From each further dimension all antecedent dimensions can be perceived as a whole; for example, cubic space or volume contains within itself length and breadth (i.e., plane surface) and height. Does it not follow that we must necessarily be seeing volume from a further, a fourth, direction of measurement, and consequently, that in order to perceive that, we would need to observe from a fifth?

So we observe the universe of phenomena, which appears to us in three directions of measurement - length, width and height - from a fourth direction, which might be what we know as duration but whose geometrical character we may only be able to perceive when we develop the ability to observe from a further direction at right-angles to those with which we are already familiar.

Phenomenal seeing, then, is normally in three dimensions observed from a fourth. That is the perceiving of appearance as volume. It is likely, however, that some sentient beings only perceive in two dimensions - length and breadth, or plane surfaces, horizontally or vertically - and that the third, volume, is an inference of which they are not conscious, although it is from that that they are looking

If phenomenality may be equated with tri-dimensional perception, then may we not assume that the essential characteristic of noumenality is perception from a further direction? Should that be so, then - geometrically regarded - what we term 'Awakening' is waking up to a further field of vision, that what we term 'Liberation' is freedom from the limitation of the cubic vision within which we have been confined, and 'Enlightenment' is the sudden brightness of a further 'universe' encompassing the three in the limited darkness of which we have been groping; i.e., that these are three terms for the displacement of the subject to a centre from which he can perceive objects in a further, richer, and more complete perspective.

If this should be so, then those who are 'awakened', perceiving a further dimension - that one from which we normally observe and which therefore is ours - are themselves perceiving from a still further direction, from a fifth. If, then, there were any entity to perceive the 'awakened', such entity would perceive the fifth dimension from a centre in the sixth.

Here metaphysics may intervene in order to point out the illusory futility of the purely theoretical notion of a perpetual regression. There could be no entity, there is only a perceiv-ing anyhow, and the whole process is phenomenal interpretation of noumenality. This, then, is within the illusory science of phenomenality, and may only enable us to understand the apparent mechanism whereby a phenomenal object can come to know noumenality.

We know - from the words of the Masters, unless from our own experience - that 'Awakening' is accompanied by the immediate, if not simultaneous, abolition of all phenomenal 'problems'. It is like knocking out the bottom of a barrel, by which all the confused, and so 'impure', contents of our phenomenal mind (phenomenal aspect or reflection of Mind) vanish. Instead of solving problems one by one, like striking off the heads of a Hydra, which grow again, all disappear simultaneously and forever (as an effect), like stabbing the Hydra herself in the heart.

But is not this the exact counterpart of what we have sought to establish geometrically? We have suggested that a displacement of the centre of the supposed entity (pseudo-centre) to a further, more profound centre will reveal a further dimension wherefrom all inferior dimensions are perceived in a greater perspective. Assuming that this is the ultimate perspective, or even if it is not, even if there be perspectives ad infinitum, is this not precisely a description of the mechanism of what the term 'Awakening' connotes?