The Golden Eye of Fiveness (2)

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Sunflower florets are arranged in a natural spiral having a Fibonacci sequence, with different values for clockwise and anticlockwise rotation. Image Wiki CC by SA 2.5 L. Shyamal – Own work.

In Part One, we looked at a very simple sequence of numbers that ‘orbited’ or homed-in on a certain value. Now we need to examine that value and look at the sheer magic of what it represents.

 

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The ‘planet’ which has captured our spaceship emerges in the third line of black numbers from the Fibonacci sequence.

This new number was 1.618. It’s derivation is summarised in the diagram above, and described in the previous post. Simply: (red numbers) we add the two previous numbers to get the next. Next: (green numbers) we offset the first line of numbers one place to the right and, using a calculator to three decimal places, we treat the offset numbers of fractions, one number above the other. The third (black) line gives the calculator results, which stabilise at 1.618.

The ‘series’ that generates it – known as the Fibonacci series – came into existence at the time the world was abandoning the old and (by then) clumsy Roman notation (I, II, IV etc) and moving to the Arab-derived numerals that we use today.

The special number 1.618 is known by many names, such a the Golden Ratio and the Golden Mean. It is a number that shows us how we can divide something to protect its ‘wholeness’ in a harmonic way. By doing this, the divided figure will always exhibit pleasing proportions when placed next to (or within) the ‘parent’ figure. For example, Leonardo Da Vinci used it, extensively, in his most famous pictures.

But there are much deeper implications to this than something that looks or feels good, important though that is.

The materialist sees the world as having numbers by virtue of an ‘accident’ that they fit how we see and describe things. The mystic looks for the experience of ‘oneness’ with the processes that created the universe. You can’t find that experience unless you look for it. The universe owes us no debt of making it happen in our minds and hearts – the search must be ours… then the doors of perception will be opened.

Imagine that we have a strip of paper that we are going to divide by cutting with scissors. Let’s say the length of the initial strip is represented by the letter ‘A’. When we cut the strip we will have three values: the initial length (A); and the lengths of the two pieces we produce. We can name the two ‘child’ pieces (a) – the longest, and (b) – the shortest.

Under all circumstances, the original length (A) would be equal to the sum of the two children (a+b) . We can write this A=b+c, the most simple kind of ‘equation’ we could every want to see.

The miraculous Fibonacci number (given the name Phi in the 20th century) gives us the means to divide the original strip of paper such that the longer of the two child pieces bears the same relationship (ratio) to the original strip, as the larger child does to the smaller…

We can keep on doing this – cutting each successive larger portion – with smaller and smaller divisions of the original strip of paper. The whole ‘creation’ will be in harmonic proportions. This generation of smaller and smaller ‘harmonic’ children is called self-similarity.

Nature uses ‘Phi’ all the time. The recent science of Fractals shows how essential self-similar division is for nature to achieve its purposes. A tree is a fractal, for example, as are our lungs. Our blood vessels can carry oxygen to our cells because they follow fractal rules of becoming smaller and smaller within the finite space of our bodies. Only by using such structures can incredibly large processes fit into small spaces. The generation of Phi is not a fractal process, but it perfectly illustrates the marvel of the related fractal structures in nature.

Examples of this in nature include the petals of flowers, such as the sunflower, and the spirals of nautilus sea shells… But there are innumerable examples.

So, how would we actually work out the Phi-derived point of where to cut our twenty-unit strip of paper? We can arrange the self-similar formula so that we have a quadratic equation to solve, but where’s the fun in that!

Instead, we can look at the workings of the older graphical method carried out with the use of compass and straight edge. This brings home the inclusive and ‘connective’ nature of working by hand and is illustrated below:

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The horizontal line A-B is the length of paper we wish to divide into the harmonic proportions given by the Fibonacci-derived Phi number 1.618. In this example, the length is 20 units.

To begin, we imagine we have turned the base line (A-B) into a square of four sides and select its right-hand vertical halfway point.

To shorten this, I have simply created point C at the correct half-value (10). The compass is placed on point C and set to the distance of C-B. We begin to draw an upward arc from B to the intersection with the hypotenuse A-C. We then set the compass to a base at the origin – A, and extend its pencil to the previous intersection with the hypotenuse. This time we draw downwards until the curve intersects with the original length A-B. The point of crossing is the length of the largest ‘child’ as above.

The length value, the golden ratio, gives us a new ‘longest child’ length of 12.36 units. We could cut at this point. The relationship of the larger child to the smaller is the same relationship as the original full length to the largest child.

This process could be repeated to infinity using the successive larger pieces. The entire family of larger pieces would inherit the divine proportions of the ‘mother’ length.

In the final post, next week, we will examine how the pentagram combines all the above properties into a single figure of dynamic value to mankind.

Other posts in this series:

One This is Two.

©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.

Perspectives on Perception

‘The sun is always an adequate symbol for the Light of Lights…’
– A.K Coomaraswamy.

1Figure 1 – ‘The Seed at Zero…?’

The Circle is Time

Six of the Nine
Process through time

Three of the Nine
Are outside time:

Divine.

