• • FINALLY, THE NUMBER LINE! • •
Now that we have a visible idea of what this model is, and understand how it represents lines of force in nature, we can return to the subject of numerology, and focus our attention on the number line that passes through to label its parts. The number line is, of course, a one dimensional diagram to be placed over the two dimensional cross-section, as a representation of the three dimensional model.
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The number line is a one dimensional representation of our spherical model’s stages.
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In the model, the spherical mobius matrix of concentric spheres was created in five steps; four in, to a center, and four out. Through our own meticulous logic, we actually condensed a universe into nine easy steps! (4 x 2 plus a center). In nine steps we created an entity of infinite proportions within the limits of a finite closed system. We began with an im-plosion from nowhere of nothingness (coagulation), and ended with an ex-plosion into everywhere of everything (big bang). And because we are on that goofy mobius cycle, the beginning and the end of these two opposites combine, making it an infinitely finite system of thought.
For those of you who felt the previous genesis logic was a bit excessive and unnecessary, this next chapter may seem a little more direct and manageable. This is because we will now be using the number line itself as a path of exploration into other patterns, and in doing so, directly establish a tangible sequence of numbers.
• ONE THROUGH NINE •
So far we have shown how an entity begins as an anti-entity (absentia), eventually centering its forces on a single point (model). A point is an idea with no dimension or form, born from nothingness. The complex stages of coagulation create this illusive point at the undefinable center of the model. Once a point is established, it will use the potential energy of the still incomplete cycle of coagulation, and the parameters of the model’s ruling forces, to create its own tangible form. Our number line will be a helpful guide to understanding how evolving forms progress from the foundation of a single point.
The Endless Ascent
First of all, the point, just by being a point, has successfully opposed, with unequal measure, the concept of nothingness from which it came (law of sequence). But as a proposition of logical sequence, we find that being just a point is not really enough, for to remain just a point would be unacceptable to the law of opposites. As a stationary and symmetrical point, a new form of symmetry must now be broken in order to comply with this law. In other words, if the resulting point does not respond to its potential by breaking its implicit symmetry, it never really materializes. Instead it just fades back into the surrounding symmetry it came from and we all go home! So in that sense, we could say that indeed a point has no meaning as just a point, a point is only a point when it is recognized as a beginning to a progression of further development. To begin this requisite development, our point will employ the potent forces of time and motion to fulfill its obligation and break this new symmetry - time and motion becoming the next concentric force of unequal measure from that of infinity on our sliding scale of relative definition.
As we continue, we notice that once a point has chosen to move, it can of course only choose one direction, one axis, or one destination at a time, thus limiting each point to the number of universes it can create - one. As the point moves out from its position of symmetry, it creates a universe of only one dimension. When it stops moving it completes a one dimensional form within that universe. This resulting form can then continue to develop, in any other direction it may choose, to create yet another form of two dimensions. Next, this two dimensional form, can then continue this wave of development in any other direction to create the next form, of three dimensions. However once all three physical dimensions of our universe are realized, only one step remains to complete the progression. The compiled dimensions must then radiate in all directions, creating and enclosing every form possible, and creating a universe of unlimited magnitude.
When the sequence of development is completed, the all dimensional radiating universe that results, becomes a logically deduced equivalent to the spherical environment of our original model’s ruling lines of force. Thus, by coming around full circle to contain the original point within a sphere, we duplicate the appearance of our original model as well as its mobius-like forces, and successfully connect macrocosm to microcosm. Altho not readily apparent, this progression from point to sphere can actually be described with the nine steps of our number line. One way to see this progression as equivalent to our number line, is to label each step with a geometric shape.
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The geometric and dimensional progressions alternate between balance and flux or pause and action as each shape is first formed, then filled in.
