In the sense that all things are perpendicular to the unity, they are similarly parallel to each other in a lateral or circular way.
All attempted descriptions of the model of existence are tangential yet parallel to the higher description of the meta-model. All that exists is the universe of all things; a logically contradictory concept. Any universe that contains all things must contain things that are not in the universe of all things, for they too are things. A self-contradictory thing is still a thing.
All experience is of the universe, in all its forms, experiencing itself through being dynamically interactive with the rest of its universe self. Each entity experiences being as both itself and not itself. Each entity experiences being directly and indirectly. The universe’s experience is of the self and the not-self together, each entity acting as both through the interactions and relationships of existence.
The part(s) of the universe that is (are) the self is (are) in all things and interact(s) with the part(s) of the universe that is (are) not the self and is (are) also in all things. All things are both the self of the universe and the not-self of the universe, depending upon the perspective of that thing. All interactions are of the universe experiencing existence as itself and as not itself. The separate experience(s) of the entities of existence is (are) both direct and indirect forms of self-experience.
Every entity exists as both a particle and a wave. The higher perspective sees existence as both and neither the particle and the wave.
Not only is this universe one of both and neither, it is actually both and neither both and neither. (a particle and a wave)
Objective and subjective dimensions' resonances both have the tendency to persist and expand. Each separate dimension's energy/information has an interest in its own benefit and increase. Objectively, energy flows downhill in entropy during an exchange. Subjective information flows uphill in syntropy during an exchange. Objective and subjective flows are in opposite directions, and the flow of exchange is in entropy and syntropy, each processed through the other.
On one level, increase or benefit to one group may reduce or reverse benefit to the other group. On another level, benefit or loss is shared by all members of the group. These distinctions create the basis for cooperation and competition. The dynamics of persistence are of hierarchical feedback from level to level as precipitated into existence. The game is to persist and propagate. All paths are explored.
The opposition of cooperative and competitive intents in an exchange system can create tensions of expansion or contraction. There is plenty of space for expansion and contraction. An attractive exchange moves objects closer, and repulsive exchange moves objects apart.
A new and higher level of response to the competitive drives of persistence is to see how there is a way to benefit the self by benefiting others that are the not self. This is a conceptual inclusion or grouping of disparate things into a greater group. This action of inclusion integrates the members of a group as a higher-level entity. Enlightened self-interest occurs when members of a group see how helping the other members is an indirect way of helping the self. This mutual altruism promotes the survival of a group as a higher entity.
Contrarily, the mere creation of a new group creates another division of the unity. Another collection of things that are not in the self-created group now exists. The existence of another group of separated things, not the self, is created when any grouped thing is created.
To the extent that entities are in the same group, they collectively benefit by cooperation. To the extent that entities are in different groups, they separately benefit by competition. Entities work toward the same purpose as some other entities, and against the purpose of other entities.
In the genetics of humanity, two similar chromosomes create a woman, and two different chromosomes create a man. The nurturing female nature of humanity is exhibited in cooperative similarity, and the aggressive male nature of humanity is exhibited in competitive difference.
An entity can exist in groups that are at cross-purposes with each other. To do this, the entity is not directly aligned with either group directly, but is at a diagonal to both groups. All things are both objective and subjective and so are on a diagonal to the field of both and neither. Higher levels of tangential self-contradiction lead to increasingly subtle and indirect expressions of reality.
Buddhists say that enlightenment cannot be sought or found directly. It comes not from words or learning, and is not an outcome of logical thought. Enlightenment cannot be described directly.
Since enlightenment can be experienced, and since that enlightenment cannot be experienced through direct description, all that is left are indirect means, which are not at all to the point.
When getting to a point, or attempting to, one follows a line of thought or a physical line. A line that is not to the point will, by default, miss the point. Such a line can only indicate the point attempting to be made indirectly.
On an indirect line there is a point that is perpendicular to the point attempting to be made. The indirect point actually made is where the point to be made is reflected back from the indirect line. The closest point on the indirect line is where it is at a tangent to the circle that exists around the point at that distance. An indirect point on a line may be tangential to many circles surrounding many points that can be made, and one indirect line by itself is not specific about which point is intended indirectly.
