolically speak to us of the merging of the finite and infinite, the fundamental principle at work throughout the cosmos.
The zero as we have established is no thing and this nothing, at the beginning of our number line, is where we are going to focus our investigation into the birth of all creation. “No thing” merely represents the state of our creation as being ethereal, or non-material. As we saw in the blog article “Eleventy One and the Magic Square of the Sun,” spirit and matter are, yet again, terms representing the two aspects of the one unified whole. Matter, which comes from the word mater, meaning mother, is also where we derive the word matrix, meaning “an environment or material in which something develops.” From the non-material realm is birthed the matrix of matter. From the all or nothing of the zero, comes forth everything. This inherent paradox of everything coming from nothing is a challenge to our modern minds since we live in the material realm. In order to fully understand this first moment of creation, we would have to dissolve ourselves into this first state, a state of transcendent being – a state of non-corporeality. This divinatory process may be done through philosophy, self-reflection, meditation, introspection, deep contemplation and travelling the inner landscapes of thought, imagination and what is often called by occultists and mystics as the astral plane. This inner dimension of thought is considered by many moderns to be a pseudo world, an artificial world that has no base in reality, yet, it is exactly in this dimension, the dimension of forms, ideas, potentials, possibilities and archetypes, where the magic of our world takes shape. Every creation made by peoples the world over; pyramids, cathedrals, temples, languages, politics, technologies, etc. were all once merely ideas birthed from within this inner dimension. Without traversing the vistas of the inward self, the outer expressions of human creativity could not manifest. The philosophy of this inherent and indubitable truth can lead one to a comprehension of the first moment of creation. Within the wholeness of the circle, at the genesis of our entire universe, the zero, being all or nothing, held within it the potential of all forms, all archetypes, all possibilities that would eventually occur during the manifestation of all that is. The circular, pregnant sphere held within it all that was, shall be and is. Everything in existence was once were merely thoughts within the supreme, supernal, ethereal or non-material consciousness of the mind of the creator. With this understanding, we may now ask one of the most profound questions of all, “How do we define these thoughts of God?”
“Numbers are the thoughts of God.” – Saint Augustine
THE ALPHABET OF THE DIVINE
In the blog article, “The Ten Emanations of God” we took an extensive look at the human hands, the first verse of Genesis in both the English and Hebrew languages and how the congruence of these elucidated the concept of the base ten-system being the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. We established and confirmed this philosophy of the base-ten system through the numerological process of digital rooting (also known as decimal parity, Pythagorean Addition or Kabbalistic reduction). Any number may be reduced down to any digit below the horizon of 9 (example: 360 becomes 3 + 6 + 0 = 9) – a process celebrated by mystics, occultists and theosophists and, most importantly, by the mathematically and mystically advanced Pythagoreans. Understanding this idea allows us to know and intuit the thoughts of the creator and, more than metaphorically, understand what was happening in the first moments of creation and every moment thereafter. Encased inside our holy / wholly circle, within our all or no thing of the zero, beneath the ethereal egg of creation, existed nine numbers. These nine numbers, along with the wholeness of the zero represent the cosmological principles at work within the entire universe. It is what we may deem, the alphabet of the divine. Every process, phenomenon and concept within our reality may be understood by these nine numbers, along with our placeholder the zero, and the interactions had between them. We may establish these cosmological principles, as many mystics and philosophers of the past have, very briefly and very concisely, by qualifying their quantities. Zero as we have said represents the all or nothing and the first moment of creation, and the placeholder for the entirety of our number line. One is a unit, all-unifying, self-replicating, the manifestation of wholeness and the only number needed to create all other numbers in existence. Two signifies duality and the unity of opposites. Up and down, left and right, forward and reverse, past and future, positive and negative, centripetal and centrifugal forces, man and women, hot and cold, good and evil are all opposites existing together to form the gradation of our experiential world. Three, as we have briefly explored represents Heaven, the creation of space, the first plane in existence and the source of all actuality in number. Four represents the Earthly field and the four-fold nature of the material world. Winter / Summer / Spring / Fall, North / East / West / South and Earth / Air / Water / Fire all come to fruition with the power and virtue of the number four. Five is recognized as the Golden Mean, Golden Proportion or balancing point recognized in the ratio of Phi (see the blog article on Phi, Metatron’s Cube and the Holy 108). The Human being has five extensions from the torso, five fingers per hand and five main material senses (Smell, Taste, Touch, Hear and Sight). The entire universe rests upon the balancing point of the number five and finds its fundamental forms via the five Platonic solids: Tetrahedron, Octahedron, Hexahedron, Isocahedron and Dodecahedron. Six gives us the six dimensions of space (Up, Down, Left, Right, Forward and Reverse) and is a number of structure, organization and arrangement. Seven represents the seven-fold vibration of the human experience. Seven chakras, seven notes of the major scale, seven days a week and seven colors of the rainbow are all present within the human adventure. Eight represents the infinite nature of the creation. This infinity, as we have demonstrated, is wrapped up within itself, forever circling and looping itself around, combining the near and the far, the as above and the so below into one continuous development. The expanding universe is contained by the number eight. Nine is our spirit. It is the endless source of energy tied to the source of all being that exists, pulsating within the temple of the human being. It represents the spirit within man, the soul of the universe and the horizon beyond which a boundless ocean of numbers lay.
