We will now move into a two-part series on the Ennead – or Nineness.
The Ennead – 9
The Ennead is described as the “The Horizon”.
It lies at the edge of the shore before the boundless ocean of numbers that repeat in endless cycles the principles of the first 9 digits.
It represents the boundary between the mundane and the transcendental infinite.
It has been called:
- The Finishing Post
- That which brings completion
- perfection, balance, order, completion
The Ennead represents the highest attainment to be achieved in any endeavor.
It is the unsurpassable limit, the utmost bound, the ultimate extension to which the archetypal principles can reach and manifest themselves in the world.
It represents the principles of the Triad taken to their utmost expression (3 x 3 = 9).
Elemire Zolla said “Every root that gives birth to words meaning ‘Oneness” will also give birth to the nine following layers of meaning representing the nine stages of manifestation.”
Keith Critchlow writes, “These stages of manifestation are part of an ‘ever present’ structure of creation that both the shaman or mystic are concerned with attuning to – and integrative understanding of the physical world is the end result of the process.”
Arithmetic Properties of the Ennead
Divisors: 1, 3, 9
It is composed of 3 trinities:
(3 x 3 = 9) and (3 + 3 + 3 = 9)
13 + 23 = 9
9 bounds decimals of infinitely repeating digits:
1/9 = .1111111…
2/9 = .222222…
3/9 = .333333…
4/9 = .444444…
5/9 = .555555…
6/9 = .666666…
7/9 = .777777…
8/9 = .888888…
9/9 = .999999… = 1
The ever-repeating nines following the decimal point (.999999…) is an infinite way of representing unity (1).
Dividing any number by the amount of nines corresponding to its number of digits turns the number into a repeating decimal:
274/999 = .0274274274274…
5234/9999 = .5234523452345234…
86554/99999 = .865548655486554…
Multiples of Nine
The multiples of nine up to 10 are: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90.
This works for all multiples of nine. Note that the 8 is excluded from the series:
12345679 x 9 = 111111111
12345679 x 18 = 222222222
12345679 x 27 = 333333333…etc.
12345679 x 81 = 999999999
If you add the 8 in you get:
123456789 x 9 = 1111111101
123456789 x 18 = 2222222202…etc.
Multiplying by 9 reveals mirror symmetry:
2 x 9 = 18 81 = 9 x 9
3 x 9 = 27 72 = 9 x 8
4 x 9 = 36 63 = 9 x 7
5 x 9 = 45 54 = 9 x 6
Nine is the only square number composed of two consecutive cubes (1 + 8 = 9).
It is the first odd square number.
The numbers 1-9 can be arranged in a magic square where every line of 3 in any direction has the same total.
There are 9 regular polyhedra.
These are the 5 Platonic solids plus 4 stellated Kepler-Poinsot polyhedra: the great, the stellated, and the great stellated dodecahedra; the great icosahedron.
The Platonic Solids
9 points can be arranged in many interesting ways:
- X (St. Andrew’s cross)
- A circle
- A traditional labyrinth can be built off these 9 points arranged in an X
9 circles arranged in a perfect 9-sided figure can fit 2 more spheres which exactly touch.
In π: 6 recurring nines (999999) appear in decimal places 762 through 767. This is sometimes called the “Feynman point” after physicist Richard Feynman.
Powers of Nine
1/81 = .012345679012345679…a repeating decimal missing only the “8”.
Divisors: 1, 3, 9, 27, 81
The relationship between the mass of Earth and the moon = 1:81.
Atomic Number – Thallium
93 = 729
94 = 6561
95 = 59049
Theology of Arithmetic – Iamblichus
As we have been doing, we will now take a look at the meaning of the Ennead as prepared by Neo-Platonist philosopher, biographer of Pythagoras, Greek mystic and mathematician Iamblichus (245-325 AD).
The ennead is the greatest of the numbers within the decad and is an unsurpassable limit.
It marks the end of the formation of specific identities.
After the ninth pitch there is no further superparticular musical ratio (the octave 2:1, the fourth 4:3, the fifth 3:2, the third 5:4, and the tone 9:8, so 9 is the largest number to appear in them).
