V

The Number Line...

• • ONE DIMENSIONAL HOMING • •

So far the number line has been used in two ways. 1) To label the concentric circles of our cross-sectioned model with equidistant pairs of numbers. 2) To create the fundamental parameters of the model in its own way, by connecting point and sphere with a geometric progression of logic. We also observed how equidistantly stationary number lines, that describe an entity, can coexist with linear, progressive number lines that describe an event. So let us now examine at how these number lines can be used to describe the salmon-like homing forces of concentric containment and coagulation in a linear form, with its equidistant number pairs.

• CONVERGENCE AND DIVERGENCE •

In previous chapters, we have described the process of coagulation with more than one analogy or metaphor. One that was particularly informative was the analogy between lines of force converging on a central point that doesn't really exist until those lines of force actually converge to define it... and the idea of salmon using their inborn instincts of homing to find their way to a source they do not know. This idea of homing is important, and needs to be translated into number line form.

When we describe the process of homing with equidistant pairs of numbers on a number line, the vision of concentric spherical stages imploding on a center, or concentric circles enclosing a central point, becomes altered into one of opposite numbers that converge upon a linear midpoint. In this way the number line becomes a one dimensional diagram revealing spherical forces, not easily seen in the original implosion / explosion theory. Here is one way to visualize these things.

The Apart/Together Model

When describing universal lines of force coagulating out of nothingness in a spherical manner, we observed how intensity increased as we approached the center of existence. We also mentioned how such an intense encounter between extreme opposites of existence and non-existence at a central point of confluence could, in theory, result in a cosmic recoil analogous to a baseball batter hitting a baseball into space. This lead us to speculate on our own special type of Big Bang theory. After establishing our own theory of beginning, we pointed out how that initial encounter of collision and recoil changes into an ongoing process of compression and radiance that continues for the life of any entity. Compression and radiance create the pulsing vibrations of life. When we translate this idea of initial collision and recoil, or ongoing compression and radiance, into opposite numbers on a number line, we use relative distance between opposites to illustrate the relative intensity of converging lines of force upon a center... or midpoint of confluence. The idea of outward radiance is then analogous to those same converging opposites breaking apart, or diverging. Thus our first example of convergence and divergence involves an elegant simplification of the homing process that I call The Apart/Together model. Seen below, it looks similar to a diagram showing how cells in our body divide! In my opinion, a fitting analogy, seeing how this diagram is meant to describe lines of force that create life as we know it.

The Apart/Together model shows the convergence and divergence of opposite number pairs, as they represent the compression and radiance or fusion and fission of spherical lines of force upon a central point of cosmic confluence.

In The Apart/Together model, we see opposites that are completely separate and isolated from each other, leading to opposites that are totally integrated... as well as steps in between. These four steps of isolation to integration describe a one dimensional procession of opposites converging and diverging. In The Apart/Together model, we view the spherical forces of implosion and explosion, or fusion and fission, as similar in fundamental design, with the only difference between them being the con-vergence of one vs. the di-vergence of the other.

At the 1/9 stage of this model, we see a condition of opposure that is extreme in separation. The numbers 1 and 9 are disparate and isolated by virtue of their extreme endpoint positions along the one dimensional number line plane, as well as the extremes of point and sphere they represent. Because of this, we come to view these numbers as opposites that are distinctly apart and not communicating, or... not transmitting their influence to each other across the separation that divides them. Like wallflowers at a school dance, sitting at opposites ends of the gymnasium. Or... like dance partners standing across from each other, not yet engaged. Maybe a Forward and Back in square dancing.

At the 2/8 stage we see another pair of opposites that, although still apart, carry an implication of communicative flux within their representative form. In The Dimensional Model, the 2 and 8 represented the first and last impetus of motion (i.e. one direction vs. all directions). Because of this, these opposites are considered to be apart but communicating... i.e. apart, but transmitting their influence across the separation that divides them, in either a con-vergent or di-vergent manner, upon the ultimate midpoint of the number line. Like dance partners holding hands with arms extended between them. Maybe an Alamande Left... or Right... in square dancing.

At the 3/7 stage, we see a pair of opposites that seem as apart as the previous two. However, when we look back at previous models we are reminded of the advent of the three dimensions of reality that occur at this stage of development in The Dimensional Model. We are also reminded of the advent of a tangible surface, as described in our Planetary Model. In this way, this 3/7 position represents a kind of skin of connectivity - this is the point at which converging lines of force first begin to touch each other and coagulate into a recognizable form. Therefore the opposites of 3 and 7 are considered together... but not yet intersecting. Like dancers dancing cheek to cheek, with bodies touching. Maybe a Promenade in square dancing.

Finally, at the 4/6 stage, we see a pair of opposites that look completely integrated. In the 4 and 6 we see a pair that is not only together and touching, like the 3 and 7, but because they represent the spiraling mass of the spherical model, they are also considered to be intersecting, or overlapping - i.e. exchanging sides or parts of each other. In this way the 4 and 6 represent the condition of marriage and reciprocity that exists between opposites that cross over the midpoint in pursuit of equilibrium (like the kids chasing each other around a tree in the Angular Momentum idea presented earlier). Like dancers in a twirl. Maybe a Do-si-do, or Elbow Swing, in square dancing.

