In this article we will delve deeper into the importance of Number.
To review the previous article, one of the clearest ways to begin to understand the Perennial Philosophy, the esoteric stream of knowledge and sacred geometry is through the study of the Quadrivium.
The Quadrivium is the Four-Petaled method of study made famous by Pythagoras consisting of:
As we have seen, the great philosophers of old revered Number above all and considered it the foundation of all other studies.
Plato said, “Geometry is knowledge of the eternally existent. Numbers are the highest degree of knowledge. It is knowledge itself.”
In the esoteric stream of knowledge, numbers symbolize universal principles regarding the movements of consciousness. Therefore they are said to contain consciousness.
Everything contains consciousness because everything is a result of consciousness.
In philosophy this is called Idealism.
Idealism is defined as “any view that stresses the central role of the ideal or the spiritual in the interpretation of experience. It holds that the world or reality exists essentially as spirit or consciousness resulting from an Infinite Mind.” That means consciousness is the creator of physical reality and all in reality is imbued with consciousness on some level.
In this belief system, numbers are carriers of information that communicate meaning far beyond mere quantities. Number symbolism is the original ‘lost’ universal language – the common language of the cosmos that explains the universal principles the universe, and all life, is based upon.
As Anthony Morris stated in his article The Numerical Universe – Order in Chaos, “…the origin of Life is the result of an inherent canonical, numerical, geometric and musical template that pervades the created Universe…”
“…the code of number behind ancient science appears seamless and, like the circumference of a circle, with no beginning.” John Michell
We will now introduce the Sacred Number Canon.
“In the known civilizations of antiquity, such as China, Babylon, and Egypt, the canon of number was venerated as the source of all knowledge and a guide to rightful conduct.” John Michell
A canon in this sense is defined as “a collection or list [of a particular item] considered to be permanently established as being of the highest quality”.
Below is an image containing many of the numbers in the Sacred Number Canon.
The sacred number canon contains numbers that consistently show up in:
- Geometry Measure
- Time Measure
- Space Measure
- Solar System Measure
The numbers we discuss are not the only numbers in the Sacred Number Canon, but they are some of the most important. The fact that these same numbers show up in so many ways hints to us that the universe is an ordered, harmonious whole that is conscious and intelligent. Without order life would not be able to exist, to reproduce, to heal or to grow. Your finger would never ‘miraculously’ heal after being cut open; your bone would not mend after a break; a child would not be able to form in the womb; plants would not be able to photosynthesize or bear fruit; electrons would not be able to arrange and continually orbit around the nuclei of atoms; stars and planets would not be able to arrange properly to nourish life…etc.
The study of sacred geometry teaches that Order leads to life. The universe is an ordered whole, unified by harmonious proportions. The universe is not chaos. Chaos is indeed apart of the Universe. Human beings can choose to experience or create chaos in their minds, their lives, or their communities. However, the Universe is not chaos itself. Random, chaotic forces are not the driving forces of the Universe that create life and matter.
Through the study of sacred geometry we begin to see that Unity, Order and Harmony are universal principles. When we learn to bring unity and balance into our lives we can find ourselves moving in harmony with the universe and find that our life moves forward with more fulfillment and grace. We can find our thoughts, emotions, actions and relationships to be more harmonious. We can find more peace, joy and prosperity in all aspects of life.
The main point is this: Numbers, Geometry, Science and Symbolism are fascinating subjects. However the main importance of them is learning how to distill the wisdom they offer and to harmonize your individualized consciousness with that of the universe. This can lead to happier, more peaceful lives and allow each individual to find the way to rise to their unique highest potential for the greatest good.
This is hands down, the most important reason for taking the time to learn these subjects, and it is a point we will return to again and again.
As human beings, this is the task set before us now.
Back to Number:
“Sacred Mathematics represents a wholly contained and internally consistent philosophy – a philosophy which describes physical reality, its cosmogony and every aspect of its science.”1
Not surprisingly, the Sacred Number Canon revolves around the Five Platonic Solids: the tetrahedron, octahedron, cube, icosahedron, and dodecahedron.
Returning to Plato, he said, “Every diagram, system of numbers, every scheme of harmony, every law of the movement of the stars, ought to appear One to him who studies rightly.”
Plato adds, “And that is why we should distinguish two kinds of cause, the necessary and the divine, and should search in everything for the divine cause, if we are to attain as blessed a life as our nature permits.” Timaeus 69a
We will now take a look at this system of sacred numbers.
