The Golden Eye of Fiveness (3)

Figure One – the pentagram, emerging at the end of our search for perfect ‘fiveness’.

“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.

Figure Two: the Emergence of the Phi “Golden Mean” from the Fibonacci series

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’.

Figure Three: Reproduction of the Olympian Zeus in the sculptured antique art of Quatremère de Quincy (1815) Source Wikipedia. Public Domain. The original statue was 43 feet tall.

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.

Figure Four: The pentagram, the embodiment of the perfection of Phi in its human form.

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.

Figure Five: the Phi ratio runs through the entire geometry of the pentagram.

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.

The Vesica Piscis – birthing place of all sacred geometry

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:

One Two This is Three

©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.

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The Golden Eye of Fiveness (2)

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.

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:

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.

The Golden Eye of Fiveness (1)

In the dream the Hermit was speaking. “I am the eye of fiveness,” he said.

I listened… dreams are not always this lucid.

“In the beginning was the division, not the multiplication; and the division contained what divided it, but in another form…”

I was listening, intently. The figure of the Hermit promised great insight…

No-thing can be a principle. It does not have to be nothing…” He paused, smiling. “But it does have to be a ghost…”

I wondered if you could blink in a dream… apparently not. He placed a dot in the centre of the sky. Then extended his arms into the shape of a draughtsman’s compass and drew, black on azure, a circle.

I smiled, understanding something, at last. “Ah, yes,” I said. “The dot is no-thing, but has existence – if only as a position. The dot is zero.” I paused, aware that my thinking was waking me up… I had to get to a point of…. memory or I would lose it all…

“The circle is everything and everywhere,” I said. “The circle – One – is the arena of existence!”

The way the Hermit faded indicated he was pleased. And then, like the Cheshire cat that left only a smile, he was gone…

That dream was many years ago. I was studying the pentagram and the way it was used in a magical school of the soul. I knew that the geometry – and hence the numeric basis – was closely linked to the organic life we all share.

But I wanted something deeper… and had asked for it.

I consider that my attitudes are roughly half ‘science’ and half mystical. That way, I avoid the worst excesses of both, such as mysticism’s inclination to be fluffy, and to espouse the most complex ‘magical’ theories, even if they are twice as forced as the simplest scientific truths.

Equally, science’s dogmatic adoption of the ‘we are the only truth‘ attitude is to be avoided. Consciousness is not rooted in numbers, but the human mechanism – the body and how it works – is.

So, if you’d like to join in, let’s go in search of what’s at the heart of the pentagram: ‘fiveness’. Stand up and take yourself into a different mental and emotional ‘space’. Tell yourself that you’re not doing something trivial, but something that’s a living key to how you are, or were, before the layers of civilisation, work and family walled us all in numbness.

Leonardo Da Vinci’s Vitruvian Man. Source: Wikki, Public Domain

Stretch out your arms and legs so you look like Leonardo Da Vinci’s famous picture of the ‘Vitruvian Man’. Each hand’s five fingers and each foot’s five toes make up four of the five points of your human pentagram. Your head – the controller, communications receiver and maker of your organic ‘me’ – forms the other. We may reasonably ask what is the fiveness of the head? The question may already have triggered an answer in your mind….

If you’ve never encountered the Fibonacci series, stay with me and I’ll do my best to explain it – very simply. It’s worth the few minutes it will take to understand it.

Fibonacci: Begin on the (Red) First Row by simply adding the previous two numbers to get the next in the sequence.

We begin with zero, then one, because the whole of metaphysics is based on their relationship. Zero is the potential for all numbers to exist. One is symbolically the ‘monad’ – the complete everything from which we come and to which we will return; but One is also the first number, so is doubly useful in this example. We could say that, in Nature, everything is a fraction, yet Nature knows no fractions… Mankind sees only fractions, yet contains the seed of that which caused that division in the first place.

From zero and one, the next term in the series of Fibonacci numbers is generated by adding the two previous numbers. So, (from 0+1) we get another 1. At this point the series starts to take shape, growing quickly as each new number emerges from the sum of the previous two.

The row of green numbers is exactly the same line of numbers as the red ones above. But they have all been shifted one place to the right. What we’re going to do now is to create a fraction (don’t panic – I’ll do the calculations!) from each of the sets of two numbers; one above the other. So the first one would be 1/0 which is an invalid number, since we cannot divide by zero in ordinary mathematics. The next one is 1/1, which is just 1. The next one is 2/1, which is 2. We can see from this that we are swaying from one ‘extreme’ to the other; between the numbers 1 and 2.

