Geometry
The Foundation
The Double Gyres
The Cones
The Diamond and the Hourglass
The Phases of the Moon
The Wheel
The Faculties
The Principles
The Foundation
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.)
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
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.
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.
Classically, this is the kind of
interrelation depicted in the YinYang 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 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 Cones
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.
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.
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.
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).
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], 17577), 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 here or here from Clemson University Press (click here if seems the
link may have changed). It is also accessible online via Liverpool Scholarhip Online and University Press
Scholarship Online (simplest to search on "Yeats" and "Vision"; direct link functional April 2016), though this
is by subscription or through a library.
Abbreviations