In this article we will continue our discussion of the Monad by moving into the symbolism of the circle.
Each number 1-10 has a geometry that corresponds to it. The geometric shape of the Monad, or 1, is the circle or sphere.
Reference Construction Lesson #3: Circles.
As Michael Glickman wrote, “Like a wise teacher, the circles use their geometry to throw us back on ourselves.”
The Circle – 360°
Keith Critchlow writes, “The most comprehensive yet simple form for defining a sacred area is the circle. It is an ‘opening to the transcendental’.”
Hermes Trismegistus tells us, “God is a circle whose center is everywhere and whose circumference is nowhere.”
The circle is the simplest and most perfect of forms.
It is the geometric representation of the Monad.
A circle is defined as “the set of all points on a plane that are a fixed distance from the center.”
A circle contains 360 degrees.
360 is a very harmonic number – it can be divided evenly by 24 terms:
2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 30, 36, 40, 45, 60, 72, 90, 120, 180
*Note – All of the first 10 numbers of the Decad are a factor of 360 except 7.
Interestingly, 360/7 = 51.4285 which is extremely close to the slope of the Great Pyramid (51.85°).
Ancient calendars (such as the Persian Calendar) used 360 days for a year. They watched the stars revolve around the North Star one degree per day.
The circle is the source of all subsequent shapes. It is the womb of Infinite Potential in which all geometric patterns develop. The circle contains the polygons of every order of geometry as seen below.
The circle represents the Infinite Unified Universe: infinite in space, time, consciousness, variety, dimension, perspective, quality and potential.
It symbolizes unity, totality, wholeness, integrity, original perfection, the Self, the Infinite, Eternity, timelessness, heaven, enlightenment, God, the infinite creator, Cosmic consciousness, Purusha, Spirit, All-That-Is.
“So whether we call the collective consciousness of all things ‘God,’ or simply ‘the consciousness of all things,’” Michael Talbot tells us, “it doesn’t change the situation. The universe is sustained by an act of such stupendous and ineffable creativity that it simply cannot be reduced to such terms. Again it is a self-reference cosmology. Or as the Kalahari Bushmen so eloquently put it, ‘The dream is dreaming itself.’”
The circle is the undifferentiated, un-potentiated infinite realm of timelessness and spacelessness. It is the field of infinite potential: still, calm, poised in wait, “an encompassing field of unbounded, infinite possibility that precedes emergence of any dualities whatsoever.”1
“The circle has been a universal symbol of an ideal perfection and divine state that always exists around and within us whether we acknowledge it or not.”2
The circle “regulates all things for us down to the humblest bounty as it dispenses beauty, homogeneity, shapeliness and perfection,” as Proclus said.
The sphere is the 3D representation of a circle.
The circle spins to become a sphere. Within this rotation, the spiral is born.
The sphere is a symbol of the cosmos and the totality of manifest creation.
The spiral is a symbol of how those things move, grow and evolve in creation.
Very large and very small things in nature tend to be spherical (electrons, atoms, planets, suns).
The sphere possesses the smallest surface area for its volume of any possible 3D solid.
Volume: 4/3 π r3
Surface Area: 4 π r2
Three Parts of a Circle
Black Elk of the Oglala Lakota Sioux said, “You have noticed that everything an Indian does is in a circle, and that is because the Power of the World always works in circles, and everything tries to be round.”
The three parts are: Center, Area, and Circumference.
These parts coincide with the three main universal principles the circle represents.
- Center = Infinity, Equality
- Area = Unity, Maximized efficiency
- Circumference = Cycles (within cycles)
“Man’s heart is the central point and heaven the circumference.”3
1. The Center
“The center is still and silent in the heart of an eternal dance of circles.” – Rabindranath Tagore
The Center: Infinity
The center is the seed; the bindu; the unknowable point, the incomprehensible center that flows both inwardly and outwardly to infinity containing within it infinite potential.
It is the foundational mystery – the Creator and creation itself.
It is both everything and nothing simultaneously.
It is the infinitesimally small and the infinitely large conjoined as a single entity.
