Shaper of Forms

It looks like bodies have been half-formed from the molten rock in this amazing photo of a lava skylight. It reminds me of the thoughts I had about the Cailleach (the old goddess) at Sligo in Ireland: “a shaper of forms, working very deep, with the earth and with the living creatures of the earth. The shaper of the mammoth and the mountain. She whom the cave painters addressed.”

w_kamokuna_skylight_02apr96_-sheet_118__26_-row_5__1

(Picture Credit: Laszlo Kestay, USGS. Public domain.)
https://www.usgs.gov/media/images/west-kamokuna-skylight

 

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Healing Dreams

I recently had major surgery, and during the early days of recovery I experienced a lot of dreaming which I think was to do with the healing process. I want to briefly describe two of these dreams.

The first dream was of a goddess, sitting in the air above my hospital bed. She seemed to be sitting on a circular cushion, and her attention was on me, and also deep beneath me, where different forms were coming into being and passing away. It was her task to see or to decide whether I was to live or die, and I was reassured when her decision became clear that I should live!

hospital

My attempt to draw the goddess figure

The second dream was of her helpers, witches, who surrounded me. The witches were seated on floating cushions or maybe branches (I was reminded on the witches in Philip Pullman’s His Dark Materials trilogy). They worked alongside the nurses and doctors, and I had the strong feeling that the whilst the healthcare professionals were looking after my body, the witches were doing something deeper, at the meeting point of mind and body. Both types of work are needed for healing.

I imagine that followers of other traditions would see these figures in a different way, but I think that the reality is there – in some way we receive healing from the goddess and her helpers, or (seen in another way) from god and his angels, or (seen in another way)  from the depths of our own mind.

Who is the goddess?

My thoughts at the time were that the goddess I saw could have been the Cailleach – the old woman of Scottish and Irish legend. In my recent field trips to the Cailleach’s House in Scotland, and particularly Sligo in Ireland, I got an impression of the Cailleach as a protective mother, a mistress of forms and life.

I was also thinking about Mari, the goddess of Basque Mythology. Mari is served by witches called Sorginak.

mari_euskal_jainkosa

Modern rendering of Mari by Josu Goñi, via Wikipedia

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The Octave and the Tree of Life

This post is part of a series about the octave as a way of understanding the world.
The previous post was about Gurdjieff’s Law of Seven.

The central image of the modern Kabbalah is the Tree of Life – an image of the relationship between the divine and the material worlds, mediated by ten sefirot.

In his 1972 book Tree of Life, Z’ev ben Shimon Halevi wrote about the Octave and the Tree of Life. The Octave, or the Law of Seven, is shown descending down the tree from Keter to Malkhut following the  traditional lightning flash path which zig-zags down the tree. This brings in some new ways of understanding both the octave and the tree.

treeoctave2

Tree of Life and the Octave

Structure of the Tree

The Tree of Life is formed of ten sefirot, ‘spheres’ or ‘lights’. They are arranged in three columns or pillars – to the one side is the pillar of light or mercy or active force, and on the other side is its opposite – the pillar of darkness, severity, passive form. The central pillar, sometimes called the pillar of consciousness, reconciles these extremes.

The sefirot are also arranged in levels. The simplest way to think of this is that the divine or heavenly world is at the top, centred on the sefira Keter, and the material world is at the bottom, centred on the sefira Malkhut. There are many ways to work with this, but one way is to think about the creation of the world proceeding down the path of the lightning flash at the moment that God said ‘let there be light’:

From Kether (the Crown) the lightning flash goes to Hokhmah (wisdom) then Binah (understanding), then it crosses the abyss – within which lies Daat (knowledge).

Stepping down from the upper world, the lightning flash passes on to Hesed (loving kindness), Gevurah (strength) and then Tiferet (beauty), the heart of the tree.

The lower triad is formed of Nezah (victory), Hod (splendour) and Yesod (foundation), leading to Malkhut (the kingdom).

The Octave on the Tree

The octave follows the lightning flash, descending from do at Kether to do at Malkhut. As you can see in the diagram, the mi-fa interval lies over the abyss (and Daat), and the final ti-do interval lies within the sephira Yesod. The central sephira Tiferet is in the place of the Gurdjieffian Harnel Aoot, the interval which in Gurdjieff’s scheme was ‘disharmonised’ by the effects of the other two intervals. Halevi calls this “the thing itself”

This arrangement of the octave has the effect of relating the notes and intervals in the octave to different elements of the tree: the notes re, fa and la are on the active pillar, set against the notes mi, sol and si which are on the passive pillar. The do notes, the two intervals and the Harnel Aoot all lie on the central pillar of equilibrium or consciousness.

