Living in our 4-D world.
When we look around us, we see a 2-D projection of our
visual field, through circuits that criss-cross our brains, onto our visual
cortex, which provides us with the cyclorama in which we behave. Our vision of the world is always like a flat
picture, but one with depth because of our binary vision.
When we close our eyes, we are not limited to seeing (with
our mind’s eye) what is in front of
us, but we can, in our minds, see all around us.
When we look at a flat picture, we are looking at it from
outside of it. If our point of view was
in the picture, we would only see the immediate surrounding pixels, because we
would be within a pixel, using computer jargon.
This concept has been well described in literature.
When we imagine the world around us while not observing it,
we may imagine ourselves immersed in it.
The new immersive, ‘virtual’, binocular perceptual inventions are
based on this principle. When we put on
the headset, we are presented with a construction of what we would see in a picture
of the direction of view, that gives the illusion of existing within the
imaginary reality. It is constructed
mathematically using rays and vectors and whatever based on the idea that the
observer is within the scene.
We are deemed to exist within a single pixel, or perhaps a
pair of close pixels, so we are similarly only able to see the surrounding
pixels. However, because most (where the
air is) are transparent, we can see a lot of structure all around.
Some people are probably better at this than others. It is part of our psycho-physiological
development that we learn to navigate the 3-D world of which our bodies are
part. How well we conceptualise
ourselves as existing within spatial dimensions must vary. Reading literature is recommended to develop this.
It is also possible to imagine the world around oneself
without being inside it, but as an outside observer of the space one
inhabits. One would see one’s physical body from all sides as
existing within the world, but one wold not be seeing the world from within
that body. It would be an ‘out of body experience’.
Many people have reported such experiences, for example swimmers who see
themselves from above while they swim up and down in the pool below. The ‘near
death experience’ includes this sort of
perception.
It must be possible for our brains to construct this sort of
perception if it occurs spontaneously for some people in specific, usually
extreme circumstances. Then, it may be
possible to develop the ability to see the world that way at will. Perhaps some Religious, meditative and concentration
techniques induce this perception giving rise to the belief that we each have a
‘soul’ that
is somehow outside or beyond the physical universe. (There are other concepts of ‘soul’ that
are not negated by this argument.)
To recap: We look at a picture from outside the frame, in a
totally different dimension. Even a 3-D
picture is viewed from outside the picture and in front of it. Our perception of the world is of a circular
or spherical projection all around us of a picture of what our eyes perceive
but a picture that has depth. We as
observers are outside the picture.
Once one has perfected the ability to perceive one’s surrounding environment from outside
it, then one can start to explore the geometry of this extra-dimensional
reality. Our almost universal, cubical Architecture
lends itself to this sort of exploration.
If we see ourselves in a room with a door in each wall, as well as a
door in the ceiling and the floor, we can easily imagine ourselves going
through that door into the room beyond. Each
room has six doors to the six surrounding rooms.
Because it is all in the mind, we are not bound to imagine
it as the animators present it, with the rooms forming an endless grid, with
door on opposite sides opening onto room after room in every direction. If we return to our 2-D heuristic simplification,
we can imagine ourselves in the picture, which we now know is not continuous in
every direction but is square. We can
move around within the flat surface and when we reach an edge, we can find a
door to the next square.
Squares can repeat endlessly on a flat surface, or they can
be wrapped round the sides of a cube.
Six squares form a cube. If we
were in one face, we could reach an edge, and stay on the cube by going through
the door at the same time as shifting direction into another dimension, so that
we are still in a flat, 2-D space, but within a plane at right angles to where
we were.
Returning to 3-D, when we open a door at one side of our
room, we can also imagine ourselves changing into another dimension, so that
our room is somehow at right angles to the room we left, even though each
appears to us, looking down on it, as a normal square room. Because we have changed direction while we
exit/enter a door, the rooms do not extend for ever, but wrap around a tesseract,
just as the squares wrap around a cube.
Eight cubes form a tesseract.
It is therefore quite easy to see oneself within the rooms,
one by one that wrap round each other.
It has to be done with eyes closed, because as soon as one looks around
oneself at the real world, the other dimension collapses and we return to our
pseudo-3D perception (2-D with depth) that looks real. When the sense of changing direction when
moving from room to room is perfected, it is possible to dispense with the
walls of the room, and see everyone at once.
This is the equivalent of having not a cube with picture-sides, but a
transparent cube that one can see inside.
Higher dimension mathematics tends to describe shapes like
the tesseract in terms of their surfaces, edges and points instead of
considering the space within. Architects
design the structure, but it is the space within that we inhabit, just as we
look at pictures from outside the surface.