With the zero being regarded as Heaven and the all or nothing this now leaves us 9 numbers within our base-ten system. 1, 2, 3, 4, 5, 6, 7, 8 and 9. These nine gods were celebrated by the Greeks and Egyptians in the Ennead. The Ennead was nine gods that represented the archetypal principles that regulated and ruled the cosmos through the laws of number. This company of nine has shown its face many times throughout the world. In Norse mythology, the god Odin hung on the Yggradsil tree for nine days. Benjamin Franklin was Grand Master of the charitable Nine Sisters Lodge. In the European Middle ages we see the Nine-Worthies, semi-legendary figures who personified the ideas of chivalry. We have all heard of Cloud Nine, being dressed to the nines, the nine lives of a feline and a stitch in time saves nine. The Christian’s mythologized the power of these nine numbers in the Christian Angelic hierarchy with those angels being the (9) Seraphim, (8) Cherubim, (7) Thrones, (6) Dominions, (5) Virtues, (4) Powers, (3) Principalities, (2) Archangels and (1) Angels. Even the ancient Mayan venerated the principles of nine. One of the most well-known Mayan pyramids is the pyramid at Chichen Itza. Chichen Itza is nine-level pyramid with a celestial observatory at the top. For a few moments on the solstices and equinoxes, the light and shadows on this pyramid forms a snake that travels down the side of the pyramid to the base, where the head of this great snake, called Quetzacoatal or Kukulcan is carved into stone. The Hebrew letter “Teth”, transcribed as a “T”, meant serpent, or the secret intelligence of all spiritual activities, and was designated by the number nine. The number 9 shows up quite often in the metrology of our universal architecture as well. The diameters of the Moon, the Sun and the Earth using decimal parity all reduce down to this number of spirit.
ZERO, ONE, TWO, THREE, FOUR, FIVE, SIX, SEVEN, EIGHT and NINE: These ten principles united represent completion, the perfection of all being and the harmony that exists within the demiurgic word of the creator, once again, apparent on the two hands that lay right before you. These ten principles are the living thoughts of a great creator being, a great mystery or grand architect who is within all things and without which, all things would cease to exist.
The ancient Vedic peoples, responsible for the oldest of Hindu scriptures, reiterated the supremacy of this base-ten system by placing nine numbers around a circle/zero and performing their math in this way. By placing 9 at the top and moving clockwise around the circle, these 9 digits encased the wholly / holy zero with the zero performing its magic as the placeholder for the rest of the digits (We will see the use of this mathematical template again later on in the text).
HUMPTY DUMPTY HAD A GREAT FALL
With these nine thoughts of god, the alphabet of the divine, encased within the first circle in existence, the sphere of all creation, mythologized in the primordial egg of Alchemical, Grecian, Hindu and Egyptian cosmologies, we can now begin to see what happened when this great egg cracked. The first verse of Genesis tells us of the two eternal concepts created by God and those being, Heaven and Earth (Genesis1:1,InthebeginningGodcreatedtheHeavenandtheEarth). Wemayunderstandthatthese two concepts represent that materiality of all that was to eventually manifest (Earth) and the ethereality of the first state of being (Heaven). These two realities existed as one within the mind of the great creator in the beginning and the Earthly material plane had not yet come to fruition. Genesis confirms this idea when it goes on to say: “And the earth was without form, and void; and darkness was upon the faceofthedeep.AndtheSpiritofGodmoveduponthefaceofthewaters.” IfEarthwasformlessand void and there was only darkness, we must assume that Genesis is trying to clue us in on the non- material, ethereal, potential realm of forms within this first sphere of all creation. No thing had existed and all that was to come to pass, all that would eventually manifest in the creation of our universe, was merely archetypal potentials, possibilities existing within the mind of God. Only upon the third verse do we find the manifestation of these concepts into the living universe, “And God said, Let there be light!” At this time we may understand that, geometrically, the sphere of creation had cracked. All of the potential existing within this sphere, or zero, with that potential recognized by the cosmological principles of our great Ennead of nine numbers, at once unleashed, creating the universe. This first moment can be poetically and philosophically expressed in numerous ways. The Grecian Orphic myth tells us of the primal generator of life, Phanes hatching from the World Egg, scripture tells us of the creation of light and nursery rhymes tell us of Humpty Dumpty taking a great fall. All of these stories being myriad poetic ways of expressing the exact same thing.