Four Worlds

This arrangement of the octave on the tree works well with the idea of the extended tree, which is a way of understanding the tree of life operating in four worlds from the divine to the material.

The extended tree (also called Jacob’s ladder) is an interlocking form of the Tree of Life where trees in the four worlds are shown as overlapping, so that for example the tree in the world of formation, Yetzirah, has its base in the sefira Tiferet in the material world of Assiah. The extended tree was first publicly presented in Z’ev ben Shimon Halevi’s books published in the early 1970s.

treein4

How the tree in each of the four worlds overlap to make the extended tree.

From the point of view of the octave, the extended tree is a series of interlocking octaves, where for example the mi-fa interval of one octave coincides with the si-do interval of the one above.

Planetary Correspondences

The octave has been related to the planets and the music of the spheres since the Pythagorean Octave. This relationship is also mirrored in the correspondences of the sefirot:

Kether (the Crown) Do  
Hokhmah (wisdom) Re Zodiac
Binah (understanding) Mi Saturn
(Daat (knowledge). – interval –  
Hesed (loving kindness) fa Jupiter
Gevurah (strength) sol Mars
Tiferet (beauty) – the thing itself – Sun
Nezah (victory) la Venus
Hod (splendour) si Mercury
Yesod (foundation) – interval – Moon
Malkhut (the kingdom) do Earth

In this scheme we see the planets arranged in effect by their apparent speed from the earth, fitting with the idea of the planets moving on a set of nested celestial crystal spheres about the earth, making music as they go.

flammarion

The edge of the firmament: wood engraving from an 1888 book by Flammarion.

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Bears Ancestors in the Pyrenees

An article I wrote for Sareoso.

Sareoso

“Lehenagoko eüskaldünek gizona hartzetik jiten zela sinhesten zizien.

Basques used to believe that humans descended from bears.” 

This interesting quotation sets the scene for a study of bear lore in the Basque areas of the Spanish and French Pyrenees. [1]

As late as the 18th century, hundreds of bears lived in the mountains of Europe, but by 1920 only about 200 were left, in the Pyrenean mountains. The last bear of this Pyrenean strain of brown bears was shot by a hunter in November 2004.  [2]

ours_brun_ld05 Female Brown Bear and Cubs

The bear is represented in the rich Carnival tradition of the Basque villages of Ituren and Zubieta, which are usually held around the end of January. In the carnival, a bear figure joins the  bell-carrying Joaldunak, and the author of the study suggests that even the style of motion and sounds made by the Joaldunak are reminiscent of a bear.

bears-in-the-plaza-during-the-ituren-carnivals

The chained bear (hartza) and…

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Why do children believe in magic while adults don’t?

My friends Lyn and Wayland, educating children in real magic!

Lyn's blog

image1 Wayland does magic with the boys

Yesterday Wayland and I did our Mabinogion workshop again, at a rural primary school near Hay in Wales.  We tell the children we have been sent by the Children of Don from our hiding place in the hollow hills to show them what real magic is.  It’s not a lie: Wayland and I share an obsession with a particular story from this collection of old British tales, written down in Welsh in the middle ages.  We do the workshop in English with some Welsh thrown in, especially for spells and charms. The children get to curse and bless, find out about the four magical ‘Hallows’ which the Plant Don brought to Britain and then use them.  They get to participate in an act of magical creation: making a woman of flowers from nothing, to make music, dance, become ‘servants of the invisible’.  They charm…

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Gurdjieff’s Law of Seven

This posts is part of a series about the octave as a way of understanding the world.
The previous post was about The Pythagorean Octave.

The philosopher and spiritual teacher G I Gurdjieff came across the law of seven in his travels in Asia around the beginning of the 20th century. Like the law of three, Gurdjieff saw the law of seven as a fundamental law of the universe, governing the progression of the vibrations which underlie all reality. The key insight is that whilst we might think that these vibrations change uniformly, in fact there are discontinuities, places where the change speeds up or slows down. These discontinuities mean that processes never go straightforwardly: impulses stall, or unintentionally change direction.

This is not just of theoretical interest, but is vital to our own well-being and self-development. To take a simple example, I might sit down with the best of intentions to write another paragraph of this article, but instead after a little while I find myself browsing images of cats. This can be seen as an operation of the law of the seven: intentions go astray.

Once we understand the law of seven, and more importantly observe it operating within ourselves, we can begin to think about how to work with the law of seven to achieve our intentions.


Gurdjieff learnt about the law of seven in the mysterious Sarmoung Monastery, built into the system of movements that he learnt there. His visit is portrayed in the film “Meetings with Remarkable Men” by Peter Brook:


 

What is the Law of Seven?

