THOLONIA 8.0.18

An instance of an archetype can only exist within the limitations of its context. That context can vary wildly, and there can be a lot of discussion as to what defines a context. For our purposes, a high-level definition is that a context is defined by the innate limits it imposes, and we define innate as that which is inherent in the archetype before it is instantiated.

For example, the concept of a car has the innate property of being a ground transportation vehicle because that is how it was designed. Its very structure is specifically intended to be a functional, efficient ground transportation vehicle before any parts were assembled. The same is true for animals and plants.

Certain social constructs may be applied to the instances of these archetypes as beliefs or interpretations, such as the Western idea that black cats are bad luck or the Eastern idea that pigs are good luck. These constructs are outside of the Form archetype. They are not material or innate properties but rather conceptual archetypes, simply ideas or beliefs overlaid onto physical instances. Males and females, by contrast, are innately different and are formed from conception to perform differently according to their respective biological archetypes. However, social constructs themselves also have archetypes, and the interaction between biological Form archetypes and social conceptual archetypes creates complex patterns. Whether certain combinations of these biological and social archetypes can create stable and sustainable patterns is left to history.

The relationship between context and concept is recursive and embedded: context applies limits to concepts, and concepts alter the context. For instance, the context of gravity is a limitation to flying, but the concept of air travel changed that context, which then changed the concept of air travel, and so on. In the world of biology, context is (usually) a force of evolutionary pressure. In the mechanical world, context is the limits and application of a material.

In the physical world, these limits are usually obvious. In the conceptual world, less so. What are the limits of ideas and concepts? One limit is their definition, which is necessary before they can even be considered a concept. Another limit is in how they are understood, which is a limitation of the conceiver’s abilities, awareness, and neurology. Aristotle and Einstein both had theories that described the Universe as finite and spherical, but these two concepts were radically different.

Another excellent example is how August Kekulé, a German chemist and one of the founders of modern organic chemistry, fell asleep during a symposium on benzene in 1890 and dreamt of atoms whirling around until they formed an ouroboros, a snake devouring its tail. The ouroboros is an ancient and mystical symbol representing the eternal cycle of life, death, rebirth, the passage of time, and the completion of effort. The symbol shows the serpent nourishing itself by devouring itself. Historically, the serpent is a symbol of the god of creation (Africa, Americas, China), immortality, resurrection (Egypt, Celtic, Americas), wisdom (Celtic), and the bearer of good, evil, knowledge, and wisdom (Greek). In short, the serpent feeding on itself represents the immortal soul’s endless growth journey in the cycle of life and death, creation and destruction.

From this vision, Kekulé discovered the benzene ring. The context of this concept was the mind and awareness of Kekulé, and the limiting factor was that being a chemist and only interested in carbon bonds at that moment, he understood from his vision of the eternal cycle of life and transmigration of souls that 6 carbon atoms form a ring. One has to wonder why such a profound symbol would have even entered Kekulé’s mind, given the countless other symbols that could have worked just as well.

Kekulé’s discovery advanced molecular biology, but he had no idea that 100 years later, the molecule of his vision would result in a “miracle material” that would revolutionize energy, medicine, electronics, food, and even sports. This material weighs almost nothing and is 200 times stronger than steel, and acts as an interface between biology and technology. This material is graphene, and it could change not only the world but also the biological structure of our being as it is already at the core of the emerging trans-humanism. If any compound were worthy of such a profound vision, it would be graphene.

From the tholonic perspective, archetypes have an existence of their own, a direction, and even an intelligence of their own (not to be confused with our human concept of existence and intelligence). Kekulé did not create this dream, as modern psychology would claim. Instead, the archetype itself advanced its cause through Kekulé.

The current understanding of an archetype is defined in the Oxford English Dictionary as:

When we speak of archetypes in the context of tholons, we are using a more general yet compatible definition that an archetype is:

These patterns are not necessarily limited to 3 (or fewer/more) dimensions. They can be, and often are, multidimensional patterns of which we can only perceive 3 dimensions as they pass through our reality. The classic example of this is the well-known “Flatland” metaphor¹. Imagine what you would see if you were a 2-dimensional person living in a 2D world and a 3D object passed through your 2D reality. You would see a series of 2D slices of that object that changed over time.

Now imagine you are a 3D person living in a 3D world (which should be pretty easy to do), and a 4D object passes through your 3D world. You will see 3D “slices” of this 4D object over time. For example, if a 4D ball passed through a 3D world, it would initially appear as a very tiny 3D ball, then grow to a large ball, then shrink to a small ball before disappearing.

In both 2D and 3D cases, you are not getting the whole picture, but in both cases, what you are getting is entirely accurate and valid for the scope of your reality.

The complete multidimensional thologram, with all its potentially infinite iterations and generations, would look like a perfect tetrahedron in our 3D world. As in the example of the 4D ball, a 4D thologram, being itself a tetrahedron, would initially appear as a small tetrahedron, which is what we, and others, are claiming all reality is conceptually built from.