The line of thought reflects upon some point. From the perspective of the point that might actually be implied, a reflection from a line can come from any direction.
All models of reality are tangential to the unity and therefor can be seen as abstractly parallel to each other from a higher perspective. The direct and the indirect are perpendicular to each other from the lower perspective. Indirect lines are tangential to the point not directly made. Two related indirect lines miss the point less vaguely than one line.
The hypotenuse line of a right triangle (as on an X, Y graph) will always have a point upon it that is tangential to the origin.
A wave in a two-dimensional field (a flat surface) has two axes, X and Y. The two components are one wave.
The hypotenuse of Pythagorus is the mirror image of the unit circle length of Trigonometry. Both are indirect expressions of the two original axes, both and neither.
No matter what the angle of the unit circle around the point, the radial line always points away from the center.
No matter what angle the hypotenuse, there is always a point on the line that reflects the center back to itself.
The hypotenuse is a constant value (one, like the unit circle) for a contrasting pair of perpendicular dimensions to share a functional relationship. The total squared areas of the two perpendiculars are constant across all angles.
Space and time are linked components of the continuum of the universe. They can be seen as similar to (and different from) each other. They can also be seen as a single higher dimensional meta-object of space-time.
The hypotenuse of X and Y is a meta-object for both X and Y separately and is thus both consistent and contradictory with itself from the perspectives of X and Y. A fixed length hypotenuse of space-time is the fundamental unit of measure for the opposing forces linear and lateral, (or angular) propagation, and is called Plank’s constant after its discoverer, Maxwell Plank.
With the hypotenuse length remaining constant, the values for X and Y may vary. As X grows longer and closer to the length of the hypotenuse, Y grows shorter.
Heisenberg showed that in complementary sets of information, X and Y, knowledge of the two kinds of information (like position and momentum) are mutually exclusive. The kind of knowledge available is based on whether the hypotenuse is more nearly parallel with X or Y. The greater the certainty of having one kind of information, the greater the certainty of a having a lack of the other kind of information. A hypotenuse yields two opposing perspectives on reality from one ambiguous tangent.
One hypotenuse traverses one quadrant of the X, Y graph. Left / right (X) symmetry and top / bottom (Y) symmetry provide three more hypotenuses surrounding the graph origin with an infinite set of parallelograms of fixed length diagonal hypotenuses, one side for each quadrant of the graph. Two sets of reflecting parallel lines exist regardless of the angular quantities in the relationship.
In trigonometry, the unit radius line of the circle changes direction around the origin. The reflective hypotenuse for each potential radial has its center collocated with the center of that rotating radius line. The hypotenuse center moves in the same direction as the radial center, but the angular changes of the two lines are in opposite directions.
As the center of the trigonometric pair (the radius and hypotenuse) moves around in a circle in one direction, The reflection back to the center from the hypotenuse line moves around the center in the opposite direction. While the radial perspective shows a constant angular motion in one direction, the reflective hypotenuse of the center (from the hypotenuse) moves around the circle in the opposite direction through each of the four quadrants.
The natural motion of the fixed length hypotenuse though a full four quadrant circle traces out a hypocycloid.
The co-located midpoint of the hypocycloid hypotenuse and the unit circle radius both trace a circle with a radius of half the length of the original unit. The area inside the inner circle is one quarter of the total area, leaving three quarters of the area on the outside of the inner circle.
The relationship of X, Y space across two dimensions, (across and along), creates the basis for a third dimension, around. The range of a new dimension is all of the perspectives from the original lower domain. A circle needs a two-dimensional field to exist in.
There is the unit circle, and collocated within the unit circle is the midpoint of coexistence circle halfway out from the center. The inner circle can have a tangent to it. When the inner diameter is half the outer diameter, the tangent line reflects around inside of the outer circle exactly three times making exactly three tangents around the origin.
The area of the outer ring half of the unit circle is three fourths of the total internal area. Three fourths of the area is in the outer ring. This tangent reflects around within the circle three times creating a three dimensional radial division of space.