A description of the law of seven is given in Ouspensky’s book In Search of the Miraculous. He quotes Gurdjieff explaining that the law was known to ancient science, and was expressed in a formula which was handed down from teacher to pupil, from one school to another:

“In very remote times one of these schools found that it was possible to apply this formula to music. In this way was obtained the seven-tone musical scale which was known in the most distant antiquity, then forgotten, and then discovered or ‘found’ again.  The seven-tone scale is the formula of a cosmic law which was worked out by ancient schools and applied to music” [1]

Ouspensky goes on to define the law in similar terms to the Pythagorean octave, but with slightly different ratios between the notes. [2] The structure of the octave is the same, with seven notes and two semi-tone intervals (mi=fa and si=do):

do – re – mi = fa – sol – la – si = do

Ouspensky explains that these semi-tone intervals are where a ‘retardation of vibration’ takes place, causing a deviation from the original direction, so that instead of going in a straight line, any process veers off:

fig_14

From In Search of the Miraculous, Chapter 7

Why we can’t do things

Gurdjieff said that the law of seven “shows why straight lines never occur in our activities; why, having begun to do one thing, we in fact constantly do something entirely different, often the opposite of the first, although we do not notice this and continue to think that we are doing the same thing that we began to do.

“All this and many other things can be explained only with the help of the law of octaves together with an understanding of the role and significance of the ‘hiccups’ which cause the line of development of force continually to change, to go in a broken line, to become its ‘own opposite’, and so on.

“Such a course of things, that is, a change of direction, we can observe in everything. After a certain period of energetic activity or strong emotion or a right understanding, a reaction comes: work becomes tedious and tiring; moments of fatigue and indifference enter into feeling; instead of right thinking, a search for compromises begins and results in suppression or evasion of difficult problems.

“But the line continues to develop — though now not in the same direction as at the beginning. Work becomes mechanical; feeling becomes weaker and descends to the level of the common events of the day; thought becomes dogmatic, literal. Everything proceeds in this way for a certain time; then again there is a reaction, again a stop, again a deviation. The development of the force may continue — but the work which was begun with great zeal and enthusiasm has become an obligatory and useless formality. A number of entirely foreign elements have entered into feeling — considering, vexation, irritation, hostility. Thought goes round in a circle, repeating what was known before, and the way out which had been found becomes more and more lost.

Why civilisations and religions fail

“The same thing happens in all spheres of human activity. In literature, science, art, philosophy, religion; in individual and, above all, in social and political life, we can observe how the line of the development of forces deviates from its original direction and goes, after a certain time, in a diametrically opposite direction, still preserving its former name. A study of history from this point of view shows the most astonishing facts which mechanical humanity is far from desiring to notice.”

“Perhaps the most interesting examples of such change of direction in the line of development of forces can be found in the history of religion, particularly in the history of Christianity if it is studied dispassionately. Think how many turns the line of development of forces must have taken to come from the Gospel preaching of love to the Inquisition; or to go from the ascetics of the early centuries studying esoteric Christianity to the scholastics who calculated how many angels could be placed on the point of a needle.” [1]

How can we work with the Law of Seven?

Ouspensky goes on to explain that it is possible for processes to develop in a constant direction if the two intervals in the octave are filled with an additional shock of the right force and character. This can happen by accident, but can also be arranged intentionally:

“[A man] can learn to recognise the moments of the ‘intervals’ in all lines of his activity and learn to create the ‘additional shocks,’ in other words, learn to apply to his own activities the method which cosmic forces make use of in creating ‘additional shocks’ at the moments necessary.”

“The possibility of artificial, that is, specially created, ‘additional shocks’ gives a practical meaning to the study of the law of octaves and makes this study obligatory and necessary if a man desires to step out of the role of passive spectator of that which is happening to him and around him.”

The law of seven and its study is at the centre of Gurdjieff’s method. Through it we can develop an understanding of the cosmos and of ourselves, and learn to begin the Work of self development.

Harnel-Aoot

The octave as previously described has two intervals where deflections take place, one between mi and fa, and the other between si and do, but Gurdjieff also mentions a third interval which has a different character, and that is the interval between the notes sol and la. In Beelzebub’s Tales [3], Gurdjieff calls this interval Harnel-Aoot, and says that it is ‘disharmonised’ by the effect of the other two intervals. (He does describe the nature of this disharmonisation, but we won’t explore that further here). So the full structure of the octave can be read as:

do – re – mi = fa – sol ≈ la – si = do

 

Next: The Octave and the Tree of Life (to come)

 


Notes:

[1] In Search of the Miraculous, P D Ouspensky, Chapter 7. Available online at http://www.ardue.org.uk/university/intro/octave.html

[2] Ouspensky uses 10/9 instead of 9/8 for the tones re-mi and sol-la, and 16/15 instead of 256/243 for the semitones mi-fa and si-do.

