T H E P E N T A G R A M
"Arise, O Man, in thy strength! the kingdom is thine to inherit / Till the high gods witness at length that Man is the Lord of his spirit."
ALEISTER CROWLEY
The pentagram is a really cool item of jewellery which some of us wear to establish our status as pagan.
Look at it closer and you may recognise something very special in the intersecting lines. The pentagram forms the basis of pagan ritual and the pantheistic belief system for a very good reason. Its proportions represent nothing less than the hidden blueprint of the universe; and are clearly present within the human form and in the structure of the galaxies - as above so below, indeed.
The ancient Greeks were more than conversant with this proportion and it underpinned their sublime system of architecture. During the so called 'dark ages' conscious awareness of the proportion was lost only to be rediscovered in the 12th century when it once again began to inform great art and architecture.
You'll find oodles of stuff about it on the web; there are a few of the less obvious aspects below.
Look at it closer and you may recognise something very special in the intersecting lines. The pentagram forms the basis of pagan ritual and the pantheistic belief system for a very good reason. Its proportions represent nothing less than the hidden blueprint of the universe; and are clearly present within the human form and in the structure of the galaxies - as above so below, indeed.
The ancient Greeks were more than conversant with this proportion and it underpinned their sublime system of architecture. During the so called 'dark ages' conscious awareness of the proportion was lost only to be rediscovered in the 12th century when it once again began to inform great art and architecture.
You'll find oodles of stuff about it on the web; there are a few of the less obvious aspects below.
There is an mathematical sequence which was first noted in the west in 1202 by Leonardo of Pisa, known as Fibonacci. In an idealised population of newly-born pair of rabbits, one male, one female, are put in a field. Rabbits are able to mate at the age of one month so that at the end of its second month a female can produce another pair of rabbits. Suppose that our rabbits never die and that the female always produces one new pair (one male, one female) every month from the second month on. The puzzle that Fibonacci posed was how many pairs will there be in one year?
At the end of the first month, they mate, but there is still one only 1 pair. At the end of the second month the female produces a new pair, so now there are 2 pairs of rabbits in the field. At the end of the third month, the original female produces a second pair, making 3 pairs in all in the field. At the end of the fourth month, the original female has produced yet another new pair, the female born two months ago produces her first pair also, making 5 pairs.
The number of pairs of rabbits in the field at the start of each month is 1, 1, 2, 3, 5, 8, 13, 21, 34 and so on. Each number is simply the sum of the two preceding numbers. This proportion has become known as the Fibonacci sequence. The proportion derived from this sequence - f = (1+v5)/2 ˜ 1.618 - is termed the Golden Proportion and occurs throughout our world and beyond. In geometric terms it is most eloquently expressed in the pentagram; making the pentagram, not just a magical symbol but a concise blueprint for universal life.
At the end of the first month, they mate, but there is still one only 1 pair. At the end of the second month the female produces a new pair, so now there are 2 pairs of rabbits in the field. At the end of the third month, the original female produces a second pair, making 3 pairs in all in the field. At the end of the fourth month, the original female has produced yet another new pair, the female born two months ago produces her first pair also, making 5 pairs.
The number of pairs of rabbits in the field at the start of each month is 1, 1, 2, 3, 5, 8, 13, 21, 34 and so on. Each number is simply the sum of the two preceding numbers. This proportion has become known as the Fibonacci sequence. The proportion derived from this sequence - f = (1+v5)/2 ˜ 1.618 - is termed the Golden Proportion and occurs throughout our world and beyond. In geometric terms it is most eloquently expressed in the pentagram; making the pentagram, not just a magical symbol but a concise blueprint for universal life.
The Swiss architect Le Corbusier, famous for his contributions to the modern international style, centered his design philosophy on systems of harmony and proportion. Le Corbusier's faith in the mathematical order of the universe was closely bound to the golden ratio and the Fibonacci series, which he described as "rhythms apparent to the eye and clear in their relations with one another. And these rhythms are at the very root of human activities. They resound in man by an organic inevitability, the same fine inevitability which causes the tracing out of the Golden Section by children, old men, savages and the learned."
The ratios of Fibonacci numbers are commonly used in technical market analysis. Changes in stock prices largely reflect human opinions, valuations and expectations. A study by mathematical psychologist Vladimir Lefebvre demonstrated that humans exhibit positive and negative evaluations of the opinions they hold in a ratio that approaches phi, with 61.8% positive and 38.2% negative. Phi (1.618), the Golden Mean and the numbers of the Fibonacci series (0, 1, 1, 2, 3, 5, 8, ...) have been used with great success to analyze and predict stock market moves. The golden ratio, or phi, appears frequently enough in the timing of highs and lows and price resistance points that adding this tool to technical analysis of the markets may help to identify key turning points.
