The Basics - Part 6: The Number 8 and the Law of Octaves
Preface
As we continue to look at numbers and how they relate to Sacred Geometry, I want to take time and do a more exhaustive study of one particularly important number---a study that goes beyond that number's strict relationship to geometry. The number is 8.
Because the meanings and correspondences to the number 8 are rich and vast, we'll take the next three monthly segments to complete our investigation. I think you will find what we uncover to be quite interesting.
Segment I: Symmetry and Renewal
Let's begin with perhaps the most famous and admired piece of architecture in the history of the Western World:
Those of us who've studied architectural history will recall that the Greeks designed the Parthenon atop the Acropolis in Athens to reflect a high level of order and symmetry. You'll remember that the horizontal lines are curved slightly upward toward the middle. You'll also recall that the columns are tilted gradually inward with their vertical sides bulging ever so slightly in the middle, and that they are placed closer together toward the corners of the building. All of this results in a visual experience that is quite pleasing to the eye.
You may also remember that there are 8 columns on the front. But, what you may not have noted is that there are 17 columns on each side. While that may seem strange, it is perfectly in keeping with our study of numbers in geometry. If you double the number of columns in the front and add one, you get 17. (8 x 2 = 16; 16 +1 = 17.) This is said to be geometrically proportional. And, taking the number 17 in the sense of numerology, if we add 1 and 7 we are back to the number 8.
The Greek architects Ictinus and Callicrates, with the sculptor Phidias, are jointly credited with the creation of the Parthenon during the rule of Pericles at about 440 BC. I'm sure there are many reasons they chose to have 8 columns on the front and back facades. But, aside from the obvious symmetrical arrangement, there is perhaps another reason: Remember that 8 is part of the infinite Fibonacci sequence of numbers. (3 + 5 = 8. The next Fibonacci number is 13.). As such, 8 relates to the spiral and to the Hermetic dictum we talked about in earlier parts of this series --- “As Above, So Below.” I think the architects were making this statement, albeit in a rather esoteric way.
Cycles of Renewal and Eight
It is interesting to note that the number 8 is the “lemniscate” symbol for infinity rotated 90 degrees into a vertical position. The lemniscate figure denotes a never ending path of movement that is cyclical in nature. Albert Pike said it “symbolizes perfection…and indicates the perpetual and regular course of the Universe.”
In the night sky, the ancients characterized 8 as consisting of the 7 moving and recurring planets superimposed upon the background of the stationary sphere of fixed stars (7 + 1 = 8). The Pythagoreans characterized the number 8 as the first cube of equal numbers (2 x 2 x 2) --- the reduplication of the first even number 2. Pike adds that they said it “signifies friendship, prudence, counsel, and justice. It was the symbol of the primeval law which regarded all men as equal.”
The relationship of the number 8 with the infinity symbol might have come about because of its similarity in appearance to the caduceus, in which two snakes form several figure eights indicating a balance of opposing forces resulting in stability.
The correspondences for the octary are historical and lengthy. I will list here only what space allows. A more expansive discussion of correspondences for 8 can be found on the Wikipedia website.
A. Religion and Divination:
Christian numerologists call 8 the symbol of resurrection because Jesus is said to have risen on the 8th day, the first day of the second week (Sunday), the day after the 7th (Saturday), and because, assigning numerals to each of the letters of the Greek alphabet, the name Jesus in Greek is 10 + 8 + 200 + 70 + 400 + 200 = 888. Therefore, they call 8 the Dominical Number.
8 is the number in Christianity of immortality and salvation…a return to the original life, but made eternal. Because 7 refers to the repeating days of the week, 8 is considered beyond time. And, there are 8 Beatitudes in the Sermon on the Mount in the Gospel of Matthew.
8 is the number of circumcision, baptism, and rebirth. In the Mysteries, they are connected. Genesis 17:10-14 says a male child shall be circumcised on the eighth day. And, the 8-sided octagon is the typical form of a baptismal font.
In Buddhism, there is the Noble Eightfold Path embodied in Eight Great “Bodhisattvas”, the Eight Aggregates of Consciousness, and the Eight Sacred Emblems or Auspicious Symbols. One of those symbols is the Eternal Knot whose geometry, like the infinity sign , symbolizes the endless cycle of death and rebirth until illumination. Another of those symbols is a wheel (the “Dharmachakra”) with eight spokes that steers the way according to Buddha's teaching.
