Assume for a moment that we do indeed live in a universe that consists of 4 spatial dimensions. How can we visualize the 4^th spatial dimension when vision itself is a 3-dimensional system? And how would movement in the 4^th spatial dimension manifest itself in our experience when our vision by nature is limited to 3 spatial dimensions?

Geometrically, the 3 spatial dimensions must be at right angles to each other, and the 4^th spatial dimension must be at right angles to the other 3 spatial coordinates. In my inner vision, this is how I visualize the 4^th spatial dimension in a 3-dimensional coordinate system. First, I make the 3 spatial dimensions: White point in Black space. Point extends and becomes a line, becomes a circle, rotates into a sphere, a sphere filled with mathematical points. Next, inside the sphere is a Point, any point, which is the axis of the 4^th spatial dimension cut in cross-section, a Line seen on end. In 3 dimensions, in the 3-dimensional sphere, the 4^th dimension is a Point and can only be seen as a Point, no matter how the sphere is turned. But in 4 spatial dimensions, the Point is a Line, a line that is cut in cross-section and seen on end (End-On Point). So the 4^th dimension is a Point in a 3-dimensional sphere but is a Line in a 4-dimensional system (axis Line of the 4^th spatial dimension). When the Point moves within the 3 dimensions of the sphere, it becomes a line within the sphere. However, when the Point moves on the inside-outside axis Line of the 4^th spatial dimension, there are two possibilities depending on whether the Point is moving inward or outward relative to the 3 dimensions of the Sphere. When the Point moves outward relative to the Sphere on the inside-outside axis of the 4^th dimension, the Point expands in place into a second sphere inside the first Sphere. When the Point moves inward relative to the Sphere on the inside-outside axis of the 4^th dimension, the sphere within the Sphere contracts to a Point, until the point recedes beyond the power of visual perception within the original 3-dimensional Sphere.

Geometrically, any Point can be viewed as the End-On Point of a cross-section of a Line that is the inside-outside axis of the 4^th spatial dimension, a Line seen on End. Expansion and Contraction in place can be viewed as movement in a 4^th spatial dimension, because the movement of the surface of the sphere is at right angles to the 3 spatial coordinates. However, even if we are willing to accept as a geometrical axiom that Expansion and Contraction are manifestations of the 4^th spatial dimension, this geometrical construct requires a fixed frame of reference in order to represent movement in the 4^th dimension. Because as soon as we add motion and movement to this simple construct, it becomes very difficult to distinguish and differentiate between movement within 3 spatial dimensions versus movement in the 4^th spatial dimension. Yet this is exactly what we are faced with because our Experience of Existence is always filtered down into 3 spatial dimensions through our vision, because vision itself is a 3-dimensional system.

When a Locus of Vision moves through Space on a coordinate, Objects of Vision appear to change in size in proportion to distance. For example, as our vision zooms through space in the Hubble telescope, a pinpoint Star appears to expand in size until it is as large as the Sun. Clearly, this is a function of movement and relative spatial proximity in 3 spatial dimensions. By contrast, within the frame of reference of our simple geometrical construct, if the Locus of Vision and Object of Vision maintain fixed relative positions in space, and the pin-Point expands in place into a Sphere, this would be an actual Expansion, which is movement on the axis of the 4^th spatial dimension. Once we depart from this simple construct, however, and introduce motion and movement into a geometrical formulation that represents the complexity of forms we experience in the “3-dimensional” physical universe, it becomes extremely difficult to differentiate between movement within 3 spatial dimensions versus movement in the 4^th spatial dimension, because movement of an Object of Vision on a coordinate toward or away from the Locus of Vision (movement in 3 spatial dimensions) and Expansion and Contraction of an Object of Vision at fixed distance from the Locus of Vision (movement in the 4^th spatial dimension) appear exactly the same in the blackness of Space.

Motion and Movement make it difficult to see structural detail and analyze structural relationships—hence we take photographs. In order to visualize the 4^th spatial dimension, we need a structural matrix that doesn’t move until we want it to move. And in order to progress from abstract geometry to definitive physical correlation, we need fixed constants as Points of Reference that correspond to actual Points of Magnitude in the Universe.

Words are fragments. Pictures are wholes. Sometimes an image can provide more insight than a broadsheet of words. 

This 4-Dimensional Model of the Universe is a purely structural model because it represents the entire universe in simultaneous time, so motion and movement called Time is removed as a variable, which will make it easier for those accustomed to a space-time mindset to visualize the 4^th spatial dimension of depth that exists in the universe. The outer circumference of the Sphere of Universe depicts the farthest visual reach by science in an outward direction to date, illustrated by the Hubble Space Telescope’s deep-field view of intergalactic space. As a geometrical concept diagram, the Hubble deep-field image serves as a visual aid to represent intergalactic space; however, adjustment in mind must be made to correct for the illusion of relative size that occurs with all visual systems. This intergalactic Sphere of Universe is intended to simultaneously represent all the galaxies in the universe as they actually are at the present time, at their actual size, location and current state-of-existence in space, without any visual magnification or temporal-distance “look back” alteration that results from introducing a visual system into a local region of space. In other words, this schematically represents the universe and galaxies as they are in actual magnitude rather than how they appear from a Locus of Vision in regional space near Planet Earth. 