Let’s continue to work these numbers to see what it is that we are swaying around… This is a bit like finding you’re a spaceship being pulled into the orbit of an unknown planet… but this planet holds one of the fundamental keys to the Universe…

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

It takes only ten ‘terms’ of the fractions from the Fibonacci series to produce the hidden planet to which our spaceship is being drawn. If you have a calculator you can check the fractions which lead to it; 5 divided by 3, 8 divided by 5, etc. Each of these divisions gets closer to a number that emerges in the greyed out boxes of term ten, above. From there onwards, the number 1.618 is present in all the results, which continue to ‘sway’ around finer and finer divisions of this mysterious destination.

In fact, we can never get at the final answer, since it is what maths calls an ‘irrational’ number – one that isn’t really a number at all, but is only defined by (in this case) an infinite (never-ending) convergence towards smaller and smaller units.

In practical terms this doesn’t matter. The three decimal places of 1.618 will do us fine. To go beyond this would involve us worrying about one ten-thousandth of a unit, which would be needed in only the most specialised engineering application, such as space travel!

But enough of the maths! We’ve landed on planet Phi… This mysterious number is so important that, like its cousin Pi, it has its own name. Phi is also known as the Golden Mean, the Golden Ratio… and a host of other historic names. It has been with us for a long time.. and very few people know its full significance.

In the next post we’ll examine what it Phi really means; and why it makes the Pentagram and Pentagon such important geometric figures in any world where harmony is important… which is just about everywhere. We’ll also consider why Phi is truly the ghost in the machine

©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.

The rotating blade of meaning (8) – final part

helicopter-meaning blog - 1

In the preceding parts of this series (see below for full list) we have seen how Arthur M. Young, inventor and chief engineer of Bell’s early helicopter design, was convinced that it was possible to construct a ‘map of human meaning’, a graphic figure that would show the relationships between the laws of physics and the observer in a new way.

In its experiments, science had always tried get rid of the observer; and yet it was the observer’s mind that constructed the experiment in the first place…. How odd, thought Young, to try to get rid of the core animating principle behind the whole thing!

His early confirmation of this came with a new analysis of the common forms of motion, starting with the idea of distance from a point, then examining the relationship between distance travelled and the time taken (velocity); then considering the rate of change of such velocity when more force (pressing the accelerator in a car) was applied to create acceleration.

Each of these could be laid out on a circle, with distance being at the right, horizontal point. Each of the others came into existence at a right angle – ninety degrees – to the previous. In parts two and three, we saw how velocity was distance (a straight line) divided by time; acceleration was distance divided by time squared (an area); and that there was something missing at the final point (the upper vertical), which would equate to distance divided by time cubed – a 3D cube – the foundation of our physical world.

As an engineer, Arthur M. Young knew that he had used formula that divided by things cubed in his control systems for the helicopters he designed. He realised that this was the point at which the observer interacted with the system, in the form of control.

His task was now to extend this circular mapping to integrate all the other equations of ‘motion’ in the greater sense. These included all the remaining formula used by physics to describe aspects of motion.

First, he had to reconcile the properties of ‘fourness’ that had led to the mapping of general meaning with the key mystical concepts of ‘threeness’

The diagram above shows the process whereby something of a ‘higher nature’, spiritually, divides itself into two ‘children’ in order to come into manifestation at a ‘lower’ level. This is a deeply mystical idea and is the basis of most of the world’s metaphysical thought.

The key to understanding this is the realisation that the ‘above’ does not entirely remain there, it ‘enters into’ its creation – the lower. Nothing is lost… in fact much is gained. The whole, the One, becomes Two, but does not lose its oneness, when seen at the original level. The result is Three… represented by the triangle, which can direct itself up or down. If down, it is in the ‘God-descending’ process of involution. If upwards, it is the planetary process of evolution.

The One undertakes this transformation only because it can extend itself in the process. The potential role for mankind is to bring this intent to fruition; matching the microcosm (us) to the macrocosm (the creator). To ‘God’, there is an involvement with the creation. Mankind has to learn first to ‘see’ God in the multiplicity of the world. To do this requires the undoing of much of our ordinary learning, based upon the desire be a living part of unity.

