Aside: Inside and Outside Spaces

Differentiating inside and outside spaces is essential to the logic of this aside.

Any Particularity (any particular entity) has both INside and OUTside spaces.

Even the most minimal entity/system (E/S) would necessarily involve a specific content (inside-space) and a larger context (outside-space).  Inside-space/content is contained within the boundary of an E/S, and outside-space/context is beyond its boundary.  The boundary both divides and connects the opposing spaces.

A bubble is boundary curving around onto itself, between an inside-space and an outside-space.

Screen Shot 2015-03-24 at 5.16.38 PMSomething as simple as a bubble must still somehow balance structural influences (such as pressure differentials) with issues of substance (for example, viscosity or tensile strength).

More on that in Brilliance of Bubbles.

Inside-space and outside-space are differentiated also by their manners of organization, relative to the Particularity.  For example, our own inside-spaces are dynamically cooperative, full of co-functioning Parts that we collectively comprise.

Particularities with whom we knowingly Participate are far outweighed by those with whom we only Participate unconsciously.

Nested Hierarchies Manipulate Inside and Outside Spaces

A fish has inside-space within its surface/boundary and outside-space beyond its individual surface/boundary.

A collective of coordinated fish (such as the ‘school’ depicted below) has a fairly-well demarcated boundary that defines its inside and outside spaces as well.

The inside- and outside-spaces of the school transcend and include the inside- and outside-spaces of its individual fish.

Spin and Span

The distance from the entity’s center to its boundary is the radius of its Span.  As the entity’s radial Span increases, its boundary Pushes outwardly (centrifugally) encroaching into the surrounding outside-space.

Notice how the circumference enlarges as the radii lengthen from the central source.

Inside-space Pulls inwardly from the boundary.  This centripetal compression can curve the radii, reducing the overall circumference.

Read more about the Geometry of Spin and Span.

In an unknown or potentially dangerous external environment, we may participate in a larger collective to actually enlarge our (centrifugal) Span (lengthen the radii and increase the circumference).  The Span of the school shown above far exceeds that of any one of its participating fish.

The fish have masked their individual vulnerabilities by collectively concocting an illusion of ominous opposition sufficient to dissuade potential predators from attacking.

Each fish has its own external surface area.  The external surface area of an entire school of fish is far less than the sum of surface areas of all the separate fish in the school.

The school of fish, through the coordination of individual fish, have minimized the individual’s exposure to predators.

The Archetypal Cosmos, quoting Fritjof Capra:

The tendency of living systems to form multi-leveled structures whose levels differ in their complexity is all-pervasive throughout nature and has to be seen as a basic principle of self-organization.

Capra’s observation affirms what Quadernity models.  OUTformation is fractal (self-similar organization apparent across multiple levels of complexity), while INformation is holographic (present at every point, accounting for leaderless systems like a school of fish or a flock of birds).

Boundaries Both Connect and Divide Spaces

Every entity/system (E/S) depends upon its own environment. No entity exists as an entirely isolated, closed system.

An Observed entity‘s near outside space (atmosphere) contains or is its direct Observer; it re-sources the entity-system within it.  An entity’s far outside-space, or environment at large, is largely beyond its control (though not beyond its influences).

As Particularities, we are the gate-keepers of our boundaries.  How we perceive ourselves in any given situation determines whether we shelter our inside-space, repelling an onslaught of intrusions from outside-space, or whether we open our boundaries to the myriad potentialities, including both resources and risks, which are ever-present in our outside-space.

The management of environmental risks and resources manipulates the boundary between an entity/system’s inside- and outside-spaces.

Inside-space of the starling murmuration, seen below, Pulls centripetally, holding the individual birds close together, while the outside-space of each bird Pushes centrifugally against the other birds.  The balance between the inward Pull and the outward Push is sustained throughout the murmuration’s unrehearsed, but never-the-less, finely-coordinated movements.

For the benefit of functioning together as a singular, more complex E/S, the participating creatures forfeit their usual amount of outside-space (akin to our own ‘personal space’, which surrounds us to the extent of about an arm’s-length radius).

