Category Archives: geometry

Ars Geometrica: First Matters…

 

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  One is All…

In Alchemy there are no short cuts.
Many are those who have spent a life-time seeking its treasure in vain.
On the other hand, everything it promises to reveal is freely given at the outset.
One need only attend properly to its stories and dictates to succeed in the quest…
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THE TREASURE OF ALEXANDER
In my native land where I was an orphan there stood a stone statue upon a golden column on which was written:
‘Behold! I am Hermes, he who is three-fold in Wisdom. I once placed marvelous signs openly before all eyes; but now I have veiled them by my wisdom so that none should attain them unless he be a sage like my good self…’
On the breast of the statue one could read:
‘Let him who would learn and know the secrets of creation and of nature look beneath my foot.’
I reflected on what this might mean and started to dig beneath the plinth…
Before long I came to a dark underground chamber in which winds arose and blew without ceasing.
I could go no further.
Exhausted by my toil and full of chagrin at my failure I sat down to rest and immediately fell asleep.
It was then that an old man appeared, resembling myself in build and appearance.
‘Arise and enter into this chamber so as to obtain a representation of nature!’ He said.
‘I cannot,’ I replied, ‘for I can see nothing in the darkness, and the winds that blow there will put out every torch flame.’
‘Then why don’t you put your light into a glass vessel…’ He said.
I immediately awoke, set a light inside a glass, as instructed, and entered the chamber.
There before me sat an Ancient Man on a Golden Throne, holding in his hand an Emerald Tablet on which was written:
‘This is the secret of the world and nature… the knowledge of creation and the cause of all things’…
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All…Ex…Andros…
Could anything be clearer or simultaneously more obscure?
How many Fairy Tales commence with a ‘Native Orphan’ who ends by first recognising and finally realising their ‘High Estate’?
And what should be made of our immobile Stone Figure which stands upon Gold?
He is a God, no less, yet he points not at heaven above but below to the earth.
Or of the Old One who appears in dream as our ‘bodily’ twin?
A simulacrum…
Nature’s representative advises we still the flickering, buffeted flame of our minds eye in order to see…
Deep in the Dark of Earth our enthroned kin who holds…
A Jewel in the Crown…
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2

 ‘Stone of the Wise’

PROJECTION OF GOLD
In truth, it is certain and without doubt that whatever is above tends toward that which is below and whatever is below tends toward that which is above for the accomplishment of the One Perfected Thing.
As all things are discovered by one, alone through contemplation so all things are born from this one, alone by permutation: its Father is the Sun, its Mother is the Moon, the Wind bears it in its Belly, the Earth nurtures it in its Heart; Power of all powers it contains the subtle and penetrates the solid and is the progenitor of all wonder in the world yet its efficacy is only perfected through embodiment.
In order that the little world may be re-created in the image of the great world the Spirit must be separated from the Body gradually by the regulated heat of a gentle flame: it rises to heaven from earth and falls back to earth from heaven and thus it acquires the inferior and superior powers for the glory of the whole world and the dissipation of all darkness…
This is the Way of Perfection…
I alone transmit this threefold wisdom which is why I am called The Thrice Raised Hermes.

– The Emerald Tablet

1

…All is One

 

Ars Geometrica…

 

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‘The alchemists disagreed on just about every aspect of the Great Work, except one: that it is impossible to succeed without the secret.’
– Patrick Harpur.

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I am reminded of ‘The Riddle of the Elements.’
The Ancient Greek Philosophers would each in turn trumpet the virtues of a particular Element claiming that it alone was primary and the source of the others, all the time, knowing full well that the solution to the riddle lay in sourcing the Four from a Fifth Element of an entirely different and more spiritual realm known as the Quintessence.
The Alchemists appear to be engaged in a similar process, describing the First Matter in terms of three ‘Spirituous Essences’, though the solution this time may be of a different order –
One in Three rather than Four from One.
They also seem to be describing the various products of a process at each stage of its operation simultaneously, thus for e.g. they might have described the process of evaporating sea-water as… Water… and… Salt… as well as its catalyst…Heat or… Fire…
Why would they do this?
To widen the scope of a mind mired in linear time?
Possibly, certainly, when one realises that the Fruit is in the Seed and not vice versa, or that the Body is in the Mind… a perspective is instilled, which opens up wide vistas to the Imagination.
Indeed, this technique only seems strange to a mind which habitually regards its own reality as an actuality.

As magicians for e.g. we might ask, in Tarot,
How is the ‘High Priestess’ ‘The Empress’?
Or, how is ‘The Fool’ ‘The Magus’?
Or indeed, in the case of ‘The Fool’, how does this key equate with any of the other major keys?
But here the equivalencies seem at the very least, much easier to accept, if not actually natural, simply because we work with these energies in an ‘Imaginal Realm’.

What the Alchemists are really doing is describing the lower in terms of the higher and in some cases what we are reading is, as it were, a Fourth Dimensional description of a Three Dimensional event.

The event itself appears to be an internal unification or better; a re-unification of polarised energies or ‘opposites’, or even, as the Alchemists would have it, a marriage, or wedding but what is the product of that wedding?

THE STONE OF MERCURIOUS

Moon’s Flux
Sun’s Seed
Earth’s Crux
Fire in the Sea
Blood from a Tree…

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Perspectives on Perception…

1 ‘The Seed at Zero.’

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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.

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3‘ Six of the Nine’.

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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..?

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4Three of the Nine’.

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

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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’.

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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?

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Apologies to Euclid….

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‘Given the option we would all choose to live in a house of the imagination…’

…A riddle is a trick played with words.

And this word ‘trick’ is interesting for it too has a three in it.

This three it seems to me is the unknown, or rather in the case of a ‘low down’ trick the not known by one but known only too well by the other.

It is debatable of course but it could be argued that whenever there is a one and another they are in one sense or another always reaching for a third.

Perhaps this reaching is an attempt to define the unknown.

Only by reaching together can they succeed.

Like a line that seeks a triangle.*

In order for the line to rise its polarities have to meet in the middle.
In order for the triangle to rise its singular-triplicities have to meet in the middle.

Why?

I hear you cry, why are the angles singular-triplicities?

Because each angle is simultaneously one of three and three in one, it is a point and also the point of two distinct bases.

Technically this ‘two base thing’ could also be designated a common-duplicity which is the reason why the little figure below works and as such, singularly, it gives us a hidden ‘fourth’, collectively, a hidden ‘sixth’.

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hares 008

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What does one point gain from another?

Reflection.

Antagonism.

Extension.

What do two points gain from a third?

Focus.

Equilibrium.

What do three points gain from a fourth?

Dimension.

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A line is a point with two ends to it.

A triangle is a line with three turns in it.

A tetrahedron is a triangle in ‘two minds’.

If the minds were houses one would be a house of the living, the other would be a house of the dead.

Or to rephrase: One mind is inner the other is outer.

For the inner to contain the outer, or for the drop to contain the ocean, requires a fourth and a sixth…

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* This triangle is always an equilateral triangle.

Baby Bear…

 

HM15 947Carreg Coetan Arthur

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 Otherwise, ‘Arthur’s Quoit.’

Of which there are a goodly number dotted about our Blessed Isles.

Which makes me wonder…

It is hard not to regard this Arthur as a giant too.

And indeed the folk record cares little whether it be a giant, or a king, or a saint who is responsible for placing the stones, only that their provenance be marked, and their links not forgotten.

The link at our previous site was with an isle and maybe if one were to sail from the isle to the mainland it would be useful to keep the stones, or the mound in sight. And if they couldn’t be seen it might have been unwise to set out at all…

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HM15 948*

The link at this one  is with the setting sun on the now obscured horizon.

Now, a quoit is a ring thrown over an upright in the game which, like a lot of games, employs distinctly coital symbolism.

It would be easy to re-construct the ring, perhaps, the earthen mound covering the chamber would only need to have been circular in shape.

But the ‘upright’ might be more difficult…

Unless it were a beam of light?

Such a notion is certainly counter intuitive but it may widen our notions of being up-standing.

We begin to wish we had paid more attention to the ray diagrams of our youth and those interminable physics lessons.

Fortunately, someone else has already done the maths, although quite how is still something of a mystery, to us at least.

According to the estimable Mr Robin Heath, the midsummer sun set of 2800 BC would cast its light through the ‘v’ at what he calls the back of the monument but which we may want to call the front.

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HM15 949*

One  has to wonder about a culture concerned enough about its environs to construct such a burial chamber.

A crucible for the last rays of the summer sun.

May it be that the structure was a calendrical instrument long before it was a tomb and that the bones eventually placed in its midst were once those of people connected to its construction and or continued employment?

When appropriate we still sometimes bury the tools of someone’s life long trade, or rather service, with ‘them’.

Such notions have  wide ranging ramifications for recent theories of psychological crystallisation, but that is another story…

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HM15 946*

This being such a small portal there was little enough room for the reader so the Companions gathered around the periphery for another recital of the ‘…Prayer’.

The reading caused shivers which, given the designation we had somewhat irreverently foisted upon the structure, seemed curiously apt.

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Practical Geometry…

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‘My goal is to teach practical geometry to our students, not as something new, but rather as a collation of older scattered material. Say what you will. I think our predecessors worked miracles. They had immense energy, and tried to get to the truth. Hard work could not dampen their ardour, nor any obstacle deter their efforts. They had deep insight into marvellous and almost incredible matters, and even in lesser ones they provided many examples of wisdom. To equal them may not be possible; not to try would be a disgrace. But enough exploration; let us address our task…’

Hugh of St Victor –  AD 1096-1141

Time After Time…

geometries 025

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… “Ah, you’ve left the matrix in this time, that’s good,” says Ben, he pauses, “Why sages?”
“You would regard Christ as a sage would you not?”
“I would indeed.”
“Christ is often pictured in a Vesica.”
“It is meant to represent the perfected aura I believe, or at least the aura of the perfected man.”
“So if we have ‘seats’ and we have ‘sages’ which in the text we assuredly do, then the vesicas are, as like as not, the sages…”
“These vesicas though aren’t at all Christ-like.”
“No, the Christ vesica is formed by the intersection of two circles. These on the other hand are formed by three. Sage leaves are also shaped like this as are many exploded seed pods.”
“Okay,” says Ben, “that’s very interesting, and the teaching?” …

