Experience of the subtle realms: Contents
10. Manifold spaces
wish now to talk about space in geometrical terms to complement the more
experiential account given in preceding chapters.
have defined matrix space as the space of the real or Euclidean shape of
physical things; the space out of which the perspectives of ordinary perception
emerge. It is the space of the true cube or cylinder or any other solid, as
distinct from perspectival space
which distorts the true shape of things. And
I have proposed that matrix space can be directly apprehended by psi awareness;
and that this apprehenesion is restricted, in ordinary consciousness, to
correcting the distortions of immediate physical perception - with respect to
shape, size and relative position. With
further training, you can extend your psi awareness of matrix space beyond the
limits of what is being looked at with the eyes - as I proposed in section 13 of
geometry of Euclid seems to define accurately enough the spatial matrix of our
immediate physical perception of the world, but
it would be wrong to identify matrix space exclusively with Euclidean
was centuries before human beings realised the distinction between mathematical
space and actual space. In 300 BC,
Euclid martialled the results of the Greek mathematicians of the classical
period into his celebrated Elements. And for over 2000 years - until the discovery of
non-Euclidean geometry by Bolyai, Gauss and Lobachevsky in the 1820s - it was
assumed that to talk about the properties of space as such, was to talk in terms
of Euclidean geometry. Geometry meant the geometry of physical space, and that
geometry was Euclid's. It was taken as self-evident that the consistency and
elegance of Euclid's system represented the final and absolute word about space.
emergence of non-Euclidean geometry was an epoch-making event in the history of
thought. A simple and liberating inspiration reached three men almost simultaneously,
but quite separately. And it marked
the turning point from an era of mental absolutism to an era of mental
relativity. Euclid's parallel postulate - that there can only be one line
parallel to a given line through a point external to it - had always seemed less
intuitively secure than his other postulates. Bolyai, Gauss and Lobachevsky
decided to give it special status no longer.
and their followers showed that by replacing it by one or other of its two contradictory
forms - there can be no line parallel to a given line through a point external
to it, and there can be many lines parallel to a given line through a point
external to it - perfectly consistent geometries could be built up with many
theorems that are quite inconsistent with the equivalent Euclidean theorems.
And it was later found that both the Euclidean and the two non-Euclidean
geometries were relative to a specialised treatment of certain aspects of the
more general space of projective geometry.
mathematical notions of certainty and absolute truth were shaken.
The relativity of postulate systems was asserted: the truth of Euclidean
geometry is not absolutely but only relatively true. The realisation of this by
scientists, mathematicians and philosophers has had an immense influence on
the mental climate of our age.
and non-Euclidean geometries deal with metric properties. They state systematically
the relations between sizes of angles, lengths of lines, areas, as these relations
appear in different figures.
geometry, founded by Desargues in 1639, is concerned solely with the non-metric
properties of figures, when these figures undergo projection and section.
Project the same circle from many different angles upon a screen, then
projective geometry will ask what properties are common to all these different
projections. The common properties
will not be metric ones, for there will be no constancy of width, of area, of
subtended angles, and so on.
geometry emerged into a fully developed science during its revival in the
nineteenth century. This was because mathematicians had greatly increased their
ability to handle the notion of geometrical infinity.
The infinite is taken actively into account in the shaping of projective
think of an archetypal projective space, free of any specific metric properties,
in which our only concern is with those properties of figures that are invariant
under any number of projective transformations.
We are not concerned with any exact measurement relations as such, but
only with ratios and relative proportions.
This is a mobile, metamorphic kind of space.
deepest law of this projective space is the polarity of point and plane, the
locus of no extension and the locus of infinite extension.
And out of the universal forms of projective space, different geometric
spaces with different metric properties can be developed and differentiated.
It all depends on what element in non-metric, projective space we select
and fix or freeze into a unique entity - a given absolute - which then determines
a sub-space with certain definite metric properties.
metric geometry, in fact, is simply projective geometry with special relation to
an absolute conic. Each arises from
the different geometric character we ascribe to the absolute or infinite
we take as our absolute in projective space an infinite plane bearing an
imaginary circle, then this invariant form will determine the metric
properties of Euclidean (parabolic) space.
This, of course, is the space we identify with the space of everyday objects.