The 3D model of the thologram is a 3D slice of a multidimensional concept. What the larger multidimensional object that we see as a tetrahedron actually looks like, we cannot say and probably cannot know. What would an 8D or 248D “object” appear as in this 3D world? It could appear as many, many different things. Look at all the ways a simple 1-generation-only self-similar 3D tetrahedral pyramid can appear in 2D orthographic projections. In this way, a single archetype can instantiate, be perceived, or understood in many different ways.

Now imagine the same tetrahedral pyramid with trillions of generations and many more dimensions! Its perspectives would effectively be infinite to us. What could it not describe?

2D example

The images below are a good example of how one archetype is expressed through different contexts. The archetype is based on the simple model previously described and shown in the diagram on the right. We begin with a 0-dimensional point. This point moves into the 1-dimensional space, which creates a line. In the figures below, we show this initial line as a circle’s (black) horizontal diameter. The radius is 90 units, equal to the number of degrees required to best describe a 2-dimensional plane. This 1-dimensional existence of a line then moves beyond the 1-dimensional space and into the 2D space by rotating itself. That movement will be expressed in the 2 dimensions of x and y, just as the 0D dot that became a 1D line was expressed in the single dimension of x. This means there will be a movement along the 1D x-axis and an equivalent movement along the 2^nd dimension of the y axis, which is accomplished via rotation, as rotation is the most efficient way to create a continuous 2D space from a 1D point (and why a circle/sphere is the most efficient continuous shape). Because we are rotating around an originating 0D point, that point will remain the center point.

To illustrate this, we will move the horizontal diameter line 5 units to the right and rotate it around its center point by 5°. These new lines are shown in red in Fig. 1. Now we see that this line is off-center. Where before, as a horizontal line, there were 90 units on the left-of-center and 90 units on the right. Now it is 85 on the left and 105 on the right. It continues its journey into the 2^nd dimension by moving another 5 units to the right and another 5° rotation. It continues to do this until the line returns to its starting position of being horizontal. Fig. 1 also shows where the center point is for each line (as yellow dots). The images that follow are instances of this archetypal pattern.

What is interesting about this shape is how it perfectly describes the archetypal shape of many things, from leaves, fruits, and seeds to number theory, fractals, and even the human brain and pineal gland. More than that, it is essentially identical to the same shape we get when we wrap a frequency around a center-point. The image on the right shows this as a overlay. This is significant because this “wrapping” is basic of the Fast Fourier Transform which can describe all shapes and frequencies, as well as fundamental to the Uncertainly Principle, Riemann Zeta function, prime numbers, and differential equations. We can speculate a bit here but looking at Fig. 4, the “Mandelbrot Set”, above, and seeing how the larger portion of the body is identical to the “winding” form, yet the entire set fits perfectly into the simple form, suggesting that the “winding” form is an instance of one subset, or one part, of the more encompassing simple form.

We have described a very simple model that we would expect to see in nature, which we do, in flying colors. Because this model can make successful predictions, we can say there is a valid hypothesis. Perhaps this same reasoning is why the ancient Sumerians thought Earth was egg-shaped and not perfectly round, as the Greeks imagined. In fact, Earth is an oblate spheroid, but it is interesting to see how they arrived at different archetypes. In the Greek mindset, Truth was based on what could be conceived, while in the Sumerian mindset, Truth was what is. This difference is also reflected in their languages and has led to many modern (Western culture, Greek-based) misinterpretations of ancient texts.

A few of the basic rules we can say about this shape that we can apply to a broader context are:

Historical footnote: The silphium plant is also a similar shape, similar to the strawberry, but with an interesting historical and cultural footnote. Its seed shape is thought by some historians to be the origin of our traditional heart symbol, though this is debated. As well as being known to cure many ailments, it was a natural contraceptive associated with love and passion. This plant was extremely valuable, which is why the Romans stockpiled it in the treasury. Coins were minted with the image of the silphium seed, which had the same shape. Sadly, that particular variety was farmed into extinction, with the last known stalk given to Emperor Nero, as the legend goes.

For the sake of completeness, the lines appear as follows when they complete a full 360°:

Revisiting Dimensions

If we are dealing with multidimensional archetypes, then let’s look at the dimensions of a tholon. To specify the location of a tholon within the thologram, we have to identify each tholon by an address based on its generation. This is an example of the dimension of location.

If we wanted to reference one specific tholon, such as the one highlighted in the image above, we would need to say it was located at 1,3,2,1 from the top, or it is the 1^st child of the 2^nd child of the 3^rd child of the 1^st tholon from the bottom. The areas blacked out are virtual tholons that do not really “exist” in the traditional sense, so we cannot navigate to them even though we can reference them. In this example, we need 4 dimensions to define the location of a tholon. Any dimension would have to record the path taken to arrive at any particular tholon. This is being mentioned to show that each generation of tholons increases the dimensionality of the thologram by one dimension.