Through this isolation to integration spectrum we see how each finite model is in fact an isolated entity, apart from all others, and isolated amid the continuum of nothingness from which it came (1/9). We can also see how each model must relate to models separate from itself. In other words, models must continually converge and diverge, as cycles continue around them (2/8). Of course when finite models converge and connect, we see how the physical contact between them is purely tangential, as surfaces touch surfaces (3/7), (only non-model forces are capable of wholistic unity). Finally, we observe how models tend to coagulate into larger entities, like families, cities and countries (4/6). Of course the larger entities that are formed by coagulation immediately repeat these conditions by virtue of the fact that they remain isolated from other larger entities (1/9), and must eventually relate to them (2/8), connect with them (3/7) and integrate to form even larger entities (4/6).

As humans, we too are all entities, isolated (1/9), relating (2.8), touching (3/7) and integrating (4/6). Thus we see how, in human terms, each of us can be broken down into constituent parts, while at the same time remaining constituent parts to a larger whole. In this way, we see how genetic integrity remains intact throughout - both literally and with respect to our models forces. This is the nature of The Apart/Together model, that of isolation(1/9), communication(2/8), contact (3/7) and reciprocity(4/6). In some ways this model is the most simplified of all our models so far, and at the same time the most powerful to build upon. By creating a model that moves from a condition of ‘apart and separate’ (1/9), to ‘connecting and intersecting’ (4/6), we incorporate the conditions of coagulation and homing into a one dimensional number line form.

Can we see the makings of any tarot icons in these notions of isolation (1/9), communication (2/8), touching (3/7) and intersecting (4/6)?. I can. To me, The Hermit (as a 9) is an icon of humanity that is clearly tapping into the concept of isolation (1/9). If The Popess or High Priestess (as a 2) is taken as an icon of inspiration (a Shekinah), she is tapping into the concept of motivation, inspiration and the transmission of electrical impulses that make an elusive point move (2/8). The connection that most people see in The Empress (as a 3 ) to that of beauty, and the beauty of nature, and the sensitivity to feel and appreciate these creations, clearly equates with the idea of creation being established at the number 3, as the end result of a 1,2,3 trinity of creation. The idea that lines of force are no longer separate, as in the 1/9 and 2/8, but are now touching also make the idea of sensitivity correlate well with this converging pattern (3/7). From there, The Lovers (as a 6) clearly represent the idea of intersecting and swapping parts of each other, as seen in this model of sides spiraling together. While The Emperor (as a 4) represents the power built up by the mass of coagulation.

Lots of people think that an archetype is the anthropomorphized, culturally embellished icon that appears on the tarot card. I don't. To me, the archetypes are these abstract, TRANS-cultural patterns... which is why this study of tarot spends so much time building this theoretical model of existence. No one needs to know any of this to use a tarot deck, just like we don't need to know how a car works in order to drive it. But, as stated in the introduction of this book, this study of tarot is not for those who only want to drive, this study of tarot is for those who want to look deeper into things than just the surface imagery of a deck. With that in mind, let's continue by examining the nature of the number 5 on this path of convergence and divergence.

The Neutral Five

In continuing with The Apart/Together model, we move on to the number 5, in the middle of it all. The middle is where coagulating lines of force meet their end in encountering each other and not being able to advance any further. In spherical form, this is what creates the definable mass of existence that we recognize as a manifest entity of existence. However... the middle, or center, remains excluded from this mass of existence, by virtue of its inability to be anything other than a neutral center. With the idea of Transcendence, presented earlier, we saw how this condition of neutrality lead to a condition of paradox, where we encountered one half of a supposed singularity that this study has chosen to call The Absentia. The Absentia, by definition, lies beyond this infinitely small point of neutrality, just as sure as it resides beyond the infinity we recognize outside us. Thus, the first thing we should observe about the number 5 is that it does not represent the inner absentia, but the point at the center which contains the inner absentia. Likewise, the number zero is not the number for the outer absentia, but for the infinite non-model of nothingness, beyond which is the outer absentia. Therefore, as our first observation we must conclude that the 5 is indeed much like a "nucleus" within the 4/6 "body" of our spherical model (a kernel within a 4/6 nut, within a three layered 3/7, 2/8, 1/9 shell).

The 5 is like a kernel within a 4/6 nut, that lies within a three layer 3/7, 2/8, 1/9 shell.

