All that exists is waves in action, a wavefront of change where there is exchange. Change is in increments of objective change along the wave and subjective change across the wave. Each direction of change (quantitativly and qualitativly) indirectly influences the other. Smaller wavefronts may become unified into a larger more complex wavefront with properties contained and not contained in the smaller waves alone; a coherent supposition, where a higher level of indirect influences may resonate and persist. Each wave, whether standing or moving, large or small, is still a wave and is abstractly the same as all other waves. The rules of existence are the same on all levels. As above, so below. In the two-dimensional division of existence, the two axes of reality, (objective and subjective), together create a diagonal unified expression that is neither yet both X and Y. The actions of existence all propagate a continuing possibility for further action and thus are the same, yet each wave front culminates in a separate and distinct event in space-time and thus each wave is different.
A one dimensional surface, (a wire), can hold the waves of any number of dimensions. The wire has two unmoving endpoint nodes and a geodesic of node points between the ends. Node points on the wire do not move as a standing wave passes across the wire. Standing waves on the line have a wavelength that is an integral division of the distance between the nodes. The wave oscillating on the line may absorb and emit energy . Resonant energy exchanges may be transmitted as change in amplitude or frequency or phase. Amplitude, frequency or phase can each be exchanged for the other. As the frequency of a segment’s waving increases, new nodes of stillness and motion come into existence between the endpoint nodes. All nodes in a line segment are evenly divided between the endpoints of the line. The ratio of distances from a node to its two endpoints is always a rational fraction. Wavelength, frequency, and phase are in the realm of harmonic rationalities and resonant energy exchanges within an entity. While the node points do not move, they do change angular orientation back and forth. Midway between any two node point pair is a part of the line that moves but does not change its angle. Between these extremes lies a transitional relationship of exchange between the concepts of distance and angle.
The numbers of geodesics in a polygon or a polyhedron represent the number of combinations between a given number of reflective endpoints. One endpoint holds no describable geodesic lines. Two endpoints hold one geodesic. Three endpoints will support three geodesics. Four endpoints will have six geodesics, etc. The number of potential lines of interaction is the descriptive for that geodesic.
The geodesics in a polygon can be arrayed perpendicularly around a point in a circle. In such a circle, the first and last endpoint overlap as all the segments overlap. With three geodesic segments, the circular representation is a triangle.
Because each geodesic segments overlaps the next, circular flow in one direction goes continuously downhill in an Escheresque spiral. This direction is seen as objective entropy. The opposing direction is then seen as subjective syntropy.
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Many geodesics may share a common endpoint. The more geodesics sharing an endpoint, the greater the number of dimensions involved. Geodesics represent potential exchange pairs. The lines are paths of exchange between endpoints. More dimensions mean more potential symmetries and paths of exchange.
Two-dimensionality limits higher order geodesics to representation as high order polygons. A third dimension allows four geodesic points to all interact directly in three dimensions without overlap as a four sided polyhedron, a tetrahedron.
A tetrahedron can be described as either; four co-mutually reflective endpoints, six geodesics- each connected to two endpoints directly and connected to the other two other endpoints indirectly, or four planes with mutually non-parallel intersections. A tetrahedron is also one set of diagonals for a cube. The standing wave geodesic lines of a polyhedron can be seen as straight or curved.
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As the surface of space-time carries projected and reflected waves to interfere and interact, the surface processes the masses and energies of the universe through each other. New things are created, simultaneously changing and not changing the materials, like knitting yarn into a sweater or reorganizing atoms into a new molecule. The physical state of existence is a harmonic extension of all realized probabilities to date. This resonance state is a dynamic object.
The present moment is the culmination to date of a complex harmonic chord progression with a correspondingly complex system of nodes and geodesics. The actualization of exchange, (the actual change in being), is between and among motionless changing node points that the waves generate. Nodes come into existence and go out of existence as the energies of persistence propagate. Interference patterns are geodesically related to their subpatterns.
There are nodes of stable intervals set at established positions along the line. There are also nodes that transition across stable established nodes. From whichever level is defined as still, there is a higher level that moves upon its progenitors. The motion of an object is relative to the other objects on that same level. The goal of creating, exchanging and absorbing harmonic tensions is to create a beautiful and logical progression of events. All points in space are potential node points. Constant motion of the time axis changes the angle of the constant length hypotenuse of self-contradictory extensions which exists between node points.
An entity is described in terms of stillness and motion, change and no change, similarity and difference, parallel and perpendicular. These are the things that change in an entity and that are themselves subject to change. Change occurs in intervals from one node to another. Intervals and cycles overlap and interact.
These intervals are described differently from different perspectives and levels of interaction. Scale is meaningless in the abstract perspective, all interactions are abstractly the same. The interval of comparative change has no single quantitative description or measure. This quantity I call ECHEGOYEN’S CONSTANT, the interval from one point to another, and not.