[3] Chapter 39 of “Beelzebub’s Tales To His Grandson”. This book, though fantastic, requires hard study! An electronic version of Chapter 39 is here.

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The Pythagorean Octave

The musical octave has been used as a way of understanding the cosmos for thousands of years. The ancient Greeks used it to represent the harmonies of the universe, and in the renaissance it was used to show hidden relationships of harmony in the music of the spheres. More recently the philosopher G I Gurdjieff used the Law of Seven to understand how processes work at all levels of existence, explaining how things can go wrong in our simplest plans, and what we can do to stop this happening. The octave can be found in the Kabbalistic Tree of Life, and Saros philosophy shows how it arises as a simple abstract pattern.

In the beginning

The story of the octave, as far as we know it, begins with Pythagoras the Greek mathematician and philosopher, who in the 6th Century BC came up with two key ideas:

  • That musical harmony is based on mathematical ratio. He found that strings of different length vibrate with different sounds, and that they sound most harmonious together when the lengths are in a simple numerical ratio: 2 to 1, or 3 to 2 for example.
  • That the universe is harmonious, with the planets and stars moving according to mathematical rules.

He reasoned that the motion of the planets should correspond to musical harmony, laying the foundation for the harmony of the spheres, which was used as a way of understanding our world for thousands of years.

the_music_of_the_spheres

Engraving from Renaissance Italy (Gafurius’s Practica musice, 1496) showing Apollo, the Muses, the planetary spheres and musical ratios. (From Wikipedia)

Plato’s Timaeus

An interesting description of the octave is contained in Plato’s dialogue on cosmology called the Timaeus. This dialogue, written around 360 BC, was Plato’s attempt at a ‘theory of everything’ describing how the world and everything in it was made [1]. The crucial part for us is where he talks about the way ‘the divine craftsman’ created the world-soul, using a mathematical division to lay out the circles which describe the apparent motion of the fixed stars and the planets around us.

The mathematical division is based on simple numerical ratios, which define a Pythagorean octave. He starts with the simplest numerical ratios, formed from whole numbers:

2 to 1   do to do (an octave)
3 to 2   do to sol (a perfect 5th)
4 to 3   do to fa (a perfect 4th)

This gives a framework of notes: do … fa sol … do

Plato then fills out the framework, taking the ratio between fa and sol as the basic tone. The ratio of fa to sol is 4/3 to 3/2 which simplifies to 9/8, so Plato adds two notes re and mi spaced at this ratio from do, and then la and si spaced by the same ratio. He ends up with this picture:

pythagoctave

The octave in Timaeus

Do-re-mi and fa-sol-la-si are all spaced by a full tone, 9/8 ratio, but there are two intervals (mi-fa) and (si-do) which are smaller, and filled by a ratio of 256/243 which is roughly a semi-tone. The white notes on a piano, CDEFGABC correspond closely to the notes of the octave. [2]

You can play around with the sounds of the notes to listen to the musical ratios using a musical instrument, or using an online keyboard. A good place to begin an appreciation of the musical intervals is this video.

The structure of the musical octave

Before moving on, it is worth summarising some of the structural elements of the octave:

  • The octave is made up of seven notes (do-re-mi-fa-sol-la-si).
  • Most of the notes are separated by a full tone, but the notes mi-fa and si-do are separated by semi tones. What does this mean? What is different about these intervals and why?
  • Considering each tone as two semitones, we can see there is a total of 12 semitones in the octave.
  • The perfect 4th and perfect 5th ratios are also present between other notes in the octave.

Next: Gurdieff’s Law of Seven (to come).


Notes:

[1] Timaeus: https://en.wikipedia.org/wiki/Timaeus_(dialogue)
See: “Music and Mathematics in Plato’s Timaeus” which describes the octave process.
See: http://www.mathpages.com/home/kmath096/kmath096.htm for an interesting description of how Plato went on to describe the universe in terms of the five platonic solids.

[2] Plato’s semitone ratio (256/243) is approximately half of a full tone ratio (9/8), because (256/243)(256/243) ≈ 9/8. The equivalence is only approximate however. In tuning a modern piano, a slightly different set of ratios are used, with a semitone defined so that 12 equal semitones give an octave (s12 = 2), and a tone is exactly two semitones (t = s2).

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