From our now-familiar chalkboard grid, we have come to understand the universal dynamics bridging every pair of contiguous dimensions, regardless of scale.
From the doubled mobius strip model, we conceptualized the Implicate and Explicate orders of the Female and Male who are entwined in their processes of Creation/OUTformation and Information.
We stretched out across the Pragmatic Schematic, as seen below, the activities of PTPR, or Pull * Transition * Push * Rest.
Contained within the two outer crescents are the opposites, Pull and Push, and within the almond shaped overlap is the necessary Transition between them. The primordial Ground State Rests beyond the overlapped circles of the PS model.
We discovered this model’s fractality as it discreetly implies that, within the singular spread of PTPR labels (see above), both Female and Male agents perform PTPR. Pull * Transition * Push occurs within their respective circles (see below) and they return to Rest in their primary position, where they may potentially Pull once again.
Relating the two models equates Pull (black PS above) with the Female Transition (colored PS above), and Push with the Male Transition; Transition with the Female Push and Male Pull; and Rest with the Male Push and Female Pull.
As you will recall*, Female Pull is called Yin and Male Push is called Yang. These are the universal forces, at the beginning (contraction/centripetal/inhalation) and end (expansion/centrifugal/exhalation) of every system/entity.
You may wish to review a previous chapter explicating The Ins and Outs of Yin and Yang.
Introduction of New Model
In this chapter we will further expand our exploration of Quadernity by introducing a colorful Cylindrical Lattice model.
At present, quantum physicists are puzzled by the non-linear behavior of sub-atomic particles, while classical physicists complacently follow the rules of linear cause and effect trajectories. Physicists in the latter camp are constrained by empiricism at the macro-scales and reductionism at micro-scales, while Quantum physicists, who allow maths to suggest anomalous behavior among unseen quanta, are surrounded by a swampy moat containing horrid creatures like the infinity, the singularity, uncertainty, acausal synchronicity, irrational numbers, teleology, chaos, complexity, and OH MY conscious observers!
Our inspired little Lattice model will become a home-grown map of Quadernity that walks us through how systemic non-linearity correlates with the apparently linear trajectories of physical entities, supposedly pushed around, and pulled upon, by various forces within the space-time of our common senses. The Cylindrical Lattice will enable us to zoom out our perspective to encompass a multi-dimensional array of influences that impact all of us and entities/systems everywhere, from micro to macro scales.
In order to account for the non-linear, inter-dimensional dynamism, which actually spans the living universe, we must make some modifications to the flat grid model of quadrants (though not to the principle of Quadernity).
A little basic algebra will be used here as an analogy, but we will go easily, step-by-step.
Algebraic equations solve for the unknown variable by performing the same adjustments to the terms on each side of the = sign. Permitted adjustments include:
- adding or subtracting the same value to or from both sides of the equation
- multiplying or dividing by the same value on both sides
- taking square roots of both sides
- squaring the values on both sides of the equation
In just the same way that we make adjustments to an algebraic equation in order to solve for an unknown variable, we are allowed to alter how we visually model Quadernity in order to reveal otherwise hidden aspects and to give it broader applicability. It is fair to revise our models, just so long as the fundamental dynamics of Quadernity are explicitly maintained.
Before we commence making careful adjustments to our Quadernity Model, it may be helpful to refresh our memories on a few points of interest that we explored in earlier chapters.
Every feedback loop, joining contiguous dimensions throughout the supreme scheme, has at its core, a couple of cooperative Subjects (one Female and one Male) who perform coordinated rounds of PTPR, as seen in the two-by-two grid of our original Quadernity Model:
In the chalkboard graphics below, we carry the opposition of blue and green arrows on the diagonals. The blue and green diagonal arrows Transition between the dual domains: OUTforming is directed to the physical domain (lower quadrants) and INforming is directed to the metaphysical domain (upper quadrants).
After an Object is produced by the Subject, She or He returns to Rest in the position from which another Pull is possible. Seen below, the black-dashed arrows, which move retrograde to the colored arrows, are visible. In other words, the blue arrow running upward diagonally in the left graphic is countered by a black dashed arrow running downward diagonally in the right graphic; and the green arrow running downward diagonally in the right graphic is countered by a black dashed arrow running upward diagonally in the left graphic.