Egyptian cosmogony shares a very similar story, though mythologized in a slightly different way. Much like Genesis (Genesis 1:2 …and the spirit of God moved upon the face of the waters…), in the beginning existed primordial or primeval waters, deemed the “waters of nun”, in which from deific means up sprang a Lotus Flower. It must be noted that phonetically nun and none are exactly the same sound and further, in Catholicism, a woman who has given her life to the servitude of God is known as a nun and the traditional garb worn by these figures is black (recognized by the darkness of the primordial waters). NUN / NONE / NO THING. Using our English cipher, Lotus equals 23, as well as Heaven, and Flower equals 24, the same as Earth. Whether we choose to use the concepts given to us of Heaven and Earth in Genesis, or if we utilize the concepts given to us by the Egyptians being Lotus and Flower, the sum of the gematria is identical.
What’s even more interesting about the creation story given to us by the Egyptians is that the lotus flower springs up from underneath water, reflective of the virgin birth of our universe. TheVirginBirth is understood philosophically in that the sphere of zero of our first moment of creation needed nothing fromoutsideitselftoimpregnateitselftogivebirthtoallofcreation. The Egyptians saw the beauty of the lotus flower as being a perfect symbolic, living example, or fractal reflection, of the first moment of creation. The divine importance of the sacred lotus flower is not exclusive to Egyptian spirituality though for lotus flower symbolism is rife in Buddhism, Confucianism and Hinduism as well.
The Freemasons also allude to this beginning of creation in the motto for the 33rd degree of Scottish Rite Freemasonic ascension. “Ordo Ab Chao” is a Latin phrase that means Order out of Chaos. Chaos is derivedfromtheGreektermKhaoswhichmeans“anabyss,avoid,agapingwideopen.” Accordingly, from this chaotic beginning, gaped open wide the form and structure and order of the Creator. Whether we speak of light emerging from the void and darkness in Genesis, or the emergence of the beautifully formed lotus flower from the waters of nun in Egyptian lore, or the order from the dark abyss of chaos in the Freemasonic motif, the story seems to be one and the same.
Upon the cracking of this egg, 9 cosmological principles, along with the zero (now becoming the placeholder and arbiter of the order of magnitude) emerged and interwove the order that is our manifested reality. In Egyptian lore we are told that “The Pharoah came forth between the thighs of the divine nine,” which alludes, very strongly, to the philosophy of the nine gods of the Ennead, or 9 numbers encased inside our egg, with the Pharaoh becoming a living representation of the all or nothing, or the zero – making the complete ten. It is most definitely not a coincidence that, using the English cipher, Pharaoh and Earth both sum to 24, reiterating the idea that what sprang forth from this egg of creation was the materiality of our existence. This first time was celebrated by the Egyptians as the Zep Tepi. The Zep Tepi, or first moment of creation, is reflected in every living being and every moment of creation. Every animate and inanimate being made by the creator embodies this first moment – the wholeness of the egg or sphere of creation, cracking into the multiplicity but simultaneously remaining whole. The tree is a perfect example of this cosmic truth. All branches of a tree, though separated from one another, all unify at the trunk into one whole being. The roots below, grounded to the foundation of all being, reflect the branches above and they all connect to form one ecosystem that is a reflection of the entire universe.
We can use the symbolism of pi, its diameter and circumference, or line and circle, to help us understand this first moment of creation, and help give us a geometric metaphor for the cracking of the great sphere or egg of creation. The diameter, or line, cut through the heart of the circle gives us two opposite hemispheres, 180 degrees each. In Egyptian hieroglyphs, we see the most interesting symbol with a pair of scissors, cutting into a sphere and the sphere, or egg, cracking or gaping open wide. Both the geometry and symbolism we may derive from pi and this Egyptian hieroglyph speak to us about the first moment of creation.
This symmetry or mirroring that we see within the geometry of pi and the unification of these two polarities by the circumference of the circle is a property utilized by nature almost every which way one looks. The human body in and of itself is mirrored. By drawing a line down the center of oneself and dividing the human body in two, this symmetry becomes very apparent. Your left eye is a mirror of your right eye. Your left ear is a mirror of your right. Our brains, nostrils, teeth, cheeks, tongues, chins, shoulders, arms, hands, breasts, buttocks and feet are all mirrors of each other. This perfect symmetry shows the intelligence of nature’s own economy. The Earth itself has a Northern and Southern hemisphere. Nature and the creative force of the creator created one hemisphere above and then simply mirrored it below to create one whole home that we call Earth. Nearly all plant and animal species on this planet follow this fundamental form in design, recognized in the symbolism of the geometry of pi. Go to your local park or go out into your backyard and pick a leaf off of a tree and the beauty, elegance and intelligence of nature’s symmetry will become quite apparent.
The unity of these two halves is what the Greek philosopher Heraclitus termed The Unity of Opposites or Coincidencia Oppositorum. Everything in nature has its opposite. Man / Woman, Hot / Cold, Good / Evil, etc. The UNITY within the two halves is what we are going to come to see is the most important part of nature’s construction. So let’s explore what happened to these two halves of pi when our great egg cracked.
“The life span for a whole universe, according to the ancient seers, is 314,159,000,000,000 solar years, or “One Age of Brahma.” – Paramhansa Yogananda, Autobiography of a Yogi
Copyright 2013 Marty Leeds
Presented with Author’s Permission