That is, Nine is said to contain the principles of concords – 4, 3, 2,: the fourth 4:3, the fifth 3:2 and the double 4:2. (4 + 3 + 2 = 9)
The ennead refers to affinity and equivalence.
Number admits nothing beyond the ennead, but everything circles around within it.
There is natural progression up to it, but after it there is repetition.
It is by no means possible for there to subsist any number beyond the nine elementary numbers.
It is called ‘Oceanus’ and ‘horizon’ because it encompasses both of these locations and has them within itself.
It is also called ‘Prometheus’ because it prevents any number from proceeding further than itself.
It is the combination of two cubes (1 and 8).
It alone of the numbers up to it has a triangular number as its square root (3).
It does not allow the harmony of number to be dissipated beyond itself, but brings numbers together and makes them play in concert.
Hence it is called ‘concord’ and ‘limitation’.
It is also called ‘sun’ because it gathers things together.
It is also called ‘assimilation’ because it is the first odd square, and squares are assimilative.
The ennead is also called ‘finishing post’ because it has been organized as the goal and turning-point of advancement.
The ennead contains the triad three times. ( 3 + 3 + 3 = 9)
It is called ‘Hyperion” because it has gone beyond all the other numbers as regards magnitude.
The ennead is the first square based on an odd number.
It is called ‘that which brings completion’.
It completes 9-month children.
More Expressions of the Ennead
Atomic Number 9 = Fluorine
Fluorine is the most chemically reactive element. It is also the most electronegative element – it attracts electrons more powerfully than any other element can.
Fluorine is highly toxic and corrosive and should not be ingested in any form.
Atomic Number 90 = Thorium
Thorium is radioactive. It has the largest liquid range of any element, spanning over 3000 degrees between its melting point (2023 K) and boiling point (5063 K).
Atomic Number 99 = Einsteinium
Einsteinium is radioactive and synthetic. It is not found naturally.
9 Represents the Ultimate Expression of Birth
Ponder on the fact that after 9 months in the womb we reach the horizon, unto which we will be born into a whole new world in order to learn, grow and spiritually evolve.
There are several Nines in the Human body:
- bundles of microtubules in centrioles, essential for cell division
- tail of a sperm half-cell made of 9 twisted threads
- 9 months in the womb (9 month gestation)
- 9 openings on the body – 2 eyes, 2 ears, 2 nostrils, 1 mouth, anus, urethra/vagina
The Ennead in Music
9:8 defines the whole tone.
The whole tone is the difference between the two simplest harmonies in the octave:
The fifth 3:2 and fourth 4:3.
Also, (3:2) x 2 = 9:8. A whole tone is a secondary interval, being derived from two perfect fifths.
There are also 9 Supreme Court justices by which we supposedly mete out the highest level of justice in the United States.
Supreme Court Justices, 2010
Baseball has: 9 players and 9 innings. The bottom of the 9th is last chance to win.
9 x 9 = 81 = number of stable elements in the periodic table, excluding chemical elements that can only be artificially synthesized.
The Multiplication Table & 9
The multiples of nine result in a map of cross-fertilization of mathematical principles.
This is called, “Casting out the Nines”.
Reduce the table down to its digital roots by summing the digits.
For example: 12 becomes 1 + 2 = 3
Keep reducing until the sum is a single digit.
For example: 56 = 5 + 6 = 11 = 1 + 1 = 2
Interesting patterns are revealed.
Credit: pages 310-311 in A Beginner’s Guide to Constructing the Universe by Michael Schneider
Some rows have all 9 digits.
Row 6 has only 3, 6, 9.
Rows that add to 9 (1 & 8) (2&7) (3&6) (4&5) form patterns that are mirror images of each other but turned at right angles.
Reducing to 9 (Digital Root 9)
Number systems express the underlying cosmic design – the architecture of the solar system.
Digits of all multiples of 9 sum to 9.
The Sum of All Angles of the Regular Polygons sum to 9.