In the graphics above, it is recognizable that, as energy is OUTformed/Created by the Female as Corporeal content (LRQ), it becomes potentially INformative to an Informable Male Consciousness (LLQ). In the lower quadrants, the Female Pushes (LRQ) to the Male who Pulls (LLQ).
In the grid below, notice how the first Female Push (3 in upper row) is aligned with the first Male Pull (1 in the lower row). Always Pulls and Pushes align. Transitions (colored arrows) and Rests (black dashed arrows) also always align. Confirm this in the models above, where two upward arrows coincide in the graphic on the left and two downward arrows coincide in the graphic on the right.
The Female Pull initiates a full cycle. A circle/cycle has 360 degrees (four x 90 degrees: represented by the four right angles (90° each) of the chalkboard quadrants, and likewise by the four grid squares through which the Subjects’ PTPR).
We learned from the PTPR chapter, that, in piggy-back fashion, the actions of Female and Male are offset by 180 degrees, so their Pulls and Pushes align and their Transitions and Rests align, as shown above.
To focus on the continuity of feedback, we begin transforming the angular 2-by-2 Quadrants into a fluid new Lattice Model, in which we illustrate the Subjects’ PTPR in the form of sine-waves.
The sine wave is not a singular thing. It is necessarily a composition of bi-level actions performed by dynamically involved partners.
The Subject moves forward to be ready to Pull what is Pushed by the companion. As this is not commonly understood, few are looking for the Rests that are invisibly situated behind the Transitions of the opposite color.
Behind the blue lines there are green Rests and behind the green lines there are blue Rests. The waves are skewed to show this.
For ease of visibility, we transform the figure above into the figure below, while keeping all the dynamics precisely the same. Pulls and Pushes make their Ex-Changes across the median axis, while Transitions and Rests, occurring synchronously, are shown now as the wave amplitude and base line, respectively.
Can you find the figure above in these ancient illustrations below? (Hint: You may have to imagine its orientation rotated from horizontal to vertical.)
Ancient artists’ deep appreciation of the form known as a double helix is evident in the illustrations above. Centered within the opposing spirals, whether depicted or implied, is a core of stability. This Axis Mundi is composed of the alternating Rests that punctuate the opposing partners’ actions, Pull * Transition * Push. The Pulls and Pushes of the interacting couple meet at the sine wave’s medial axis to functionally conjoin their contiguous dimensions.
Breathing is a Complex Process
When we pay attention to our breaths, one thing we easily recognize is that our individual breaths continue sequentially.
Inhalation Pulls O2 inward and down into the lungs, and exhalation Pushes CO2 upward and out; between there is a Transition (seen at the troughs below). Between the Exhalation that completes one breath and the Inhalation that begins the following breath, there is a palpable Rest (seen as the horizontal dashed line).
We do not immediately exhale the air that we just inhaled. If that were so, what good would it do for us to breathe? The oxygen we take in must oxygenate our cells. When the cells import oxygen, they export deoxygenated gas, rich in CO2. In other words, the CO2 delivered back to the lungs for exhalation was a byproduct of the previous breath, not the current breath.
How did the Transition convert the O2 that we inhaled into the CO2 that we exhaled?
Air is Pulled, Transitioned and Pushed by the Female, as depicted above with green lines. We could think of the blue lines (seen below) as the air; however, the air itself does no action on its own; it is not a Subject who Pulls, Transitions and Pushes. Therefore, the blue lines should not represent the air; instead they should represent a Male Subject who is actively participating in the process of exchanging gases. In just a bit, we will learn how this is true.
Individually trace the green and blue sine-wave curves below. At the Male peaks and Female troughs there is a Transition.
Depicted in the Pragmatic Schematics below (one Female and the other Male), this Transition is called an Intra-Change.
What we want to do now is to put the two magnets together, the green Female alongside the blue Male, as if together they form a single magnet that Pulls from the Female end and Pushes at the Male end.
Note that in the central almond-shaped ‘mandorla’ we now have an Ex-Change rather than an Intra-change. The Intra-changes are the Transitions, one Female and one Male. They have been moved into the outer crescents.