As a point of neutrality, the 5 can be seen as part of either side, or... part of neither side. In this way, we can view the 5 as both a gap, or a hinge - a point of division of a point of unity. Thus, on the one dimensional number line, the number 5 is like a fracture... filled with glue, holding equidistantly similar sets of numbers together, like the wings of a butterfly. And... because of its infinite in between state, it remains a neutral mediator between these two sides. Because of this, we conclude that as a matter of necessity it must belong to both sides of our number line equally. But, at the same time, we must also acknowledge the fact that, in being neutral, it can only serve one side of the number line at an given moment in time. In other words, if we were to divide the 5 equally between the two number line halves we would only repeat what is already there, two sides with a middle. This means that, as a middle, one of the fundamental characteristics to be found within the number 5 is going to be that of endless alternation between sides. In other words, since the 5 cannot serve both sides at once - it must forever alternate its influence between the two.

The 5 is like a glue holding the equidistant pairs of opposite numbers together - or apart! The 5 is a neutral mediator between sides. It does not belong to either side. In belongs to both sides.

When this linear idea of back-and-forth alternation between sides is applied to our three dimensional model, we see how the alternating effect of the 5 is in accordance with the rapid succession of implosions and explosions within the form of the spherical model itself, as the compression and radiance, or fusion and fission of coagulation becomes a process that continues for the life of any entity. Thus the 5 becomes a mediator between the "in" and "out" of this implosion/explosion process, or the "left" and "right" as opposites on a number line are used. On a grand cosmic level, the speed of this alternation can at times become so fast as to appear completely neutral and stationary, giving further associations of neutrality to this midpoint position. On more mundane levels, this alternation creates moments in time that require endless choices. It is at these moments in time that we make endless course corrections to our life path... deciding consciously or unconsciously this way or that... or attempting, consciously or unconsciously, to remain neutral.

For an analogy of the alternating effect that we encounter at the number 5, we can observe a phenomenon known as retinal rivalry. Retinal rivalry occurs when two different images, say one black and one white, are shown to different eyes of the same brain. Since the brain is not capable of seeing both together it ends up alternating between the two, continually changing one into the other and back again, as they compete to dominate the single brain. This phenomenon can also be seen in the examples of the figure/ground illusions, and an optical illusion that goes by the name of Nekar’s cube.

The figure ground on the left, and the Nekar’s Cube on the right demonstrate the concept of retinal rivalry. Constant alternating back and forth without resolution, that is what the 5 is all about.

In many popular tarot decks, the card labeled Temperance (usually numbered 14, which reduces to 5) is shown with two goblets, pouring water from one to the other, and presumably back again, thus symbolizing the alternating nature of this middle position... not to mention the alchemistic idea of opposites mixing and blending. Likewise, the card labeled The Pope, or Hierophant, (usually numbered 5) is often shown with two monks standing before him competing for attention in much the same way as the two sides of our number line. Thus, we see the Hierophant or Pope as alternating his attention between these two monks, as well as holding sides together, while remaining neutral.

The Neither, Either, Both Model

The neutral point that we are identifying as the center of a spherical model, or the midpoint of a linear number line model, is created by converging lines of force that can converge no more. With the idea of Transcendence, presented earlier, it was speculated that, through infinite neutrality, we could - in theory - connect, or transcend... via a remnant of impossible singularity captured by the mass of existence, to the outsides we left behind while on our path of inward coagulation. In addition to this idea of transcending through, it was also theorized that we could bounce off of this infinite point of absentia and radiate the built up energy of a coagulated mass as lines of force emanating outward... back, to the infinity from which they came. Thus, in addition to being an excluded middle, the 5 comes to also represent the beginning point of this emanation of energy outward from a center or core of existence. As lines of force emanate, they diverge. As we continue, we will observe how an emanating midpoint of a number line can also be used to create a model of divergent action that can be added to our repertoire of forms. This next model is called The Neither, Either, Both model.

The absentia is the ultimate “Neither” - it is neither black nor white, neither everything nor nothing. The Five is the ultimate “Either”, alternating back and for between either black or white or everything and nothing. The 4 and 6 are a marriage of “Both” black and white or everything and nothing. The rest are in some degree of opposition, diverging or converging.

In this model, The Absentia (held within the 5) is seen as having a special place of excluded opposition to that of the finite number line. Thus we view The Absentia as an ultimate "neither" to the rest of the number line - as in neither here nor there (or neither chicken nor egg)... (see Predictable Paradox presented earlier). The 5 on the other hand, has already been described as an alternating midpoint... alternating in rapid successions that are in accordance with the implosions and explosions, or fusion and fission of spherical coagulations that continue for the life of an entity, as its pulse of life. Because of this, the 5 is viewed as an ultimate "either" - as in either this side of the number line or that side. Next we observe how the 4/6 cluster of the model’s mass can be viewed as a combination, or marriage of opposites, as they spiral together, down the Mobius/Magnetosphere cones, creating a double helix of opposing forces, like chocolate and vanilla in the blender. Because of this association, the 4/6 is viewed as a reciprocal combination of opposites - as in both this side and that... trading with each other or alchemistically mixing. Finally, we see how the 3/7, 2/8 and 1/9 reflect progressive distance away from a previous goal of definition, as described by The Apart/Together model. Thus, as a pair that is no longer apart, and not yet intersecting the 3 and 7 stand for qualities of sameness and simultaneity between sides, while the convergent or divergent 2 and 8 represent the idea of bifurcating nature and fractal geometry. While the 1/9 pair represents the outer reaches of the model’s form and the idea of isolation, distance and limits of influence from one "thing" to another.