Sadly, it is beyond the scope of these few blogs to provide more of the mathematical and logical mapping that Arthur M. Young carried out. Many of the techniques were invented by him. He was seeking what he called his ‘Rosetta Stone of Meaning‘. We can, therefore, cut to the chase and show the finished thing:

The figure comprises the original square cross of our original process of human meaning overlaid with four triangles. The result is twelve points on the circumference of the circle – exactly the number that astrology uses in its map of the year and the signs.

What had Arthur M. Young achieved with this reconciliation of physics, metaphysics and the place of the observer within both?

First and foremost, he had shown that our state as observer of ‘the’ world was not a single state, that there were incremental stages of consciousness corresponding to his maps of meaning. He showed that raw experience was the first product of our perception and that it occurred before our consciousness of anything. Whatever is ‘out-there’ has to register before our mind can begin to process it. After that, as the Rosicrucians often said,  ‘mind assigns it dimension’. This produces a literal depth of perception that a different part of the mind can then categorise.

It does this so it can group like things, giving related sets of experience. As an infant (as discussed in Part 7) the most important of these is what will hurt us. The organism has to endure, and there are many things in the out-there that can hurt or kill it.

Over time, we confuse the two organic fear of survival with what we like and dislike. In this way our registered experience become confused with what is being ‘valued’ as good and bad – in the Genesis story this is the fruit of the tree of good and evil. Ultimately, there is no good and evil, only what is. But our personal growth demands we take the long learning curve to real knowledge of our place in existence: gnosis, as the ancient teachers named it.

Arthur M. Young showed us that our consciousness – that jewel at the centre of our organism, needs threeness and fourness to divide its ‘circle’ of meaning into twelve parallel aspects. Once these are known, there is nothing that can fall outside their realm. The totality of our existence is mapped into this glyph – and it is of great significance that this corresponds with the twelve-fold divisions of the wheel of astrology – the most ancient of the ‘power-glyphs’.

What is humanity in this picture?  As organic beings, we are wholly of this planet. The good Earth lends us her bright materials, and the seed from afar takes root and grows. It’s highest function is to be fully conscious, and, within that, to use the inbuilt gradients to set a course for ‘heaven’. Many storms await, but captains are made of storms, not books on navigation – though the latter are vital if this life-layer of humanity is to learn to give its fullest love back to the globe that nurtured it.

Information about Arthur M. Young, 1905-1995

This series of blogs are based upon the book: The Geometry of Meaning, by Arthur M. Young.  ISBN 1-892160-01-3.

Many of his talks are available on YouTube.

Previous posts in this series:

Part One,   Part Two,   Part ThreePart Four

Part Five   Part Six

Part Seven

©️Stephen Tanham

Stephen Tanham is a director of the Silent Eye School of Consciousness, a not-for-profit organisation 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.

You’ll find friends, poetry, literature and photography there…and some great guest posts on related topics.

The rotating blade of meaning (7)

Now we have finished with our incursion into maths, and I know that will be welcome…

Why have we been talking about such non-spiritual things as acceleration, velocity (speed) and distance? The answer is that these aspects of motion are at the heart of how we learn about the world, and how we interact with it. In learning, we forget how we learned and become absorbed in the results.

When the infant reaches out to get the hot cup she shouldn’t touch, and her fingers fail to grasp it, but push it away, she is using acceleration in the force she is trying to exert with her fingers. The small training cup may move but a larger and hotter teapot wouldn’t. The difference is not in the child’s fingers but in the mass (heaviness) of the teapot. A burn may be the result. It’s important to be able to gauge the mass of things – cycling into a tree or a wall is more painful than a hedge.

When the young boy, against his parents’ wishes, finds himself following his friends across that busy road, his life depends upon his ability to gauge the distance and how fast (velocity) he can run before the approaching vehicle kills him. If he’s successful, his parents will never know – and he is free to carry on learning.

If, halfway across that road, he sees that he has misjudged the speed of the approaching car, then he still has one chance of survival left to him: he can begin to run faster, in other words, accelerate. By generating more power (force = acceleration) in his leg muscles, he can propel his body forward, faster than before, and then faster, again, until the limit of his straining organism is reached. The swerving car passes him, its wing mirror rips the back of his coat, its horn is blaring, the driver frantic… but the boy is alive, and has learned something that will affect the rest of his life. In accelerating by choice, he has exercised something not present in position, distance, velocity or acceleration: he has developed control using his desire and free will to survive – using his mind and the mechanical capabilities of his body.