And in this space there can only be one line parallel to a given line
through a point external to it, the angles of a triangle always add up to 180
degrees, and so on.
we make our invariant absolute an imaginary quadric, this governs and determines
the metric properties of the non-Euclidean space known as Riemannian (elliptic)
space. In this space there are no
other lines parallel to a given line through a point external to it; and the
angles of a triangle always add up to more than 180 degrees.
concrete representation of this kind of space is provided by the surface of a
sphere. On a sphere, a straight
line - defined as the shortest distance between two points - becomes a 'great
circle', which is the shortest distance between two points on a spherical
surface. On a sphere there are no parallel lines of the Euclidean sort, for each
great circle intersects every other at two points.
And when any three great circles intersect to form a triangle,
the sum of its angles is always greater than 180 degrees.
if we make invariant in projective space a real non-ruled quadric, this determines
the metric properties of the non-Euclidean space known as Lobachevskian
(hyperbolic) space. Here there is more than one line parallel to a given line
through a point external to it; and the angles of a triangle always add up to
less than 180 degrees. A concrete
representation of this kind of geometric space is provided by the concave
surface of a pseudosphere.
everyday objects we ascribe the geometrical properties of Euclidean space,
because this is the simplest of logically possible forms, and seems to make
sense of our immediate perceptual experience.
But the logical simplicity of Euclid fails to do justice to the inherent
complexity of the physical universe at large.
attempts to conceptualise the space which astronomical telescopes probe, as in
the general theory of relativity, led to the view that a non-Euclidean
geometrical space of the Riemannian type might have greater relevance. What
type of geometrical representation - Euclidean, non-Euclidean or
pseudo-Euclidean - is best suited to symbolise the wider view of the physical
universe is still under discussion.
significance of Einstein's idea of applying a non-Euclidean geometry to the universe
at large was that it made fully explicit the relativity of spatial concepts.
It broke up the idea of one absolute, universal and homogeneous space
exhibiting everywhere Euclidean properties.
It suggested, rather, that the geometrical properties of space are
relative to the standpoint of the observer, his assumptions, the range of his
vision, and the purposes he has in mind. Different spaces can have different
properties as a function of different intentions and beliefs.
Or to put it another way, the properties of any space are inseparable
from the structures of the consciousness that embraces it.
account starts to echo the doctrine of powers view - that different spaces are
different forms of the archetypal creative energy of universal consciousness.
said in the introduction to this chapter that it would be wrong to identify
matrix space exclusively with Euclidean space.
I can now say why. When my
awareness embraces the matrix space of this room, say, by being simultaneously
in all its eight corners, the structure of my awareness is informed by the logic
of Euclidean metric geometry.
as we have seen in the previous section, this Euclidean matrix space is itself a
limited and limiting 'perspective' of consciousness on a subtler, deeper and
richer matrix space: the non-metric, mobile, metamorphic, projective space of
ratios and relative proportions. And
here the structure of my awareness is informed by the logical polarity of point
see now if we can relate this geometrical account of space to the experiential
account of the expansion of consciousness given in earlier chapters,
especially the section 13 of Chapter 7.
can liberate my awareness spatially in two distinct steps.
I can expand it from limited perspectives in physical space to a more
extensive awareness in Euclidean space - of the 'fixed' subtle matrix of
physical forms. And then I can
expand it beyond that to the archetypal, projective matrix of the Euclidean
matrix - to the subtler, mobile subtle matrix
of the fixed subtle matrix of physical forms.
clairvoyant exploration of the Euclidean matrix of, say, a room already seems to
be done from the projective matrix, with many viewpoints from the lines of
interacting planes. So we view the
first step from the standpoint of the second.
we have to be cautious about this geometricising of experience.
We must be careful not to identify experiential space with geometrical
space. Geometrical knowledge develops and changes.
It can inform and illuminate our experience of different kinds of space.
Yet we may have spatial experiences that transcend the limits of geometrical
advance. And we can have misfits:
we may apply the wrong kind of geometry to certain kinds of spatial experience.
the case of four dimensional space, imagination and analytic thought seem on
their first encounter to be incompatible. It
is easy to define a space of four dimensions in terms of coordinate or
analytical geometry. It has four
independent directions or dimensions at right angles to each other; and four
coordinates will be needed to identify spatial entities in it.