It is eternity, the eternal present.
It represents the singularity point in which the potential of the entire Universe of Space and Time is contained.
It is also the singularity at the core of “black wholes” on all scales that serve as the nucleus of atoms on the microcosmic and the nucleus of galactic systems on the macrocosmic. This is discussed in detail in the Science section of Cosmic Core.
Randall Carlson writes, “Corresponding to these external singularities there exists an inner, spiritual nucleus of infinite potential, in the form of the Bindu, the gateway to the Superconsciousness.”
“Consider the point as symbolizing your own “center”. Through meditation and self-contemplation we can seek a more subtle center, our higher or deeper self, the power that motivates the actions, emotions, thoughts, and desires.”4
The Center: Equal expansion in all directions from the center (equality)
“One is echoed in all things and treats all equally.”5
The center expands outwards (and inwards) equally in all directions. It implies equality in all aspects of the universe, all beings, all thoughts, all emotions, all events…everything.
Equal in importance. Equal in validity. Equally loved and cherished. Equal, but different.
This implies that each grain of sand, each speck of dust, each worm, bee, spider, insect, pig, dog and horse, each animal, each human, each planet, each star…everything is equally important and equally accepted. Everything is equally supported as each move at their own pace on their own journey of transformation.
Each of the infinite movements from the center (radii) are at a slightly different angle or perspective, giving rise to the infinite subjective perspectives of reality.
Randall Carlson tells us that the point “has meaning in the metaphysical/spiritual dimension, representing the ‘siva-bindu’ the point round which the kundalini serpent lies coiled; on the Hermetic/Alchemical level, it represents the germ of transmutation; on the level of nuclear physics, it is the extraordinary power contained within the atomic nucleus, and in the Cosmological dimension it represents the ultimate singularity containing the potential of the entire universe of Space and Time.”
The Universe & Infinity
“Euclidean geometry means that the universe is either finite and surrounded by nothingness OR it is infinite and has no boundary…Infinity and Nothingness are notions the profoundness of which tax the limits of our brains. They represent the unattainable limiting concepts of existence itself.”6
“Infinity is an inconceivable having actuality.” Conrad Ranzan
The Mainstream View of Infinity
Currently mainstream scientists claim ignorance on the subject. They do not know and do not claim to know. They say it could be either way.
Physics equations won’t work unless an infinite universe is supposed, yet the expanding universe hypothesis only works for a finite universe.
They have an unsolvable problem and therefore claim ignorance on the matter.
Roger Penrose sums it up well, “We do not know whether the universe as a whole is finite or infinite in extent – either in space or time.”
According to the philosophy of the esoteric stream of knowledge and sacred geometry it is assumed the universe is infinite.
Infinity is Unified
“The universe is infinite. This has yet to be proven or disproven, but we can assure you that there is no end to your selves, your understanding, what you would call your journey of seeking, or your perceptions of the creation. That which is infinite cannot be many, for many-ness is a finite concept. To have infinity you must identify or define the infinity as unity; otherwise, the term does not have any referent or meaning. In an Infinite Creation there is only unity. You have seen simple examples of unity. You have seen the prism which shows all colors stemming from the sunlight. This is a simplistic example of unity.”7
The Key of Unity is Infinity
Unity does not mean everyone becomes homogenized.
Within Unity, individuality is a universal right.
Unity alludes to a greater, deeper connection between all consciousnesses.
Unity does not mean all consciousnesses are the same, or need to be the same.
Within Unity there is room for Infinite unique expressions.
Evolving towards Unity does not mean everyone must become the same; be the same; think the same; act the same. Everyone must become more of themselves within the framework of knowing we are all connected, and acting accordingly with compassion, empathy and understanding.
When you recognize the connection you recognize how your thoughts, words, and actions affect all others.
If one could recognize the true meaning of Unity, they would not harm another, or take advantage of another.
This is Multiplicity within Unity – the Archetypal Principles of 1-10 of which the Monad contains all.