These are vital things, and they are key to how we learn and continue to learn. They give us our basic capabilities; and they help us to make sense of the world – our individual world – for we can know no other. Can we relate them to Arthur M. Young’s core diagram of how we learn the meaning of anything?

 

Let’s take a journey into ‘micro-time’. We enter a new house. In the corner of the first room there is a shape. It looks like a triangle, but so do many things. This is our first ‘taste’ of the previously unseen object. We examine it in more detail, believing that knowledge of its construction and function is important. We are at the stage of the Objective General in the above diagram.

We notice that triangle is actually three dimensional and has little ‘dimples’ in its material, We have good evidence that this object is made from a compressed paper derivative. We are now at the level of the Objective Specific.

Further study shows that there is light escaping from the edges of the object, and that its colour is a vivid orange. This is the Subjective General – because we are now imposing on it values (colour etc) that are actually part of our own minds – none of us sees exactly the same shade of orange, for example.

In a flash of recognition, we know its purpose: it is a lampshade, and it has been switched on.

This example shows how we perceive, though we do this in ‘micro-time’ and automatically. If we encountered an object whose like we had never seen, our minds would have to evaluate it in this way, step by step – but that process, too, would be automatic.

The  ‘automation’ in our consciousness is necessary. Without it, we would be exhausted with all the routine ‘processing’ our brains would have to do. Its negative cost is that our world very quickly loses its magic unless we deliberately ‘look-again’ at things.

This science of perception was already well known to scientists, psychologists and mystics. Arthur M. Young’s interest was in the fact that it could be viewed as a diagram of meaning, as above.

He superimposed the attributes of motion that we have discussed in the last three posts onto the circle in the same way. Remember that each of the sequence: distance, velocity, acceleration, and now, control, had been seen to emerge from a 90 degree shift from the previous state – a ‘right-angle’, as the ancient builders described it. This followed the way the line (a number) became a square (the number squared), and then a cube (the number cubed).

What resulted was this:

 

We move clockwise from Distance to Velocity to Acceleration. This is the point where classical physics ends. But Arthur M. Young was an engineer and knew that you had to add control (and thus the Observer) to have the whole system work – as in the creation of the helicopter. Control needed to be at the top of the circle, with another 90 degree shift from Acceleration.

With this discovery, Arthur Young knew that the circle had to be capable of holding all the relationships to not only how we know objects, but how we interact with objects. More importantly, these relationship would each have their own angle in the circle. The above diagram shows how the fundamental quality of time had a 90 degree relationship with this master-symbol, and could map itself four times around the circle before returning to its original state.

Young had been fascinated by the history of how Egypt’s treasures had been discovered. He remembered that an artefact named the ‘Rosetta Stone’ had enabled the same description to be mapped between the ancient Greek and Egyptian languages, opening up the written story of that mighty civilisation.

He decided that his search was of a similar nature. Could he extend how Time was mapped into the circle to the other fundamental qualities of physics, such as mass and length?

In the next and final post of this series we will summarise the conclusions he came to, and show his Rosetta Stone of universal meaning.

Previous posts in this series:

Part One,   Part Two,   Part ThreePart Four

Part Five   Part Six

©️Stephen Tanham

Stephen Tanham is a director of the Silent Eye School of Consciousness, a not-for-profit organisation 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.

You’ll find friends, poetry, literature and photography there…and some great guest posts on related topics.

The rotating blade of meaning (6)

 

Bell_30 sm St(Above: the original Bell 30 which established commercial helicopter technology, and was invented and developed by Arthur M. Young. Picture Wikipedia, public domain)

In our last post, we looked at those most frightening objects: numbers which are squared and cubed. This exercise in cruelty was an attempt to remove the fear of these things in order to put them in a very special place: Arthur M. Young’s conception of how consciousness worked – and its simplicity.

Arthur Young discovered that how the human mind grasped ‘meaning’ could be represented in a very simple graphical figure; one which gave greater depth to our understanding of consciousness. As well as being a scientist and famous inventor (the Bell helicopter was his creation) Young was a master astrologer – a very unusual activity for a scientist. He did not feel that astrology was antithetical to science, and admired the way the ancient science tried to encompass the whole of mankind’s experience rather than just the workings of the material world.