The outermost surface of this Sphere of Universe corresponds to standard cosmological models of a “closed universe” having closed spatial geometry in which space is positively curved. According to current scientific thinking, only the surface of the cosmological model of a “closed universe” has physical significance because the surface of the sphere corresponds to the 3-spatial dimensions of the physical universe. By contrast, the 4^th spatial dimensional Radius of Universe, which is at right angles to the 3-dimensional surface, has always been considered a mathematical artifice of an unobservable 4^th spatial dimension that doesn’t exist in the real world, but which was needed to diagrammatically represent the solution of equations for curved 3-dimensional space. As a matter of fact, however, not only does this 4^th spatial dimension actually exist in the real world but this 4^th dimension of depth is scientifically observable and measurable and mathematically definable in terms of physical constants that form the fundamental structure of the universe.

The 4-Dimensional Model of Universe above serves as a visual introduction to the concept of the Spectrum of Magnitudes. In this Spectrum of Magnitudes Model, the 4^th dimensional radius of the universe corresponds with the actual physical structure of the universe and the inner spatial dimension that actually exists in the universe. Stars are made of atoms and atoms are made of quarks, and there is a fixed physical inside-outside structural and spatial relationship between these Magnitudes of Mass. Furthermore, these Magnitudes of Mass are physical constants that are mathematically definable as Points of Magnitude. As these Magnitudes of Mass are structurally arranged and spatially aligned inside each other on an inside-outside axis according to invariable physical laws, which results in their respective composite structure and form, the inside-outside alignment of these Magnitudes of Mass physically constitute a 4^th spatial dimension of depth. As all spinning Magnitudes of Mass are Spheres and Points in Space in actual physical existence, by defining these Magnitudes of Mass as mathematical Points of Magnitude it becomes possible to formulate a geometrical model that directly corresponds to the 4-spatial dimensional structure of the physical universe.

The 4-Dimensional Model of Universe above illustrates three different views of the Spectrum of Magnitudes aligned on the inside-outside axis of the 4^th spatial dimension, which corresponds to the 4^th spatial dimensional Radius of Universe. The wedge section in the illustration shows the full depth of the universe from two frames of reference: 1) the 4^th spatial dimensional alignment and inside-outside spatial relationships of all Magnitudes of Mass in the space of the entire Universe (upper half of wedge); 2) the 4^th spatial dimensional alignment and inside-outside spatial relationships of Magnitudes of Mass on a single axis line within a single Star in a single Galaxy (lower half of wedge). In the lower half of the illustration, the Spectrum of Magnitudes is plotted linearly on a single inside-outside axis line of the 4^th spatial dimension, on a spatial coordinate that extends from galaxy to star to hydrogen atom to quark and beyond, assuming there is space inside quarks. For the purpose of illustration (lower half of wedge), two separate views of the spatial interrelationships between the—Star—Atom—Particle—are depicted that show the inside-outside spatial relationship that exists between smaller component Magnitudes of Mass and their respective larger composite Magnitudes of Mass. The star and hydrogen atom and quark are represented as shaded Spheres of Magnitude, sphere within sphere within sphere, to illustrate the inside-outside spatial relationship of these constituent Magnitudes of Mass. The star and hydrogen atom and quark are also represented as Points of Magnitude on the inside-outside axis of the 4^th spatial dimension to illustrate the periodic linear relationship of these Magnitudes of Mass in Space. This linear alignment emphases the intervening space that exists between these Magnitudes of Mass in the 4^th spatial dimension. I will subsequently demonstrate how this alignment of defined Points of Magnitude, which forms and formulates into a Spectrum of Magnitudes, defines a pattern of periodicity that exists between all magnitudes of mass that form the structure of the universe.