Islamic scholar Frithjof Schuon remarked, “Geometrical figures are so many images of unity; they exclude one another or rather, they denote different principal qualities; the triangle is harmony, the square stability; these are concentric not serial numbers.”
We will delve much farther into number symbolism and the archetypal qualities of numbers in later articles.
It all begins with an incommensurable point.
The point expands into a sphere, represented by a circle.
The circle is Infinite. It expresses Unity and Infinite Potential, or the Infinite Potential of Cosmic Consciousness at rest, waiting, silent and still.
This concept of the Point and Circle as the Source has been called by many names and shows up in every single spiritual tradition throughout time:
Unity, The One, The First, The Seed, The Essence, The Builder, The Foundation, The Space-Producer, The Silent Force, Mirror of Wonders, Chi, Brahman, Dharmakaya, Tao, Quantum Physical Vacuum, the Void, The Still Eternity, The Immutable Truth and Destiny, Infinite Potential, Prana, Akasha, Purusha, Dzogchen, Infinity, Divinity, Spiritual Reality, Infinite Consciousness, Cosmic Consciousness, God, Allah, Spirit, Great Spirit, Kosmos, Holy Ghost, Holy Spirit, Loving Energy, Spiritual Energy, Logos, The Universe, Cosmic Mind, Source Field, Source Realm, Zero-point energy, Infinite Intelligence, the Metaphysical Realm…and on and on…
This is an inexpressible concept therefore you may call it whatever feels right to you. Or don’t name it at all.
Wars have been fought and torture has been committed over this concept of naming what cannot be named, and forcing others to interpret truth through all too narrow channels.
Never forget Shakespeare’s famous line, “What’s in a name? That which we call a rose by any other name would smell as sweet…”
To return to the circle:
The circumference of a circle, in the sexagesimal system, is 360 degrees.
The sexigesimal numeral system is based on the number 60. This system originated with the ancient Sumerians (Chaldeans) in the 3rd millennium BCE. As far as we know, the ancient Sumerians were present from approximately 5500 BC to 2004 BC.
One important reason base-60 was chosen is due to the number 60 being a ‘superior highly composite number’ which means it is an extremely harmonic number with many factors – to be exact, “a natural number which has more divisors than any other number scaled relative to some power of the number itself.”2
There are 12 factors of 60:
There are 24 factors of 360:
Circumference of a circle = 360 degrees
360 degrees of arc = 21600 minutes of arc (360 degrees x 60 minutes)
21600 minutes of arc = 1296000 seconds of arc (21600 minutes x 60 seconds)
To begin to gain an understanding of sacred geometry it is extremely important to recognize the following geometric numbers and to learn to notice them as they show up over the course of studying esoteric knowledge.
It is also important to note that adding zeros to a number does not change its symbolism; it only changes its magnitude, raising it to a ‘higher power’. For instance, 216 has the same basic meaning as 2160, 21,600, 216,000, 2,160,000…etc.
Regular Polygons & Angles
As Galileo said: “The universe cannot be read until we have learnt the language and become familiar with the characters in which it is written. It is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word.”
Michael Schneider writes, “The universe is not like a room filled with geometric shapes. These forms are the shape of the universe, the shapes of space itself.”
“Space has shape,” as Bucky Fuller said.
The importance of this quote will be better understood once we delve into the science aspect, particularly the astronomy section, of Cosmic Core.
Below is a chart representing the regular polygons from 3 to 10. Regular Polygons are two-dimensional shapes where all sides and all angles are equal.
Take a look at these polygonal shapes, all which are familiar to human beings. These shapes are archetypal patterns within our consciousness representing an Ideal, or Universal Principle. Upon contemplation we have an innate understanding of them once we begin to remember their importance.
Notice the numbers associated with each familiar shape. The sum of the interior angles are the sum of the angles of each shape.
For instance, a regular (or equilateral) triangle has three sides and three angles of 60º each.
3 x 60 = 180°.
Hence, the number of a triangle is 180.
Familiarize yourself with each number and attempt to memorize the number of each shape. These numbers, and the Platonic Solid Numbers discussed next, are the basis for the Sacred Number Canon and they will continually pop up throughout the study of sacred geometry and the esoteric stream of knowledge.
|Shape||Sides||Each Angle||Sum of Interior Angles|
Next we have a chart of the Five Platonic Solids and one Compound solid, the Star tetrahedron.