Another way of thinking of the connected magnets is to see them as a torus, the shape below.
The torus is a symbol suggestive of how the Male and Female are singled-out and linearly related in their “Public Daytime Relationship” (center of torus where one Exchange occurs: Female Pushes/Male Pulls) and how their Rests are mingled-in in their non-linear “Private Nighttime Relationship” (the interconnected web, where the other Exchange occurs: Male Pushes, and Female Pulls).
Dual Aspects of the Cardio-Pulmonary System
Let us now examine the torus above in light of cardio-pulmonary respiration in which the heart and lungs are entwined.
Begin with the Female Pull (left side of the torus). As Subject of the Circulatory system, She inhales/Pulls oxygen-rich air from beyond Her body, as depicted by the torus’s web, in which all gasses are mingled in. She Transitions/Intra-Changes the oxygen into the blood and sends it over to the heart, which then circulates/Pushes the oxygenated blood, via arteries and capillaries, to the most distant cells in Her body.
Reprinted for your convenience: Inside the torus, the cells of the body/Female/circulatory system expel/Push deoxygenated gas into the blood which returns it to the heart. An Exchange occurs when the Male Subject of the pulmonary system Pulls from the Female‘s Push the CO2-rich gas from the blood in the heart. He then Intra-Changes it over to the lungs, where it is Pushed/exhaled as waste-gas out of the body (right side of the torus).
In each cycle there are two Ex-changes and two Intra-changes. Ex-changes are between the Subjects as they Pull from and Push toward each other. Intra-changes involve the Subjects’ own internal Transitions, which occur while their partner returns to Rest.
In the graphic below, the stars outlined in black show the Intra-Changes. Green star outlined in black indicates the Female‘s Transition and the blue star outlined in black indicates the Male‘s Transition.
The green star outlined in blue indicates an Ex-Change from Male to Female. The blue star outlined in green indicates an Ex-Change from Female to Male.
The two points … which are the fundamentals of every cycle are: the point of beginning at the wave axis [Ex-Changes], and the point of interchange between positive and negative opposites at the wave amplitude [Intra-Changes].
Walter Russell identifies two points, one on the axis and the other at the amplitude. Quadernity shows that both the Female and the Male have these two points on their half of the sine wave; therefore, there are a total of four fundamental points.
Comparing Closed and Open Systems
Compare the open feedback system (left below), which perpetuates life, to a closed feedback loop (right below) that quickly dies out:
As an open system, our breathing can be seen as a progression, shown by the illustrations on the left above. The closed system on the right shows what would happen if we were to inhale only our own exhalations: we would soon die out, just as surely as a pendulum returns to equilibrium.
Open, Multi-Dimensional Systems
From the word ‘spirit’ is the root word, spire, found in the words inspire and expire. Spirit means breath or wind.
When we count our breaths, beginning with a Pull/inhalation at birth/inspiration, and ending with the Push/exhalation at death/expiration, we must include the exchange of gasses with our environment. Our breathing is both open (ongoing) and multi-dimensional.
A new question is brewing.
Q: How does the environment acquire the O2 that we naively take for granted?
A: O2 is released into the atmosphere by plants as they go through a process called photosynthesis.
The graphic below allows us to account for interactivity between additional levels, such as photosynthesis. Follow the brown arrow from bottom to top.
Please notice the following factors in the graphic above:
- We have labeled alternating Female and Male sequences of Pull * Transition * Push, just as they always interact in Quadernity.
- The bottom blue half-wave connects to the top blue half wave. Altogether there are two X-shaped iterations of each, blue Male and green Female.
- Occurring within the intersections of each color is a Transition. The labels reveal different functions at each Transition up the ladder.
- Only one side of each half-wave has been labeled, so far.
What is happening on the other side of the half-waves? Another process is similarly sequenced. In addition to their exchange of gasses, flora and fauna are also related by their exchange of nutrients. The layout below shows this exchange. Follow the brown arrow from top to bottom to see that this process is also open and multi-dimensional.
PTPR Progresses Linearly and Non-Linearly
Two consecutive breaths are depicted below, enclosed in overlapped circles. This image serves as a reminder that PTPR advances linearly/horizontally, as well as non-linearly/diagonally.
