We will now begin a three-part series on the Octad, or Eightness.

# The Octad – 8 – Periodic Renewal

Eight is highly dependent on Seven.

It is represented by the process of the Octave.  We have discussed the Octave already in the previous articles.

The idea of the octave represents the concept of “Same but Different”, or “Equal but Different.”

The Octad refers to self-renewal and limitless growth.

It is also interesting to note that 8 is the Infinity sign turned on its side.

# Arithmetic Properties of the Octad

Eight is promiscuous.

It has more divisors than any other number in the Dekad.

Divisors: 1, 2, 4, 8.

1 x 2 x 4 = 8

The Octad is called “justice” and “evenly even”.

It can be continually halved all the way down to unity.

Oddly-even cannot be halved to unity, for example: 6.

Only 1 & 8 are composed of 3 identical divisors within the dekad.

1 x 1 x 1 = 1

2 x 2 x 2 = 8

1 & 8 are the volumes of the only 2 cubes in the dekad.

Every cube has 8 vertices.

The cube’s dual – the octahedron – has 8 faces dividing space equally in 8 directions.

8 is the 7th Fibonacci number (3+5).

It is the only positive Fibonacci number, aside from 1, that is a perfect cube (2 x 2 x 2).

A cuboctahedron has 6 square faces and 8 triangular faces.

There are 8 semi-regular tilings.

# Powers of Eight

## 82 = 64

• 4 x 4 x 4 x 4 = 64
• Divisors of 64: 1, 2, 4, 8, 16, 32, 64
• 64 represents an octave of octaves.

• It is the smallest number with exactly 7 divisors.
• It is the first perfect square and perfect cube.
• Atomic Number 64 = Gadolinium
• 64 Tetrahedral Grid – Isometric Vector Matrix

• 64 6-part codons specify amino acids in DNA.
• 64 Transformations in the I-Ching

• 64 Arts of the Kama Sutra

• 64 Squares on a Chess board

# Atomic Number 8 = Oxygen

Oxygen is the third most common element in the Universe, behind hydrogen and helium.  It is the most abundant element in the Earth’s crust, accounting for almost half by mass.

Plants and animals rely on oxygen for respiration.

Oxygen is extremely reactive and forms oxides with nearly all other elements except noble gases.

# Atomic Number 80 = Mercury

Mercury is the only common metal that is liquid at room temperature.  It evaporates slowly at room temperature.  It has a high surface tension and when spilled, breaks into tiny liquid beads.

Mercury and most of its compounds are toxic.

# Atomic Number 88 = Radium

Radium is a silvery white metal that is highly radioactive.  The metal and its compounds glow in the dark.

# Other Eights

We are all familiar with the ubiquitous stop sign.

In computer processing there are 8 binary bits in a byte.

There are 8 electrons in each orbital shell (except for the first shell which contains only 2).  Please remember, electrons are not ‘things’.  They are ever-moving, ever-oscillating, ever-spinning processes of potentials.

The octahedron shows up regularly in the realm of molecular structure.

Octahedral molecules have eight faces.  All bond angles are 90º or 180º.

Example: SF6 Sulfur hexafluoride

Crystals are often octahedral shaped.

Examples: spinel, fluorite & diamond

On average, male & female voices are 1 octave apart.

We hear, on average, about 10 octaves of sound.

# 7 & 8

Seven is the musical scale & Eight is the octave.

1/49 (7×7) = .020408163265306122448979591836734693877551 (42 repeating digits that grow in octaves.)

The repeating number can be obtained from 02 and repetition of doubles places at two places to the right:

This produces a repeating decimal built on the process of doubling.

# The Figure -8

The Figure-8 “represents a polar cycle perpetually swinging between extremes and crossing itself in the middle as the diagonals of a square.”1

Turned sideways, it is the glyph for “infinity”.

# The 8-ball

The 8 is the “oddball” at the exact middle of the 15 balls.

“To be ‘behind the eight ball’ is to find oneself in the middle of a dilemma with 7 elusive solutions on each side.”2

# The Theology of Arithmetic – Iamblichus

As we have been doing, we will now take a look at the meaning of the Octad as prepared by Neo-Platonist philosopher, biographer of Pythagoras, Greek mystic and mathematician Iamblichus (245-325 AD).

The octad is the first actual cube and the only number within the decad to be even-times-even. (2 x 4)

All the ways in which it is put together are excellent and equilibrated tunings.