Young reminded us that our picture of the ‘world’ is our own; and is formed as a composite of information from our senses and our mind. This includes the way we react to it, as well. Let’s absorb this. There is no world, except the one we make. We are incapable of a full consciousness of the ‘out there’. That is not to say that we will always be limited in this way, but the present development of our species forms a very subjective picture: what I think, as opposed to what is. And we need to remember that it is very much a picture, though it has more dimensions than the area of the ‘picture’ we constructed in last week’s blog (Part 5).

There are certain things that have always been with mankind. A good example is the sky with its sun, moon and the mysterious planets – those ‘wanderers’ in the night sky that behaved very differently from the constellations around which ancient peoples spun their stories.

Arthur M. Young had determined that there were four stages, or aspects of how the pictures formed by our consciousness. Now, we must bear in mind that all of these are projected by the mind onto what we paint as ‘out there’. These stages have been carefully constructed during the course of our evolution, so Young felt justified in placing them at the centre of things.

One of the drivers of evolution was how we reacted to the motion of objects, friends and predators. To Young, the motion-related issues of distance covered, velocity and acceleration were related to three of the four aspects of meaning that we humans need to fully comprehend what is happening to us, and how we should interact with it. We examined this in Part Three and Part Four, like this:

(1) Distance travelled is seen to be the baseline of motion. It is analogous to our simple line of blocks in the last blog. The diagram is reproduced below:

Arthur Young line alone

(2) Velocity (or more commonly Speed) is Distance divided by Time, as in miles per hour. In other words, it’s a rate of change. With a constant speed (as in car staying at 70 mph on a motorway) the motion is at a constant rate. In our simplification of the formula we saw that Velocity is equal to Distance divided by the Time taken to cover it. in the diagram below, the distance is simply the length of the top line of blocks.

Arthur Young 3+3 +RightAA

3) Acceleration is the rate of change of the previous aspect of Velocity. A car travelling at a constant 70 miles per hour is not accelerating.  If our car, which had been travelling at constant 70 miles per hour, suddenly accelerated to overtake a wagon, there would be an increase in not only the distance, but also the velocity. This equates to the distance divided by time squared. We have seen that anything squared is equal to a square. Here’s our square from last week:

Arthur Young Nine Full wallAA

In each case of the above aspects, we have evolved our understanding by creating a ninety degree (a right angle) turn. We moved from a line (1+1+1) to an area, a square, by turning our evolving shape through ninety degrees and extending all of it by the same length.

Have we finished what we can know? Our blocks have been carefully drawn to show that another transformation is possible. One more turn through ninety degrees is, effectively, extending all the squared blocks backwards into the diagram three times (1+1+1) as we hinted in the final diagram from last week, reproduced below:

Arthur Young Nine Full27cubeAA

Do we know this figure? Most certainly – it is a cube. We got to it by dividing distance by time cubed. We live in a world of cubes; that is , we live in a three-dimensional world. Arthur M. Young proposed that there is a missing type of motion related to this final transformation of the aspects of motion.

In the next part of this story, we will look at the nature of this third derivative of distance and time; and the vital link it provides between a scientific world of ‘only matter’ and the presence of the observer as an intelligent part of creation…

To be continued…

{Note to the reader: These posts are not about maths or physics; they are about a unique perspective on universal meaning created by Arthur M. Young. If you can grasp the concepts in this blog, your understanding of what follows will be deeper.}

Previous posts in this series:

Part One,   Part Two,   Part ThreePart Four

Part Five

©️Stephen Tanham

Stephen Tanham is a director of the Silent Eye School of Consciousness, a not-for-profit organisation 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.

You’ll find friends, poetry, literature and photography there…and some great guest posts on related topics.

The rotating blade of meaning (3)

arthur young fence four sm

For this series of posts to make sense – and be spiritually useful in our lives – it must challenge the way we see and therefore ascribe meaning to situations. That challenge must also apply to what we are, as well, since how we used to see, in innocence and wonder, lies, now, below the surface of our active adult consciousness, yet comprises its foundations. Everything we perceive has a human process of perception to it, shared by us all, but differently configured within our individual psychologies. This happens so fast and so automatically that we are not aware of it, but the child is still within us.

There were four of us in the small conference room, high in the executive suite of one of the corporate buildings belonging to the giant telecommunications (telco) company. We were a small but important supplier of complex management software to the giant company.

And we’d had enough…

The four people around the table were present to discuss the legal case that was brought by ourselves and due to enter its court stages in a few days’ time. We were not bluffing. We never had been. As the principle of the business, I was there to demonstrate this stance; and that we were not being intimidated by their size. My opposite number was a senior sector head and a very decent man. The legal crisis had been passed to him to resolve. As always, it was sad that the proceedings had taken so long to get to the attention of a reasonable person, but that’s often how it goes. We knew we were burning our bridges and we knew that we would never work with that Telco, again. It was, potentially, as confrontational as it gets…

The two people with us were lawyers. One of our own and the other acting for the Telco. Our lawyer sat to my right around the small table. The Telco lawyer was at the side of the corporate exec. Together, we formed a cross, just like in our previous post.

basic cross map for arthur young

If we grow up in a commercial world, we come to expect that our ‘betters’ will sit across that desk or table when they are ‘dealing’ with us. The face to face, 180 degrees position is one we learn very early in our lives. We do it because it is only face to face that we get the full range of signals that tell us what we need to survive, to communicate and to love… It has always been said that love is close to its opposite…

The lawyers were there to advise, they were not able to affect the primary axis between me and the Telco manager, but they could suggest mediation.

young compass diag

If we consider another, and familiar example of a ‘four’ diagram, we can immediately relate to another aspect of this fourness. In the above diagram, we recognise the compass directions from typical map, or even – these days – a smart phone. We know from our reading of maps that we can move along the north-south axis without changing where we are in the East-West direction. The one does not affect the other, yet has great potential to mediate. If it is late and we are hiking to our safe destination, the other axis will play a crucial role.

solomon

One of the finest examples – given by Arthur Young, himself, is that of the story of the wise King Solomon mediating between the two wives over the ownership of a baby. We all know the story of how the king asked whose baby it was; and both women replied it was theirs. This is represented by the vertical axis of ‘Possession’ – they were each pulling to get the child. One of them was lying but Solomon could not know which without invoking the other axis, which, in this case, was Love. So, he did so, and deliberately suggested that he cut the infant in two, so that each wife could have half. The real mother was horrified at the proposed loss of life of her son and offered to let the other woman have the child rather than see it killed. The movement along the other axis, Love, resolved the situation, and the cleverness of the solution has come down to us through legend.

Or did the story always contain a pointer to the architecture of real meaning?

Arthur Young’s passion was to unite the worlds of science and mysticism. In this research, he was beginning to see way to do it. In the next part, we will consider how he invoked the different aspects of space and time to assist him.

Part One,

Part Two 

To be continued…

©️Stephen Tanham


Stephen Tanham is a director of the Silent Eye School of Consciousness, a not-for-profit organisation 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.

You’ll find friends, poetry, literature and photography there…and some great guest posts on related topics.

A chip off the old block? (part 1 of 2)

cube of space+wake you smaller

We have a phrase in English; that someone is a ‘chip off the old block’. Its meaning is that someone of merit is continuing the ‘family’ tradition. I suppose it could also refer in a wider context to someone in a group or organisation doing the same thing.

A group of scientists are promoting a ‘new’ theory: that of the ‘Block Universe’ or “Evolving Block Universe’. It’s not entirely new. The idea of a static universe where the only change is the evolution of the conscious inhabitants has been around for a while; and touches on some of the deepest ideas in philosophy and metaphysics.

Just think about that for a moment to grasp the sheer strangeness of the concept. Look around you and watch the shifting view, the tiny changes, the way you move your coffee mug, shift your position on the chair, drive the car through an autumnal landscape…. But you don’t do any of that, according to Block Theory. Instead what you are experiencing is your journey of consciousness along a hyper-road which maps and separates what is possible (with reference to where you started) to where you might choose to be next.

Only you change… and even then, only your consciousness; the hyper-globe in front of you reveals itself in an experience of movement – including your own body and organs. But… and it’s a big one… nothing out-there is really changing – we are just choosing what to see next amongst the possibilities. And, startlingly, this may be the ultimate purpose of the brain.

Within this world, the present has reality; the past has a lesser reality but is at least consistent; but the future does not exist. Reality belongs to where consciousness is. Conventional Block Theory conceives of a supremely thin wedge of passing time that is now… but philosophers dismissed this long ago as meaningless. There is not, nor can there ever be, a wedge of the ‘present’ small enough to contain the conscious now. In simple terms the observation may be in the present, and recorded in the brain; but the observer, by definition, isn’t… The observation becomes immediate history.