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A point, of course, is a point. When it is moving it is called a ray. When it stops it is a line or line segment. If every point along the line segment moves in a perpendicular direction, the same amount as the ray, it will simultaneously create a square and a plane. If every point on the plane moves the same amount again, it will simultaneously create a box and a cube. After the cube of this progression is formed, we find that we have now completely enclose and defined the original center. When the center, which contains the inner absentia, becomes enclosed by the finite nature of the cube, it causes the explosion of energy described earlier in the fountain analogy (big bang). In zero gravity, this explosion is uniform in direction and creates the final two shapes of a ball and a sphere. Another look at this geometric progression will show how it can be segmented into nine alternating steps of balance and flux. Let’s look again at those nine steps;
1) no Dimensions = balance
2) one direction = flux
3) one dimension = balance
4) any direction = flux
5) two dimensions = balance
6) any direction = flux
7) three dimensions = balance
8) all directions = flux
9) every dimension = balance
Or,
1) a point
2) a ray
3) a line
4) a square
5) a plane
6) a box
7) a cube
8) a ball
9) a sphere
The Dimensional Model
What we have just witnessed, is how the dimensional model moves us, from no form or dimension at all (1), to every physical dimension possible (9), in nine steps. As pointed out, the mechanism that drives this process is the impetus of the number 2, that breaks the inertia of non-manifestation, to begin the steps of implosion. It is the number 2’s ability to cause the nothingness around it to implode, combined with the number 8’s ability to explode the resulting manifestation back to nothingness, that is the propelling force of the entire model. The 2 and 8, are like the intake and exhaust valves of a cosmic engine, feeding the combustion chamber of the model's core (4/5/6), through the one way valves of the 3 and 7. The fuel consumed, is the eternal nothingness of dormant matter not yet put into motion. However, unlike a real engine and actual fuel, this supply of energy is not so much used up, like engine fuel, but only made to change form as it passes through the confines of our model, eventually returning as it came to nothingness, to be used again.
The number line represents steps toward manifestation, the dimensional mode shows us how the three dimensions of ‘reality’ do not begin until the 3/7 stage of development. The three dimensions of reality that exist between the numbers 3 and 7, represent the measurable conclusions we can make about the temporal, corporeal mass and the type of reality associated with it. The progression from one dimension (3) to three dimensions (7), represents the building up of that mass into a form worthy of the label ‘reality.’ The emergence of reality from nothingness, reinforces the idea of the 3/7 sphere as a spiritual as well as physical number. From these observations, we can see how our definition of reality depends on which side of the 3/7 skin we are making our perceptions, and how vague or defined that skin is.
The dimensional model describes both the 4 and 6 as moving in ‘any’ direction. This association is attributed to the seemingly optional, much more mechanical force used in building up the mass, as opposed to the compulsive, automatic, immediate and direct energy of the impoding and exploding 2 and 8. Actually the steps from 4 to 6 are just as mandatory and compulsory as the 2 & 8 by virtue of the incompleteness of the whole cycle of creation. But because of the mixture of elements that occur within the spiralling mass, we see how the building of the mass becomes a process where applied effort reflects the mechanical nature of component parts as they work together in an atmosphere of reciprocity, gradually building toward critical mass.
Together, the steps of the dimensional model create a cycle of endless augmentation that periodically culminates, at a ‘critical mass,’ with an explosion and dissemination of acquired content. This cycle can complete its desired augmentation in one pass, or repeat endlessly. The examples of progressive models that follow are mostly of a single pass, although repeated applications of each can create continued results if desired.
The Geometric Model
The geometric progression is the visual model that accompanies the dimensional model. These two models together are so similar in design as to be a perfect marriage of ideas. Geometry, being one of the most definitive forms of expression possible, makes the dimensional/geometric combination a good language/visual model to build upon. Let’s review its progress.
At the beginning of the geometric progression is the point. The point is that infinitesimally undefinable area of the model with ‘no form,’ which, when set into motion by the compulsive action of the number 2, marks the beginning of shapes to come. The process of changing from ‘no dimension’ to the ‘first dimension’ happens by breaking the inertia and symmetry of the number one. This is the responsibility of the number 2. The number 2 marks the first occurrence of motion and time within the model and its steps of implosion. As this occurs, we observe how the model consumes this theoretical ‘atmosphere’ of time and motion as its fuel. Like a fish passing water over its gills, it draws in these companion elements. The explosive end result of this is the space displaced and the energy produced, as the intake and exhaust of the time-space continuum drives the model.
As soon as the first three numbers have illuminated the first dimension of reality (at the number 3), the process of building to the last dimension (at the number 7) begins. Thus we see how the three dimensions are compiled, just like building a house, such that when the final dimension is solidified, the models internal mass is formed. At this point we could say that the model is in fact finished. But whereas the work of building the model may be finished, the essence of the model is not considered complete until it relates back, to the environment that created it. Outward expression of the model occurs as the solidified cube of this geometric progression yields to the power of ‘critical mass,’ - the result being an explosion of energy, back to the nothingness from which it came (7,8,9), creating the final all dimensional ball and sphere, and ending the whole progression.
When we apply this information to existing tarot decks, the endless ascent of the number line becomes the path of the fool’s spiritual journey. He starts as a naive point of ignorance (1), and ends up with the culminating experience of the Hermit’s sphere of knowledge (9). The explosive nature of the 8 is then analogous to his enlightenment - nirvana!
