Exploring the many worlds of Wave Space geometry has led me to speculate on the two extremes of our own reality, i.e., micro or quantum space and cosmic space. The basic analogy between Wave Space and the "real" world is summed up in Fig. 6.1. Here, the quantum world is viewed as a high frequency, densely packed nodular space compared to our essentially "linear", Newtonian world. This analogy seems to fit well when we consider Einstein positing a cosmic space which takes the form of a vast curvilinear geometric structure and the quantum scientists who view the microcosmos as a wave/particle paradigm of incredibly high frequencies.

Figure 6.1 World Reality Scale

Figure 6.2 Minimum IWS Geometry

Let's consider the limits of Wave Space geometry. From the previous discussion, the macro limit would be a Cartesian grid, Newtonian reality, which is our basic frame of reference. Beyond our frame of reference, in the microworld, we assume the bottom limit of Wave Space geometry.

The minimum wave configuration is w/a=2, and its spatial configuration in IWS is given by the two equations, 
     (1) G(X₂2) and 
     (2) G(X, 2X₂^p22), Fig. 6.2. 
It should be noted, here, that the two equations give the same geometry but are physically different: The X₁ field line, the straight line portion of (1), is considered a wave with w_X1/a_X1= ¥, i.e., as a curve with an infinite radius of curvature. The straight line portion of (2) occurs with q=2, putting the secondary wave X₂, 180^o out of phase. This minimum configuration gives four elements per wave cycle, an equal distribution of common to nodal elements, or e_c/e_n= 1, and a maximum density of nodal elements. From this, e_c/e_n increases, as our reference scale increases, to our macroworld level and beyond, e_c/e_n ® ¥. Also, as e_c/e_n increases, the nodal density decreases and the space between the widening nodal regions takes on the appearance of a Cartesian grid, illustrated to some extent in Fig. 2.3. In this region, we presume the predictable, Newtonian world we are familiar with. Let me further suggest that in this geometry of widely separated nodal regions, that the nodal regions are analogous to the black hole regions of our own universe. This speculation may or may not be that far fetched if we consider Wave Space geometry in three or more dimensions rather than the two of this paper.

Another parallel to our world is, because of the density of nodes at the quantum level, and their bifurcating factor, a microshape or particle/wave packet would have more possible paths to follow in a given distance and therefore be harder to predict its position or velocity at a given time, unless we knew the precise geometry of the space and the laws that govern it. Also, a microshape moving in a densely nodular space, as in Fig. 6.2, would be more difficult to identily due to its continual morphing from nodular to non-nodular space.

The above, of course, is pure science fiction; but even the physicists don't know what the quantum world is like; they have a strong feeling and good reason to believe it is quite different from our own experience. Many feel the quantum world to be a complex paradigm of wave fields; and, even on a cosmic scale, Einstein posits a curvilinear geometric structure. However, Einstein's conclusion, as I understand a it is that mass, or mass as energy, interacts with and distorts the surrounding space. In applying Wave Space to "our" space, I have to conclude that it is the space that creates and defines the mass, or to be more accurate, the illusion of mass. It is the interweaving and interdependence of complex geometries that create and contribute to the totality of reality itself.