Thus, by using this Neither, Either, Both model with the Apart/Together language model, we can again visualize the five stages of the spherical model itself. With the Apart/Together model we redefine our parameters, and can now see how our original five step progression of creation, coagulation and definition is not only one of reverse-entropy stabilization from ‘no concept at all’ (outer absentia) to the finite concepts of the model and its excluded middle (inner absentia), but also a progression from total isolation and beyond (outer absentia >> apart & separate), to total integration and beyond (intersecting & exchanging >> inner absentia). And with the Neither, Either, Both model we observe how the core of existence that is built up by coagulation can also emanate its force back into the nothingness from which it came. Let's look at another way of diagramming these ideas, specifically the idea of a model that emanates its influence outward from a core...

Here is a combination of the Apart/Together model and the Neither, Either, Both model, showing the simultaneity of the 3/7 stage and the crossing over of the 4/6 stage... like chocolate and vanilla in the blender! Hey, I just noticed something... this diagram looks very similar to The Tree of Life diagram used by the Kabbalah! Interesting. The idea is certainly the same. Out of the ineffable comes a binary system of opposites, that connect the mundane to the divine, and ultimately returns to its origins.

Absentia: As a model that emanates from its center out, the Neither, Either, Both model accurately identifies the condition of The Absentia as the ultimate "neither," - as in neither here nor there. By being an ultimate "neither" the inner absentia is like the eye of a hurricane amid the spiraling mass of the model. It is calm, empty and sits completely apart from the activity around it.

The 5: As we examine the next stage of this model, we find ourselves radiating out from this center, to describe the condition of the alternating 5 which holds The Absentia within. As an ultimate "either" this position describes to us the alternating or pulsing action that both accepts and emits waves of flux - creating the heartbeat of our living model, or the put, put, put of our cosmic engine! - an idea we will expand upon shortly.

The 4/6 sphere: In the "Both" part of this model, we describe integrated opposites, united in co-mingling fashion by the alternating 5, like two colors of playdough rolled together, or two people shaking hands. At this point, the idea of "strength in numbers" applies, as a built up mass of conglomerated existence must now express its power outward to its origins. Thus emanation of acquired content becomes as manditory as the reverse-entropy path of initial creation, coagulation and definition that got us here. Thus... as we depart from the center, we see how manifest definition begins to "unwind," along a path of actual entropy, as the next three steps show us how opposites relate before spiraling together into the all important mass.

The 3/7 sphere: In all our models, the 3/7 stage is where we encounter the surface of the mass or the "skin" that contains the three dimensions of manifestation, or "reality" as defined by manifestation. By being a point of transition between positive inside and negative outside charges, the 3/7 position becomes another in between of sorts. On our path inward, this position represented a point at which lines of force touch, and begin to define a tangible form. Now, on our path outward, this position represents the point at which our accumulated mass of manifestation begins to express itself back into the nothingness from which it came as lines of now diverging force.

As a point on our path where we express our accumulated mass of existence back into the nothingness that gave us life, this position comes to represent that point where we (incarnate beings living between two mobius-like points of absentia) theoretically touch our individual ideas of Go-o-d - or D-evil. Wholistic apprehension, or "seeing God," is thus the result of achieving oneness within our concentric spheres of theoretical containment. When followed by the explosive nature of an 8, as seen in the Geometric and Dimensional models covered earlier, God’s "touch" lifts us up and out of our three dimensional finite prison, and into the spacetime atmosphere of the 2/8 heavens.

Viewed equidistantly this 7,8,9 trinity of expression represents a spiritual awakening, i.e. breaking out of the mass (5,6,7), into the heavens (8), and on to infinity (9). While at the same time, the 1,2,3 trinity of creation is seen as an expression of Gods inward touch toward the manifest world, i.e. reaching into our world, to create a finite entity out of an intangible absentia. Thus the 1,2,3 trinity of primary creation is seen as the first act of the hand of God, while this 7,8,9 trinity of expression becomes the final act of each creation back to its creator.

The 2/8 sphere: Moving on, we now view the 2/8 stage inwardly, as a representation of the imploding impetus of time and motion in the 1,2,3 trinity of primary creation, and outwardly, as the energy and space displaced by all manifest entities that warp the fabric of spacetime in order to exists. Thus, in the 1,2,3 trinity of creation, time and motion are described as imploding from nowhere. While in the 7,8,9 trinity of expression, energy and space are said to radiate back... out... to the beginning... where we end this whole alchemistic process of coagulation and dissolve. When viewed equidistantly, we see how time and space occupy the same theoretical sphere, thus becoming spacetime. Because of this, we view the 2 and 8 as a spacetime "atmosphere" of sorts, surrounding the model with a layer of concentric containment.

