Under the masthead title, Chalkboard Models and Other Insights, the first chapter called Pull * Transition * Push * Rest, Nature’s Ubiquitous Sequence taught us a universally important sequence of actions (abbreviated PTPR) that pertain to all dynamical systems.
In the graphic below of the Pragmatic Schematic (abbreviated PS), locate the three actions (Pull * Transition * Push) inside the new model and notice that the Rest is found outside, beyond the overlapped circles.
A good example of PTPR from human-scale biology is found in nerve transmission. Below a single neuron has been overlaid upon the PS. Though not a perfect fit, we can still grok how PTPR describes the sequential functions performed by a nerve cell.
Follow from left to right in the image above: Molecular neurotransmitters are 1) Pulled/received as INput by dendrites. The cell body decides whether or not to relay the nerve signal to other nearby nerve cells. (How it does that is beyond the point of this narrative.) To propagate the signal received, the cell body 2) Transitions from receiving to sending forth that signal. The electrical pulse dies at the axon terminal, so from that point the neuron must 3) Push/produce neurotransmitters as OUTput. The three actions (P-T-P) constitute the electrical pulse, which, from start to end, is contained within the neuron itself.
Just outside of the nerve cell–between it and adjacent neurons–the electrical pulse is 4) at Rest. The small space between adjacent neurons is called a synapse. To propagate the signal across this synaptic gap, the signal must be converted from an internal electrical pulse into external chemical molecules. The OUTput neurotransmitters then traverse the interstitial medium to be received as INput by dendrites of nearby nerve cells.
Without the aid of chemical transmitters, the nerve cells alone cannot propagate their signals. The nervous system, as a whole, includes and transcends both its individual neurons and its neurotransmitters.
PTPR in Breathing Revisited
When we first learned of PTPR it was in relation to the process of breathing. Each of our lives, and each of our breaths, begins with an inhalation/Pull and ends with an exhalation/Push. If we carefully attend our process of breathing, we can perceive the Rest between individual breaths. Rest comes after a Push and before a Pull.
On the other hand, after a Pull and before a Push, comes a Transition. In this Transition the direction of air flow reverses, from the Pull of air into the mouth and down into the diaphragm, to the Push of air up from the diaphragm and out through the mouth.
We do not breathe out the same air we just breathed in (what would be the point of that?). Between the inhalation of oxygen rich air and the exhalation of carbon dioxide rich air there must be a point at which an exchange of gasses occurs.
In normal respiration, the Transition that achieves a change of direction and an exchange of gas is so fleeting as to be nearly imperceptible.
Transition Emphasized by Pendulum Balls
In the brief video below, the Transition between an initial Pull of the leftmost pendulum ball (alpha ball) and the eventual Push of the rightmost pendulum ball (omega ball) has been extended in duration by adding a few interim pendulum balls through which the force* must pass.
- Initially, the leftmost ball (alpha) was Pulled from its original Rest (low center) to the beginning of a nascent arc (upward left), where the ball was briefly suspended in the arc’s alpha Rest position. Note that the alpha Rest of the alpha ball was low center, while the alpha Rest of the arc was upward and far left.
- As the ball was released it fell towards its desired Rest. Were it not for being tethered by a string to the entertaining little apparatus, the elevated ball would have fallen straight downward. In free fall, an object accelerates toward earth at a rate of 9.81 m/s² (m = meter; s = second) meaning that for every second the downward velocity increases by 9.81 m/s. A meter is equivalent to 39.37″. Multiplying by a factor of 9.81 we get a velocity of 386.2197″ per second, increasing every second by another 386.2197″ (or roughly 32′) during the fall to earth. For ease of math we will assume our pendulum ball is elevated 3.862197 inches; consequently it would fall in one-hundredth of a second. Without the additional balls or the tether, the alpha ball would have dropped straight down and rolled away until the acceleration it had acquired was exhausted by friction. Due to its tether, the ball falls in an arc to the right. Besides being tethered, the alpha ball’s trajectory is interrupted by the four additional balls. Without the interruption of these four balls, the alpha ball would have climbed in an upward arc along the curve of a circumference determined by the length of tether (radius) restraining it. The alpha ball’s acceleration (a) times its mass (m) equals the momentum (f) it transfered through the three intermediate balls and into the fourth, or omega ball. F = ma.