- circle – 360
- triangle – 180
- square – 360
- pentagon – 540
- pentagonal angles, 36, 72, 108
- hexagon – 720
- heptagon – 900
- octagon – 1080
- nonagon – 1260
- decagon – 1440
The Sum of All Angles of the Platonic Solids sum to 9.
- tetrahedron – 720
- octahedron – 1440
- cube – 2160
- icosahedron – 3600
- dodecahedron – 6480
The Sum of All Angles of the Archimedean Solids sum to 9.
- Icosidodecahedron – 10080
- Great Rhombicuboctahedron – 16560
- Great Rhombiicoidodecahedron – 42480
- Cuboctahedron – 3600
- Rhombicuboctahedron – 7920
- Snub Cube – 7920
- Rhombiicosadodecahedron – 20880
- Snub Dodecahedron – 20880
- Truncated Tetrahedron – 3600
- Truncated Octahedron – 7920
- Truncated Cube – 7920
- Truncated Icosahedron – 20880
- Truncated dodecahedron – 20880
The Sum of All Angles of the Catalan Solids (duals of the Archimedeans) sum to 9.
- Triakis Tetrahedron – 2160
- Tetrakis Hexahedron – 4320
- Triakis Octahedron – 4320
- Pentakis dodecahedron – 10800
- Triakis Icosahedron – 10800
- Rhombic Dodecahedron – 2160
- Trapezoidal Icositetrahedron – 8640
- Disdyakis dodecahedron – 8640
- Rhombic Triacontahedron – 10800
- Trapezoidal Hexecontahedron – 21600
- Disdyakis Triacontahedron – 21600
- Pentagonal Icositetrahedron – 12960
- Pentagonal Hexecontahedron – 32400
Astronomical Lengths sum to 9.
Radius of the Moon in miles = 1080
Diameter of Moon in miles = 2160
Radius of the Earth in miles = 3960
Diameter of Earth in miles = 7920
Radius of the Sun in miles = 43200
Diameter of the Sun in miles = 864000
Cycles of Time
1 ‘Great Month’ of the Precession of the Equinoxes = 2160 years
1 ‘Great Year’ = 25,920 years
Time and space are thus linked by 9, but only if you measure in miles.
Miles are derived from the human yardstick.
1 mile = 1000 human paces (a pace is two steps – a step with left & right foot).
The ratio between the average human pace and the length of the average human foot is 5.28.
1000 paces then gives us 5280 feet = 1 mile.
Our feet anchor us to the earth. Our pace moves us across the Earth.
Not to denigrate the metric system – there are many fascinating number synchronicities in the metric system as well. Both measuring systems are special and valid. There should be no competition among them as far as which one is “best”. They are both good.
Nines – Religion, Myth, Folklore
Keith Critchlow writes in Time Stands Still, “The two most recurrent and significant numbers in shamanistic cosmology are seven and nine.”
Nine is featured in religion and myth throughout the world.
9 Circles of Hell – Dante’s Divine Comedy
J.R.R. Tolkien’s Lord of the Rings Trilogy: 9 Rings, 9 companions of the Fellowship, 9 Ring Wraiths
9 Muses – Greek
History (Clio), Astronomy (Urania), Tragedy (Melpomene), Comedy (Thalia), Dance (Terpsichore), Songs to the Gods (Polyhymnia), Epic Poetry (Calliope), Love Poetry (Erato), Lyric Poetry (Euterpe)
9 Orders of Angels – Western
Angels, Archangels, Virtues, Powers, Principalities, Dominations, Throne, Cherubim, Seraphim
9 Personalities – Middle Eastern
Perfectionist, Giver, Achiever, Tragic Romantic, Observer, Contradictor, Enthusiast, Leader, Mediator
- God Odin – ruler of 9 Norse worlds
- He hung 9 days on the world axis to win the secrets of wisdom for mankind.
- Every 9 years a fertility feast lasting 9 days was held.