The 1/9 sphere: Finally, at the extreme ends of all of this, we find the 1/9 sphere, poised to begin, or end, this whole mess. On a spectrum of one dimensional homing, the 1 and 9 represent the most irreconcilable, antithetical separation possible. But because moving to such extremes only pushes us toward the outer absentia, antithetical associations like point and sphere actually end up being identical in kind - a result of paradox... the force that begins, ends, unites and divides all of this... making this the key to the endless ascent of all number lines, as illusions of progress attempt to move us as far from each evolving point as possible... only to return again, through the Point = Sphere paradox of The Absentia!

• RECIPROCITY •

In continuing with our analysis of the model’s mass and center, and its reciprocal, alternating qualities, the idea of reciprocity becomes an important concept to address. Reciprocity comes in many forms. Even the Yin and Yang symbol that we borrow from The Chi incorporate reciprocity into its simple design, as these two characters resemble our previous analogy of kids chasing each other around a tree (see Angular Momentum presented earlier). This un-ending game of "tag" was used to describe the result of finite opposites converging on an un-obtainable midpoint of definition in a spiral-like fashion. But this is not the only form of reciprocity to observe in our model or number line. In a spherical form we can observe that; because all points radiate a sphere of influence, and all spheres of influence ultimately converge upon a single point, a reciprocal relationship exists between the insides and outsides of our model’s concentric spherical form.

Every point radiates a sphere of influence. Every sphere of influence encloses, contains and converges upon a point.

From this concept alone, we can see how it makes our "point" and "sphere" essentially the same in character, thus enabling each to be transformed into the other without changing the form of the linear models that exist between. Swapping point for sphere, or insides for outsides just inverts everything, like turning a reversible coat inside out. Thus, this reversible nature of our theoretical model of existence resembles the untwisting of the twisted half of a Mobius band, only to find that we have now twisted what was untwisted! Thus making reciprocity another signature of nature to address in detail.

Particle and Wave

As an example of reciprocity in nature, the particle/wave characteristics of light offer us a scientific analogy for the place our model has in the universe. For many years people have debated on whether light is made of particles or waves. It always seems to exhibit characteristics of both. Conclusions that lead to acceptance of both, also lead to a pattern of reciprocity within our model. Here’s how.

Science has observed that wave frequencies can be combined, to form distinct, definable patterns that can then take on characteristics of particles. It has also been observed that particles move through space to form patterns with wavelike configurations... thus leading to the notion that light is both wave and particle. When we attempt to assimilate this controversy into the stages of our model, we naturally consider a wave to be less tangible than a particle and as a result associate it with the external reaches of the model and the "waves" of concentric development that emerge from nothingness. The internal mass, however, has already been described as a particle, a particle created from these imploding waves of nothingness that surround it! Thus from the vantage point of our model we see how; waves can combine, or coagulate, to form particles and how particles will emanate, or disseminate, in waves. By standing at the transitional 3/7 surface of the model’s "skin" we can see how we, become situated on the fine line between the reality of the mass (particles) and the intangibility of the not yet coagulated (waves)!

Light Waves

Light waves go from short to long, or from very fast oscillation of cycles-per-second, to very slow... or, from extremely intense to extremely weak. When the intensity of the oscillating waves becomes too much, or too little to perceive, they are essentially the same - just like point and sphere! As an analogy of form, we would say that the intense end of the light wave spectrum belongs with the converging, radiating mass, and the weak end with the outer portions of the model as it fades into nothingness.

The internal mass is a particle created from the imploding waves of nothingness that surround it!

5) The most intense cycles-per-second wave is the Cosmic. Cosmic waves are considered the source of all other light waves. Placing the cosmic waves at the number 5 gives us an idea of just how fast the alternating midpoint of our number line shares its influence between theoretical halves! The alternating effect of course comes from the peristaltic wave-like continuance of implosion and explosion, or solve et coagula through an entity.

4/6) The next most intense wave on this spectrum belongs to the 4/6 sphere. These are the Gamma and X-ray waves. The predominant characteristics of Gamma and X-rays is their ability to penetrate, revealing the fragility of things considered solid. Gamma and X-rays go right through human tissue and cause disturbances in molecular and atomic continuity that can be deadly. If we accept that the model represents forces in nature as well as within humans, then we would equate the ability to penetrate solid objects with that of "mind over matter," and Karate masters who perform impossible feats of destruction upon "solid" objects. Whether karate masters actually produce gamma rays before striking a solid object is irrelevant. The point is, as a metaphor, the intensity of the model’s cluster, whether it be within the heart of a human, or at the center of a galaxy, is an intensity of great magnitude and penetrative capability.

