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:


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.


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)



[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.


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:


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).


[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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Cailleach’s bed by the hearth

There’s an interesting article on the Old European Culture blog about alcoves found in old houses in parts of Ireland. The alcoves, built next to the warm hearth, were apparently called cailleach, which of course reminds us of the name of the old veiled one, the goddess.

Whether this is coincidence or not, it reminds me of the little house in Scotland made to keep the Cailleach and her family warm through the winter, and I imagine a time when each house would have a place for the Cailleach near to the fire.


The source for the article is a record of a house plan in Galway from the Irish Folklore Photograph Collection. The note reads:

“The bed outshot was a common feature of houses in north-west Ulster and north-west Connaught, consisting of an alcove in the back wall of the house beside the hearth. The purpose of this small extension to the house was to provide additional sleeping accommodation and it was often occupied by elderly people. A common name for the outshot was the cailleach, which according to folk etymology derives from “cúil theach” (the back of the house).”




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Winter Solstice

In the dark mid-winter,
warm underground,
light pulses,

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The Living Mountain

Nan Shepherd was a Scottish writer and hill-walker, who described her experience of the Cairngorms as a kind of meditative participation in the landscape.

Last night I watched a beautiful and moving BBC TV documentary about her, and one of the quotations seemed to me to go to the heart of walking-as-meditation. She wrote, in a letter to a friend in 1940:

“To apprehend things – walking on a hill, seeing the light change, the mist, the dark, being aware, using the whole of one’s body to instruct the spirit… it dissolves one’s being. I am no longer myself, but a part of a life beyond myself.”


Beinn a’Chaorainn by Mark Knapton at English Wikipedia

The BBC TV Documentary, in the Secret Knowledge Series is called The Living Mountain: A Cairngorms Journey and there is an interesting article about the documentary and Nan on the BBC News website here.


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The Cailleach at Sligo

This summer I visited Sligo on the Northwest coast of Ireland, looking for traces of the Cailleach, the crone of Irish legend. What I found there was a prehistoric ritual landscape of breathtaking scale, and finally an intimation of the Cailleach herself. At the centre of the landscape is Carrowmore, a collection of 30 neolithic passage tombs. To the northwest the great hill of Knocknarea dominates the landscape.

From the top of Knocknarea a huge prehistoric cairn, the tomb of Queen Mebd, looks down on the monuments of Carrowmore.


Looking up to the cairn on Knocknarea from the centre of Carrowmore

In the opposite direction lie the Ballygawley mountains. The soft curves of these hills suggest to some people the shape of a giant woman lying down. In legend, the hills are associated with the Cailleach Bhérra – the old woman of Beare.


The Ballygawley mountains from the centre of Carrowmore

The Cailleach

The Cailleach is an important figure in Irish and Scottish folklore. As the old woman, the veiled one, or the hag, she is associated with many landscape features and prehistoric sites. In folklore she is of great age, remembering previous generations and landscape changes on a geological timescale. For example in one story, she remembers when the ocean was a forest, full of trees. [1]

As well as great age, she also has giant stature and supernatural strength. Although she is old, she renews her youth every generation by bathing in a deep pool before sunrise on beltane. [1]

She is also a shaper of the landscape, and there is a story of her throwing large rocks around in a contest with another cailleach. The contest takes place at dawn, while the people of the place are all still asleep. The story explains the landscape: anyone who comes to that district today can still see a pile of large rocks on the hilltop, with no other rocks anywhere near them.

Gearóid Ó Crualaoich suggests that this story is “a metaphor for the terrifying cosmic energies that have gone into the rendering of the physical landscape of human times into its shape and form, energies beyond the tolerance of humans who live their lives in a smaller and, hopefully, safer compass. The physical features of the landscape today, however, and legends about its formation, remind the human community of the otherworld dimension of their environment, a dimension available to them in the legends and other imaginatively creative narrations of cultural tradition.” [2]

As mentioned above, the Ballygawley mountains southeast of Carrowmore are associated in legend with the Cailleach. One of the peaks is named after the Cailleach Bhérra and there is a passage tomb there called the Cailleach’s house. When viewed from the centre of Carrowmore, an interesting alignment comes into focus.

The centre: Listoghil

At the centre of Carrowmore is a large passage tomb called Listoghil. Originally the monument would have appeared as a large cairn or mound of stones. There would have been a passage giving access to the centre of the cairn, where six large upright stones supported a massive roof-slab.  The monument has now been partially restored, so that the central chamber can be seen surrounded by walls of cairn-stones held back by wire fencing. In effect a visitor walks into a cut-away version of the original cairn to find the central chamber.


The central monument of Listoghil, with the partially restored cairn in the background (originally the monument would have been completely covered by stones with just a passage leading in from the left).

Researchers at Listoghil have recently discovered a fascinating seasonal alignment. The passage into the centre of the cairn, now represented by the entry path to the monument, is directed towards a distant point called the saddle on the Ballygawley mountains.


Looking out from the centre of Listoghil along the passage towards the saddle on the Ballygawley mountains.

Sunrise Alignments

At the autumn equinox, the sun rises exactly in the east, but then each morning the sun rises a little bit more towards the south, until it reaches the most southerly sunrise on the mid-winter solstice. It then begins to swing back towards the east. From the centre of Listoghil, this movement of the sunrise takes place over the Ballygawley mountains, and the sun rises over the saddle around Samhain, so that the rising sun shines in to the centre of Listoghil. By mid-Winter the sunrise has moved along the mountains to the Cailleach’s House, before turning around for the journey back. By winter’s end, as the sunrise comes back towards the east, the light once again shines into Listoghil around Imbolc.


Ballygawley mountains showing the progression of the winter sunrise

In his book Listoghil: A Seasonal Alignment? [3]  Pádraig Meehan describes a moment when he saw the Samhain sunrise:

31 October 2008 was a beautiful crisp morning, one of the year’s first frosts. In the moments before sunrise the Ballygawley Mountains appeared to burn, and fingers of sunlight threaded the sky. The four peaks of the Ballygawley Mountains huddled on the horizon, the passage tombs at each of their summits clearly discernible; Aghamore Far to the north, Sliabh Dhá Éan, Sliabh Dargan and Cailleach a Bhérra. As the light intensified before sunrise the sense of expectation increased. Suddenly, a brilliant sliver of sun-disk appeared, close and immediate. The land darkened under the fire. On October 31, the sun rose just off-centre left in the saddle and shone directly down the ‘passage’ of Listoghil, and through the chamber. Queen Meadbh’s cairn on Knocknarea was illuminated by sunlight approximately one minute before the sun reached the central tomb in Carrowmore.

Meehan relates that there is a local story describing the form of the rounded hillocks of the Ballygawley mountains as the hag lying on her back, so that the sunrise travels up her belly and breasts to rest at her head at midwinter. Seen from the slopes of Knocknarea, the hills look to me more like a figure lying on her side with her legs drawn up.


Ballygawley mountains from Knocknarea. If the figure is lying on its side, then the hills from left to right would be hips, elbows, shoulder and head.

In either case, there seems to be a relationship painted by the landscape of the sun rising over the Cailleach’s body during the winter months, and a polarity between Knocknarea and the Cailleach’s body, with everything centred on Listoghil. In fact the progression of the sunrise along the Cailleach’s body is mirrored by a progression of sun-sets behind Knocknarea during late spring and summer.

Interestingly, the poet and esotericist W B Yeats seemed to be aware of this polarity. In the opening of his poem The Hosting of the Sidhe, he has the faerie host riding from Knocknarea and over the grave of Clooth-na-Bare (the name he used for the Cailleach a Bhérra).

In the central chamber of Listoghil, the passage is partially blocked by a stone with a blunted peak, which forms a triangular spear of shadow in the chamber when the sunrise shines down the passage. Pádraig Meehan describes lying on his back and watching the shadow cross the roof slab. He wondered “Did a ritual specialist once lie in this way to observe light and shadow in the chamber? Or was the entire event, or sequence of events, arranged not for the living, but for the dead?”


The blocking stone in the central chamber

The view from Knocknarea

The climb up to the summit of Knocknarea is steep, but worth the effort. On a clear day there are views of the sea on three sides, with the Ballygawley mountains in the south-east. Looking down the hill the monuments of Carrowmore seem tiny and insignificant.


The view from Knocknarea towards the north

The cairn at the top is huge, built from large stones.  It is the largest unopened cairn in Ireland and is thought to conceal a neolithic passage tomb dating back to 3,000 BC. Queen Medb of Connaught is supposed to be buried in the cairn, standing up with her spear and shield. According to Wikipedia, Mebd was originally a sovereignty goddess, whom a king would ritually marry as part of his inauguration. Her name, cognate with the English word ‘mead’, means ‘intoxicating one’. This perhaps then was the summer face of the goddess, with the Cailleach as her winter person.


Medb’s Cairn on Knocknarea

Michael Quirke, a local woodcarver and folklorist introduces a third person to this local form of the goddess: Findabair as the maiden. In this video he also mentions another local name for the Cailleach: Garavogue which is the name of the river running through Sligo.

The Stones of the Cailleach

I just want to finish by talking a little bit about an impression I got of the Cailleach from this visit. The rocks that I saw both at Carrowmore and on the top of Knocknarea had an organic quality. For example, look at this boulder, part of one of the Carrowmore circles:


It’s made of gneiss – a rock formed under extreme temperature and pressure. Its shape flows, in curves and bands suggestive of half-formed living shapes. This is the same rock from which the ‘Cailleach’s body’ – the Ballygawley mountains – is formed.

Here is another rock, this time from the top of Knocknarea:


I think this is fossilised coral, and there are many fossil rocks like this in on Knocknarea, again suggesting an idea of half-formed living things in the rock. The third type of rock is more about touch than appearance. This is the type of rock sometimes found in caves, with a layer of small crystals one one side, somewhere between sandpaper and velvet to the touch. This type of rock was also on Mebd’s cairn on Knocknarea.

Letting this all percolate in the back of the mind brought about a picture of the Cailleach as 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.



[1] The Cailleach Bheurr and Loch Bà, pp. 113-120 of Ó Crualaoich, Gearóid. The Book of the Cailleach: Stories of the Wise-Woman healer. Cork: Cork UP, 2003.

[2] The story of Cailleach Bhéarra’s Shower of Stones, pp. 104-105 of Ó Crualaoich, Gearóid. The Book of the Cailleach: Stories of the Wise-Woman healer. Cork: Cork UP, 2003.

[3] Listoghil: A Seasonal Alignment? by Pádraig Meehan is available at the Carrowmore visitor centre, but is seemingly out of stock on online retailers. Much of the same information from the book is available online at http://intarch.ac.uk/journal/issue32/meehan_toc.html


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