But it is difficult to imagine or visualise it.
line, the surface and the volume are respectively spaces of one, two and three
dimensions. We see at once that
two points bound one line, four lines bound one square, six squares bound one
cube. But if we continue this
sequence and say that eight cubes bound one four-dimensional figure which will
have a symmetrical eight-sided aspect to four independent directions - then the
imagination gives out. Any attempt
to visualise such a figure flounders in chaotic incoherence.
there is another, more experiential, approach with which the imagination can do
some business. We know that
from our three-dimensional point of view we can look inside, grasp fully the
total form of, a two-dimensional figure such as a circle or square. If our line of vision is at right angles to the central point
of any such plane figure, then for all practical purposes we see it as it really
is: we see its true Euclidean shape, inside and out, all at once. But a
two-dimensional being could only get a limited, partial and distorted view of a
bit of the inside, or a bit of the outside.
analogy, we can imagine that an intelligence in four-dimensional space can look
inside, grasp fully the total form of, any three-dimensional volume such as a
cube or a sphere. Whereas our three-dimensional perspective of a cube is only a
limited and distorted view of part of the outside of it, every part of its
contents could be seen from a four-dimensional standpoint.
The whole thing could be seen, inside and out, as it really is, all at
once. But this is what is involved in entering matrix space, as described in
section 13, Chapter 7; and in entering fully one's own matrix body as described
in section 2, Chapter 9: embracing a three-dimensional volume fully, inside
and out, all parts being simultaneously entertained in awareness.
we can say that four-dimensional space is a non-perspectival awareness, all at
once, of the total spatial gesture of a three-dimensional figure.
On this account, the fourth dimension of space is a certain holistic
state of awareness. In the fourth dimension, space and consciousness are
fourth dimension - a direction at right angles to the three directions of
physical space - is an inclusive and encompassing way of being aware of these
three directions: it is a spatial
form of consciousness. Now the
account of four-dimensional space given by analytical geometry is such that an
equation with four variables could represesent a three-dimensional stretch in a
space of four dimensions. In other words, equations with four variables give an
algebraic account of consciousness
of matrix space. This launches us
into the mathematics of altered states of consciousness.
But I am not competent to proceed further.
is one basic question I have not so far considered.
What is the relation between this holistic four-dimensional grasp, all at
once, of a three-dimensional shape and the multiple clairvoyant views of such a
shape from peripheral lines on the clairvoyant plane of vision?
is equivalent, at the physical level, to the difference between feeling one's
body shape from within by sensation from its tissues, and looking at its shape
with one's eyes. In my physical body I have these two complementary modes of
spatial experience: feeling or sensing my place in space, and seeing where I am.
And mediating between them is moving through space.
I can be in space, see in space and move in space.
same modes of spatial experience seem to apply at the subtle level, but each in
a much more emancipated form. For
subtle awareness, it seems that I can be
in space, in the holistic four-dimensional all-at-once sense, not just here
where my subtle body is, but there where some other entity is.
And I can see in subtle space
not just from one central viewpoint, but also from many peripheral viewpoints.
And may subtle body movement in subtle space can at times seem as rapid
as thought itself, and can negotiate different spaces that express different
forms of consciousness and energy.
you have a four dimensional grasp of a three dimensional figure. This means,
according to section 4 just above, that your awareness grasps the true shape of
the figure all at once, inside and out, as it really is.
What does it mean if your awareness then expands into a further and
fifth dimension of space? What is
it to have a five dimensional grasp of a four dimensional figure? Or, to put
it another way, what is it to know all-at-once your knowing all-at-once of a
three dimensional figure?
thing it could mean is that you shift into a space within
four-dimensional space. The word
'within' here is used by analogy. I
don't mean 'within' in the sense of within the house or within the box - that is
ordinary three-dimensional talk. It
is more akin to what I mean when I say that the gaze is within the eyes, a
person is within his body, or life is within the leaf.
But is also a bit more rigorous than these examples indicate.
I go out of my body into the other world (not just having an ectosomatic view of
this world) I am in a quite distinct domain which is not located 'in' physical
space, in the ordinary sense of this word 'in'.
It is not in it like an orange is in it, or the moon is in it.