As each bird or fish gives some of its individual outside-space to the outside-space of their respective murmuration, or school, by which:

  1. they achieve their closest possible proximity for safe, unified navigation,
  2. reduce their surface exposure, and
  3. enlarge their ‘footprint’ to seem less vulnerable.

These objectives are met spontaneously and leaderlessly, without planning, communicating, or thinking!

Relationships may be lateral, as spouses in a marriage, or employees in a cooperative; or relationships may be hierarchical, as a cell within a body, a planet within a solar system, or a thought entertained in the context of an established mindset.

Everything, from the infinitely complex universe down to the simplest, infinitesimal quantum, operates within at least one relationship–the one they have with their environment.

In both lateral and hierarchical relationships, each party impacts the other(s) in ways that are either direct/obvious or indirect/subtle.  Direct associations with blatant, consistent effects become predictable (flipping a switch lights a room, drinking some water quells thirst); whereas, indirect associations may subtly accumulate until an abrupt phase change takes us by surprise (global climate change, collapse of a financial bubble, diagnosis of advanced cancer).

Explosion and Implosion

An explosion, as seen from the outside, is the disintegration of Matter (LRQ).  Fragments of material are Pushed forcefully through a previous boundary, spanning matter particles into what had been the outside-space of the object before explosion.

When seen from the inside, explosion can be reframed.  What had been outside-space (relative to the object) enters through the object’s boundary, expanding the radius of the exploding object’s inside-space.

Thinking about explosion as an increase of inside space will aid in our contemplation of implosion.  Implosion, the opposite of explosion, decreases inside-space and increases outside-space, relative to the imploding object.

Spinning within a closed boundary contracts the Subject’s inside-space, expelling it to the outside-space.  Watch the slo-mo video to see for yourself how the matter falls in on itself, while what was inside-space moves into the outside-space.

Did you notice how the bulk of the building’s material disintegrated and fell nearly straight down onto the foundation?

In an implosion, as compared with an explosion (shown a few paragraphs above), a relatively small quantity of material is projected outwardly.  Instead of blowing out chunks of MATTER, it is the inside SPACE that is forced out during implosion.

Implosion decreases inside-space and increases outside-space, relative to the imploding object.  Additional examples of decreasing inside-space include: swarm behavior, coalescing material, molecular collapse and nuclear fusion.

Referring to the loss of inside-space Symmetry Magazine states:

If we lost all the dead space inside our atoms, we would each be able to fit into a particle of lead dust, and the entire human race would fit into the volume of a sugar cube.

In PTPR, Rest is OUTside and Transition is INside

Quadernity’s PTPR (Pull * Transition * Push * Rest) illustrates a universal pattern, one that we recognize at the human scale in our breaths and in nerve transmission.


  • Between the inhalation/Pull and the exhalation/Push INside of a single breath, there is a Transition in which gases are exchanged.  (We inhale to receive oxygen and we exhale to eliminate carbon dioxide.)
  • Before the inhalation and after the exhalation of each breath, there is a Rest.  OUTside/beyond the P-T-P of the breath, there is a Rest.  Yet, something must link the breaths together sequentially.  Breathing is the process which transcends the P-T-P and includes the R.

Nerve Transmission:

  • In the INside-space of an activated nerve, an electrical pulse travels from the Pull of dendrites to the Push of axon terminals.  For an incoming signal to become an outgoing signal, the cell body must Transition it.  The cell body has the job of determining if a signal received from the neuron’s dendrites should get propagated from the neuron’s axon terminals to other nearby neurons.
  • In the neuron’s OUTside-space (surrounding it, and between it and adjacent neurons) the electrical pulse Rests.  Beyond the individual neurons, chemical molecules facilitate signal transmission from one nerve to the next.

On our familiar scale we recognize another specific example.  Metabolism comprises dual, inverse processes: the catabolic process breaks down complexity into simplicity, and the inverse anabolic process builds from simplicity up to complexity.  Catabolism and anabolism are inextricably united in metabolism.  Metabolism requires a dual cooperation of PTPR.  Metabolism transcends and includes catabolism and anabolism.  All life forms depend on metabolism.