It results from the two which are even-odd, one potentially, the other actually (2 and 6) and it results from the first two odd numbers – 3 and 5.

It is called ’embracer of all harmonies’ because it is the first to have been attuned and multiplied so as to be equal-times-equal-times equal (2 x 2 x 2).

There are eight spheres of the heavenly bodies and eight circles which astronomers most need to understand and which are most useful for knowledge.

The four greater ones are the equator, the zodiac, the horizon and the meridian (which passes through the poles).

The four lesser are the Arctic and Antarctic circles and the summer and winter tropics.

The ogdoad contains the limit for creatures which have feet, and after it there is indeterminacy: there are scorpions and crabs and similar creatures among those which have a definite number of feet, but any subsequent creatures are among those which are simply many-footed.

Counting from the middle of the mouth, there are eight teeth in each quadrant (32 in all).

The ogdoad is called ‘mother’ for even is female.

With the ogdoad things come by love and friendship and wisdom and creative thought.

The ogdoad is ‘untimely for birth’ because labor in the eighth month is fruitless and hence is called ‘untimely’.

It is also called ‘Euterpe’ the ‘well-pleasing’ Muse, because it is the most changeable of the numbers within the decad, since it is even-times-even and is divisible up to the monad itself, which is naturally indivisible.

The ogdoad is called ‘safety’ and ‘foundation’ since it is a leader, because two is a leader.  The seed of the ogodad is the first even number.  When multiplied by the tetrad it makes 32.

The 8th sphere encompasses the whole – hence the saying ‘All is eight’.

The number 8 is the source of all musical ratios because eight represents the octave.

# Eights in Religion

The eighth step is often associated with spiritual evolution, deliverance, salvation, transcendentalism, and transfiguration.

# Ancient Egyptian Ogdoad – Hermopolis

Four pairs (8) of unmanifest gods and goddesses are responsible for giving birth to the manifest universe.

“I am One that transforms into Two, I am Two that transforms into Four, I am Four that transforms into Eight.  After this I am One again.”  Egyptian (Hermopolitan) creation myth

# Eight Elements and Associated Qualities – Aristotle

earth = solid; water = liquid; air = gas; fire = electronic plasma

cold = contraction; hot = expansion; wet = dissolution; dry = crystallization

# Eight Immortals – Taoist

youth, old age, poverty, wealth, the populace, nobility, the masculine, the feminine

The Eight Immortals crossing the sea, from Myths and Legends of China. Clockwise in the boat starting from the stern: He Xian’gu, Han Xiang Zi, Lan Caihe, Li Tieguai, Lü Dongbin, Zhongli Quan, Cao Guojiu and outside the boat is Zhang Guo Lao.

“Furthermore, they have been linked to the initial development of qigong exercises such as the Eight Piece Brocade. There are some Chinese martial arts styles named after them, which use fighting techniques that are attributed to the characteristics of each immortal.   Some drunken boxing styles make extensive use of the Eight Immortals archetypes for conditioning, qigong/meditation and combat training.  One subsection of BaYingQuan drunken fist training includes methodologies for each of the eight immortals.”3

# Eight Trigrams – I-Ching

1. chi’en (heaven, creative)
2. Tui (attraction, achievement)
3. Li (awareness, beauty)
4. Chen (action, movement)
5. Sun (following, penetration)
6. K’an (danger, peril)
7. Ken (stop, rest)
8. K’un (earth, receptive)

‘Former Heaven Sequence’ represents the ideal pattern of transformation in the cosmos.

Each trigram is the complement of its opposite.

# Eightfold Path – Buddhism

1. right understanding – free from superstition and delusion
2. right thoughts – elevated and worthy of intelligence
3. right speech – kindly, open and truthful
4. right action – peaceful, honest and pure
5. right livelihood – bringing hurt or danger to no living being
6. right effort – in self-training and in self-control
7. right mindfulness – the active watchful mind
8. right concentration – deeply meditating on the realities of life

Eight symbols of a scholar

Eight directions of the wind

# Eight Limbs of Yoga – Vedic

1. morality (yama)
2. observances (niyama)
3. postures (asana)
4. breathing (pranayama)
5. sense withdrawal (pratyhara)
6. concentration (dharana)
7. devotion (dhyana)

# Wicca

Eight Sabbats, festivals, seasons or spokes in the Wheel of the Year in Wicca

# Islamic Mythology

• Sa’di’s Gulistan or Rose Garden has 8 chapters
• eight angles holding up the throne of Allah in heaven
• eight gates of Heaven

# The Octad as “Great Mother Goddess”

The eight is an ancient symbol for the Great Mother Goddess.