In these one through nine progressions, we have shown an alternate method for creating our spherical model. We have also shown the nine steps of numerology, and we have done so in a way that is faithful to our original paradox. The paradox here lies in the fact that the original point and the resultant sphere are in essence the same, just as the inner and outer points of absentia were considered the same. Because point and sphere are the same, we could say that the whole progression never really takes place! Or to be more accurate, that all the steps occur in unison with wave-like continuance, providing the same end result.
Also, by containing the original point within the resultant sphere, we see how the elements of recursion are also maintained within this seemingly linear progression. And, because the broken symmetry of the point creates an equally symmetrical sphere, we see how that sphere must immediately repeat the action of the original point or, again, the whole model will cease to exist. Because of this, we come to view the resulting sphere as nothing more than another point, beginning a further, and endless, progression of development (it’s both a chicken and an egg!). Finally, the fact that we traverse nine ascending steps and end up where we began, becomes an additional reflection of the finite prison the mobius paradox creates. But that’s not all there is to this geometric progression.
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Hey look, another spiral! Because the radiation of the model into the continuum of nothingness that surrounds it is infinite, the sphere that results from the Geometric Progression is really nothing more than another point, beginning another and endless progression of points and spheres. This of course is only possible because of the ‘impossible’ absentia that exists between each sphere and its following point, and the chicken and egg in the same place, at the same time qualities of that absentia that governs our ‘possible’ universe by its necessary opposure in a binary cosmos. Hey, I’m not makin’ this up.
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The Film Loop
If we look again at the geometric progression just proposed, we notice a distinctive pattern of alternation in its nine steps. We notice that as each shape is created, it must also be filled in or solidified. In other words, you must first consider the perimeter of each shape, and then the stuff in the middle. By alternating back and forth, each shape becomes alternately in or out of balance with its neighbor, reflecting the wave-like continuance of violation and restoration.
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“A point in every direction is the same as no point at all” - The Pointless Man, or Pointed Man, depending on your point of view (The Point - Harry Nilsson).
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Also, because our original steps of development (the cosmic Waltz) dealt with intangible ideas (absentia, nothingness, model), we observed how each of these steps was able to maintain a simultaneous state of balance and flux. Whereas now we see how this changes to a state of alternating balance or flux. Each odd number representing a state of balance, each even number representing the necessary imbalance put upon it, to get to the next stage. As a final analogy, we can see how this alternating of action and non-action, found within these progressions, can be compared to a strip of movie film, where the action is contained within each frame, and the non-action is the space, or pause, between each frame
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When we twist the film loop into a Mobius shape, we traverse nine ascending steps and end up where we began!
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When we put this nine piece length of film, with its four windows of action and five in-between spaces, on a mobius strip, we can see how point and sphere run one into the other, creating the endless ascent just described. Finally, when we imagine this strip of mobius film as a mobius sphere, we see how the four concentric spheres of development, and five ways of being, are again rediscovered!
Two Lines in One
This is the path of the geometric and dimensional number line pattern. As we continue, progressions like this will be many and varied, and their ability to describe cycles in nature will become apparent. However as we bring up the idea of using a number line to describe cycles in nature, we must not forget that this same number line continues to be used as a stationary description of our model’s concentric spheres. Because of this we must acknowledge that there are in fact two types of number lines for us to study; those that progress from point to sphere, and those that remain stationary equidistant representations of our model’s fundamental form. But because we described our model, and the coagulation that created it, as both an entity as well as an event in time, we must also conclude that both types of lines are indeed compatible, and capable of being discussed as one.
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That’s right, there is more than two ways to skin a cat. Here are several different ways to view a number line.
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To confirm this superimposed capability we need only look back at these first examples of number line progressions to see how indeed the number lines of dimensional and geometric forms were both progressing through, and at the same time, maintaining equidistant similarities in their design. For example: by moving from point to sphere, as well as into and out of three dimensions, the dimensional progression successfully combined both types of number lines into one form (see Dimensional model). In this number line we not only saw a definite progression from nowhere to somewhere, but also became aware of equidistant similarities, such as the similarity of a point and sphere at the beginning and end of the line, connecting one to the other by way of essential sameness.