In standard cosmological models of a “closed universe”, the entire physical universe is represented by the outer circumferential surface of a Sphere of Universe, such that the outermost circumference represents 3-dimensional space containing the entire universe and the 4^th spatial dimensional Radius of the Universe has always been considered a mathematical artifice that doesn’t correspond to anything observable in physical existence. For the purpose of creating a cosmological model of the full breadth and depth of the universe that geometrically encompasses all Magnitudes of Mass in existence (upper half of wedge), all Points of Magnitude (Magnitudes of Mass) in the universe are plotted as a radial graph of the Spectrum of Magnitudes on infinite axes of the 4^th spatial dimension. This 4-dimensional geometry forms a Sphere of Universe that contains concentric rings of 3-dimensional Space occupied by corresponding Magnitudes of Mass, aligned according to magnitude of mass on the inside-outside axis of the 4^th spatial dimension, which corresponds with the 4^th spatial dimensional Radius of Universe. Each locus on the radial axis of the 4^th spatial dimension corresponds with a Point of Magnitude in physical existence (—Stars—Atoms—Particles—), which form a circumferential Line of Magnitude at each respective locus (Stellar Line, Atomic Line, Particle Line), each of which is a circumferential ring of 3-dimensional space that extends the breadth of the entire physical universe. As an image, this 4-Dimensional Universe is like a spherical onion in which 3-dimensional shell layers consisting of isotropic Magnitudes of Mass in Space are systematically aligned and arranged inside each other, such that the 3-dimensional shell layer of intergalactic space can be peeled off leaving a shell layer of stars, the stars peeled off leaving a shell layer of atoms, the atoms peeled off leaving a shell layer of subatomic particles. If we reverse the direction of this layering process and sequentially layer the physical universe into existence according to Magnitudes of Mass, this layering process becomes far more significant, because according to this theory of evolution, this sequential materialization of Magnitudes of Mass is exactly how the physical universe has grown and evolved into its present evident form. The physical universe has grown and evolved into existence from inside outward from Particles to Hydrogen Atoms to Stars to Galaxies, and from thereon into the mainstream sequence of stellar and atomic co-evolution that sequentially materialized the periodic table of atoms into physical existence that has in turn assembled into the atomic-molecular physical universe.

At first glance, the 4-Dimensional Model of the Universe above may look like a cosmological model of a “closed universe”, but it isn’t. In the 4^th spatial dimension, this is an “open universe” because the radial axes of the 4^th spatial dimension extend outwardly without limit, passing through each spherical shell layer of 3-dimensional “closed universe” to the furthest outermost reach of Cosmos evolution. Although for the time being I need to stay focused on the geometrical formulation of the 4-dimensional structure of the universe, it is worthy of note that this radial axis line of the 4^th spatial dimension also reflects the temporal Line of Evolution of the galaxies that collectively constitute the physical universe, which like everything else in Nature have grown individually from inside outward into their present physical forms, as I will show with unmistakable clarity from the wealth of astrophysical evidence we have available to us.

Through the 4^th spatial dimension of depth, the Universe can be brought into more accurate composite and component focus for all Magnitudes of Mass in Space. This ability to focus within each 3-dimensional plane of depth on the axis of the 4^th spatial dimension is very important because there has been a misconception by modern science about what the 3-dimensional topography of their cosmological models actually represent in the real physical world. These topographies are usually illustrated as intergalactic space because it is believed by science that they geometrically encompass all magnitudes of mass and space in the universe, but from my perspective that just isn’t so. The current cosmological models only accurately represent one thin 3-dimensional magnitude of the universe, and to think that they represent all magnitudes of mass in the universe is a slip of imagination, a slip of mind that results from a visual confusion about the dimensionality of the universe which is shared by the whole of our species. The mind of science looks at these intergalactic topographies of the universe and slips to the conclusion that the 3-spatial dimensions of intergalactic topography accurately represent the full spatial depth and encompass all magnitudes of mass that are contained within the physical universe. Although those cosmological models accurately depict a single layer of 3-dimensional universe, they encompass only the surface and not the spatial dimension of depth that this universe is made of. Hence they accurately represent the light-speed relevant magnitude of 3-dimensional intergalactic space but they do not represent the interatomic and subatomic particle magnitudes of 3-dimensional mass and space within the universe, because 3-dimensional surface models do not correspond to the 4^th spatial dimension of depth that constitutes the structure of the physical universe.

In the 4-Dimensional Sphere of Universe Model illustrated above, which can depict any number of circumferential lines of 3-dimensional space, the parameters used to demarcate the inside-outside axis of the 4^th spatial dimension are Points of Magnitude in a Spectrum of Magnitudes composed of defined Magnitudes of Mass that form the structure of the universe. If these Points of Magnitude can be arranged into a geometrical system according to their innate mathematical periodicity, these physical constants—Stars—Atoms—Particles—constitute a structural Spectrum of Magnitudes that corresponds to the precise structure of the physical universe. The Sphere of Universe illustrated above serves as a conceptual model that I will endeavor, to the best of my ability, to convert into a workable geometrical and mathematical model, so that the theory and hypotheses herein contained will be mathematically approachable and scientifically testable. With that goal in mind, I will now define the Spectrum of Magnitudes and attempt to formulate a mathematically workable geometrical model of the 4^th spatial dimension.

 Origin and Evolution of the Universe, a Unified Scientific Theory by Paul Hollister, M.D. Copyright 2004

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