The ratio of straight space to curved space in angular divisions of the circle depends on the number of harmonic divisions created around the circle.
The repetitive flow around a point is a feedback system for resonant propagation. In these flat examples, the circular two-dimensional motion can be seen as moving through one axis of time and one axis of space. One view of our four dimensions sees a similar repetitive motion through one axis of time but three axes of space.
A triangle inscribed in a circle, itself describes an inner circle at half the radius of the outer circle. One quarter of the outer circle’s total area is found in the inner circle.
A square inscribed within a circle has its own inner circle with half the area of the outer circle. If another square is inscribed, and then another inner circle, the second inner circle of the square has the same area as a single inscribed circle from an inscribed triangle.
Squaring a circle twice is equivalent to tri-angling the circle once with a triangle.
As shown above, self-reflection from the center origin of a graph occurs with each of the four hypotenuses at any slope around a point. Every perpendicular line pair rational position on the grid acts as a direct reflector for every radial from that point.
Self-reflection within a grid square occurs from four directions from any position within the square. The four 90 degree corners are natural direct reflectors.
Exterior reflection of space and interior reflection of space are different perspectives of the same geometry of linear process.
Divisions of the whole circle other than four 90-degree radials can also mark out equal angles of radial sweep around a point. 60, 90, and 120-degree rotations allow unit length extensions into space to continue self-similar patterning on the plane.
Any number of radials around a point can divide the circle. The orientations and extensions of dimension in being, in space-time, are at a stable balance when opposing forces receive equal uniform resistance.
The more radials around a point, the less the angle of sweep exists around a circle between radial lines. The occupation of space can occur with any polygon.
The number of corners in a polygon is same as the number of sides of that polygon. Since the number of sides of a polygon is always the same as the number of corners of that same polygon, every polygon is its own ‘dual’. That is, every polygon can be rotated half way out of phase with itself and have a one to one correspondence between sides and corners of the two positions of the polygon. Two regular identical polygons, rotated out of phase with each other, can be of a relative size that their edge lines will cross. Each polygon has its edgelines lines crossing the lines of the (by its perspective, out of phase) other polygon.
Every point in space has an infinite number of radials through it. Every point in space also has an infinite number of circles surrounding the point.
All expressions of space are perpendicular to all expressions of time. Every point on the tangent line (where the circle and radial meet) is at a given distance from, and at a given angle to the central point. At specific ratios of uniform lengths and angles, a plane is covered with three self-perpetuating, resonant, geometric organizations of space and time. These arrangements are seen as the triangle, square, and hexagon. The intersections for each of these repeating patterns of extension into space are motionless node points. Flat planar space can be seen as a grid with uniform divisions or patterns of potential running across it.
Three dimensions of space are more complex than two dimensions. A three dimensional dual has the number of corners of one polyhedron matching the number of facets of another polyhedron. The cube and the octahedron are duals of each other. Only the tetrahedron is its own dual.
There are at least four ways to describe the point location of an object in two-dimensional space; the Cartesian X, Y two-distance coordinate system, the two radial coordinate system, the single radial-distance coordinate system, and the three-distance coordinate system, where the intersection of only two circles would leave uncertainty.
Lines can be reflected and projected by other lines. Radial lines come from a point. Lines are of reflections and projections from one point to another. Tangent lines miss the point. Tangent lines reflect and project relative to the circles radius around a point. A radial line from one perspective can be a tangent line from another perspective.
Memory traces are enduring wave interference patterns of projections and reflections whose resonant vibrations have caused recognition in consciousness. Pattern recognition is being able to resonate against past patterns to compare for such things as harmonic tensions, stress relationships, and classes of resolution, seeking the higher pattern.
The resonance traces can be seen in the infinite set of tangents of the circular expansion from a point. The resonant echo can be seen in a particular radial’s set of tangents in a particular reflective or projective pattern, or it can be seen going around or through divergent radial lines. The resonant pattern can be simple or complex.