In the dimensional progression we also saw how the first and last of the three dimensions, began and ended on the concentric circle that corresponds to the perimeter of the three dimensional mass (3 & 7). Within both of the equally distant numbers of the mass itself (4 & 6), we saw the optional energy of moving in ‘any’ direction, enabling us to seek a path of least resistance through its spirally substance. And finally, the opposing qualities of ‘one’ direction vs. ‘all’ directions, just outside the mass (2 & 8), equated with the energy of imploding nothingness vs. exploding everythingness. This is an example of how one line can represent stationary equidistant qualities as well as endlessly ascending progressive qualities at the same time.
The geometric progression, on the other hand, while including the same three dimensions as the dimensional model, became a much more real point-to-sphere type of line, because the resulting sphere could literally be seen as the starting ‘point,’ of a continuing progression (see Geometric model). The alternating steps of action and non-action reveal to us the equidistant design of this point to sphere progression.
As we continue, very little distinction will be made between stationary, equidistant number lines, and cyclic point to sphere number lines, as they continue to describe the entity/event we call our model. Hopefully this will not provide too much confusion.
• THE NUMBER LINE IN SPACE •
So far the few examples given of number line forms have all been used to describe the finite nature of the model, as it describes the finite nature of our tarot universe. But, as number lines are used to describe both entities and events, let us not forget that there is still a formless non-model to be reckoned with. The non-model is of course the exact opposite of the finite model and in being so will continue to defy description except by way of contrast to finite forces. But what exactly (or not exactly) is the form of the non-model?
Well, one way to conceive of the non-model’s form is to think of the four stages of the ‘mobius film loop’ just described, as a set of four railroad cars on an infinitely long track. By converting, in our mind’s eye, to this alternate analogy, we can see how each railroad car becomes a representation of the action of ‘sequence’ found in the mobius film loop analogy, while each door between becomes the pause that occurs from one frame to another. The infinite track then represents the continuum of nothingness that contains the finite stages of the train.
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In the railroad car analogy, the railroad cars are finite and segmented, the track is continuous and infinite.
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The Wholistic Number Line
Earlier we referred to the non-model as being off the scale of the number line and gave it the number zero. Now, with this train-on-track analogy, we can see how the non-model actually passes through the same nine steps as the model. But, because of the non-model’s inability to contain itself (being a frameless ground), we find that it actually ends up blending with the nothingness it comes from, and as a result becomes virtually indistinguishable from its background, like a piece of glass in a jar of water, or a picture of a polar bear eating vanilla ice cream in a snow storm.
The way we convey this idea of a frameless ground to a sequential finite mind is by opening all the doors of the railroad car analogy, and observing how the infinite view down the track can now merge with the analytical steps of each individual car. In this way, individual steps can be seen as blending together into one wholistic unity. This is the form of the non-model.
The Analytical Number Line
By comparison, the doors of the finite model are all closed, symbolizing the analytical step-by-step mind as it passes through the stages of the finite number line. With this analogy, we see how finite progress is limited, as the last door of this progression halts all continuation, mysteriously returning you to the beginning, via the mobius ‘film loop’ twist and the effects of endless ascent. The endless expanse of the track is then an illusion that lies beyond your finite perception and can only be imagined or surmised - the result of an infinite track on a mobius band. Thus through the train analogy, the model, and its number line equivalents, can now be seen as devices for separating and segmenting wholistic apprehension into finite pieces, for finite minds to grasp.
When we get to the part of this study where we want to build a deck of cards to illustrate these concepts, suits of the Minor Arcana will be see as either analytical or wholistic.
• THE ENDLESS PIANO •
The train-on-track analogy is good for showing us the difference between the analytical steps of separate cars, as compared to the wholistic unity of opened cars that enabled the infinite track to visually run through the train, thereby combining the formless non-model and the finite tangible model into one. Another analogy useful to describing the relationship between non-model and model is that of an octave, on an endless piano! Similar in form to the train-on-track analogy, the octave-on-piano analogy can be used to expand this model to non-model relationship with additional analogies in form.
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The number line is like an octave on an endless piano. The octave remains an octave no matter how high or low it goes along the infinite range of modulation. The octave (... and our model) displaces all but itself.
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One Octave
In this new analogy, we view the finite number line as but a single octave, on an endless piano of possible octaves. Each octave on this endless piano oscillates between the extremes of its range. Moving through all possible octaves modulates this range. In this way, oscillation and modulation become comparable to the analytical and wholistic, or model and non-model. In other words, modulation is infinite and always there, like the railroad tracks of infinity, but does not have any meaning until a chosen octave brings it into play. Likewise, any octave you choose can only oscillate at one pitch. Moving to another octave is like moving our nine car train along the track of infinity - the pitch changes, but the octave remains an octave wherever it goes. In this way genetic integrity, and the displacement of the number line from within its infinite ground remains intact. But there is more to this analogy than just repeating the conditions of finite displacement within a continuum.
