Geometric forms have always been of interest to magicians, containing within their shapes, numbers, proportions and interrelationships, insights into the nature of the universe. The simplest elements of form – the point, the straight line and the circle – each have numerous symbolic associations as do their derivatives, such as the square, the cross and the sphere. Greek mathematicians explored the properties of the set of five regular convex solids which can be circumscribed by a sphere. Each of these so-called Platonic solids was associated with a traditional element: the octahedron, for example was associated with elemental Air (and the colour yellow) whilst elemental Water (and the colour blue) was associated with the dodecahedron. The proportions of these figures frequently contain the Golden Section.
Colquhoun’s interest in the Platonic solids is evidenced by her writings. In an unpublished essay Dimensional Interrelations: a Meditation on the Platonic Solids (1), she described a method of analyzing these figures. Her attention was particularly focused on the cube, a three dimensional figure which could be reduced to the two dimensional figure, the square, and, potentially expanded, into a fourth, spiritual, dimension.
A second source of the mystical knowledge that was contained within the cube lay in the Sefer Yetzirah, an early book of Jewish mysticism and an important qabalistic treatise that dealt with the origin of the universe. Translated by Westcott, one of the founders of the Golden Dawn, it was a primary source for the Order’s Knowledge Lectures. In the Sefer Yetzirah the universe is represented as a cube. Occultists mapped onto the cube, its planes, edges and diagonals, a vast repertoire of signs and symbols. This ‘Qabalistic Cube of Space’, contains in its structure, for example, the number four (sides) and the number three (dimensions). Its six faces, together with the interior centre point, can be assigned to the seven double letters of the Hebrew language and the seven planets. Its twelve boundary lines can be assigned to the twelve zodiacal signs and the twelve single Hebrew letters. The six faces, eight corner points and twelve boundary lines make a total of twenty-six, the numerical value of YHVH, the Tetragrammaton. The taro trumps, the paths of the Tree of Life, the houses of the zodiac and many other attributes and symbols can be plotted onto the cube. It can be regarded as a symbol of the philosopher’s stone; the completion of the Great Work of the alchemists, and the Perfect Ashlar of the Freemasons. Meditation on these properties would expand the magician’s network of esoteric associations and develop their understanding of the universe.
Colquhoun must have spent hours in such meditation, and also in practical experimentation. She was particularly intrigued by the shapes that are made when a two dimensional figure is folded into a three dimensional form, and when a three dimensional figure is opened out and becomes two-dimensional again. A square, projected or developed into three dimensions, becomes a cube with six faces. A paper cube, opened and flattened, becomes a Latin cross of six squares. The cross alludes to the crucifixion, death and rebirth. A variant of the Latin cross, the cubic cross of five cubes, (one in the centre and one forming each arm) when developed into three dimensions, becomes a figure with twenty-two outer, visible, facets. Assigning to each facet the number of a path of the Tree of Life, the appropriate Hebrew letter, taro trump, astrological symbol and painting it in the appropriate colour results in a model that summarises many of these hermetic relationships. It will be an object of considerable magical power.
A cross can be easily drawn on card or squared paper and then folded into a three-dimensional cube. In ones imagination, perhaps, three-dimensional cubes can be folded into a four-dimensional hypercube, the so called tessaract. This is the logic of the watercolour Towards the Tessaract (1978) in which the additional dimension is hinted at partly by ambiguity in the perspective drawing and partly by the use of transparent colour washes. In an earlier, but similar work with multi-dimensional ambiguities, (Figure in a Colour Cube c.1941) Colquhoun placed a human figure with arms outstretched within the confines of the cube, suggesting the place of Man in the cosmos.
The triangle is a traditional hermetic symbol. A triangle with the point uppermost, painted red, is the triangle of fire and light. It is male and symbolizes spiritual aspiration. A triangle with the point downward, coloured blue, is the triangle of water. It is a symbol of the feminine and represents intuition and the unconscious mind. This, the interplay between make and female, is undoubtedly the symbolism that underlies Machine for Conjuration (c.1940).
The superimposition of two triangles makes the Seal of Solomon. This can be seen in Volcano (1972), which also deals with elemental fire and water. According to Böhme, the Seal is the most meaningful sign in the entire universe. Colquhoun herself wrote that the Seal is ’the symbol of spirit manifested in matter, of God united with Man, the inner spiritual life with the outer practical life and the male united with the female, becoming the power that liberated Man.’ She made the heterodox comment that the Seal symbolizes the fallen Adam with Sophia, showing that the work of rebirth and unification has been completed.
Golden Dawn magicians had a number of techniques for creating talismans, sigils and for translating magical names into geometric forms. The angular line in Torso (1971) is very reminiscent of an angelic name drawn on a magical square. Similarly, it has many of the hallmarks of a figure made by tracing Hebrew letters on the petals of the Rose Cross. In this particular work, however, the inspiration is the lataif-e-sitta, the six subtleties, recognised by Sufis.
Colquhoun believed that there is no reason to suppose that spirits and elementals evoked by these means should be humanoid. She speculated that geometric shapes were more likely. (2) The automatic drawing Elemental (1942) may represent just one such being.
For a short period during the early 1950s, Colquhoun’s interest in geometry included a specifically Christian aspect. This is evident in works such as Ikon I - Crucifixion (1954); Ikon II - Ark (1954) and Heads of Angels (c.1952). Many, if not all of these works, were executed in connection with a project to execute some murals for Maze Hill Congregational Church in Greenwich, in conjunction the the architect Trevor Dannat. The works consist of geometric forms, especially squares and circles. In common usage, the circle is a symbol of the infinite. Because it is endless, it has come to be regarded as perfect and representative of the divine. The square, with its links to the cardinal points and the four elements, represents earthly things and is often used to stand for mankind. Combining the two as Colquhoun does, has a special significance: the elimination of imperfection in the reconciliation of the polarity between the heavenly and the infinite with the earthly and the man made, with the consequent achievement of harmony.
Notes
1. At TGA 929/2/1/21.
2. Colquhoun, I. The Sword of Wisdom. MacGregor Mathers and the Golden Dawn. Spearman, London 1975. See p. 261.
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