Yet still impact
And impinge in time
By impelling this processional motion.

3Figure 2 – Six of the Nine.

The Six of the Nine can be represented by the six faces of a cube:
Enfolded outlooks on the world.
The Three of the Nine can be represented by the three dimensions of a cube:
…Dimension is always an adequate symbol for Divinity.
The Seed at Zero can be represented by the cube itself in miniature:
A little world encapsulated by a larger one..?

4Figure 3 – Three of the Nine.

What is the antithesis of one?
None, two or many…?
It is tempting to answer money… that is, ‘my one’ or ‘my own’ as opposed to The One, which ‘belongs’ to everybody.
Or even The High One which is almost honey.

For many years I laboured under the misapprehension that to glean the gist of a thing was to
have the mere rudiments of it which is almost the exact opposite of the word’s actual
meaning. This can happen because of the context in which words are used and context
which has at least two viewpoints if not many more is really just another word for perspective.

The World is predicated on number.
Mineral, Plant and Animal growth are all governed by number.
Music is number in time.
Geometry is number in space.

Neither the World, Music nor Geometry initially ‘looks’ very much like number but that is what they are.

The qualities of number are the key to understanding this, which really means their properties and their relationships, each one conceived as distinct from all the others yet linked by natural sequence and logical progression.

Strictly speaking there are only seven numbers.
Zero is not a number because it is the negation of number:
It is rather both Tomb and Womb of number…
One is not a number because it is everything, without which there would be no thing:
Not One Thing…
Nine is not a number because it is a completion and possesses all the qualities of Zero:
And although numbers go on for ever they always repeat from Nine…

But Geometry can help here too because the way we see things affects the way we think about things and vice-versa. Whenever we come across a reversible we have reflection and the world, it has been claimed, is merely a domain of perceived reflections.

Plato’s Cave is the classic simile for this idea.
In order to affect the shadow-play of the world-screen one has to access the light source.
The outer can only be affected by changing the inner.

This can be ‘seen’ to be the case by experiencing the following ‘optical illusion’.

2

When the outer cube ‘flips’ the inner cube remains unaffected.
But if the inner cube ‘flips’ the outer cube has to flip too.
Can you see it?

Good… isn’t it?

Stella Interiori

‘…One becomes Two, Two becomes Three…

And out of the Third comes One as the Fourth…’

– Mary the Prophetess.

77Figure 1 – Plate One of Duvet’s Apocalypse.

The Apocalypse of St John serves as more than just a Coda for the New Testament.
Its constant cycling and recyclying of ‘sevens’ also re-works the creation of Genesis,
subsequent Hebraic festal traditions and the calendrical speculations of the Prophets.
We give below a taste of the seven-fold structure which runs throughout the whole of the mighty work…

“It was on the island of Patmos.
I was meditating on the seventh day when I heard behind me a voice as of many waters, “I am the beginning and end, first and the last.”

I turned to see who it was that spoke and I saw a figure resembling the Son of Man.
He was standing in the middle of seven golden candlesticks.
His beard and his hair were like white wool
And his eyes were flames of fire.
His countenance was bright, as the sun when it shines at its height.
He was clothed in a long white robe
And wore a golden girdle about his breast.
In his right hand he held seven stars.

His words rang out of his mouth clearly with the poignancy of a double-edged sword:

“I am he that lives and was dead.
I possess the keys to death and hell.
I shall live forever more.”

I fell down at his feet and they were like fine-brass forged in a furnace.

He laid his hands upon me, “You must write down all you see in a book, and send it
to the Seven Churches of Asia.
Let all the churches know that I am he who searches the reins of the heart and gives to every one, according to their works. Tell them to remember from whence they have fallen, to return to their first love lest I come upon them like a thief and remove their candlestick from its place, thus speaks the ‘Amen’: ‘I know your works, I know that you have a name, I know that you live, and yet, you are as the dead!’

To the guardian of the Church of Ephesus write,
‘He that is the beginning and end, first and the last says this:
‘I know your labours and your patience, yet this I have against you, that you love the Deeds of the Nicolaitans which I hate.
Turn within!
For to those that overcome the tribulations of the world will I give to eat of the tree of
life which is in the paradise of God. Let those with ears hear the words of the Spirit.’”…

– Revelation.

The Kabbalah is a Ten not an Eleven.
The Octave is an Eight not a Seven.
The Tetragrammaton is a Four and not a Three.
The World is a within and a without.

The Word is a Whole; the Not-Whole is the World.
How to make the World Whole?
‘Turn within.’

Metanoia…

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Figure 2 – Future and Past.

Our Cube of Space constantly turns or flips.
One moment the Future holds sway
The next moment the Past.

The Past and Future are
‘Death and Hell’
The Old and the New,
But what of the True?

Where is the Present?
Where is the Now?
Where is the Spirit?

Within.

To be present is to be centred within…

Within is a Temple:
A temple is a Church;
A church is a Kirk:
A kirk is a Circle…

…But what kind of circle can be considered a Star?

Next up we will look in more detail at some of the Geometries involved…