In the graphic below, we have highlighted the entire linearly-advancing sine wave (both halves: green/physical and blue/environmental) within a non-linear progression. Please follow the labels to verify that PTPR reiterates in either case, both horizontally and diagonally.
The full sine wave (bolded above) is incomplete as a metaphor for breathing, as it divulges neither the exchange of gasses within the body nor the exchange of gasses between the plants and the environment beyond the body.
Exquisitely apparent is the non-linear aspect of breathing, which involves numerous dimensions (faded lines) that interconnect along the diagonals.
Where are the Rests in Multi-Dimensional sequences? A Rest comes after a Push (which ends a series of actions) and before a Pull (which initiates the next series of actions). Follow along the diagonal paths marked by the brown arrows to see that the Rests of one process (you do not see that color) are obscured/overshadowed by the triple actions (Pull * Transition * Push) performed by the opposite process (the color you do see).
Just because the Rests are hidden does not mean they are not there. Not knowing they are there means not asking where they must be, and this prevents many a scientist from achieving a breakthrough discovery. :/
The Life Lattice: A New Depiction of Quadernity
Appreciate, in each of the images below, the artistry symbolizing the entwined opposition of two complementary forces, archetypally represented as the primal Mother and Father.
The double helix comprises loops of two inverse, nonlinear systems, which feed into each other.
To account for the reiteration of dual, complementary cycles of PTPR, such as the means by which flora and fauna exchange gasses and nutrients, we arrive at the Life Lattice Model below.
Please take your time to follow along both of the pathways. The black arrow-heads indicate the direction of Pushes and Pulls between the two colored partners. At the Transitions, which occur within the same color, move diagonally from left to right. At the wave’s peaks and troughs, the Life-Lattice connects non-linear dimensions to the linearly advancing dynamic.
You will recognize that both paths, up and down, follow diagonals that slant to the right, showing their mutual progression. The two processes, however, move inversely; one moves from the top downward on the diagonal, and the other moves from the bottom upward on the diagonal.
The blue half-wave at the bottom of the Lattice connects to the blue half-wave at the top of the Lattice. By connecting them, we form a cylindrical tube of sorts. The short video demonstrates how the diagonal movements are a spiral progression.
The tube shown is an incomplete section. As you can surmise, the spiraling diagonal arrows continue their progression indefinitely.
This Lattice Model of Quadernity maintains, from our original two-by-two model of Quadernity, the functional interchanges between opposing cooperatives (shown as color-coded wave-forms). Added are the features of dimensionality and reiteration, which are necessary to reflect real-world dynamical interactions.
Complexity in Dynamical Systems
Given the single-loop metamorphic phases of the Lepidopteran shown in this chapter, plus the water and rock cycles, and the planting and harvesting seasons that we read about in the chapter called Pull * Transition * Push * Rest, the Ubiquitous Sequence of Nature, we may overlook higher degrees of complexity in dynamical systems.
The meso-cycles of interactive PTPR, such as illustrated by the single sine wave above, incur micro/intra and macro/extra influences, at the Transitions (peaks and troughs), such as illustrated by our new Lattice Model. Transitions are not a one-way exchange; therefore, the meso-level affects, and is affected by, both the up-line dimensions (above/open to outside, extra) and the down-line dimensions (below/open to inside, intra).
The ancient Emerald Tablet of Hermes proclaims:
Truth! Certainty! That in which there is no doubt!
That which is above is from that which is below, and that which is below is from that which is above, working the miracles of one.
As all things were from one.
From the microscopic level of our cells, to the macroscopic level of our solar system, there exists dynamic interactivity. This big loop of interrelated dimensions shows an hierarchical arrangement of corporeal phenomena.
The purple arrows in the flow chart form a loop from the micro/subatomic to the macro/cosmic, and back. Along with the elephant, we and other earthly critters are about halfway between the micro and macro scales. Relative to the spectrum of all corporeal existence, the meso-scale includes the totality of life on earth.
For reference, a human toddler stands about three feet tall; that is one meter. The Planck unit is the limit for the smallest size (1.6 x 10^-35 meters) of any discrete thing. And, our known universe (8.8 x 10^26 meters) is the biggest measured thing. An intriguing article, written on this topic by a student from UCSC, can be read here.
