We set out in this post to 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.
From our now familiar chalkboard-grid, coupled with our understanding of the universal dynamics between contiguous dimensions, Pull * Transition * Push * Rest, or PTPR, we transform the original Quadernity Model, with its two-by-two angularity, into a lovely Lattice with fluid curves.
We will go easily, step-by-step. No worries…it’ll be fun!
From the simple grid model of quadrants, we must make small modifications (not to the principle of Quadernity) in order to account for the multi-level dynamism that actually spans the living universe.
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 who perform coordinated rounds of PTPR, as seen in the two-by-two grid of our original Quadernity Model:
The green and blue diagonal arrows Transition between the physical domain (lower quadrants) and metaphysical domain (upper quadrants).
In the chalkboard graphics below, we carry the opposition of blue and green arrows on the diagonals. The black-dashed arrows, which move retrograde to the colored arrows, are now added. 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.
The black-dashed arrows indicate retrograde movements, allowing the Subjects to re-position and reset their potential for another Pull. The ‘reset’ that ‘returns’ a Subject to Rest in His/Her initial quadrant (where He/She will again initiate another round with a Pull) implies the possibility of an ongoing feedback process.
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.
The original grid nicely illustrates the four functions performed sequentially (PTPR) by both Female and Male Subjects; however, Rests do not actually move backwards. The Subjects’ return to a state of Potentiality in Rest indicates the completion of its cycle. The Subject does not actually return to a previous spatial position, as the 2-by-2 grid of Quadrants might lead us to erroneously think.
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 actions of the opposite color.
Behind the blue lines there are green rests and behind the green lines there are blue rests. We must skew the waves to see 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 as the wave amplitude and base line.
Now, do you see this 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 expect to see a Female process without an accompanying Male process. Ah, yes, we must breathe air to live! The bodily movements are shown in green and the movements of air into and out of the lungs are a logical candidate for the blue lines (Father Sky).
How did the Transition convert the O2 that we inhaled into the CO2 that we exhaled?
Individually trace the green and blue sine-wave curves above. At the Male peaks and Female troughs there is a Transition. Depicted in the Pragmatic Schematic, this Transition is called an Intra-Change.
The images above show Pulls at the left of the Pragmatic Schematic and Pushes at the right. We are reminded of a couple of magnets, situated side by side. (Hold that thought; we will come back to it.)
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.
The gasses are Pulled, Transitioned and Pushed; they are not a Subject doing the actions; therefore, the blue lines should not represent the gasses, as we had thought when first composing the sine-wave above.
Who is the Male Subject participating in breathing, this all-important, life-giving process?
To think this through, we sequence the breath, using our trusty Pragmatic Schematic. The PTPR labels from both the green and blue schematics above are combined into a single PS below.
In contrast to the two separate magnets from above, this time the two magnets are conjoined. (Please add this impression to the previous and hold them both a little longer.)
As Subject of the Circulatory System, the Mother/Female/Body acquires and circulates O2.
As Subject of the Pulmonary System, the Male/Father/Sky extracts and expels CO2 from the body.
The gasses that undergo Intra-Changes and Ex-Changes are objects, simply going with the flow.
Diastole is a vacuum-like condition by which the heart retrieves de-oxygenated blood from throughout the body, sucking it through capillaries and into veins, and Pulling it into the right cavities of the heart. From there, the blood moves through a series of valves and into the lungs where CO2 is extracted and the blood is reinfused with oxygen. The re-oxygenated blood is then shuttled to the left cavities of the heart, from which it gets pumped back out to the body. (Notice the essential role the lungs play in Transitioning blood from a de-oxygenated state back to an oxygenated state.)
With a systolic contraction the oxygenated blood is Pushed out from the heart through arteries and capillaries to nourish the organs and tissues of the body. After each contraction the heart Rests while it elastically rebounds, creating diastole again.
Breathing entails a lot more than we actually sense.
We finally come back to our patiently-held impressions of the single, sequentially oriented magnets and the magnet which contains both north and south poles at its center. (If you cut a magnet in half, you will have two magnets, each with north and south poles, so this is factually true.)
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 (Female Pushes/Male Pulls), seen inside at the center of the torus, and how their Rests are mingled-in in their non-linear Private Nighttime Relationship, shown as the interconnected web, into which the Male Pushes, and from which the Female Pulls.
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.
Inside the torus, the Male Subject of the pulmonary system Pulls from the Female’s Push. The cells of the body/Female have expelled/Pushed deoxygenated gas into the blood and returned it to the lungs. The Male Pulls the CO2-rich gas from the blood in the heart, Intra-Changes it over to the lungs, after which He exhales/Pushes the 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 involve both partners as they Pull from and Push toward each other. Intra-changes involve Transitions that occur within each partner while the other Rests.
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 the points on the axis and at the amplitude. Quadernity shows that both the Female and the Male have these two points, making a total of four fundamental points.
Comparing Closed and Open Systems
Compare the open feedback system (left below) that 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 color are obscured/overshadowed by the triple actions performed by the opposite color.
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 right to left or vice versa. 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 (as did the past graphics with brown arrows). The two processes, however, move in opposite directions. 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
Should we suspect this degree of complexity in other dynamical systems? Given the examples on this post, the planting and harvesting seasons, as well as the metamorphic phases of the Lepidopteran, we may lean toward the affirmative.
Because the water and rock cycles, discussed in the chapter, Pull * Transition * Push * Rest, are ongoing, we must recognize in them that micro and macro influences Transition into their own meso-cycles of PTPR.
Transitions are not a one-way exchange; therefore, the meso-level both affects, and is affected by, the up-line dimensions (above/outside) and the down-line dimensions (below/inside).
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.
Having firmly grasped the notion that countless other dimensions exist between the gross representations of varying scales that are pictured above, such as cells, tissues, body systems and organisms, we may come to wonder, “Are various degrees of consciousness (impossible to illustrate) similarly hierarchical?”
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.
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?
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.
In upcoming chapters we will continue to build new models to elucidate their implications in human scale, and as above, so below.