Platonic Solids will be covered in extreme detail as we move forward. Like the regular polygons above, it is recommended that you familiarize yourself with these shapes and their associated numbers.
|Plato’s Element||Platonic Volume||Shape of Face||Faces||Edges||Corners||Sum of Angles||Dual|
|“Heaven” or Aether||Dodecahedron||pentagon||12||30||20||6480||Icosahedron|
Platonic solids are three-dimensional volumes, or ‘regular polyhedra’ made up of ‘regular polygons’.
Regular polygons (the 2D shapes above) have equal angles and equal side lengths.
Regular polyhedra (the five 3D Platonic solids) have equal regular polygonal faces and identical vertices (angles).
The Five Platonic Solids are extremely important shapes. Along with the circle/sphere, spiral and torus they are the most important geometric shapes to understand.
They are the only shapes:
- with equal side lengths
- with equal interior angles
- that look the same from each vertex (corner point)
- with faces made of the same regular polygon (triangle, square, pentagon) 3, 4, 5
- that all fit perfectly in a sphere (circumsphere) with all points resting on the circumference (This means the Platonic solids will all fit exactly in an appropriately sized sphere with all points exactly touching the circumference.)
Note the sum of the angles and how those numbers relate to the sum of the angles of the regular polygons above.
To calculate the sum of the angles:
For example, the dodecahedron has 12 regular pentagonal faces of 540º each. 12 x 540 = 6480°. Hence, the number of the dodecahedron is 6480.
Note the other associated numbers with the dodecahedron:
- 12 Faces
- 30 Edges
- 20 Vertices (corners)
- 540 – the sum of the pentagon
- 108 – the interior angle of the pentagon
- 72 is also an associated number as 180-108 = 72. There are 72º in the exterior angles of a pentagon.
For the purpose of this article, let it be known that 72 and 108 are preeminent numbers of the Sacred Canon. They are both derived from the pentagon and they are both factors of twelve:
(12 x 6 = 72) (12 x 9 = 108)
Twelve is important for many reasons: One being that 12 spheres fit perfectly around a 13th if they are all the same size. This creates a spherical cuboctahedron.
Another is that 13-circles-around-1 represents the important ‘Fruit of Life’ symbol.
Another being the 12 houses of the Zodiac and 12 Ages of the Precession of the Equinoxes which create and guide earthly time cycles. Much more will said about these subjects in later articles.
And yet another being its association with the Platonic solid edges, vertices and faces.
Note the twelves involved with each Platonic solid:
Numbers associated with the dodecahedron: 6480, 540, 108, 72, 30, 20, 12
Numbers associated with the octahedron: 1440, 180, 60, 12, 8, 6.
Numbers associated with the icosahedron: 3600, 180, 60, 30, 20, 12.
Numbers associated with the cube: 2160, 360, 90, 12, 8, 6.
Numbers associated with the tetrahedron: 720, 180, 60, 6, 4.
Furthermore, all Platonic solids, Archimedean solids and Catalan solids are factors of 72.
Remember, 12 x 6 = 72.
Before we move on, it is helpful to notice some of the important factors of 72:
72 x 2 = 144 72 x 14 = 1008 72 x 110 = 7920
72 x 3 = 216 72 x 15 = 1080 72 x 120 = 8640
72 x 4 = 288 72 x 18 = 1296 72 x 140 = 10080
72 x 5 = 360 72 x 20 = 1440 72 x 150 = 10800
72 x 6 = 432 72 x 30 = 2160 72 x 180 = 12960
72 x 7 = 504 72 x 36 = 2592 72 x 200 = 14400
72 x 8 = 576 72 x 48 = 3456 72 x 230 = 16560
72 x 9 = 648 72 x 50 = 3600 72 x 290 = 20880
72 x 10 = 720 72 x 60 = 4320 72 x 450 = 32400
72 x 12 = 864 72 x 70 = 5040 72 x 590 = 42480
72 x 13 = 936 72 x 90 = 6480 72 x 2100 = 151200
Another important number is 432.
432 Hz had a particular significance to Pythagorean tuning in music, which will be discussed at another time. The numerical value of a frequency is dependent on the length of one second in time, which, it is argued, is arbitrary. However, it is not arbitrary if you base it on astronomical observations and cosmological cycles as the ancients did. One second was an exact division of the amount of time it took the Earth to make one complete revolution around the Sun.
Interestingly, in 1967 the second began to be defined in terms of the natural periodicity of the radiation of a cesium-133 atom. The International Committee of Weights and Measures announced in 1967, “The second is the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom.”