Fibonacci numbers apply to honeybee's. Not all honey bees have two parents. In a colony of honeybees there is one special female called the queen. There are many worker bees who are female too but unlike the queen bee, they produce no eggs. There are some drone bees who are male and do no work. Males are produced by the queen's unfertilised eggs, so male bees only have a mother but no father! female bees have 2 parents, a male and a female whereas male bees have just one parent, a female. Let's look at the family tree of a male drone bee. He had 1 parent, a female. He has 2 grand-parents, since his mother had two parents, a male and a female. He has 3 great-grand-parents: his grand-mother had two parents but his grand-father had only one; and here we see the Fibonacci numbers.
Male bee parents: 1 2 3 5 8
Female bee parents: 2 3 5 8 13 |
The DNA molecule, the program for all life, is based on the golden section. It measures 34 angstroms long by 21 angstroms wide for each full cycle of its double helix spiral. 34 and 21, of course, are numbers in the Fibonacci series and their ratio, 1.6190476 closely approximates phi, 1.6180339.
DNA in the cell appears as a double-stranded helix referred to as B-DNA. This form of DNA has a two groove in its spirals, with a ratio of phi in the proportion of the major groove to the minor groove, or roughly 21 angstroms to 13 angstroms. A cross-sectional view from the top of the DNA double helix forms a decagon: A decagon is in essence two pentagons, with one rotated by 36 degrees from the other, so each spiral of the double helix must trace out the shape of a pentagon. The ratio of the diagonal of a pentagon to its side is Phi to 1. So, no matter which way you look at it, even in its smallest element, DNA, and life, is constructed using phi and the golden section!
DNA in the cell appears as a double-stranded helix referred to as B-DNA. This form of DNA has a two groove in its spirals, with a ratio of phi in the proportion of the major groove to the minor groove, or roughly 21 angstroms to 13 angstroms. A cross-sectional view from the top of the DNA double helix forms a decagon: A decagon is in essence two pentagons, with one rotated by 36 degrees from the other, so each spiral of the double helix must trace out the shape of a pentagon. The ratio of the diagonal of a pentagon to its side is Phi to 1. So, no matter which way you look at it, even in its smallest element, DNA, and life, is constructed using phi and the golden section!
If you're sitting around the kitchen or waiting for your meal at a restaurant you might marvel at this unexpected appearance of the famous Golden Ratio. Gather three identical items, knives, straws, breadsticks or any other identical lengths and find the center of two of them. Place one vertically and then put another's tip at it's middle point, so that they lie along the same horizontal bottom. Place the tip of the third knife at the center of the second knife, and lean it down along the same bottom line. Believe it or not, the distances along the horizontal line form the Golden Ratio, where the whole length (A+B) relates to the large part (A) as the large part (A) relates to the small part (B). It's a perfect mathematical balance relating the parts to each other and to the whole by the same, unifying rule.
Pantheism is the view that the Universe and God are identical. Pantheists thus do not believe in a personal, anthropomorphic or creator god. The word derives from the Greek (pan) meaning 'all' and the Greek (theos) meaning 'God'. Pantheism denotes the idea that 'God' is best seen as a process of relating to the Universe. The central belief in the Cosmos as an all-encompassing unity and the sacredness of Nature. The icon used as the World Pantheist Movement (WPM) symbol is the spiral as seen in the curves of the nautilus shell juxtaposed with the spiral arms of a galaxy, showing the link between the cosmos and the biological. The spiral represents a variety of things; evolution, eternity, spirituality, growth. Sometimes the Nautilus spiral alone is used which is a graphical embodiment of the Fibonacci series and the golden ratio.
The pentagram is considered by some western occultists to trace its esoteric significance to an astronomical observance of the pattern of Venus' conjunctions with the Sun. This is not possible. A superior conjunction occurs when Venus is behind the Sun and the inferior conjunction is when Venus is between Earth and the Sun; in both cases Venus is not visible. But it is true that plotting the recurrence of Venus' westward elongation from the Sun, over five consecutive synodic periods, will create the points of a pentagram. This period is approximately 584 days long, each period determining a different point of the observed pentagram - taking approximately eight years, five days to complete the figure. One would get a pentagram by picking any sunrise date on which the morning star is prominent and then repeating the observation at 584 day intervals following that date.