“The ‘concrete’ reality for traditional societies was metaphysical and grounded in the gods, whereas in our contemporary Western society it is literal and grounded in mechanisms. Hence our contemporary repetitive concrete ‘boxes’ – the tower blocks, flats and offices – proclaim an equality of identity to such a degree that they become mechanically identical and therefore anonymous, thereby denying the first law of the natural order of manifestation – variety and multiplicity in Unity, or uniqueness in unicity.”8
The Geometric Parts of a Circle
- The distance from the center of a circle to any point on the circle (half the diameter)
- All radii of the same circle are congruent. (All points on the circle are at the same distance from the center point.)
- A circle can have an infinite number of radii.
- A radius perpendicular to a chord bisects the chord and the arc.
- The angle made when the radius is wrapped around the circumference
- In a half circle there are π radians, also 180 degrees.
- π radians = 180 degrees
- 1 radian = 180/π = 57.2958…
- To go from radians to degrees: multiply by 180 then divide by π.
- To go from degrees to radians: multiply by π then divide by 180.
- There are 2π radians in a full circle.
- A line segment with endpoints on the circle.
- A radius that bisects a chord is perpendicular to the chord.
- A chord that passes through the center
- Diameter is twice the length of the radius.
- A circle can have an infinite number of diameters.
- d = 2r
- A line that intersects the circle in two points
- Perpendicular to radius
- If a line is tangent to a circle, it is perpendicular to the radius drawn to the point of tangency.
- The distance around the circle
- C = 2πr
- a portion of the circumference
- The arc measure is the measure of a central angle.
- In the same circle, or congruent circles, congruent central angles have congruent arcs.
- An angle made from points sitting on the circle’s circumference. See image below.
- An inscribed angle in a semicircle is always a right angle. See image below.
2. The Area
There are no divisions within a circle except for the ones we artificially impose upon it.
Area: Maximized efficiency
“A circle expresses the most practical and efficient geometric space for natural and human creations to occur. Of all shapes, a circle encloses the most space by the smallest perimeter…or…the most enclosure with the least exposure.”9
A = πr2
A = (π/4) x d2
Where A = area
r = radius
π = the ratio of a circle’s circumference to its diameter, commonly expressed as 3.14159…
Bruce Rawles tells us, “There is no point of view given greater or lesser importance, and all points on the surface are equally accessible and regarded by the center from which all originate. Atoms, cells, seeds, planets, and globular systems all echo the spherical paradigm of total inclusion, acceptance, simultaneous potential and fruition, the macrocosm and microcosm.”
Keith Critchlow writes that the circle, or area of a circle has a universal meaning “of the unity of a ‘sacred’ space representing that which is situated outside time and outside space in a primordial state, ‘prior’ to space and temporally ‘in the beginning.’”
This reflects the idea of the unpotentiated Infinite potential of the metaphysical – time/space – that which is outside time, or timelessness.
Algis Uzdavinys wrote, “Unity is possible through the contemplation of geometrical figures, diagrams and symbols (analogous to the Hindu Yantras and Mandalas) projected into the Imagination which occupies, according to Proclus, the central position in the scale of knowing.”
3. The Circumference: C = 2πr
The circumference implies movement – not just any movement – circling movement or cycles.
In three dimensions this movement creates spirals or spiraling cycles.
Not just cycles, but cycles within cycles, within cycles, to infinity…
Cycles, circulations, circuits, orbits, vibrations and rhythms are a part of unity (the circle), therefore a part of every aspect of reality. There is no way to avoid this.
There will always be high points and low points, rising and declining phases.
Cycles within cycles within cycles are an inherent part of nature, life, humanity, evolution and creation. There are no exceptions.
Cycles will be discussed in greater detail in Article 14.
Circumference/Diameter = π or C/D = π
Circumference = π x d C = πd
“The ratio of the circumference of a circle to its diameter, Pi, is the original transcendental and irrational number. It cannot be expressed in terms of the ratio of two whole numbers, or in the language of sacred symbolism, the essence of the circle exists in a dimension that transcends the linear rationality that it contains.”10
The circle contains the limited and unlimited in one body, or the material and the immaterial, the visible and the invisible, the finite and the infinite.
When either the radius or circumference is measurable in whole, rational units, the other is an endless decimal with non-repeating units (pi = 3.1415926…)
Sri Aurobindo writes, “Pi is no irrational decimal recurrence, helplessly repeating forever its figures, but an expanding series of powers of the Infinite.”
Pi is an ‘irrational’ number: “A number that cannot be expressed as a ratio between two integers and is not an imaginary number. If written in decimal notation, an irrational number would have an infinite number of digits to the right of the decimal point, without repetition.”
Robert Lawlor tells us, “The rational and irrational numbers resulting from a circle represent two completely different states of being. The rational whole numbers were related to manifestation and were the terms to be used in calculation. Every aspect of the phenomenal world was seen to be a fixed, instantaneous moment caused by the interaction of complimentary components, a moment trapped between light and dark, life and death, day and night, between formation, disintegration and reformation.”
The irrational numbers “symbolize the constant, creative process of acting and reacting energy.”
We only know 10 trillion digits of pi, a mere speck in the grand scheme of things.
Yet Steven Strogatz says, Pi “puts infinity within reach”.
Pi = 3.14159265358979323846264338327950288419716939937510582097494459230781…
The first 144 digits of pi add up to 666.
Pi is encoded into the Great Pyramid at Giza: The vertical height of the pyramid has the same relationship to the perimeter of its base as the radius of a circle has to its circumference. If you take the perimeter of the base and divide it by the height multiplied by 2 you’ll get Pi (1760/560 = 3.14).
The number 360 is at the 359th digit position of pi.
At position 763 there are six nines in a row – called the Feynman Point.
The first six digits of pi (314159) appear in order at least six times among the first 10 million decimal places of pi.
The first 3 decimals sums 6, the first perfect number and the triangular number of 3.
The first 7 decimals sums 28, the second perfect number and the triangular number of 7.
Plato obtained a fairly accurate value for pi: √2 + √3 = 3.146.
The Babylonians found the first known value of pi: 25/8
The most convenient value for pi is: 22/7 = 3.142857
104348/33215 is the fraction with the closest approximation = 3.141592653921421
355/113 is an easier value, and still quite accurate = 3.141593
The Nilakanthaa series – Indian mathematician (1444-1544)
The Nilakanthaa series exhibits the Principle of Alternation. Each term bounces below pi and above pi getting closer to the true value as it goes up:
Term 1 = 3
Term 2 = 3.166666666667
Term 3 = 3.133333333333
Term 4 = 3.145238095238
A Sanskrit Poem and Pi
The following is a phonetic translation of an ancient Sanskrit poem11:
gopi bhagya madhuvrata
srngiso dadhi sandhiga
khala jivita khatava
It means: “O Lord [Krishna], anointed with the yogurt of the milkmaids’ worship, O savior of the fallen, O master of Shiva, please protect me.”
Each one of the Sanskrit sounds corresponds to a numerical value:
ka = 0
ka ta pa ya = 1
kha tha pha ra = 2
ga da ba la = 3
gha dha bha va = 4
gna na ma sa = 5
ca ta sa = 6
cha tha sa = 7
ja da ha = 8
jha dha = 9
These sound values applied to this particular poem results in the number:
.3141592653589793238462643383279 (32 digits)
This is the exact number of pi divided by 10 carried to 32 digits…supposedly unknown in ancient times.
The Great Pi Conspiracy
Mark Wollum provides “compelling empirical evidence and multiple mathematical proofs that the real value of pi differs from the textbook number by approximately one-tenth percent, and is based on the mathematical constant known as the Golden Ratio.”12
Wollum tells us that the true value of pi is paramount to understanding the interactions of all our constructs of reality, since they all involve rotational energy.
The whole story can be read here: The Great Pi Conspiracy.
This new value of pi is said to be:
π = 4/√φ or 3.144605511…
This is a very interesting perspective that we are not saying is correct or incorrect. Decide for yourself.