3/7) The next group of waves belongs to the 3/7 sphere. This is of course where we find the visible light spectrum and the ultra-violet and infra-red that enclose it. Unlike X-rays, Visible light does not penetrate, but instead is absorbed and seen as color on the surfaces, or skin, of objects. The uniqueness of the visible light spectrum, the way it illuminates our daily lives, makes the 3/7 position special to the idea of reality, as well as life. We could say that it is in fact here, and only here, where "reality" actually comes into focus, and becomes "one" with our perceptive capabilities... making this position analogous to a "radio station of reality" on a dial of relative incomprehensibility. Thus, the 3/7 position is a theoretical dividing line between ideas like reality and fantasy. Reality of course existing within the 3/7 skin, and fantasy existing beyond the 3/7 skin. This association to fantasy and reality would of course make this position, and the numbers 3 and 7, of great significance to creative, spiritual, mystic and religious people. And so they are.

2/8) If Gamma and X-rays penetrate, and visible light is absorbed, then surely the short, medium, and long radio waves will bounce off - and so they do. They bounce off buildings, clouds and satellite dishes with predictable regularity, making them useful for communication of great expedience across great distances - communication that is as immediate and direct as the "path of least distance" they represent through the 2/8 "atmosphere" of the model.

1/9) Finally, the final set of waves belongs to the 1/9 position. They are associated with all the slower waves too weak to penetrate, absorb, or bounce off. They are simply there, surrounding objects the way the 1/9 "magnetosphere" surrounds the model.

Point to Sphere

The light wave spectrum is a good analogy for how it describes the center, or insides of our spherical model as very intense, and the outsides as very relaxed. While, the idea of waves of energy becoming infinitely fast or infinitely slow shows how the ends of this spectrum lead to the same place... in two different locations! - the paradox of The Absentia. The Absentia is off the spectrum in either direction... with the universe being all the vibrations of opposites that reside between. As vibrations of the universe intensify, the phenomenon we have called coagulation takes place, and what we call manifest entities appear out of nothingness. As coagulating lines of force meet, they create a point, which, as we saw in the Geometric and Dimensional models, either dies, or begins a continuing process of building out to that of a sphere. In the Geometric and Dimensional models this path of building to a sphere was described in nine ascending steps. But... the last two models we've covered have made that same traverse from central point to outer sphere of influence, or outer sphere to inner point, in only four steps. What gives? The fact is, that both approaches are equally legitimate ways of describing this point to sphere path. Just as we earlier described two types of number lines as being capable of being thought of as one, these two forms of point to sphere traverse are also capable of being thought of as one.

The number 5 is not the only critical point of in betweeness. The 3/7 stage is also a critical point of transition between negative outsides and positive insides. When we superimpose a nine step scale over the five step scale we can see how 5 and 3/7 relate as critical points of separation or unity between sides. Below is a mandala showing how this idea of a 5 steps and 9 steps being superimposed can repeat infinitely. This mandala repeats this idea 4 times over an all encompassing 5th set making a total of 9 centers from one end to the other. A point to sphere progression happens from one end of this mandala to the other, from one half of this mandala to the other... from one quarter of this mandala to the other... etc. etc.

Thus, with the diagram above, we observe how the number 5 is not the only critical point of in betweeness, and how the 3/7 stage is also a critical point of transition, a critical point of transition between negative outsides and positive insides... a transitional stage that creates a theoretical "skin" around the resulting mass of manifestation that resides inside. The diagram above shows how superimposing a nine step scale over a five step scale reveals the 5 and 3/7 stages as relatives in the separation or unity of sides... and both the 5 to 1/9 and 1 to 9 as relatives in the beginning and end of sides. This shows us, again, how running off the end of the 1 through 9 scale leads to The Absentia... which leads to transcendence... which leads to point and sphere, or sphere and point being in essence the same. With this knowledge we can stop chasing our tail by forever pursuing the really big or the really small, and just live within the universe given to us, and vibrate at whatever frequency is appropriate for each situation.

But... before we leave this diagram of superimposed number lines, let's observe how the five coagulating stages align perfectly with the odd numbers of the point-to-sphere stages. In a previous path of analysis, we observed how odd numbers became important lines of demarcation, and even numbers became areas enclosed by lines of demarcation. Now we have another reason to see odd numbers as important lines of demarcation. And... in creating these lines of demarcation with a model that is meant to describe varying levels of wave propagation, we are lead to another important pattern of nature...

Interference

By describing the concentric steps of coagulation in terms of wave-like patterns upon a center, we can speculate on the idea of wave interference as a contributor to the alternating effect of active and passive stages of development in our model and number line (as seen in The Film Loop analogy, The Dimensional model and our Two Step logical model). Such a speculation would reinforce the idea of implosion and explosion co-existing within the same theoretical space, by offering evidence of opposing paths of longitudinal wave propagation that would create for us the intermittent interference patterns of cancelled and doubled light pockets. These would then correspond to the pause of the 1/9 sphere of influence, the action of the 2/8 motion, the pause of the 3/7 transition and the action of the 4/6 spiraling mass.

Inward bound coagulating waves meet outward bound radiating waves and create pockets of interference at the critical stages of development... which we then illustrate, or diagram, with four circles and a point.

