Geometry


The Foundation

The Gyre continues

The Double Gyres

The Cones

The Diamond and the Hourglass


The Phases of the Moon

The Wheel

The Faculties

The Principles



The Foundation

The Basic Gyre

When Yeats published ‘The Second Coming’ in book form in 1921, he decided that he needed to explain the source of some of his imagery and thinking. He couched the account in terms of the fiction of Michael Robartes and Owen Aherne (see The Fictions of the Two Versions), giving a succinct summary of some of the main elements in the System that was emerging in his collaboration with George. Robartes gives Aherne ‘several mathematical diagrams’, ‘squares and spheres, cones made up of revolving gyres intersecting each other at various angles, figures sometimes of great complexity’, but the explanation for these ‘is founded upon a single fundamental thought. The mind, whether expressed in history or in the individual life, has a precise movement, which can be quickened or slackened but cannot be fundamentally altered, and this movement can be expressed by a mathematical form’ and this form is the gyre. (See text of the note at the bottom of the page.)

The Basic Gyre: Wax & Wane

Robartes/Yeats compares the inevitable pattern of this movement to the growth of a plant or animal, each species having its own variation of the fundamental paradigm, and each individual within a species being affected by its resources and circumstances, and he compares the paradigm to the laws of genetic inheritance discovered by Gregor Mendel.

The gyre starts at its origin and moves progressively wider in a spiral, while time adds another dimension, creating the form of the vortex or funnel. Once the gyre reaches its point of maximum expansion it then begins to narrow until it reaches its end-point which is also the origin of the new gyre. Another way of seeing the same thing, if time is not taken as being fixed in one direction, is that once the maximum is reached, the gyre begins to retrace its path in the opposite direction.

The gyre can therefore be seen as a single vortex which grows and dwindles, but the more commonly used figure is a double vortex, where two vortices intersect and the apex of one is at the centre of the other's base.


The Double Gyres

The Double Gyre Horizontal

Yeats's thought is fundamentally dualistic and, although the single gyre contains a fundamental dualism in the two boundaries of its form, the base and the apex, it is more natural for Yeats to use a doubled form. Since the apex or minimum of one element implies the maximum of its dualistic opposite, these double cones intersect so that the two gyres are the complementary opposites of each other.

The Double Gyre Vertical

In this formulation, if each gyre is depicted as a single principle, then the gyre moves from the total preponderance of one principle over the other, through increasing admixture of the second principle to equality at the point where the surfaces cross each other, until the minimum of the first and the maximum of the second principle are reached. At this point the reflux starts, so that there is never more than a momentary predominance of either principle, and the system is constant movement.

Yin-Yang

Classically, this is the kind of interrelation depicted in the Yin-Yang mandala or in any form of wheel expressing two polar opposites. As in the representation of the Yin-Yang polarity, the maximum of one gyre contains the minimum of its opposite at its centre, so that, even as this minimum briefly touches zero, it is still inherent within the whole.

Yeats uses the cycle of the Moon's phases as the visual symbol of the interplay between his two defining principles, the Tinctures, primary and antithetical, the poles of which are symbolised by the dark of the Moon and the full Moon. Although this is shown as a disc divided into shaded and white halves in A Vision (AV B 80), it is more accurate to depict it as a disc where black and white are the extremes, with shades of grey in between.

The Wheel

The two diagrams represent the same idea, of two interacting principles which increase and decrease in a reciprocal relationship with each other. There are no fixed stages and the change is gradual rather than discrete, however once the cycle is applied to human life, death and birth mark radical changes of state for the human soul, and it becomes both natural and necessary to mark these divisions, which Yeats takes as the twenty-eight stages symbolised by the Phases of the Moon (see the Wheel). Even within history, where the transitions are not marked and are clearly gradual, the Phases provide a useful notation to show the point that the cycle has reached, so that they are maintained, or adapted to a twelvefold scheme (see the historical gyres).

Especially with regard to history, it can sometimes be clearer to see the double intersecting cones extended over time, so that they become a chain rather than an isolated unit. This can appear to minimise the cyclical nature of the interaction, but can be helpful in disentangling the various cycles in operation at any one time (see History and the Great Year).

The Extended Gyre

The Cones

The Simple Cone

For diagrammatic ease, the gyres are usually integrated into cones in A Vision, and represented on the page as triangles. This serves very little purpose beyond simplifying the tangle of lines which would otherwise dominate any of the diagrams, and making the delineation of the Faculties’ movements clearer (see the Faculties on the Cones). The intersecting triangles can come to appear as some esoteric form of slide-rule, if it is not remembered that these represent a three-dimensional shape, which itself represents a four-dimensional system, which is in constant movement.

Cone1

Because of the dominance of this image in Yeats's mind, even when he comes to refer to the supernatural opposite to mundane reality, he uses the term the Thirteenth Cone. There may also be some influence from Renaissance thinking here, where various writers posited intersecting pyramids of light and dark to represent the interpenetration of the divine and mundane, and to see in these two pyramids a ladder of descent from and ascent to the Godhead. Robert Fludd, the English Rosicrucian, created a fascinating series of diagrams which show the relationship of the Macrocosmic world of the divine to the Microcosmic world of the human.

Fludd's intersecting pyramids The 2D Cones
from Fludd, Utriusque Cosmi. . . Historia The Double Cones

The Diamond and the Hourglass

Although the double cone dominates the diagrams found in A Vision, the more important representation of the gyres in the Automatic Script was that which was called the ‘Diamond’ and ‘Hourglass’, which is effectively a doubled form of the double cone. The Instructors objected to the term ‘Diamond’, but Yeats retained it anyway.