The author states, “A new value of pi based on the golden ratio will support the interconnectedness of our physical constructs of the universe, and be much more eloquent than the old one. A new pi should allow for more accurate energy assessments, predictability in rotational systems, and perhaps lead to an entirely new physics paradigm, based on interactions of rotational energies.”
Concentric Circles (Spherical Waves/Standing Waves)
We will now briefly discuss circles within circles, otherwise known as concentric circles.
Concentric circles are circles with a common center.
Keith Critchlow tells us, “The ‘dimensions’ of the transcendental world are expressed in concentric rather than serial form.”
In other words, everything in reality has a common center.
Remember Hermes Trismegistus, “God is a circle whose center is everywhere and circumference is nowhere.”
The annulus is the region between two concentric circles of different radii.
The pattern of rings around a Point can be called a Holon.
A holon is something that is simultaneously a whole and a part. “A fractal is close to the idea of a holon, as it is a part that represents a whole at the same time.”13
The Hungarian-British author Arthur Koestler (1905-1983) coined the word holon in 1967 in his book The Ghost in the Machine.
The symbolism is interesting when you think of it in terms of consciousness.
Koestler said that ‘holons are self-reliant units that possess a degree of independence and handle contingencies without asking higher authorities for instructions. i.e. they have a degree of autonomy [free will]. These holons are also simultaneously subject to control from one or more of these higher authorities [Unalterable laws of the Universe such as Unity].
The first property ensures that holons are stable forms that are able to withstand disturbances, while the latter property signifies that they are intermediate forms, providing a context for the proper functionality for the larger whole.
Finally, Koestler defines a holarchy as a hierarchy of self-regulating holons that function first as autonomous wholes in supra-ordination to their parts, secondly as dependent parts in sub-ordination to controls on higher levels, and thirdly in coordination with their local environment.”14
Think again about this relating to consciousness. If each human is an independent individualized consciousness able to make decisions on their own and function successfully in their individual local environments, and each is granted a wide range of free will yet is still subject to control and influence from a higher order, this would make the evolution of consciousness a holarchy.
That is, each human has free will. This free will is vast in its scope yet there are limits to it. None can escape Unity. Everyone, whether they believe it or not, is interconnected with everything else. None can escape the evolution of the soul, whether they remember that the point of life is to learn, grow and evolve towards unity. On another level, in each life none can escape the characteristics of their species according to their DNA. That is, none can become a duck or cat or spider in a lifetime that they are a human. None can regrow limbs or suddenly sprout wings if they are human. Each species is bounded by the DNA of that species while they are in that type of body. Yet each entity is still granted total free will in the way they choose to live their lives, their belief systems, and the speed and method with which they choose to evolve, and so forth.
Consciousness is a holarchy bounded by the Divine Unity of which we are all a part.
There is an idea (the Golden circle of Business) that concentric circles represent a business plan. Business is a never-ending circle of repeating cycles. Dale and Ben Midgley tell us, “While poor decisions beget more poor decisions, all of which radiate throughout the entire organization, good decisions do the opposite; they beget more good decisions, which affect the entire business.”
This analogy can be expanded to a life, realizing that good decisions radiate throughout our entire life creating a better life; or expanded further to an analogy of the entire universe. Good decisions we make ripple outward from our selves, radiating through the entire creation, affecting all parts helping to make it a better world, or universe. Vice versa, negative thoughts ripple outwards adding to negativity and suffering.
Karen French posits the Holon of concentric circles as a representative of the dynamics of time.
“Each sequential Circle moves around the Center just as every measure of cycle in time – a second, an hour, a year and an eon – moves around the Moment.”15
Concentric circles are seen in nature: ripples in water, tree rings, layers of deposits in agate crystals, spider webs, onion rings, time lapse of star traces around the Pole star, rings around Saturn, planets around the sun…etc.
“Many waves of interest, such as sound waves, light waves, [shock waves and radio transmission waves] move in three dimensions. These produce expanding concentric circles and are called spherical waves.