We could then theorize that the resulting pockets of interference would be organized or regulated by the 3/7 transitional stage (see Apart/Together, and Neither, Either, Both models), as this point of development would now represent a filter of sorts, demanding that the terminal midpoint of the number line (the 5) only send back incoming waves in an opposite pattern, to pass through the 3/7 stage in only one allowable direction or another. Such orderly passage would again result in combined wave lengths and interference patterns, and reinforce the concept of reciprocity between the outside and insides of the model.

Summary

This is how we view the equidistant qualities of the number line and the ideas they bring to our three dimension model. Not just a stagnant stationary labeling of parts, but a living, pulsating entity of life. Converging and diverging upon a central core. Like breathing in and breathing out, our model LIVES!

The model of four circles and a point is meant to be an idealized "map" of an invisible terrain. In being a map, some might view its four simple stages as oversimplified, as there are obviously things going on between each idealized stage of development. But now, with the patterns just covered, we have a scientific analogy to help justify our simplification of what we see as four circles and a point. These four circles and point are not just arbitrary stopping points in a completely made up design, they have now been created for us... by our observance of more than one logically deduced pattern in nature. Our Two Step model lead to lines of demarcation and points between. Now this idea of wave interference leads to the same conclusion. This... in my opinion... makes this model of existence extremely archetypal in nature. Thus, I propose it as an archetypal armature upon which to build out to more mundane, human, anthropomorphized expressions that eventually find their way onto little pieces of paper in a tarot deck. The image on the card is not the archetype, or, "original pattern or model from which all things of the same kind are copied or on which they are based" as Dictionary.com put it in their definition of archetype. The archetypes are these patterns, or parts thereof, which point to vibrations of the universe we all resonate with when creating works of art designed to express who we are.

• THE LIVING MODEL •

Solve et Coagula

Solve et Coagula is an alchemical term that appears occasionally in tarot decks of the past, in connection with the card labeled The Devil. The Devil carries with it the number 15. As in all numerology, multiple numbers are always added together and reduced to a single digit. In this case 15 = 1 + 5 or 6. This means the Devil card is describing the 4/6 mass of the model and its characteristic behavior of coagulation and eventual radiance, as the mass of our model becomes alternately fused and exploded. Solve means to dissolve or break apart, disintegrate, fission... and coagula obviously means to coagulate, come together, fusion. Solve et coagula describes the diminishing intensity of paradox toward finite definition. Coagula is to define, Solve is to fade back into the symmetry of nothingness that surrounds all coagulated entities.

Coagula) Through coagula we approach the mass of an entity, and by approaching the mass or cluster of an entity we feel the resistance of the mass pushing us back. At the same time, we also feel the incompleteness of the homing cycle, pushing us in. Near the center, we encounter tremendous forces capable of fusing the mass - that’s Coagula.

Solve) On our way out, we sense a relaxation of the fused, twisted, compressed area of the mass. At the surface, we feel the perfect peaceful pause of the neutral membrane of transition. Ahead is the open area of the model’s atmosphere and its characteristically direct path of "least distance" and "near simultaneous" passage. Further and further away from all this, is the nothingness from which we came - that’s Solve.

Some choose to describe this back-and-forth path as a fall from grace, followed by enlightenment. They see coagulation of a manifest form as a finite prison from which it is our life's goal to escape. And while I agree that our manifest forms are a finite prison of sorts (and have used that term already), I do not agree that it should be our life's goal to escape. Our life's goal should be to understand what is going on, and then live the life we are meant to live within this finite form, not to loath it and spend all our energy wishing we could be somewhere where the grass is supposedly greener and the light of life brighter. Life is a gift, not a punishment. Be here... now.

Karma

Karma is a concept that is similar to the Fountain analogy used earlier in this study of patterns. Karma is like the invisible absentia that passes through the model, to change form and return, or... like the "message in the bottle" story. A man alone on an island, with a plea for help cast adrift in a bottle. The bottle travels out, away from its source. When it is found it causes a return journey, by a recipient, to a source it has never met. The sender of the message does not know if he will get a response, or if he does what kind, or from where. All he can do is send the message and wait, wait for his karma to return. Of course if he sends the same message every year, or every day, his chances of a response increase. Likewise, if he could control the randomness of the ocean and send messages in all directions, the chance of a response would increase again. Of course if he were in zero gravity, he would want to send messages in an all directional spherical pattern. As it happens, this is exactly what our model does during the perpetual implosions and explosions of Solve et Coagula.

Of course not all models implode and explode, or compress and radiate with the same potency. Thus, the ability to send and receive messages can be compared to casting a hook into the water in hopes of catching a fish; the stronger the mass of the model, the farther it can cast, and the more it can reel in. In this analogy, the "hook" lands in the water at the 1/9 stage of the spherical model. Reeling it in correlates with the 2/8 stage of immediate and direct passage, and the idea of opposites coming together. Next, like lines of force meeting and touching in the Apart/Together model, we meet the catch at the surface, or 3/7 stage of spherical development. And finally, without hesitation, we gather it into the boat and add it to the growing mass that represents the 4/6 stage of development.