This trace is a sequence of points patterning specific times and spaces. Pattern sequences from one point to another can occur along an infinite number of paths through an infinite number of points, but the most direct route is the renormalized general description. From one point on an X, Y graph to another, motion can be in either direction.
A line can be a tangent to a circle around a point or a radial away from a point. The tangent line is perpendicular to the radial line, and one is the same as the other. Angular motion of the tangent line is the same as linear motion away from the radial point. Slope change in the tangent line is only a consideration when the origin of the tangent line is local.
Sequential motion of a point strictly in a radial direction will have tangent lines to that point that are all parallel to each other, never crossing, with a given linear quantity between any pair of points on the line of motion. Motion of a line strictly around a single point will have radial lines that all meet at a single point, with a given angular quantity between any two lines.
No line is just a tangent or just a radial. Every line is both a tangent and a radial. Perspective allows a line to be seen as one or the other.
All flows are not just X or Y, but X and Y. The line of flow will be at some diagonal slope to the X, Y coordinate system.
A two to one slope has a wave’s line of travel going twice as far along one axis as the other axis while the line moves but the slope is still. This straight-line flow of slope can be in flat space or in curved space. Curved space comes back around to repeat a flow across the same space. If the curvature is just X or just Y, the resulting objects are cylinders. If both X and Y curve around to allow angular flow along both axes, the resulting shape is a torus.
If the line of flow along a curved space appears to be nearly exclusively along one axis, it can be seen to curve back around and be parallel to itself on its next cycle, and the next. The line itself is always at some diagonal, but may appear to move almost exclusively along one dimension. If the cycle is observed for may similar passes of adjacent parallel lines along one dimension, a timed point along that cycle will show fixed a set of points at the same place in the cycle to all describe a single line that is lateral to the original flow. The marked repetition of an explicit diagonal line of thought along one direction of motion will yield a lateral line of implicit inference in the across that same direction of motion. A true perpendicular to the rotating spiral is a spiral in the other direction around the closed surface. The closer one direction gets to being completely across the flow in one direction, the closer the perpendicular gets to being completely along that same direction of flow. The perpendicular of a spiral line is another spiral line going in the other direction.
The tube that the line spirals around goes along in one direction that is a different frame of reference than the grid that is offset onto the tube.
This same lateral direction of patterned flow exists even when the linear slope across the grid is greater and the lateral line is less obvious. Every rational harmonic of X and Y has a related lateral structure existing along with and against the objective structure.
When a straight line passes across the plane, the repeating change in quantities of X and Y define the slope ratio for that rational pattern. There exists within the parts of the ratio, dimensional extensions where a standing wave might develop. Such a repeating pattern of X and Y is an object. A given slope is of a particular object. The more subtle the ratio between X and Y the more complex the object created. A two-dimensional pattern may appear to repeat over and over on a flat surface, or the two-dimensional surface can be reflected back to the origin within a single grid square.
Passage of a line across a two dimensional geometric figure is analogous to passing a plane across a three-dimensional geometric figure, as is the passage of a three-dimensional surface through four-dimensional object. Exchanges are along the geodesics between node points, whether in some sequence, or all at once.
The facets on a high order polyhedron (one that looks like a sphere) when viewed locally appear to be a grid on a flat surface. Exchanges across the high order polyhedron’s surface then appear to be motion from node points to node points on the grid. Quantum exchanges along node points can be between individual nodes or groups of nodes that are collectively a single node, or groups of groups of nodes, etc…
Geometry is the study of angles and distances on surfaces. Topology is the study of the curvature of surfaces. The relationship between geometry and topology is that a topological object, like a sphere, is a high order geodesic and a geometric object, like a cube, is a low order geodesic shape. Both sphere and tetrahedron possess qualities of topology and geometry. The different attributes, though the same, have differing influences on differing scales.
A wave traveling on the surface of a topological object is via the geometric node points of the geodesic surface. Both actions are that of a lower-dimensional surface passing across a higher-dimensional object.
When viewed from a global perspective, a high order polyhedron surface is curved. When viewed from a local perspective, the surface is flat.