- The omega ball receives/Pulls the acceleration that was Pushed from the alpha ball. Without the tether, the omega ball would have traveled horizontally rightward in reaction; being tethered by a string, it was forced instead to arc upward as it moved rightward.
- The omega ball decelerates as it travels upward. Having exhausted the momentum in its climb, the ball briefly pauses at the omega end of the overall arc. Beyond the swing of this arc there is no more motion. Beyond the arc there is only the arc’s Rest. Rest (R) transcends the triple actions P-T-P. The alpha/beginning and omega/ending of the arc are enclosed within the transcendent Rest that is before its beginning and after its end.
The Pragmatic Schematic (PS) below represents graphically the initial pendulum swing, arcing from upper left (arc’s alpha point) to upper right (arc’s omega point).
The omega ball, having exhausted all the acquired acceleration, naturally wants to return to its own Rest position, the lowest, center-most position possible. Naturally, this omega ball would also free fall straight downward were it not for the tether. Being tethered, the mass of the omega ball accelerates in the opposite direction, arcing from right to left.
The omega ball Transitions the re-acquired momentum through the three central balls and back into the alpha ball. The alpha ball appears to be Pushed from its Rest position, rather than being Pulled from it, as it was initially. This is an illusion though, from our perspective.
Acceleration is transferred. This means one ball Pushes acceleration and another ball receives/Pulls that acceleration.
In this five-ball pendulum set, acceleration is Pushed from the alpha ball through three interim balls that show no reaction and is conveyed at last into the omega ball, which does react by arcing upward. This process repeats, back and forth, until all the energy of acceleration is gradually depleted by friction and the resistance of air pressure. At such a time the balls become still again, Resting as close as possible to the low center position.
The Rest position of the balls is low center; it is where they would stay if there were no outside influence.
Take note that there is no need for an additional outside influence to initiate the return half of the cycle because there is now feedback between the alpha and omega balls.
Before the video began the balls were at Rest, mingled in, stationary in their lowest energy state.
What initiated the behavior of the pendulum balls?
The initial Pull was introduced from beyond the system. Though it cannot be seen, a human hand provided this initial Pull. When the alpha ball was singled out, the uplifting force contributed acceleration to that ball.
Without additional input of energy to offset the entropy, the pendulum is a closed system. A closed system is subject to disorganization (entropy) as initial resources are steadily expended. Open systems acquire sufficient resources to continuously maintain the strength of its cycles.
To sustain the oscillating movements of large display pendulums, such as the Foucault’s Pendulum in the Science Museum of Richmond, VA, magnets are employed, effectively turning the closed system of pendulum balls into an open system that dependably maintains the acceleration in both directions.
Learning from Magnets
Acknowledging the obvious fact that the leftmost alpha ball began with a Pull, and the rightmost omega ball ended with a Push, we are reminded of what happens at the two poles of a magnet.
Do you notice the similarity of the magnet within the PS and the neuron within the PS, which was shown at the top of this page? Look at the arrow heads. The left terminal Pulls and the right terminal Pushes.
From outward appearances there is no effectual difference between a single magnet and conjoined half-sized magnets as seen below.
Mentally, compare this exchange with the exchange of gases, and change of direction, that occurs in the Transition between the inhalation (Pull) and the exhalation (Push) of each of our breaths.
Likewise, the exchange of acceleration and direction of movement (from downward to upward) between the alpha and omega balls can be seen as a Transition.
Paired Pulls and Pushes always require a Transition through which a transfer of something is accomplished (gases in respiration, acceleration in the pendulum balls).
Female and Male in the New PS
Dynamic activity indicates two interactive participants. In Quadernity, we understand the coupled systems act together as a Female and Male.
In the PS below, the left circle is colored green to represent the Female. The right circle is colored blue to represent the Male.