In theory, karma is the end result of praying, chanting or whatever method someone chooses to send their message adrift. But it can also be used to help explain destiny, coincidence (synchronicity), and the idea of pre-destiny. With karma, each of us can be seen as a universe casting out hooks and reeling in each other, to our respective boats. By reeling in our destiny from a distant origin, we pull ourselves through time.

All of Human Behavior

So... by way of Karma, and our passage through an existing model, we have shown how Solve et Coagula works. We have also eluded to the idea of fundamental parameters effecting all of human behavior. In determining where possible influence to human behavior may occur, let’s take another look at our model’s form.

If you were to guess what sphere of the model influenced you the most, which do you think it would be? Would you want to be standing alone on the 1/9 outer perimeter of concentric forces, isolated from all others looking in, as in "the spectator sees more of the sport?" Or would you want to be flying, through that open area of the 2/8 atmosphere? Or maybe you would want to be within the realm of that perfect peaceful pause, feeling the energy of the mass radiating out through the 3/7 membrane of transition. Or perhaps you would want to be right in the thick of things, part of the thronging 4/6 mass - like someone who enjoys crowds, involved in the exchange between sides. By examining the model this way, our analysis begins to sound more like a personality questionnaire. This is an example of how the model attempts to describe patterns that I believe govern all of nature, and how all of nature can be described within the stages of the model.

When we apply all this information to numerology, we will see how numbers, and the fundamental parameters they represent effect human nature. Because of this, I like to think of our fundamental parameters as a kind of aura around the body, with five charkra points up the spine.

When we apply this idea of an archetypal armature of patterns in nature to the tarot cards, we will use these relative positions to describe contrasting ideas like; the independent personality, standing apart from the crowd (1/9) like a hermit, vs. the social interaction of being totally absorbed and involved with others in an intense exchange (4/6) like lovers. This is why Solve et Coagula is such an important concept to remember. We all vibrate, pulse, implode and explode in accordance with these fundamental, elemental, primordial, archetypal patterns of nature. Thus... if we REALLY want to know what the icons of tarot are about, it would behoove us to examine these patterns and know them... inside and out.

For those who already know the tarot card symbols, determining connections to the model in this way may be a bit easier than following a path of geometric shapes. For example, we can see how the independent personality is already symbolized by the card labeled The Magician and numbered 1 in the tarot deck. Likewise, in equidistant design, (as we now know equidistant similarities to be significant) the number 9 card, labeled The Hermit, also carries with it the notion of standing alone, apart from the crowd. By contrast, the 6th card, labeled The Lovers, symbolizes an often literal intercourse of opposites about a midpoint of definition, while the equidistant 4th card, labeled The Emperor, clearly defines the power and potency of the radiating mass and all its substance.

Solve et Coagula shows how all of human behavior will fall somewhere along a sliding scale of relative definition. For example; some people like to live in the heart of the city with people all around them, others like to live in the country miles from their nearest neighbor. Both are connected to each other and to the forces of the model. The man in the city needs to get outside that cluster to be alone (solve), the man in the country needs to go into the city to meet other people (coagula). Flying across the country at night, the lights below show us urban clusters of varying sizes, breaching the continuum of the single darkened land mass in much the same way as stars cluster together in space to form galaxies, demonstrating man’s need, as well as the universe’s need, to coagulate and define. In this way, even the hermit, or lone star becomes part of the eventual cluster it attempts to defy.

Solve et Coagula shows how our model comes to be, even without individual, segmented stages of development.

Solve et Coagula reveals the dualistic, binary nature of the model and its forces of creation. The idea of pulling together to define a form, and then disseminating that form back to nothingness, shows the reciprocal point to sphere connection between the finite and infinity. Even without individual stages of development labeled with numbers of numerology we can see the various forms of our theoretical model of existence in the behavior of humans. These patterns are there, whether there are any humans to give them form or not. Do not think that you are not affected.

Summary

Thus ends our examination of number line patterns. The Endless Ascent, The Film Loop, Two Lines in One, Railroad Cars and The Endless Piano with its octave, pitch, chords and scales all showed us what the number line LOOKED like. Ideas like Apart/Together, Neither, Either, Both, Particle/Wave, Point to Sphere, and Interference breathed life into our model’s form. Finally, with ideas like Solve et Coagula, Karma and all of human behavior, we introduced the idea of how abstract patterns in nature can be used to describe human behavior, and in doing so suggest that the parameters that govern human behavior are the same as those that govern the patterns of our model.

Overview

If you choose to continue with this study, we will shift gears a bit, and begin to examine some patterns that reveal the progressive nature of a number line. Number lines that progress from 1 to 9 show us how flexible our model is in describing all of human nature. If you are interested in hearing a few words on how the Apart/Together model might be seen as an archetypal influence to anthropomorphized icons of tarot, try reading the edited down version of this page called Why Abstract Patterns?