In Islam, there are 8 angels who carry the Holy Throne of Allah. In the Hindu religion, the Goddess Lakshmi possesses 8 forms, and there are 8 seats of wealth. There are also 8 Chinese Immortal Deities.
The Gnostic “ogdoad” had 8 stars which, among other things, represented eight divine beings, the 8 Egyptian and Phoenician principles, and the 8 corners of a cubic stone.
In numerology, 8 can be both the number of building and the number of destroying.
8 signifies physical stability. It is the number of earth (4) doubled. In plane geometry, it is represented by two superimposed squares rotated 45 degrees generating a polygon called an octagon:
There are 8 trigrams in the I Ching which multiply to 64 (8 x 8) hexagrams.
The Jewish holiday Hanukkah is celebrated for 8 days because, as the story goes, an oil lamp with only enough oil to burn one day miraculously burned for 8, thus signifying a renewal of the Jewish people.
8 is associated with the Great Goddess because it takes eight years for Venus and Earth to synchronize against the backdrop of the zodiac. And, “Strength”, picturing the Goddess taming a lion, is the 8th card in the Tarot deck.
The Goddess is associated in mythology with Arachne, who challenged Athena to a weaving contest and was victorious. As punishment, Athena then transformed Arachne into an eight-legged spider. (Actually, all arachnids including spiders have eight legs. In the sea kingdom, an octopus has eight tentacles.)
B. Architecture and Planning
In the currently popular study of Feng Shui, the 8 winds are symbolized by the octagon. Pagodas and gazebos are usually eight-sided. In fact, the octagon is exhibited in numerous ancient structures like the Tower of the Winds in Athens:
The Athens guidebook sourced for the photo above says: “The famous Tower of the Winds … is a part of the ancient Roman Agora. It was believed by later generations to be a place of great magic and to be the grave of Phillip of Macedon but it was actually a meteorological station from the first century built by the Syrian Astronomer Andronikos Kyrrhestes. It had a hydraulic clock fueled from a reservoir on the south side and inside was a mechanical device that represented the sun, the moon and the five known planets. The frieze which represents the winds and their personalities is the most interesting part of the building ….”
The central point in old Athens was, in fact, the Tower of the Winds. It served as a gnomon (sundial) from which the layout of the city was generated by angular projections from the sun's shadow at different times of the day and the season. The Greeks called such a central point the omphalos (navel) of the city.
The 1st century Roman architect, Vitruvius (we remember him from Leonardo's adaptation of the Vitruvian Man from Part 2 of this series), perhaps the most influential architect of all time, derived the design of his ideal city following just such a classical central point method of geometry.
Here is a 17th century city plan using Vitruvius' octagonal shaped model:
Source: Sacred Geometry by Nigel Pennick, Capall Bann Publishing, 1994, p. 89.
A particularly fascinating example of an octagonal building is Holy Roman Emperor Frederick II's medieval Romanesque Castel del Monte in the Apulia region of southeastern Italy completed in 1240 AD.
Wikipedia says: “The fortress is an octagonal prism with an octagonal bastion at each corner. Each wall has 8 rooms and an eight-sided courtyard occupies its centre. The octagon is thought to be an intermediate symbol between a square (representing the earth) and a circle (representing the sky). Frederick II may have been inspired to build to this shape by either the Dome of the Rock in Jerusalem, which he had seen whilst on Crusade, or by the Palace Chapel of Aachen Cathedral.” [See more at: http://en.wikipedia.org/wiki/Castel_del_Monte_(Apulia).]
It is, indeed, quite likely that Frederick was inspired by the Jerusalem's Dome of the Rock. It was completed in 691 AD, making it today the oldest existing Islamic building in the world.
In fact, Islamic architecture and ornamentation use a geometry of 8 to express the Compassionate Breath of God. Frederick spoke six languages, including Arabic, and had read the Koran. He no doubt was aware of the esoteric significance of the octagon and the number 8.
Any of you who have been to the American Institute of Architects' Headquarters in Washington, DC, will recall that the organization was originally housed at the corner of the present property in a building that now serves as a gallery and meeting place for various AIA functions. Aptly so, it's called The Octagon.
Next time, in Part 7 of AL's Corner, we'll proceed to Segment II of our study of the number 8 and how it relates to Sacred Geometry.
Copyright Alan S. Glassman, 2008 (all rights reserved)
Where Every Issue is a Green Issue
rotated 90 degrees into a vertical position. The lemniscate figure denotes a never ending path of movement that is cyclical in nature. Albert Pike said it “symbolizes perfection…and indicates the perpetual and regular course of the Universe.”