An expanding ripple can be on a curved or flat surface. (Any surface is both, depending on how close or far it appears to be.) The perpendicular sine wave travels on the surface along the radial lines away from the origin point. The circle’s sine wave expands away from the center. Globally far from the center, a local radial section across the front of the wave will be flat and perpendicular to the direction of travel crossing the surface at a given slope. At closer more local scales, the wave is discrete quantum exchanges from node to node.
The sine wave itself is time invariant. That is, the image of the wave looks the same forward or backwards. What is not time invariant is the wavefront’s curvature across the local part of a full circle. One direction is positive, The other is negative. No matter how little curvature there is, the curvature is in the direction of the original point, the direction of probable cause. The other side of the wave of passage is the direction of probable effect.
If the wave, starting at a point, travels completely across the polyhedron, the energy of that wave will meet again on the other side of the polyhedron at a point. This processes is time invariant. Sub microscopically, it happens continuously. Quantum particles are completely time invariant. In the macroscopic world, however, a wave will lose or transfer its energy before reaching the other side of the geodesic, and time-flow cause and effect becomes directional. Objective entropic decay in one direction is subjective syntropic increase in the other direction.
Only three regular polygons will tile the local flat surface without gap or overlap. These are the triangle, the square and the hexagon. A flat tiling around a single point will use three hexagons, four squares, or six triangles. These patterns describe the allowable standing wave resonances on the surface of the sphere.
With these three polygons, points at the corners of the tiles define the plane’s nodal geodesic surface. The new points in the tiling infer new points of resonance for more tiling of the plane. From each extension of a tile, more tiling extensions of space can be described. Waves travel along a surface through its potential divisions of that surface. The potential node points pass energy as exchange in both directions at once. The tile node points are terminals of harmonic exchange.
To gain curvature on the tiled surface, affecting the topology through geometry, the number of polygons around a point can be reduced. Four squares around a point are flat, but three squares around a point make the corner of a cube.
Angling and reducing the number of facets around a point can create objects that are (in the simplest regular form) the five platonic solids.
The lines connecting corner points on the polyhedron carry wave exchanges around the object in three dimensions instead of two. More dimensions allow for more complicated exchanges. The shape of the polyhedron shows the wave sets it will carry.
The cube and octahedron are a pair of expressions for one symmetry of space. They are each platonic solids and duals of each other. Polyhedron pairs that are duals of each other have the corners of one object radially collocated spatially with the facets of the other object.
The cube has eight corners and six facets, while the octahedron has six corners and eight facets. Both objects have twelve edge lines. An edge line on one object matches perpendicularly to a corresponding edge line of its dual object. Duals have all the edges on one object each perpendicular to a corresponding edge on the other object.
The other platonic dual set is the dodecahedron and icosahedron pair, with facet counts of twelve and twenty each, respectively. They both have thirty opposing edge lines.
The fifth and simplest platonic solid is the tetrahedron. This is a four-sided figure with four corners. The tetrahedron is the only solid that is its own dual. A tetrahedron has six edge lines to interact with another tetrahedron.
On a tetrahedron there are six paths of exchange between four points of reflection and projection.
Each corner point has three lines going from it to the three other points.
Each facet centerpoint is surrounded by three lines that go around the facets and are tangent to the center of the facet and tangent to the center of the tetrahedron.
When two same sized tetrahedrons are placed out of phase with the other, all six lines of exchange on each tetrahedron cross all lines of six lines of exchange on the other tetrahedron. No matter the orientation of one tetrahedron to the other, the two sets of six lines can always cross and touch. The point where two edge lines cross and touch each other are resonant node points of stillness common to both polyhedrons.
The tetrahedron structure depicts the tensions of a three dimensional standing wave object. The geodesic lines of exchange in the tetrahedrons resonate harmonically. Still node points on one line can change location along that line and influence still node points on the dual line that crosses it through indirect mutual reflective feedback.
The position of the harmonic progression nodes in the lines on each tetrahedron indirectly influence the position of the other tetrahedron’s harmonic progression nodes, and as the crossing nodes move, so does the spatial orientation of one tetrahedron to the other. This is the dynamics of the four-dimensional crystal.