Living is a process that transcends and includes the individual lives that endure alternating sequences of breaking down and building up their embodied parts.  Living is a complex hierarchical process that transcends and includes the births and deaths of individual organisms.  Life integrally transcends and includes the countless differentiated lives that rise and fall within it.

In Magnetism, Rest is OUTside and Transition is INside

The magnetic field, in a bar magnet’s outside-space, links the south pole of one magnet to the north pole of another.  An infinite number of magnets can be connected, one after another, just as breathing stitches one more breath to the string of breaths preceding it, then one more, and one more…

Magnetism transcends and includes bipolar magnets, just as breathing transcends and includes the inhalations and exhalations of individual breaths and living transcends and includes the building up and breaking down of organisms.

Imagine what would happen if a simple bar magnet (such as seen below) is approached at either end with the north pole of another magnet.  Pretend you hold the second magnet in your hand.  As you bring it toward the sketched magnet on the pretend-table below, the north pole of your magnet would be pulled toward its south pole and pushed away from its north pole, just as the arrows indicate.

The bar magnet is overlaid upon a PS below.  As shown, the magnet’s south pole Pulls from the outside-space (beyond the physicality of the magnet) and its north pole Pushes back into that outside-space.

In the context of magnets, one would not expect the south pole’s Pull to be yin/Female and the north pole’s Push to be yang/Male; however, with the aid of Quadernity, we understand how the magnet is just another example of a dynamical system comprising both Female and Male PTPR.

In the magnet’s central Transition the Female Push hands off to the Male Pull.

Inside the Venn Diagram (upper row below), the position labeled BOTH correlates with Transition (lower row below):

Outside the Venn Diagram (upper row above), the position labeled NEITHER correlates with Rest (lower row above).

Connecting and Dividing INside and OUTside Spaces

Locate these terms in the Pragmatic Schematic (PS) below: EITHER/Spin, OR/Span, BOTH/Spin & Span as equilibrium, and NEITHER Spin nor Span, the stillness/quiescence of the Ground state beyond the PS.

From the Ground state, all dynamical systems appear as pairs of entangled solutes that fall from solution when seeded (inception: Female receives Male in the outside-space, the metaphysical level) and heeded (perception: Male receives Female in the inside-space, on physical level).

Compare magnetic poles to the outer crescents of the Pragmatic Schematic (PS).  We see Spinning and Spanning in the PS and Pulling and Pushing in the magnet.

The terms Pull and Push are meaningful only with regard to what happens when the poles of two magnets are put together.  North and South are arbitrary designations.  Opposite poles (N & S) attract or Pull each other together; whereas, N-N or S-S Push each other apart.  In the image above, the outer Pull and Push indicate what would happen if exposed to the north pole of another magnet.  If we bent the two halved-magnets into semi-circles, their four poles would join together in two sets of S-N, forming a full circle.  In such a case, the S-N juncture would be nowhere exclusively, rather it would be everywhere throughout the circular magnet.

A single magnet can be cut anywhere and each of the smaller magnets will also have a “north” and “south” pole.  When joining two halved-magnets together, as in the image below, we see a north-pole/Push and a south pole/Pull connected in the center.

Similarly, a Push meets a Pull where the two circles of the PS overlap (reprinted below). This interior region is called mandorla or Vesica Piscis.

Content and Context

Earth exists within the atmospheric Heavens; therefore, Earth is content (inside-space) within the context (outside-space) of the Heavens.

At the level of Quadernity, both physical Earth and metaphysical Heaven become contexts (domains/outside-spaces) for their own peculiar types of content (inside-spaces).

Earth can now be understood as both context for its own kinds of content, and, on a greater scale, as content within the context of its atmosphere.

At the level of an infinite cosmos, we discover what relates the content (inside-space) of the cosmos with the context (outside-space) of Eternal Comprehensive Perfection (ECP).  Within the totality of all, there is an intrinsic dynamic — an irreducible unit we are calling Quadernity — by which the MaleFemale collaborators enmind and embody the Absolute.

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