- 9 Norse giantesses, strode 9 paces at a time, lived at the edge of sea and land
- 9 worlds all connected by the world tree Yggdrasil in Norse mythology
Yggdrasil – the axis mundi or World Tree in Norse Mythology
- 9 Muses (epic poetry, history, erotic poetry, lyric poetry, tragedy, song, dance, comedy, astronomy)
- The City of Troy was beseiged for 9 years.
- The goddess Demeter is depicted with 9 ears of wheat, searched 9 days for her daughter Persephone before locating her in the underworld.
- Persephone allowed to spend 9 months above ground and 3 months below.
- The underworld was considered so deep an anvil dropped would fall for 9 days then reach bottom.
- The birth of Apollo and Artemis by Leto took 9 days and nights. It came about when Hera sent a gold and amber necklace 9 meters long.
- Virtuous virgin Artemis chose 2 nine-year old girls as companions.
9 days and 9 nights initiates took part in ritual and drama duplicating Demeter’s search
The return of Persephone, by Frederic Leighton (1891)
There are 9 gods or “neteru”.
They emerged from 4 pairs of unmanifest gods to oversee the world’s creative processes.
They symbolized humanity as “nine archer’s bows”.
Furthermore, the pharaoh was often represented by 9 bows.
Medieval Europe – 9 types of crowns in heraldry
Ecclesiastical architects also recognize 9 styles of crosses.
Bahai’i Faith – 9 symbolizes completeness
The 9-pointed Bahai Star
Buddhism – nine virtues of Buddha
These are: accomplished, perfectly enlightened, endowed with knowledge and conduct or practice, well-gone or well-spoken, knower of worlds, the guide unsurpassed of men to be tamed, the teacher of gods and men, enlightened, blessed
- 9 orders of angelic choirs
- 9 circles of heaven
- 9 orders of devils
- 9 rings of hell
- 9 gates of hell
- 9 rivers pouring into the 9th ring where Lucifer lives
- 9 days for Lucifer and his angels to fall from heaven
- 9th hour of the clock Jesus died
- Jesus appeared to his disciples 9 times
- 9 Celtic maidens
- 9 virgins attended Bridget
- Beltane fire rites attended by 9 groups of 9 men
Native American, Aztec, Mayan
- 9 cosmic levels
- 9 story temples – 9 levels of the underworld, realm of our unconscious
- Man emerged from the Yellow River carrying the lo-shu or 3 x 3 magic square with numbers 1-9
- 9 palaces of Ming T’ang or Hall of Light
- 9 great social laws
- 9 classes of officials
- 9 sacred rites
- 9 story pagodas
- 9th hour of 9th day or 9th month – festival of the “double yang” honoring the ninefold creative powers of heaven
- 9 forms of the dragon (a symbol of magic and power)
- 9 points of the heart channels in Traditional Chinese Medicine
- 3 x 3 grid used as ground plan for temples dedicated to Vishnu
- Buddhist monk’s staff has 9 rings
- 9 influences of Indian astrology
- nine universal substances in Vaisheshika (earth, water, air, fire, ether, time, space, soul, mind)
- 9 is considered a complete, perfected and divine number in Hinduism
Islam – Ramadan in the ninth month
Roman market held every 9 days – novendinae
November the 9th month of the Roman calendar
The golden Bush Barrow lozenge has internal angles of 80 and 100. This suggests 9-fold geometry.
Sunrises & sunsets at Stonehenge also vary from 80 to 100 degrees.
Nines – Folk sayings
- 9 lives of a cat
- cat-o-nine tails – symbolic maximum punishment
- go the whole 9 yards – to go all the way
- on cloud nine – experiencing highest joy
- dressed to the nines – dressed completely & perfectly, omitting no detail
- a stitch in time saves nine – take care of small problems as they arise to avoid having to redo the complete job later
99 expresses the horizon of the Ennead on a higher level.
- 99-year leases
- 99 year prison sentence – conveys an ultimate term
- Abraham was 99 years when the Lord spoke to him
- 99 Beautiful Names of God in Islam. The highest pronounceable name (#99) is “The Compassionate”.
- 99 beads of an Islamic rosary