“Her substance clothes the archetypal patterns by crossing the four elements with four opposite qualities.”4

She is often depicted as a spider (from ‘spinner’).

She is less often depicted as an octopus.

There is the Grandmother Spider of Native American mythology; spider emblems found in Crete, Germany, Mexico and Peru; and weaver and spinner goddesses such as the Egyptian Neith, Nutet and Isis, the Greek Athena and the Three Fates, and the Mayan Ixchel.

From the ancient  Moche people of Peru, circa 300 CE

Spider depicted on a shell gorget by the Stone Grave people, from a mound on Fain’s Island, Tennessee.

Pre-Columbian spider image from a conch shell gorget at the Great Mound at Spiro, Oklahoma

Other Pre-Columbian spider amulets found in the Midwest mound country of the United States.

“What might we see, how might we act, if we saw with a webbed vision?  The world seen through a web of relationships…as delicate as spider’s silk, yet strong enough to hang a bridge on.” ~ Catherine Keller, From a Broken Web, 1989

Michael Schneider writes in A Beginner’s Guide to Constructing the Universe, “In her terrible aspect, the spider goddess is the ensnaring feminine dangling from the heavens to trap the unwary in her web.  Foreboding doom, she ultimately provides her catch with a fate of spiritual transformation and renewal.”5

In its archetypal form, the spider represents the weaver.  The weaver represents the foundational force of oscillation from time/space to space/time (warp and weft), or the continuous weaving back and forth of consciousness and matter.

Weaving represents oscillation, and everything in the universe continually oscillates.

Below is a small taste of the Octad found in Nature.  Read the articles in the sections on plants, insects and animals to see many more examples.

The Octad is found in the faces of many flowers.

8 Petals: Lesser Celandine (1), Zinnia (2), Bloodroot (3), Cosmos (4, 5 & 6), Clematis(7), some poppy seed heads (8)

Some fruits have an 8-fold structure.

Star anise

Persimmon – A 4-petal flower yields 8-point geometry.

Tahitian Gooseberry

Some algae has 8-pointed geometry.

(1) Pediastrum tetras = Stauridium tetras; (2) Pediastrum rotula; (4) Pediastrum octonum; (5) Pediastrum cruciatum; (8) Pediastrum elegans.  Credit: Ernst Haeckel

The Earthstar fungus (Myriostomacoliforme) has 8-fold geometry.

Many diatoms have 8-fold geometry as well.

Credit: Samuel Colman

Plate 21: Acanthometra.  Credit: Ernst Haeckel

There are also many radiolaria with octad geometry.  The following examples are shaped like octahedra.

Ovulus coralli

Credit: Bernotat & Co.

Hexapodus inflatus – Octahedral

Credit: Bernotat & Co.

Plate 41: Acanthophracta.  Credit: Ernst Haeckel

Eight-fold geometry is found glass sponges and jellyfish.

Credit: Michael Schneider

Plate 35: Hexactinellae – Glass sponges.  Credit: Ernst Haeckel

Plate 17: Siphonophorae – colonial organisms composed of small individual animals called zooids.  Credit: Ernst Haeckel

Jellyfish

An octopus has 8 tentacles; so does the squid.

Crabs have 8 legs with 2 pincers.

Spiders have 2 sections, 8 legs, and 0 antennae compared to insects with 3 sections, 6 legs, and 2 antennae.

The Octad (8) in also found in the Human Body.  On average:  The thumb, wrist, neck & waist form a series of doubling octaves:

• thumb base circumference x 2 = wrist circumference
• wrist circumference x 2 = neck base circumference
• neck base x 2 = waist circumference

The octave is found in the way waves break.

Waves will break when the distance to the bottom below the wave equals exactly half the surface distance between two waves, their wavelength.

1. Schneider, Michael, A Beginner’s Guide to Constructing the Universe, Harper Perennial, 1994
2. ibid.
3. https://en.wikipedia.org/wiki/Eight_Immortals
4. Schneider, Michael, A Beginner’s Guide to Constructing the Universe, Harper Perennial, 1994
5. ibid.