Within this meta-loop are countless feedback loops, like the seasons of our year, or the water and rock cycles. Loops within loops within loops…
Perhaps you are musing that I am kinda loopy. Ha, ha. I admit it; the truth is we all are! Without our many layered loops, our conscious–corporeal lives would be impossible.
What follows is a famous video from 1977 that traces, by powers of ten, from our human scale to the infinitesimal and back up and outward to the cosmic level. If you have not seen this previously, you are in for a treat:
Having firmly grasped the notion that countless other dimensions exist between the gross representations of varying scales that are pictured above in the graphic with the purple loop, such as cells, tissues, body systems and organisms, we may come to wonder, “Are various degrees of consciousness (impossible to illustrate) similarly hierarchical?”
A paper published recently (March 2021) in the magazine NeuroQuantology offers answers. Link to pdf of the paper:
The Tao te Ching says that even darkness, or what is not perceptible to us, is nested hierarchically:
Darkness within darkness, the gateway to all mystery.
What is sub-sensible to us humans (who reside halfway around the purple loop) may be quite sensible to our cells earlier on the loop. And, what are to us, as individuals, supra-sensible signals, can evoke statistically predictable behaviors among crowds of us, or communities, or ecosystems, further around the loop.
Linear Trajectories are Abstractions
Sine waves provide a clue that singled-out entities comprise two aspects that oscillate around a core ground state in which they are mingled-in.
Of a particular trajectory’s dual aspects (depicted by the sine wave above), one is measurable (closed/within, like the cardio aspect). The other is transcendent (open/beyond, like the pulmonary aspect), and is often disregarded, even though it is part of the cooperative, complex system (like the complex cardio-pulmonary system).
In your mind’s eye, can you visualize the sine wave that alternates between any two contiguous levels/dimensions, such as consciousness and corporeality, joining the two and carrying them onward, sustaining them into the future?
In this chapter about the Lattice Model of Quadernity, we explored how a single entity can appear to have a measurable trajectory, only by disregarding all the influences within and beyond it, without which, of course, it would not exist.
Taking the wave-particle duality of light as an example, ask yourself, “Can the trajectory of a single photon ever exist without its metaphysical wave?”
A Couple of Gifts for Hanging In to the End!
Please allow the aesthetic of Moorish tiles and lanterns to bespeak the beauty of our brand-new Lattice model.
And, here is a lovely little video (only 4 mins.) explaining the sacred geometry of Islamic patterns, such as those above. May the profound symmetry of this ancient art touch your heart and inspire your soul.
So far, you have acquired understanding from the chalkboard Quadernity model of how two contiguous domains are combined into a single fundamental unit. Relatively speaking, the domain represented by the upper quadrants are more ethereal, while the domain represented by the lower quadrants is more dense.
You also have learned about open and closed systems. It is not difficult to imagine that the open system is less dense than the closed system. Closed systems depend upon open systems for their continued existence. There is no such thing as a closed system in isolation, yet science foolishly bases its experiments on the false premise that a system can be completely isolated from extraneous influences.
From the original chalkboard model to the new cylindrical lattice model, we have extended our perception of Quadernity from two dimensions/domains to four dimensions/levels of interactivity.
Also, we have gone from two interacting Subjects cooperating within one entity/system to two interactive doubled systems: the cardio-pulmonary systems exchange blood gasses, and flora-fauna systems Exchange nutrients.
Next, we shall proceed to a whole new unit. The Mathematical Models of Quadernity will help us learn the limitations of our habitual linear thinking and develop proficiency in non-linear thinking, without which we cannot begin to solve the ominous, complex issues threatening our home planet, and therefore ourselves and our families and friends.
Hopefully, this sense of urgency will help overcome any concerns you may have about mathematics and/or numbers. I myself, have no schooling in advanced maths; therefore, you can rest assured there is no math in this unit beyond what was learned in high school, and even if you have forgotten that, don’t worry! Everything is broken down, step-by-step, to its ultimate simplicity. Because of its importance, I wanted to leave no one behind.
P.S. In the upcoming unit, you will enjoy lots of fun videos, astonishing revelations, and solve a mysterious enigmatic formula!