Observed properties of a tetrahedron are quite instructive. The closest packing of spheres is in a tetrahedral array. A tetrahedron is the simplest and most stable three dimensional object. Two opposing tetrahedrons form the crossmembers of a cube, which has six single surface reflectors, twelve two surface reflectors, and eight three surface reflectors.
A tetrahedron shows the symmetries that tile the plane: From one perspective, perpendicular to two opposing edges, a tetrahedron has the silhouette of a square. From another perspective, perpendicular to a facet, a tetrahedron has the silhouette of a triangle. Crossing diagonals on the facets of a cube are made of two crossing tetrahedrons, and the diagonal silhouette of the cube as a whole is a hexagon when seen perpendicular to any of the cube’s four three dimensional opposing corner diagonals.
The passage of a plane through a geodesic plots not just the parts, but also the perspective of organization. For that pattern to exist, its parts must each have an exchange in sequence discovered by the passing plane’s perspective. Exchanges between the parts can be seen from different perspectives.
A plane, passing through a tetrahedron perpendicular to its square perspective, maintains a constant length perimeter as the ratio of height and width exchange quantities. A plane passing through a tetrahedron perpendicular to its triangular perspective maintains a constant ratio of area to height as the volume changes. These are different resonance structures in the tetrahedron.
Four spheres pack into a tetrahedron. By the two symmetrical ways to pass a plane across the tetrahedron of spheres, four is counted two plus two, and also counted as one plus three. The exchange arrangement goes in both directions from both perspectives.
The tetrahedron can grow in the number of spheres needed for its creation. The next higher order tetrahedron has three spheres in a row along the edges. There are three layers to pass through, two different ways. That is three plus four plus three, or one plus three plus six.
From the perpendicular perspective, this higher order tetrahedron makes exchanges from three spheres in a line to a two by two arrangement, and then to three spheres in line at ninety degrees to the first line. The six new spheres needed for this tetrahedron exist in two different symmetries. One additional sphere occurs between each of the two opposing perpendicular lines of spheres, and the other four spheres form the square of equal perimeter interface between the two perpendiculars lines of spheres. The primary addition was two plus two. The next level of addition goes three plus four plus three.
From the triangular perspective, the old tetrahedron makes exchanges from one to three and back. The new tetrahedron goes from one sphere to three spheres to six spheres. All six new spheres occur in one plane together, and have their own internal perpendicular planar symmetry of one plus two plus three. Triangular three-dimensional addition is one plus three plus six.
Every point in space is surrounded by an infinite set of circles, radials, and tangents to circles. Every radial has an infinite number of perpendiculars from as infinite number of directions.
A point in space may have two circles expand out away from it starting at different times. There may be, then, an outer circle and an inner circle that both expand away from the center. This expanding set of circles will be called a circle pair.
Within a circle pair, a line that is tangent to the inner circle will be a secant or chord line to the outer circle.
If the inner circle diameter is near zero, the length of the inner circle tangent line that is a chord to the outer circle approaches the diameter of just the outer circle.
If the center circle expands relative to a fixed outer circle, the chord between the two circles grows shorter. As the inner circle approaches the outer circle, the tangent approaches zero.
Now, if these two circles both expand at a rate that leaves a constant length tangent chord between them, then the area between the two circles remains constant. The area between any pair of concentric circles is a function of the tangent chord length between those two circles.
This fixed length tangent of a circle pair is the fixed length hypotenuse unit of quantum measurement. We see the universe as expanding. We see both circles as expanding. If the tangent length stays the same between the circles then the area between the circles stays the same. What we see is a fixed length tangent, the basic quantum of measurement and exchange. A fixed two-dimensional area also represents this fixed one-dimensional length. The area that is the square of the hypotenuse remains constant and equal to the sum of the squares of the X and Y quantities that describe that hypotenuse, and pi is the factor of rotational extension around a point. This relationship between length and area aids in understanding the relationship between rolled up membrane surfaces and unit length strings in superstring theories.