But the other world domain I visit clearly does have some kind of spatial
relationship to this world: for going out of the body to that domain is itself
a spatial transition.
is, I suppose, logically possible for there to be two distinct spaces that are
not themselves spatially related. Indeed,
one contemporary theologian, John Hick, has conceived the after-life in this
way: as a kind of instantaneous resurrection at the moment of death in a space
of which it makes no sense to ask where it is in relation to the space of this
life. But my experience is
different, not I hasten to add of dying, but of going from this world to the
other: as I say, this 'going' is a spatial business.
seems to me that the other world is within, in the sense of interpenetrating,
this world: an interpenetration that somehow supports this world and provides
the framework or matrix for it; and also an interpenetration that in other
respects is quite independent, functionally, of this world - in the sense that
many things can go on in the other world without having any obvious effect on
what is going on in this world.
also means that you can in some sense say where
some independent other-world domain is in relation to the
space of this universe. This 'where' may be fixed or mobile. So I may say
there is a domain of subtle space within
the physical area between the earth and its moon: this would be a fixed kind of
co-location of the two worlds.
Or I may say that there are domains of inner space that 'move through'
the physical area, say, of the solar system: here the co-location shifts around.
well as other-world domains interpenetrating the space of this universe, they
also, of course, have more inclusive logical or geometrical parameters than
physical space. And the energy
frequencies of events within them are also different: usually, it seems, much
extending this notion of the interpenetration of spaces, we may say that we
enter a six dimensional space when we are conscious in and of a first
other-world domain that interpenetrates a distinct and second other-world
domain, which in turn interpenetrates the all-at-once four dimensional matrix
of the physical realm. Each more
comprehensive space is a matrix of the space it transcends. And just as in the
four dimensional matrix of physical space you can know any three dimensional
volume both within and without all at once; so also in the fifth dimensional
matrix you can know any four dimensional space simultaneously from the 'inside'
and the 'outside'; and so on in the sixth. Figure 10.1 gives simple portrayal of
the hierarchy of spaces, grounded in mahabindu,
the Great Point.
Figure 10.1 The
hierarchy of spaces
hierarchy of spaces is, on the doctrine of powers view, also a hierarchy of the
structures and energies of universal consciousness. Each higher dimension
comprehends all the other dimensions within it, is more intense in its degree of
consciousness, and manifests higher frequencies of energies.
we get a conjectural model of a
universe of manifold spaces: there is the first subtle realm which transcends
yet interpenetrates the second subtle realm, which in turn transcends yet
interpenetrates the four-dimensional subtle matrix of the physical world.
And all this structured diversification is of consciousness itself, of
which my consciousness and your consciousness are
illusorily restricted parts. We
can break out of the illusion, and get going on the wider reaches of spatial
speaking, the first and second subtle realms mentioned here correspond to the higher
subtle level, and the interaction between the second subtle realm and the
subtle matrix to thelower subtle level,
of Grof's cartography of transpersonal states
(Grof, 1988: 39).
grasp the first three dimensions of space in one go. We don't first learn to
master one dimension, the line, then two dimensions, the plane, then three
dimensions, the solid and the enclosed or open space. We take them on board in a
cluster. They come in our ordinary consciousness together.
believe it is essentially the same with the second three dimensions of space,
the fourth, fifth and sixth. When I enter my levity line and thence into
all-at-once four dimensional awareness of the subtle matrix of my physical
body, at the same time I have five dimensional awareness of the way in which my
subtle body proper interpenetrates my subtle matrix and thence my physical body.
Also at the same time I have at least incipient six dimensional
awareness of subtle domains within and beyond my subtle body frequencies:
because I can choose to open myself up to these higher frequencies and make my
six dimensional awareness explicit.
is nothing particularly mysterious, problematic or esoteric about this
experiential cluster of the fourth, fifth and sixth spatial dimensions. It's
just a matter of doing the exercises that open up your awareness at the matrix
level, and noticing how the cluster comes.
At any rate, it is not really any more mysterious than how the first
three dimensions of line, plane and solid all come together.
first cluster initiates us into spatial extension
- the without of space. The second
cluster initiates us into spatial intension
- the within of space. I give the
word 'intension' here a new technical meaning. In relation to any domain of
subtle space, it refers to three things: the degree or intensity of
consciousness of which that space is the form; the degree or frequency of its
energies; and the degree to which it includes, by virtue of its
multi-dimensional structure, other spaces which it interpenetrates and yet
birth launches us into the first cluster, physical death into the second cluster
- when our consciousness starts to function explicitly in the subtle body.
But we need not wait to be born into the subtle body at death.
We can start to become our own ally now, awakening ourselves to explicit
subtle action in the midst of earthly life.
Experience of the subtle realms: