The Three Dimensions of Space
Now, about those “three dimensions of Space,” how exactly do we experience them in concrete and tangible ways. What features of Space do we experience immediately, just as the senses present them to us?
Well, in the first place we experience ourselves as existing in an emptiness of space. Space, in the first place, is an expanse which encloses us. In a room we are in a space-enclosure. Under the night-sky we are enclosed within the expanse of universal space, extending to galactic regions and beyond.
Fine, but all this is so obvious it seems positively and patently dumb to point it out. However, it is not dumb, for it becomes enlightening when we realize that this is the only kind of Space we normally experience — or believe ourselves to experience. To put it another way, we are educated to think that expansive enclosing-space is all of Space. And we are taught to think of height, breadth and depth as the ‘three dimensions’ of this enclosing-space in which we are spatially situated. But it is more accurate to describe height, breadth and depth as the three inertial frames of enclosing-space. They belong to this inertial, static, empty space and to it exclusively. They are not dimensions at all, but merely the defining-lines of enclosing-space.
In short, height, depth, and breadth are not dimensions of Space, capital S. They are merely the inertial frames of one kind of spatial continuum, enclosing space. S-1: space enclosing, open space.
So much for enclosing space, but is this really the only kind of space we experience? Pat experience often presents us with occasions to refer to surface space, as when we consider where to find a place to park. Thus there is a kind of space which occupies the surface of things, or actually constitutes the surface of things. Since we are educated to think of enclosing-space as all the space there is, we find it a little odd to consider surface-space as having its own unique character. But for a moment let’s allow that it does. S-2: surface space, continuity of surface.
Is there yet again any other kind of space, distinct form enclosing-space and surface-space, as we have dubbed them? Well, there is the space occupied by objects, such as the stone sculpture on the table. Material objects differ in density and hardness, but they are all alike in that they “take up space” and in D-4 everyone knows that no two things can occupy the same space at the same time. This tells us that the space occupied by materiality is another kind, unique unto itself. We can call the space-enclosed, by contrast to space-enclosing. This is simple and neat terminology which, by the way, preserves the design-feature of opposition (or polarity) between Space (enclosing-space) and Materiality (space-enclosed). S-3: space enclosed, the space bounded by the surfaces of physical objects.
Are these kinds of space truly distinct, or are we just making all this up? Indeed they are different as we can see by letting precise grammar tell us how we are situated in quite distinct ways to each of them:
We experience ourselves as located physically IN enclosing-space, ON surface-space and OUTSIDE space-enclosed.
With the exception of the physical body (a most notable exception, grant you) we can never experience ourselves inside materiality. The realm of materiality remains closed to us, the opposite of Space which is open in its main aspect of enclosing-space. Enclosed-space is always bounded by surfaces, actually by surface-space. An apple is a good example of enclosed-space. What happens if we “cut open” the apple? We do not get inside enclosed-space, we merely change its surface boundaries. It is quite impossible ever to get inside enclosed-space, unless you are already there — and we are already there only in one instance, that of the physical body itself.
It takes a little quiet gazing to appreciate how the space enclosed by solid objects constitutes a unique kind of space in its own right. It is a space within a space, for the object by which space-enclosed is identified is itself situated in enclosing-space. Surface-space, on the other hand, is not a space within a space but a space-in-between. It is always and ever-in-between enclosing space and space-enclosed. It is the space of infinite and various contour. Human skin is in the realm of surface space, while the body-organs are in space-enclosed and body itself is in enclosing-space.
Odd or even silly as these descriptions seem, they form the basis of a completely new orientation to the world around us, from which an authentic human physics can be created. Conceptually, we are hide-bound to think of space as empty, to see enclosing-space as the only space. But in D-4 what we really find is Triple Space consisting of opened, surface and bounded volume. This is the tactile, perceptual, organic reality of Space, but we are not educated to experience it as such.
Returning to the conventional spatial frames: depth, breadth, and height. What is S=1 enclosing-space as we know it naturally and normally but depth-alone? It is sheer and complete, static and vacuous depth. This we measure by the inertial frames of up-down, right-left and back-front, but these are merely defining-lines, not inherent properties of this depth-space.
What about S-2 surface-space? If it be accepted that enclosing-space comprises sheer depth, or depth-alone, how about regarding surface-space as breadth-alone: what is surface-space but sheer breadth, a perfectly flat spreading-out of space? In a precise experience of surface-space, you come to realize how it has no thickness, no depth. Place your hand on the table. With your fingers, you touch a surface of no thickness. Beneath your fingers, if any depth is present, it belongs to space-enclosed. Between the volume occupied by the solid-wood of the table and the emptiness of enclosing-space in which you are situated, there is only the membrane of surface-space. Breadth-alone. Palpable to your senses, right under your fingers.
There remains space-enclosed, located wherever materiality appears in the S-T continuum. It can be called the space of materiality. It is not open, like enclosing-space, but it is always closed, bounded. As the only remaining dimension of Triple Space height-alone, one might be forgiven for inferring that space enclosed correlates by semblance to height-alone. While the other correlations are readily seen, this one is difficult. It clues us to the mysterious nature of material mass, which is a great enigma even to modern science. For instance, it was recently discovered that the galaxies may have masses extending far beyond their visible limits — called galactic coronas. If this proves to be so, it will be necessary to rethink and recalculate the entire dimensions of the universe from scratch…
The enigma of material mass is hinted in the odd notion of “height alone.” What can this mean? In height we have the implication of hierarchy, of one thing situated above another in an all-inclusive system. Hierarchy implies degrees of evolution, degrees of difference in evolutionary events. Now in the case of enclosing-space, which is all-depth, there is no difference of this kind. It is quite the same in all directions, and quite neutral. In the case of surface-space, this is an infinitely contoured and configurated plane of spatial extension, but it too is neutral to difference: for instance, both a glass and the water in the glass present surfaces and as surfaces they are all-breadth. If there is any difference in texture, this is due to the materiality bounded by the surface-space, not to the nature of the surface-space itself. Thus, materiality exhibits itself as embodying a hierarchial composition, “height-alone”. In the 4-D continuum this is evident in the masses of various densities we find all around us, and in which we ourselves, as bodies, are included.
The entire gestalt sketched here can be summarized as follows:
TRIPLE SPACE : Cosmic Womb S-T Continuum, D-4
Depth-alone ——> S1, enclosing space = all depth, static, open, vacant, ALL AROUND
Breadth-alone —-> S2, surface-space = all-breadth, expanse of a continual plane, no thickness, IN BETWEEN “contoured”
Height-alone —–> S3, space-enclosed = all-height, variant mass, ALL WITHIN, “closed,” Hermetically sealed
So Triple Space petrifies into S1, congeals into S2, and condenses into S3. These are, accurately speaking, the three Dimensions of Space in D-4 which can be experientially verified and investigated endlessly with the human mind and senses.
This completes the topography of D-4, for the moment. Although we have had to consider some rather far-out notions regarding the unknowns of cosmic evolution, everything we have considered has been referred back to the givens of patent and palpable experience, direct sensation. In taking this approach we can restore our awareness to a more accurate, organic knowledge of the world.
It is not difficult to see Triple Space as vacant, contoured and closed, but it can be difficult to break the unconscious habit of seeing it that way. Once we begin to see it that way, the shift we feel is truly revolutionary, as well as revelatory. The world becomes interesting in a new way when we can see and feel how surface-space and space-enclosed are true dimensions in their own right. Through this new orientation new sensations can arise, as when we really get the feel of surface=space as a realm of no thickness. If these sensations are carefully cultivated, the world can take on a floating feeling.
We develop a human physics from what is observable, and in the very process of doing so, we change the way we experience the observable. This is the first faint hint of alchemical transmutation, unfolding within the realm of the senses themselves.