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geometries 027

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…“The teaching is to open up and get out of the way like a directional cross of four chalices which point, or empty, into the centre.”
“Haven’t I seen that somewhere before?” says Ben.
“It’s a device which runs along the bottom of the stained glass window in the West Wing of ORC,” say I.
“Ooh, I like the notion of a West Wing to ORC,” says Wen rejoining the fray.
“But that is not the teaching in the text is it?” says Ben.
“No, but when you do the elemental, directional thing with the teaching in the text you get to the centre anyway…” say I.
“Let’s have a look now,” says Ben, “A plentiful sowing…A dutiful flowing…A beautiful glowing…An artful knowing…”

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“What sows?” says Wen.
“Wind sows,” say I.
“What flows?” says Wen.
“Water flows,” say I.
“What glows?” says Wen.
“Fire glows,” say I.
“What knows?” says Wen.
“Mind knows,” says Ben…

*
…“What knows?” say I.
“Body knows,” says Wen.
“What flows?” say I.
“Feeling flows,” says Wen.
“What glows?” say I.
“Face glows,” says Wen.
“What sows?” say I.
“Hand sows,” says Ben…

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“What sows?” say I.
“Water sows,” says Ben.
“What glows?” say I.
“Earth glows,” says Ben.
“What flows?” say I.
“Air flows,” says Ben.
“What knows?” say I.
“Heart knows,” says Wen…

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…“What knows?” says Ben.
“Spirit knows,” says Wen.
“What flows?” say I.
“Spirit flows,” says Ben.
“What glows?” says Wen.
“Spirit glows,” say I.
“What sows?” say Wen, Ben and I in unison.
“Spirit sows,” say Ben, Wen and I…

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Morgana, who has been observing our performance with increasing incredulity, laughs out loud and claps her hands together, “If you can reproduce that in the talks,” she says, “we’ve cracked it!”

– The Aetheling Thing.

Ego and Essence…

ss

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“Individuality, however we may hug its chains, is a partial and definite modality of being: ‘I’ is defined by what is ‘not-I’, and thus imprisoned.”

– A.K. Coomaraswamy.

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In philosophy there is a famous dictum relating to thesis, antithesis and synthesis.
To synthesise and to decipher symbolism requires contemplation.

Contemplation involves the mind in a simultaneous three-fold operation.
Review, Analysis and Enquiry.
When performed with honest intent the ‘unknown’ reveals itself.

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The Codices of the New Testament offer great scope for contemplation.
In the last of our Glastonbury Talks we looked at the work of Maurice Nicoll.
Nicoll’s psychological approach to storytelling opens to us Esoteric Christianity.

Exoteric Christianity insists upon the historical authenticity of the Gospels…
…And posits the notion of a vicarious salvation via belief.
Esoteric Christianity insists upon neither of these two tenets.

Below we reprint a comprehensive analysis of the story of the Marriage of Cana.
This was one of the stories we looked at in Glastonbury.
Our point of departure was the psychological approach outlined by Nicoll.

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Marriage at Cana

1. The Third Day…was a marriage at Cana of Galilee and the Mother of Jesus was there and also Jesus was called…
2. And wine having failed the Mother of Jesus said to him, ‘Wine they have not.’
3. Jesus said to her, “What… to me and to thee Woman? Not yet is mine hour come.”
4. His Mother said to the Ministrants, “Whatever he may say to you… do.”
5. There were six water jugs of stone placed according to the purification of the Jews holding each three measures.
6. Jesus said to them, “Fill the stone jugs with water.” And they filled them… up to the brim.
7. And then he said to them, “Draw out now and bear to the Director of the Apartment.” And they did so.
8. And the Director of the Apartment tasted the water becoming wine and knew not whence it is, yet the Disciples knew from whence they had drawn it, the Director of the Feast did then call the Bridegroom and said to him, “everyman at first the good wine sets forth and when they have drunk freely only then the inferior but you have kept the good wine for now.”
9. This, the first sign of Jesus in his manifest glory at Cana in Galilee.

– John 2…

Relationships

Mother-Son = Stone = ‘Letter of Law’
Bridegroom – (Bride) = Water = ‘Spirit of Law’
(Husband) – (Wife) = Wine = ‘Divine Law’

Psychology

Director of the Apartment = Ego
Director of the Feast = the New Man
Ministrants = Unredeemed aspects of personality
Disciples= Redeemed aspects of personality
Woman = Active Receptivity.

Teaching

All aspects of the personality are redeemed by active receptivity to Divine Dispensation.

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The Dance of Fire and Water III…

‘…As all things are discovered by one,

alone through contemplation,

so all things are born from this one,

alone by permutation…

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… Its father is the Sun,

its mother is the Moon,

the Wind bears it in its belly,

the Earth nurtures it in its heart…’

The Emerald Tablet