Those interested in metaphysics of any sort will recognise much of what is taught and experienced in their Work in this ‘new’ theory. We do not have a centre of consciousness, we are a centre of consciousness. In fact, within us there are two conscious centres: the first is a self that is grown in reaction to the world we experience – even though we are choosing it – The second is a deeper, super-conscious ‘presence’ which is not really a centre at all, it just retains an outer identity for the lifetime in which it is linked to the organic being and its personality.

Why is it called ‘Block Theory’? Here it gets interesting. There are two theories based on this idea of a three dimensional cube of length, breadth and height; where time is the expansion, but only via interaction with consciousness. The second, or derived theory is named ‘Evolving Block Theory’.

The use of  ‘Expanding’ suggests that this newly envisioned cosmos is actually growing… Mystics may recognise the idea that the universe or ‘God’ expands through the consciousness of its creation growing from within. It’s a staggering thought, that God is ‘not finished’, but evolves, too! Such a view has, of course, caused much controversy over the years.

Previous centuries have contained cosmological views that are very primitive in the light of modern science; but science is only now learning to value the presence of consciousness in the whole world-picture. Interestingly, some of the most ancient philosophies and religions were the very opposite and placed the development of consciousness, itself, at the centre of knowledge of the ‘world’.

The idea that the universe has past and present realities but no future except that which is unfolding in the now dovetails nicely with some of the better science fiction stories. One in particular that fits is the Hugo Award winning Hyperion series by Dan Simmons. In the story, Hyperion is a simple, colonised world to which a future civilisation sends an horrific artificial monster; a cyborg so dreadful that the whole of the Earth-derived space ‘Federation’ is drawn into a cataclysmic battle around its destiny. The cyborg – the Shrike – has been sent backwards in time to show the children of Earth the consequences of mindlessness, violence and lack of compassion. Although written in 1989, it is chillingly prescient about today’s society. The Shrike’s victims are impaled on a ‘tree of metallic thorns’ where their suffering is endless. I would imaging many abandoned souls on this Earth would describe their plight as similar…

From a mystical point of view – and in keeping with Block Theory – we may speculate that all that people of sufficient positioning and power within society would need to do would be to choose a different path, together. But then we may consider that we have no power nor right to change someone else’s path. We only have responsibility for our own. Mystics have taught for millennia that when we change our own thoughts, we change our own worlds.

This brings to mind the nature of real choice. most of the choices we make are as a result of our conditioning: they are automated responses based on pleasure and pain. This conditioning, and its resulting force – habit, is a necessary feature of our organic existence and as such is important for our survival. However, when faced with the idea of a voluntary higher evolution, we may choose to approach the nature of choice from a different perspective; especially in the light of theories such as the Block Universe. We will explore this further in the concluding part two.

From the point view of our choice of accelerated evolution, if Evolving Block Theory has any truth in it, then our personal possibilities have just expanded greatly. In fact, we only need make the right choices in order to radically change our lives.

On a chessboard a pawn may, with a few moves, gain the back row – the 8th rank, and transform itself into any of: Bishop, Rook, Knight or Queen of the same colour Only the King remains beyond this alchemy, though a Queen may mate with a King… We may reflect on this and wonder at how these deep and significant patterns are threaded through our history in ways that keep them in front of our unawakened gaze, like seeds awaiting their time in the sun… The important parallel is that to completely change our lives would take far fewer moves than we imagine.

If the block theories have merit, then we may be able to transform ourselves into personal ‘kings and queens’. As ‘royals’ in our own lives, we would have our own kingdom and would have no desire to control others and thereby restrict the freedom of those we should be helping along their own path.

To borrow from Isaac Newton: we may find our selves (our consciousness) crossing the paths belonging to Giants. Through the right choices: the Buddhist ‘right action’, for example, we may find ourselves ‘on the shoulders of giants’ in the sense of inheriting their wisdom – and choosing, with all our being, to follow it… Our journey through the Block of the intelligent universe as the fourth dimension may just have become a lot more lively!

To be continued…

©️Stephen Tanham


Stephen Tanham is a director of the Silent Eye School of Consciousness, a not-for-profit organisation 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.

You’ll find friends, poetry, literature and photography there…and some great guest posts on related topics.


 

The slow-quick Big Bang

Big Bang? - 1

Most people are familiar with the Big Bang. It’s a name adopted by the scientific world to describe the origin of the universe, a point of ‘singularity’ at the centre of the original black hole where everything, including space and time, came into existence.

Wikipedia defines it as:

‘The initial singularity was a singularity of infinite density thought to have contained all of the mass and space-time of the Universe before quantum fluctuations caused it to rapidly expand in the Big Bang and subsequent inflation, creating the present-day Universe.’

Except it didn’t…

Not everyone agreed with the idea of the Big Bang. One of its chief opponents ironically gave it its name: Professor Sir Fred Hoyle. The ‘big bang wars’ of the 1950s onwards were very bitter, as an outspoken Yorkshireman battled with the Cambridge establishment, of which he was a member, though he eventually resigned, saying it was impossible to work with the politics, there.

Hoyle was a brilliant astro-physicist who had objected to the idea that the universe had a start point. He argued that nature never did that; that time was a subjective thing and that everything should continue to be set within the understanding of Einstein’s laws, which required that time and space didn’t just disappear… or appear. The counter-theory, which had the weight of historical opinion behind it, was named the ‘Steady State’.

With the discovery of the cosmic microwave background in 1965, which showed that something like the Big Bang had happened billions of years ago, the tide turned against Hoyle and his ‘Steady State’ colleagues. This was despite the fact that Hoyle had previously showed that the heavy atoms needed for human life originated, not in the primordial big-bang soup, but in the suns of local solar systems – a kind of stepping down of cosmic matter and energy to originate life within the stable realm of a sun, which then nurtured that life as it gave up its own… in the form of radiant energy.

Professor Sir Fred Hoyle was excluded from a Nobel prize that included his main co-worker at the time. The reason was never given, but speculation was rife that the Nobel committee was uneasy with Hoyle’s multiple pastimes, including his creation of various science fiction books which dealt with intelligent and benign aliens.

Hoyle left Cambridge for the more liberal pastures of the American academic life, eventually retiring, with his wife, to the hills above Ullswater in the Lake District; not too far from where I’m writing this blog. He continued to oppose the Big Bang but was to far from its mainstream of thought to attack it.

In contrast, the Big Bang continued its roller-coaster of success, tracing the origin of the Universe back to millionths of a second after its creation…

…until the past few decades, when insurmountable evidence began to accumulate that you could not actually trace this creation scenario back to its absolute origin, at all.

Like most people, I had no idea that the Big Bang train had come to a halt, and yet what follows has apparently been known for four decades… That hunted singularity where space, time, and all the matter and energy within began did not exist.

The trail, as you approach the singularity where everything breaks down, is something like this: it becomes too hot for atoms to form; there is so much energy that matter and antimatter pairs can form; individual protons and neutrons break down into a quark soup and the heat and densities are so high that the whole Universe becomes denser and fits into the inside of a single atomic nucleus that we would recognise, today.

Finally, this collapses to a single point that occupies no space at all – a singularity at which the very laws of physics run off to infinity and everything breaks down. This was the ultimate vision of the Big Bang – the origin from which everything exploded outwards and forwards in time.

It’s sobering to think that nearly everything except that last instant has been confirmed as true. The three problems are: (1) that the Universe is perfectly uniform in background temperature; yet hasn’t had time to be so; (2) Has no curvature at the extremes, despite extensive searching; (3) There is no high-energy wreckage from these earliest of times…

The answer, put forward in 1979 by a theoretical scientist named Alan Guth, was stranger than science fiction. Instead of a radiant mixture of the highest energy particles at that singularity, there was no singularity and there were no particles. All that would become the Universe was bound up in the fabric of space, itself.

In space, itself….

This has been described as form of ‘vacuum energy’ which subsequently causes the Universe to expand at an exponential rate, without the need for a Big Bang, at all.

No-one really knows what this means. But it matches the ancient Hindu picture of eons-long expansion and contraction far more than it matches the Big Bang.

Professor Sir Fred Hoyle died on his beloved hills near Ullswater in August 2001. I would have loved to hike up those hills to tell him that, while he wasn’t exactly right, he wasn’t wrong either…


For more information I can recommend this excellent article on Medium, by Ethan Siegel:

Stephen Tanham is a director of the Silent Eye School of Consciousness, a not-for-profit organisation that helps people find the reality and essence of their existence via low-cost, supervised correspondence courses.

His personal blog, Sun in Gemini, is at stevetanham.wordpress.com

©️Stephen Tanham