What changes, along with ratio of radii to chord lengths, during the expansion of a circle pair, is the number of tangents that reflect around the circle. At specific ratios of radial length to tangent length the reflections around a point are reinforced by whole number harmonics. This allows for a set of circularly reflected standing waves.
A disk rolling on a surface remains upright, holding a resistance to the force of gravity to lower the disk’s center of gravity. If the disk is spun backwards to the direction of motion across the surface, the disk remains upright as the frictional forces of rotational deceleration and linear deceleration compete. When the frictional forces equalize, either the direction of spin in the wheel will have changed or the direction of travel across the floor will have changed. On a spinning turntable surface, a disk spun backwards will reverse both its direction of spin and direction of travel continuously around the spinning center of this surface, with a circle as the limit of the disk’s travel. Different size disks have different size patterns around a similar sized limit circle for a given speed of rotation around the center of rotation.
Entities are standing waves with any and all number of divisions of the whole. Entities’ different numbers of divisions resonate against each other by one facet from each of the two entities being a single composite pulse that is some fraction of one entity and some other fraction of the other entity. The ratios of one to the other can vary vastly. Changing the ratio between interacting circle-pairs changes the resonance of the interactions between them.
Common resonance structures for standing waves include the circle diameter, inscribed triangle, square, pentagon, pentagram; all self-reinforcing inscribed patterns. All regular polygonal structural lines of flow can be reflected around by the outer circle back onto itself, as long as the inner circle does not interfere. As the circle-pair expand, first the simplest geometries are blocked, then higher resonances. At great expansions, only the highest resonances endure. A wave traveling around inside the outer circle interferes with itself for feedback and persistence.
All possible ratios of radius to tangent occur in the fixed area of an expanding circle pair. When the inner circle starts at zero radius, the internal fixed area of the circle pair is the same as the area of the whole outer circle. The tangent between the circle pair is then equal to the diameter of a single circle with the same radius. The tangent equals one and the outer radius equals one half. The inner radius is zero. The ratio of radii to tangent is one half to one for the outer circle, and zero to one for the inner circle.
As the circle pair expands, the radii of the two circles successively become larger than the tangent chord length. With enough time, the radii become so large that the unit length of the tangent becomes virtually zero in relation to either radii. The difference in length between the two radii has shrunk to virtually zero. The radii to tangent ratios become nearly infinite.
Local closeness of a tangent to the center of the circle is in relationship to the swept angle of that single segment around the point. The greater the tangent length in relation to the radius length, the closer the tangent line is to the center, and the fewer tangents it takes to go around the point.
Everything is a wave. The wave circle can be seen as an expanding surface pulse flowing away from a point. This circular wave that is the outer circle can reflect back into the circle. Even though the wave is circular, the paths of expansion on the wave are all straight. The flows of the inner wave go in straight-line reflections around the inside of the outer circle. Any point inside the outer circle provides a starting point for a circular wave to find straight geometric reinforcement at any angle. Wave starting points near the edge of the outer circle only allow for iterations around the circle that do not cross.
The simplest two-dimensional geodesic is the triangle. Next simplest is the square. Two circle inscriptions of the square are the same as one inscription of the circle in a triangle.
All lines of discourse on the nature of things are at a tangent to the true point of unity’s singularity and will miss the mark. In Olde England’s archery, to miss the mark is to ‘sin’. The first circle was sin one, and the next circle was sin two, etc.
The vocabulary of King James colors modern terminology for wrongdoing. Biblically we all fall short of the aim of being a squarely centered reflection of God. To face self-reflection directly as the godly unity is beyond mortal abilities, as we exist on the diagonal and experience God only indirectly. Some people find it difficult just to meet the reflective gaze of another person squarely.
We are made in the image of God, abstractly, but so are all things.
No matter how
precise a description of the unity is attempted, it will fail to hit
the mark exactly. Even the closest imagery is at a tangent to the
truth and will, by its nature, miss the point....
And this great
truth of the certainty of any description of reality to miss the
point, itself completely misses the point.