“It is highly dishonourable for a Reasonable Soul to live in so Divinely built a Mansion as the Body she resides in, altogether unacquainted with the exquisite structure of it…”Robert Boyle
In Part One, and Part Two we looked at a the emergence of a special number, Phi, that allowed the division of any ‘whole’ – like a figure in a painting or a building – into a series of proportions that divided it, but also retained its original relationship to the overall dimensions. the original ‘parent’. The number cannot be written, exactly, because it is ‘irrational’ – really an infinite relationship whose digits never recur. But the table below shows its emergence, to three decimal places, from the Fibonacci series. See Part One for the details.
This magical number, often called the Golden Mean or the Golden Section, was named Phi after the Greek artist and sculptor, Phidias, best known for his design of the statue of Athena within the Parthenon in Athens and the celebrated status of Zeus at Olympus. Both works were famous for their beauty… and also a sense of ‘specialness’. The reason for the latter is less well understood, yet central to our final consideration of this essence of ‘fiveness’.
Phidias, or the school he belonged to, had discovered that the human body followed ‘divine proportions’ – all based on the magical number of Phi – approximated as 1.618.
In the human form, the primary unit of this ‘divided divinity’ was the vertical distance between the brow of the face (the top of the eye, as in ‘eyebrow’) and the tip of the nose. Taking this as a base, the the vertical distance from the brow to the crown of the head is Phi times the base unit -the brow to tip of nose.
Moving the other way, the Phi ratio applies between the nose tip to the base of the neck. Travelling down the body, the same ratio applies – but with increasing lengths – from the neck to the armpit, then the navel, to the reach of the fingertips, and, finally from the fingertips to the soles of the feet. Using this analysis, there are seven harmonic sections to the human body.
Phidias used these proportions to create his breathtaking art. His approach was copied by many throughout history, including Leonardo Da Vinci, who had also inherited a love of another symbol that encapsulated the uniqueness of this magical proportion – the pentagram.
The origin of the pentagram is lost in ancient history, but was known as an astronomical symbol around 6,000 years BC in the land that became Sumer – possibly to represent the visible planets: Jupiter, Mercury, Marks, Saturn and Venus.
Its rise in Western history is due to the adoption by the School of Pythagoras (approx 500 BC), who shaped so much of our philosophical thought. The Pythagoreans knew the mathematical properties of the Golden Ratio and its relationship to the pentagram. Pythagoras was said to keep his own small pentagram with him at all times.
To conclude this series of three posts. Let’s examine the pentagram in the light of what we have learned about the Golden Section –
This five-sided ‘star’ can stand alone, or can sit within either a pentagon or a circle. The simple iPad geometry app I’ve used to create these diagrams (Geometry Pad) allowed only one measurement to be shown while the snapshots were being taken. We need to combine the measurements shown in Figure Four and Figure Five.
Look at the line running from G to I. It has three divisions caused by the intersections with the other vertices. From Figure Four we see that the distance from G to the first intersection is 5 units. Figure five shows us that the next section is of length 3.095 units. Allowing for the slight inaccuracy of the graphics we can divide the smaller by the larger and get 1.618, which is the value of Phi – the Golden Section.
This is only one instance. The pentagram is entirely constructed from Phi and Phi squared. As we have seen, it is truly the glyph of the human, and its Phi-based symmetry is too closely allied to our proportions to be considered an accidental result.
It is beyond the scope of this post but the pentagram first emerges – graphically – from the interaction of two circles, as above. First comes the point, then the line, then the triangle, then the square – then the pentagram. It occupies a very special place in Creation…
I believe we will go on discovering further depths to the pentagram in the years to come.
Other posts in this series:
©Copyright Stephen Tanham
Stephen Tanham is a Director of the Silent Eye School of Consciousness, a not-for-profit teaching school of modern mysticism that helps people find a personal path to a deeper place within their internal and external lives.
The Silent Eye provides home-based, practical courses which are low-cost and personally supervised. The course materials and corresponding supervision are provided month by month without further commitment.
Steve’s personal blog, Sun in Gemini, is at stevetanham.wordpress.com.
I do love reading about this, and though it is still difficult for me to understand, I honestly sense something sacred about it all. Thank you for such good writing about it. I can understand about the harmonic aspect and about how artists were able to use this to create the human figure with an amazing sense of correctness in the figures. I understand the golden mean, Phi and fibonacci. Is it because we are made with perfect balance? Does this have an application out there in the universe that we know this golden mean, etc.? Does it affect how we act in this life? Does it have a greater meaning for us that applies to other things? I know there must be more in the way of relationships, and I am just not seeing right now now that works. I am sure it is there though, so I will do some meditating and trying to see more clearly what this signifies. Thank you most kindly.
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Thank you, Anne. Let your meditation be seeded with that which creates from no-thing; which fills that space with the potential for conscious existence; which enters into its own creation, replicating itself at each level with that which is a mirror, though different in degree… x
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That’s beautiful, Steve. Thank you most kindly.
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Thank you for this fascinating series, Steve. Always been fascinated by the Golden Ratio and the Fibonacci sequence, very simple in its construction but infinitely complex in its results and potential. You have me reaching for my compasses!
Oh,good, Micheal! A worthy subject. Glad you liked the blogs.