Category Archives: geometry

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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An Aye for an Eye?…

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“Sure, ’tis a terrible thing to choose one or t’other.”

The Aurally Man

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Alchemy as process has a number of stages.

And nobody seems able to agree on how many!

This might not though be a disagreement of number but of measure.

An hour possesses sixty minutes and three-thousand-six-hundred seconds, after all.

If we make our focus three, we get…

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A point worth considering: all the triangles are of equal size.

Individually this seems obvious but, perhaps, not quite so, relatively.

A shortcoming alluded to in the phrase, ‘vagaries of the human eye’.

Which is another point worth considering.

The human eye follows lines like a moth to flame.

This is one of the reasons why the ‘Blessed Head of Joshua’ is eyeless.

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All – Ex – Andros…

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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 our Earth the enthroned kin who holds…
A Jewel in the Crown…
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Image result for lemniscate

The Eye-Guy’s Eye…

Human Eye

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…”I don’t get it.”

“In Geometry, before one can draw a human eye, one has to draw a cat’s eye.”

“I still don’t get it.”

“It’s a process.”

“And in any process things have to happen in a certain order…”

“You said that without using your brain.”

“…First one thing, and then another.”

“And that.”

“But what thing and what other?”

“Ah ha! In this case, Night and Day.”

“Cat’s-Eye and Human Eye!”

“There’s more to it than that though.”

“In what sense more?”

“In a magical sense.”

“Old magic?”

“Well, it would have to be, very old magic.”

“Whoo-Hoo!”

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The Eye-Guy…

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SPOILS OF THE ABYSS

 When Pryderi, Lord of Underhill, was treated for the

 injury done to his arm by Tyrnonos, Thunder-of-Water,

 his leech, Nudd, found that he was unable to save the limb; so

 he hacked it down to a stump and put a silver hand on Pryderi which

 was so cunningly crafted that it had all the movement of a natural hand.

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Yet still Pryderi had no end of pain and trouble with the arm

and he was forever lying sick in his bed from the grief of it…

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“Not a particularly auspicious start, and no sign of our ‘Eye-Guy’.”

“Give it time.” …

“Did they have ‘bionic’ hands in those days then?”

“A ha… I don’t know, did they have ‘bionic’ hands in those days?”

“I think not.”

“We are dealing with the Crafty Folk here, remember?”

“I still think not.”

“So, to what can the silver hand or arm refer?”

“It would be useful to know which we are dealing with, actually.”

“Some sources specify hand, some specify arm, and this lack of precision may itself be the clue to our non literal interpretation. You’d think they’d know!”

“You would.”

“Let’s settle on limb, then. To what can the silver-limb refer?”

“If it’s silver it could have something to do with the moon?”

“I think that’s a very auspicious start.”

“Or a tree?”

“Even better, what sort of tree?”

“A birch tree.”

“Now, I know that is an incredibly auspicious start.”

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Dance of Fire and Water: Relations…

‘…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

Dance of Fire and Water: Tablet…

 

‘In truth, it is certain and without doubt,

that whatever is above tends toward that which is below…

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… And whatever is below tends toward that which is above,

for the accomplishment of the One Perfected Thing…’

The Emerald Tablet

 

Dance of Fire and Water: Planets…

Image result for moon symbol

White represents the Crescent of the Soul:

a vision of the tides of life, their ebb and flow…

Image result for Mars symbol

Red represents Matter over Spirit:

when to act in peace and war, we all must know…

Image result for Mercury symbol

Grey represents Spirit which mediates between Soul and Body:

a communion of truth and wisdom…

Image result for Jupiter symbol - orange

Orange represents Expansion through Wisdom:

and tempers justice with compassion, to protect and to serve…

File:Venus symbol (green).svg

Green represents Spirit over Matter:

acting from love with a generous heart…

Image result for Saturn symbol

Black represents Contraction through Matter:

as the bread of life is sown and reaped…

Image result for Astrological sun symbol - yellow

Yellow represents the Circle of the Spirit:

an outer light and the greater light within…

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