One Pitch
On a true musical octave, the first and last notes are always in phase. And so, by analogy, we can now see how the same is true of our number line, as the point and sphere of the cyclic number lines bring us through a path of ascension that ends on a note of equidistant similarity (see endless ascent and the geometric model).
In our endless piano, the range of modulation (or potential octaves) is as endless as the range of the infinite non-model that contains all octaves.
The pitch of any one octave is determined by the frequency of alternation within the center or midpoint. In explaining pitch, we determine that; whatever the speed of this alternating center, the outer sphere will always be in phase at the other end of that octave.
Chords and Scales
By using the octave analogy, we can again separate model and non-model forces. But, within the octave itself, we can also observe the two types of number lines described earlier.
Within a single octave, we can see how stationary equidistant number lines reveal patterns that can be thought of like chords on this theoretical octave, i.e. equidistant and concordant in some manner or another, like point and sphere. While the 1-9 cyclic number lines, can be thought of like scales on the same octave, showing patterns of analytical progression through from 1 to 9.
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Some number lines progress from end to end like scales on a piano. Other number lines show equidistant similarities like chords on a piano.
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Thus, by analogy, the endless piano reveals to us yin and yang differences within a single number line form (in the form of chords and scales). Chords will equate with stationary symmetrical models, and scales will equate with analytical moving progressions through events in time. Modulation equates with the wholistic non-model, and oscillation with the analytical model. The ‘everpresent’ quality of modulation reminds us of the infinite expanse of non-model forces, while on the other side, the limited range of any octave, and the limited life of notes that are actually played, reveals the transient qualities of the finite model, as well as reminding us of the containment of the model within the non-model continuum.
The Spirit Lives/The Reality Dies
By combining the train car analogy with the piano octave analogy, the idea of wholistic unity and analytical segmentation, occurring within the same theoretical space, enables us to visualize the more familiar idea of ‘Spirit’ and ‘Body’ occupying the same space at the same time. With these analogies, our tangible bodies and conscious minds become the analytical train segments, while our intangible spirit and unconscious minds become the formless presence that passes through - the endless railroad tracks of infinity. Thus by identifying the non-model as everpresent, wholistic and infinite, and the model as transient, analytical and finite, we can see how the non-model’s everpresent symmetry becomes broken by the model’s transient flux. In this way we see how the non-model obliges all by giving birth to a finite model (the body), while each model in turn gives life to the intangible characteristics of the non-model (the spirit)! As this cycle goes on and on we begin to understand how it is possible for every living thing to be the same under the skin, while at the same time remaining a uniquely transient expression of universal patterns. In other words, we begin to see every finite ‘thing’ in the universe as but a transient octave of infinite expression. Each one unique in its overall appearance and duration of existence. Each remaining distinct from others by way of finite laws, while at the same time maintaining an invisible connection by way of common ancestry along the same ‘piano’ or ‘track.’ Thus “The Spirit Lives (endless piano), and The Reality Dies” (transient octave).
Later, when we apply this information to our tarot deck design, each suit of the minor arcana will be thought of as either analytical or wholistic, or, tangible and spiritual, or, segmented or connected. This will allow subtle differences between like numbers of differing suits to be logically explained. It will also allow us to expand our vocabulary to include intangible concepts that would otherwise be destroyed by analytical thought.
Summary
This concludes our brief view of what the number line LOOKS like. With the idea of endless ascent we recreated our abstract model’s point and sphere and with the addition of the film loop idea we also restate the influence of paradox as a signature of nature. Then, with ideas like two lines in one, railroad cars and the endless piano we show, on a one dimensional number line plane, how model and non-model co-exist as analytical and wholistic representations of the same thing. But as these ideas only explain what the number line LOOKS like, we must now examine how the number line WORKS, as a functioning entity with forces equivalent to that of our spherical model.
Overview
If you choose to continue with this study, we will examine how the equidistant qualities of a number line can be used as a representation of the homing forces we observed in our salmon and fountain analogies, as paired numbers are shown to converge and diverge from a mid-point equivalent of our model’s spherical core. Then we will move on to examine how the cyclic endlessly ascending type of number line, can be used as a representation of cycles in nature, and in doing so reveal a signature of nature that is critical to both tarot and life in general. Then, a few words on how these ideas may effect man and personalities.
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