Hyperspherical Polarity

The term pseudosphere is used in science and geometry to refer to a spherical array of an infinite number of vectors, each equal in length.  A hyperspherical polarity is simply a pseudosphere in a higher dimension (like a four-dimensional pseudosphere) whose vectors are infinite, representing a pure polarity -- a polarity between a singularity and a higher-dimensional infinity. So, the Hyperspherical Polarity refers to the polarity between the Universal Singularity and the Infinite Void. The "space" around the Universal Singularity represents pure nothingness where the concepts of space and time as we know them are meaningless. (Keep in mind that even the empty space in our physical Universe is much more than nothingness.)

Imagine, as far as it is imaginable, the state of the Universe at the Planck time of the Big Bang (a mere 10^-44 second after the Universal Singularity at t=0), where all physical forces of the Universe are still unified. Although this point in spacetime history is associated with an extremely tiny size, we can also relate the present hypersurface of our still expanding Universe to a hypersphere, which we tend to image as being a good deal larger. As far as the hyperspherical polarity itself is concerned, any notion of size or spatial extension is completely meaningless.

The Singularity of the Big Bang is not localized in spacetime -- space and time did not exist at t=0, and we cannot point to the location of the Big Bang in space (except in a "pseudo" sort of way by pointing in every direction at once into the blackness of infinity all around us). In the same way, the Hyperspherical Polarity is a purely ethereal dynamic condition that cannot be localized in spacetime, and yet is the source of our entire physical Universe of experience, from the Big Bang to the present, no matter where or when we happen to be.

It is important to realize that what we are visualizing is a single state of polarity which is spherical in nature. Rather than being composed of an infinite number of rays as such, it is more like a single polarized spherical condition with an infinite radius -- a pure homogeneousness, a single reality representing all possible realities superimposed.  The Hyperspherical Polarity is an undifferentiated and timeless projection.

An equatorial ring-aspect sliced from a four-dimensional sphere would actually be a spherical plane in three-dimensional space, in exactly the same way that a ring sliced from your light-cone is a spherical plane surrounding you in space. Your consciousness is represented as the singularity in the center of the three-dimensional spherical plane, which also happens to be the singularity at the tip of the light-cone in the higher-dimensional Minkowski model, which also happens to be a singularity on the universal hypersurface of the present.

Although a four-dimensional hypersphere is beyond a precise representation in our three-dimensional space and is essentially transcendental to our experience, we can still expand the geometric concept even further than that.  Just as a three-dimensional sphere is a ring on a four-dimensional sphere, that four-dimensional sphere could just as easily be a ring on a five-dimensional sphere, which could be a ring on a six-dimensional sphere, as so on, ad infinitum, an infinite number of higher dimensions beyond the hypersphere itself. Also, note that a ring-aspect is actually a circular array of an infinite number of rays by itself, and that there are an infinite number of possible ring-aspects on a single hypersphere, just as there are an infinite number of rays, and that each ring-aspect has an associated ray perpendicular to the plane of the ring.