The Diamond and the Hourglass

In A Vision this form of representation is most important in the discussion of the Principles, the spiritual constituents of the human being, which come to the fore in the after-life. In this system the axes of the two shapes do not necessarily coincide, and they rotate about a common centre, within a sphere. The Diamond itself represents the original Principle of the Celestial Body, within which the Spirit moves as a single gyre. These together form the Solar element of the system of the Principles, while the Hourglass represents the Lunar element. Both the Passionate Body and the Husk move within this double gyre, one half representing life and the other half the after-life (see the Principles and the After-life).

The Diamond and the Hourglass




 

Note on 'The Second Coming', Michael Robartes and the Dancer (Dundrum: Cuala, 1921).

Wade 127; the book was finished on All Souls' Day, 1920, and bears the date MCMXX on the title page, but was actually published in February 1921.

Full text of the note on 'The Second Coming', Michael Robartes and the Dancer:

Robartes copied out and gave to Aherne several mathematical diagrams from the Speculum, squares and spheres, cones made up of revolving gyres intersecting each other at various angles, figures sometimes with great complexity. His explanation of these, obtained invariably from the followers of Kusta-ben-Luki, is founded upon a single fundamental thought. The mind, whether expressed in history or in the individual life, has a precise movement, which can be quickened or slackened but cannot be fundamentally altered, and this movement can be expressed by a mathematical form. A plant or an animal has an order of development peculiar to it, a bamboo will not develop evenly like a willow nor a willow from joint to joint, and both have branches, that lessen and grow more light as they rise, and no characteristic of the soil can alter these things. A poor soil may indeed check or stop the movement and rich prolong and quicken it. Mendel has shown that his sweet-peas bred long and short, white and pink varieties in certain mathematical proportions, suggesting a mathematical law governing the transmission of parental characteristics. To the Judwalis, as interpreted by Michael Robartes, all living minds have likewise a fundamental mathematical movement, however adapted in plant, or animal, or man to particular circumstance; and when you have found this movement and calculated its relations, you can foretell the entire future of that mind. A supreme religious act of their faith is to fix the attention on the mathematical form of this movement until the whole past and future of humanity, or of an individual man, shall be present to the intellect as if it were accomplished in a single moment. The intensity of the Beatific Vision when it comes depends, upon the intensity of this realisation. It is possible in this way, seeing that death itself is marked upon the mathematical figure, which passes beyond it, to follow the soul into the highest heaven and the deepest hell. This doctrine is, they contend, not fatalistic because the mathematical figure is an expression of the mind's desire and the more rapid the development of the figure the greater the freedom of the soul. The figure while the soul is in the body, or suffering from the consequences of that life, is usually drawn as a double cone, the narrow end of each cone being in the centre of the broad end of the other.

It has its origin from a straight line which represents, now time, now emotion, now subjective life, and a plane at right angles to this line which represents, now space, now intellect, now objective life; while it is marked out by two gyres which represent the conflict, as it were, of plane and line, by two movements, which circle about a centre because a movement outward on the plane is checked and in turn checks a movement onward upon the line; & the circling is always narrowing or spreading, because one movement or other is always the stronger. In other words, the human soul is always moving outward into the objective world or inward into itself; & this movement is double because the human soul would not be conscious were it not suspended between contraries, the greater the contrast the more intense the consciousness. The man, in whom the movement inward is stronger than the movement outward, the man who sees all reflected within himself, the subjective man, reaches the narrow end of a gyre at death, for death is always, they contend, even when it seems the result of accident, preceded by an intensification of the subjective life; and has a moment of revelation immediately after death, a revelation which they describe as his being carried into the presence of all his dead kindred, a moment whose objectivity is exactly equal to the subjectivity of death. The objective man on the other hand, whose gyre moves outward, receives at this moment the revelation, not of himself seen from within, for that is impossible to objective man, but of himself as if he were somebody else. This figure is true also of history, for the end of an age, which always receives the revelation of the character of the next age, is represented by the coming of one gyre to its place of greatest expansion and of the other to that of its greatest contraction. At the present moment the life gyre is sweeping outward, unlike that before the birth of Christ which was narrowing, and has almost reached its greatest expansion. The revelation which approaches will however take its character from the contrary movement of the interior gyre. All our scientific, democratic, fact-accumulating, heterogeneous civilization belongs to the outward gyre and prepares not the continuance of itself but the revelation as in a lightning flash, though in a flash that will strike only in one place, and will for a time be constantly repeated, of the civilization that must slowly take its place. This is too simple a statement, for much detail is possible. There are certain points of stress on outer and inner gyre, a division of each, now into ten, now into twenty-eight, stages or phases. However in the exposition of this detail so far as it affects their future, Robartes had little help from the Judwalis either because they cannot grasp the events outside their experience, or because certain studies seem to them unlucky. '"For a time the power" they have said to me,' (writes Robartes) '"will be with us, who are as like one another as the grains of sand, but when the revelation comes it will not come to the poor but to the great and learned and establish again for two thousand years prince & vizier. Why should we resist? Have not our wise men have marked it upon the sand, and it is because of these marks, made generation after generation by the old for the young, that we are named Judwalis."'
Their name means makers of measures, or as we would say, of diagrams.

Variorum Edition of the Poems, 823-25. It is given in full in Richard Finneran, ed., W. B. Yeats: The Poems (2nd ed., 1997), 658-60, and (without the diagram) in A. N. Jeffares, W. B. Yeats: Poet and Man (1949), 197-98, (3rd ed. [1996], 175-77), though with variations of punctuation and sometimes wording.



The essay "'Everywhere that antinomy of the One and the Many': The Foundations of A Vision," by Neil Mann in the collection W. B. Yeats's "A Vision": Explications and Contexts, edited by Neil Mann, Matthew Gibson, and Claire Nally (Clemson University, 2012), provides useful further exploration of this subject.
This title is available for free download from Clemson University Digital Press.


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