They changed the definition at this time “to improve the stability of timekeeping in a manner that would be invisible to the general population.”3
Note that the second is not a ‘length of time’ per se. It is a ‘specific division of a larger, precise cycle’.
Furthermore, if you tune a musical instrument to A = 432 Hertz (Hz), all the other notes will be integer (whole) numbers. If you tune to another frequency, such as A = 440 Hz, every other note is a fractional number.
Notice how one system inherently contains more harmony than the other.
This does not mean one is “better” than the other per se. It means one is more harmonious and synched up to greater universal cycles (the year & Great Year). It is amusing that this is such a contentious subject for many. Take from it what you will.
Now note the importance of 432 in unifying the regular polygons with the cube and the cosmological cycle the Precession of the Equinoxes.
The Cube = 2160 = 360 x 6
- 432/2 = 216
- Cube = 2160º
- 2160 years = 1 Great Month (1 Zodiacal Age) in the 25,920 Great Year (Precession)
- 2160 = The diameter of the Moon in miles
- 2160/2 = 1080º = octagon
- 2160/3 = 720º = hexagon
- 2160/4 = 540º = pentagon
- 2160/5 = 432
- 2160/6 = 360º = square and circle
Incidentally: 4322 = 186,624 miles/second. This is the speed of light to 99.99% accuracy.
432 the only whole number when squared comes into .01% accuracy measuring the speed of light (186,282 miles/second).
We will now take a look at how these numbers show up in other ways.
Gyorgy Doczi writes, “As the measuring of length was linked to the proportions of the human body, so the measuring of time became based upon the durations observed in the rhythmically occurring movements of the heavenly bodies. These observations led to the realization that there exists a heavenly or cosmic order, to which human life is related, and upon which it depends, this order manifesting itself in the movements of the stars and in the recurring patterns of the calendar.”
- Earth Motion #1 – rotation about the axis (day cycle – 24 hours)
- Earth Motion #2 – revolution around the sun (year cycle – 365.242 days)
- Earth Motion #3 – Precession of the Equinoxes (galactic cycle – 25,920 years)
- One solar day = 24 hours
- 60 seconds x 60 min = 3600 seconds/hour
- 24 hours x 60 min = 1440 minutes/day
- 1440 min x 60 sec = 86400 seconds/day
- 720 min x 60 sec = 43200 seconds/half day (division of light and dark hours)
- 25920 seconds = 432 minutes
- 432 minutes = 7.2 hrs
- 12960 seconds = 216 minutes
- 6480 seconds = 108 minutes
- 25920 hours = 1080 days
- 25920 days = 72 years (of 360 day sacred calendar)
- Current average human lifespan = 72 years (1 day of the Great Year)
- Average human resting heartbeat = 72 bpm
- “Room temperature” = 72° F
- Precession of the Equinoxes
Keep noting the harmony and order inherent in the system of time and how time itself is related to Geometry (the simple shapes of the regular polygons and polyhedra). If you don’t fully understand these concepts, don’t worry. They will all be thoroughly explained in the Science section of Cosmic Core. For now, we are looking at numbers and noticing how the same numbers continue to show up in many interesting ways.
- One foot = 12 inches
- One square foot = 144 square inches
- One cubic foot = 1728 cubic inches (12 x 12 x 12)
- One square yard = 1296 inches (36 x 36)
- One cubic yard = 27 cubic feet or 46,656 cubic inches (36 x 36 x 36)
- (Note: 46,656 = 72 x 648)
- Origin of the mile
- Mile is from Latin mil meaning thousand or 1000 paces.
- 1 pace = a step with right and left foot.
- Each pace averages 5.28 feet.