In this case the wavelength is the distance between each concentric circle. The lines that locate the crests are called wave fronts and they are spaced precisely one wavelength apart.”16
Very far from the source small sections of the wave fronts appear to be straight lines.
The inward and outward pulsation of these spherical waves forms the torus vortex.
Concentric circles also represent the quantized states of energy that exist around all matter/life due to the toroidal field of energy that creates that matter/life. We discuss the quantized ‘shells’ around electrons, atoms, molecules and galaxies in the Science section of Cosmic Core.
“In 2003, NASA’s Chandra X-ray space telescope spotted a pattern in the gas that fills the Perseus Cluster: concentric rings of light and dark, like ripples in a pond. Astrophysicists say those ripples are the traces of incredibly low frequency sound waves.”17
“When two pebbles are dropped into the water some distance from each other, circular patterns of the parents waves join to create ellipses that grow wider and wider, until – beyond the confines of this picture – they also become circles. Meanwhile, the first circles are becoming transformed: from closed circles, centered upon themselves, they are growing into parabolic arches, reaching out beyond themselves toward the infinite.” Asks Gyorgy Doczi, “Is this merely a pattern of pebbles, of vibration, or is it also a metaphor for love, for the power of shared limits, and for the creative act itself?”
Concentric Circles as Ancient Multi-Cultural Art
Concentric circles are also seen as a form of prehistoric art from around the world. They can be found in Ireland, Wales, Northern England, France, Portugal, Finland, Scotland, Spain, Italy, Greece, Denmark, Sweden, Switzerland, Australia, Gabon, Africa, Hawaii, India, Israel, Mexico, Mozambique and the states of Arizona, New Mexico and California.
These sites are from 3000 to 10,000 years old, some perhaps older.
The image below is from Alice Springs, Australia:
This one is from Northumberland in England:
Here is one from the Big Island of Hawaii:
This one is from Gabon in West Africa:
One from New Mexico in the United States:
One from Arizona in the United States:
An example from the Pomo site in California:
One from Sardinia off the coast of Italy:
And one from the Carschenna site in Switzerland:
These are just a few examples out of thousands.
Jack Andrews says, “The concentric circles found all over the world are an eye opening to the realization that the people of our earth are interconnected and we are all of one human family. It is our hope that these discoveries of ancient symbols will continue to bring us all together in peace and we will see the wonderful connectedness of us all along with the cultural diversity that makes us all unique.”
- Mahony, William, Exquisite Love, Sarvabhava Press, 2014
- Schneider, Michael, A Beginner’s Guide to Constructing the Universe, Harper Perennial, 1994
- Shabistari, Mahmud, The Secret Rose Garden, Phanes Press, 2002
- Schneider, Michael, A Beginner’s Guide to Constructing the Universe, Harper Perennial, 1994
- Lundy, Miranda, Sacred Geometry, Bloomsbury USA, 2001
- Ranzan, Conrad, The Dynamic Steady State Universe, Physics Essays, Vol. 27, 2014
- Elkins, Rueckert, McCarty, The Law of One, Session 1.7, https://www.lawofone.info/results.php?s=1
- Critchlow, Keith, Time Stands Still, Brecourt Academic, 2nd edition, 2007
- Schneider, Michael, A Beginner’s Guide to Constructing the Universe, Harper Perennial, 1994
- Rawles, Bruce, Sacred Geometry Introductory Tutorial, https://www.geometrycode.com/sacred-geometry/
- Melchizedek, Drunvalo, The Ancient Secret of the Flower of Life Vol I, pg 16
- Wollum, Mark, The Great Pi Conspiracy, 5 February 2015, Veterans Today, https://www.veteranstoday.com/2015/02/05/pi/
- French, Karen, The Hidden Geometry of Life, Watkins, 2012
- Pearson Education Inc, Pearson Addison –Wesley, 2008
- Smith-Strickland, Kiona, There Actually Is Sound in Outer Space, Gizmodo, 28 October, 2015, https://gizmodo.com/there-actually-is-sound-in-outer-space-1738420340