We understand from our Chalkboard 2×2 Model of Quadernity that both Male and Female perform PTPR.
The two halves of the cycle, each consisting of Pulls * Transitions * Pushes (PTPs) are shown in green and blue. The first half of every arc PTPs from up to down, then the second half PTPs from down to up. Both halves of the first arc move from left to right across the PS. This is followed by the second arc, which moves backward from right to left across the PS. Two full arcs take us full circle/cycle.
With this understanding we color-code the conjoined magnets and compare them with a Sine Wave.
Compare the diagram of an open system (left below) which continually renews its resources, with the diagram of a closed system, (right below) which gradually runs down the initiating energetic influence.
The two semicircular arcs are halves of a full cycle/circuit/circle. The arcs have been shifted to show their opposing directions on opposite sides of an axis.
Remember from the chalkboard model of Quadernity, the dashed arrows indicate a return to the Rest state, which happens after expending/releasing/Pushing excess energy. The pendulum balls stay at Rest until energy of acceleration is again transmitted into them.
The closed system (right above) correlates to the (non-magnetized) pendulum behavior. The return half of the cycle (in blue) is rotated on the axis to be seen above the first half of the cycle (in green). Within a full cycle/circle of a closed system, the direction alternates: left-to-right and right-to-left.
In the PS model of Quadernity, an exchange within the mandorla (almond shaped area of overlap) occurs as the Female Push is met with the Male Pull. The Female OUTput becomes the Male‘s INput during this Transition between opposite movements/forces.
The Female and Male enjoy their Rest states, outside the Pragmatic Schematic, which is similar to the synaptic gap, from the previous example. Inside the PS, the Female and Male are active. From the Rest state, the Female Pulls (Yin) and into the Rest state, the Male Pushes (Yang).
Check out this aside: The Ins and Outs of Yin and Yang.
Four Seasons through the Lens of Quadernity
In each of the four seasons, the Mother and Father dance together rhythmically, staggering their PTPRs so that their Pulls and Pushes align and their Transitions and Rests align. The Transition of one system carries its partner-system over its Rest.
As we compare the four seasons, as shown in the photos above, with how they line up in our trusty Pragmatic Schematic below, we note that the two different relationships (as established in Divine Divisions) enjoyed by the Mother and Father are more apparent in the graphic than in the photos.
In the photos, the Female Pushes visibly ripe produce from the plants, to be harvested by the farmer (Male Pull). In the spring photo, however, the processes are invisible. The Female Pulls the Male‘s seed and secretly prepares it to grow and produce. Ensconced in the warmth and darkness of the Mother, the seed is invisibly Transitioned into a productive plant.
Invisible and Visible Moon Phases
Like the story of the seasons, delivering visible produce from invisible potentiality, the moon cycles from invisibility into visibility and back again.
The earth rotates on its axis, completing a cycle in ~24 hours. During this rotation, part of the earth is bathed in sunlight while the rest is cloaked in darkness. The sun does not rise and fall as it appears to do from our vantage point; instead, we rotate out of, and into, our own shadow. The sun is ~93 million miles from earth whether our place on earth is temporarily facing toward the sun or away from it.
The moon’s cycle around earth takes ~28 days. During this span of time, the moon is said to wax and wane, though it does neither. The moon retains its size and shape throughout its cycles.
The moon rotates on its axis once in the same time it takes for it to revolve around Earth. This means that always the same side of the moon faces Earth.
Half of the moon is always lit. When we see all of the half-moon that is illumined, we call it a full moon. When we see all of the half-moon that is unillumined, we call it a new moon. During other times of the month we see varying degrees of the moon’s dark and lighted sides.
In showing the moon images, arrayed across the PS, its entire cycle appears in a linear advance, waxing from the beginning, reaching fullness in the center, waning toward the end, and then Resting until the next cycle begins.
The moon helps us recognize that just because something is unseen does not make it unreal; and the Pragmatic Schematic helps illustrate how dual systems (comprising Female and Male partners) sustain their dynamic activities and confluent processes.