- 1 mile = 5280 feet (1000 paces of 5.28 feet)
- 1.5 miles = 7920 feet (72 x 110 = 7920)
- 7920 miles is the diameter of the Earth
- Astronomical Units (AU) & Light Years (LY)
An inch is to a mile as an astronomical unit is to a light-year. (99.8% accuracy)
- 1 AU = the average distance the Earth is from the Sun
- 1 LY = the total distance light travels during 1 Earth revolution around the Sun
- 63,360 inches = 1 mile
- 63,241.1 AU = 1 LY
Space Measure in the Solar System
It is also interesting to note how 7920 shows up in DNA and the group of 20 amino acids common to all human, plant and animal biology. “The number of protons and neutrons utilized by the entire “Game of Amino Acids”, and required for life to be perpetuated, totals 7920 exactly.”4
108 in the Solar System
- Sun diameter = ~ 108 Earth diameters
- 108 Sun diameters between the Sun and Earth
- radius of the Moon = 1080 miles
- diameter of the Moon = 1080 x 2 miles (2160)
- 10080 miles = diameter of the Earth + Diameter of the Moon
- Diameter of Mars = 1080 x 4 miles (4320)
- Diameter of Jupiter = 10800 x 8 miles (86400)
- Orbit of Jupiter = 1080 x 4 days (4320)
- Saturn’s orbit = 10800 days
- Saturn’s hexagon edge length = 1080 x 8 miles (8640)
Archimedean and Catalan Solids
Below is a chart of the 13 Archimedean solids, which will be discussed in greater detail in subsequent articles. For now, notice the numbers involved:
|Volume||# of Faces||# of Edges||# of Corners||Sum of Degrees|
|Sum of All||165,600|
The sum of the degrees for each Archimedean solid is a factor of 72.
The same holds true for their duals, the Catalan solids.
|Catalan Solid||Archimedian Dual||Faces||Edges||Vertices||Sum of Angles|
|Triakis Tetrahedron||Truncated Tetrahedron||12||18||8||2160|
|Tetrakis Hexahedron||Truncated Octahedron||24||36||14||4320|
|Triakis Octahedron||Truncated Cube||24||36||14||4320|
|Pentakis Dodecahedron||Truncated Icosahedron||60||90||32||10800|
|Triakis Icosahedron||Truncated Dodecahedron||60||90||32||10800|
|Disdyakis Dodecahedron||(Truncated cuboctahedron) Great Rhombicuboctahedron||48||72||26||8640|
|Disdyakis Triacontahedron||Great Rhomb-icosidodecahedron||120||180||62||21600|
|Pentagonal Icositetrahedron||Snub Cube||24||60||38||12960|
|Pentagonal Hexecontahedron||Snub Dodecahedron||60||150||92||32400|
|Sum of All||151,200|
We have taken a look at the Sacred Number Canon and noticed how the same numbers show up again and again in many different ways. We have specifically seen how the numbers of the simple regular polygons and polyhedra are related to the measure of time and space. As we continue along this path of knowledge we will see how these same shapes show up in all aspects of science and life, from the microcosmic to the macrocosmic.
These numbers and simple shapes allow us glimpses into a matrix upon which the whole evolving creation is sustained.
It is necessary to note at this point that the esoteric stream of knowledge unifies both creation and evolution, giving credence to both. They are both important parts of understanding reality and the ugly, bitter creation vs. evolution feud can be long-last put to rest once we understand how both forces work together to produce the reality we experience.
The esoteric stream of knowledge also teaches that the ‘Creator’ is not a separate, judgmental anthropomorphic deity far removed from the Creation. The Infinite Creator, ‘Creative Force’, ‘Cosmic Consciousness’ or whatever you would like to call it, is present in all matter and life. It is that which resides within.
Recall Article 2 and the brief discussion of Dynamic Symmetry, Scale Invariance and the Fractal-holographic Nature of Reality.
The whole is present in all its parts.
The point is Unity and Harmony. Everything in the universe is connected. Every point in time and space is connected. Everything is bound together harmoniously (that is geometrically).
Recognizing harmony as a universal principle encourages one to learn to live more harmoniously. This means everything comes back to ethics – learning to live a harmonious ethical life for the greatest good; learning to be kind, compassionate and forgiving while rising to your unique individual highest potential.
This is the core of the teachings of Jesus, Buddha, Krishna, Plato, Pythagoras and many, many other wise teachers throughout the course of history.
“There is a design and a designer, but they are so combined, the one within the other, the one within and the one without, that it is impossible to separate them. The creator is within its creations, and the creations themselves are gifted with creativity. The world comes to know itself, to discover itself, for the planner left room for divine surprise, and the plan was nowhere foreordained.” The Seth Material
- Ward, Dan Sewell, Library of Halexandria, Sacred Mathematics, http://www.halexandria.org/dward010.htm
- Sullivan, Donald B, How does one arrive at the exact number of cycles of radiation a cesium-133 atom makes in order to define a second? Scientific American, https://www.scientificamerican.com/article/how-does-one-arrive-at-th/
- Morris, Anthony G, The Numerical Universe – Order in Chaos, Nexus, April 2015, http://www.academia.edu/27331840/Nexus_Article_July_2015