For example, to identify the position (P) of one tholon at the 45^th generation, we would need a dimension that looked something like:

But it is even a bit more involved because this dimension only points to one particular tholon within which is its own 3D space. In the thologram, we cannot use a Cartesian coordinate system (i.e., x, y, z) because that would require a coordinate system that extends past the boundaries of existence, and we know that there can be no metrics in nothingness. We can only use quadray coordinates (e.g., a, b, c, d) based on a tetrahedron to identify a point within the tholon.

Does this mean our 3D reality is embedded within a parent 3D reality? According to the thologram, yes, although I have no idea how this can be tested.

An analogy we have to this idea of a 3D reality within a 3D reality is VR (virtual reality), where we can create countless 3D worlds within our 3D reality. Another analogy is how a hologram can create a 3D space from a 2D surface, and there can be many 3D spaces on top of one another recorded on that same 2D surface.

These analogies that are used to describe this tholonic concept are similar to the previously mentioned Black Hole Big Bang Theory (BHBBT), which proposes that our universe, which emerged from the Big Bang, actually exists inside a black hole within another universe that emerged from another previous Big Bang, and so on. This describes 3D universes embedded within 3D universes, ad infinitum, or embedded self-similar universes.

Synergetics

What some people today call sacred geometry our ancestors simply called geometry. Contrary to what we learned in school, geometry is as much a study of philosophy as form, space, and mathematics. Plato, Pythagoras, Parmenides, and several other great philosophers were well-schooled in geometry, but the marriage of philosophy and geometry goes back even further in history and across every culture. Take the quadray coordinates system as an example. This system is based on 60°, which comes from the 360° (60° × 6) model of a circle. One could make a case that the Ancient Mesopotamian base-6/60 number system, which gave us the 360° circle, was an early version of this idea. In fact, one could make the case that the 20,000-44,000-year-old Ishango Bone of the upper paleolithic era discovered in the Congo was an early version of a base-60 system. This bone is considered to be among the earliest instances of the concept of the number “1”. On this bone are counting marks, 60 marks on one side and 60 on the other. One has to wonder if 60 was not chosen for a reason beyond what we might traditionally imagine.

Synergetics is a modern-day example of how geometry forms the basis of the structure of creation, life, and how everything interacts with each other. Buckminster Fuller coined the term synergetics in his three-volume work “Synergetics. Explorations in the Geometry of Thinking”², wherein he explains how using a 60° coordinates system can explain both physics and chemistry, but more importantly, he believed that it also explained reality. In his words:

He explains how a tetrahedron’s points and lines (60° coordinates) describe all elementary phenomena. Moreover, he claims that synergetics can measure our experiences geometrically and that we can employ geometry regarding both metaphysical and physical knowledge.

The math of synergetics, according to Fuller, “works omnirationally, energetically, arithmetically, geometrically, chemically, volumetrically, crystallographically, vectorially, topologically, and energy-quantum-wise”³. In addition, it is pretty compatible with the empirical world, where all atoms can be described by the patterns of tetrahedrons, octahedrons, rhombic dodecahedrons, and cubes. One clever Dublin School of Technology engineer hypothesizes that thermodynamics and space-time could be unified with quadray coordinates⁴. It is worth noting that each of the geometrical shapes that Fuller claims can describe atomic structure can be made with the tetrahedron.

The thologram, which is based entirely on the tetrahedron and synergetic quadray coordinates, is a model of knowledge, thought, and ideas. It is important to remember that the map is not the territory. These models of reality are like maps that describe the terrain. There are elevation maps, density maps, road maps, water maps, contour maps, temperature maps, population maps, economy maps, and crime maps. San Francisco even has human feces maps! They all describe the same territory from different perspectives. The thologram is one of these perspectives, but even this one perspective can be seen in several ways. How many ways are there? I do not know, but the elementary three-square geometry problem (“what is the total of the angles α, β, γ?”) has been proven synthetically in 54 ways⁵, and that is just with three simple squares (the answer is 90°)! As you can imagine, there is virtually no end to the relationships, patterns, rules, etc., that can be discovered.

What separates knowledge from apophenic delusions (“apophenia” is the tendency to perceive connections and meaning between unrelated things and is considered a sign of early-stage schizophrenia) is whether a relationship, pattern or law can be tested to achieve predictable results. On the other hand, we do not want to fall victim to randomania either (“randomania” is the unofficial term for people who attribute to chance that which is clearly the result of order, the inability to see patterns where they actually exist. I suspect this disability could also be a sign of some sort of mental illness, though this remains speculative).

We agree with Mr. Feynman, but we also have a broader definition of “experiment”. Reality is reasonable by default; otherwise, it would not exist, but it is not always quantifiable and often incompatible with current science.

Types of archetypes

The 2D images of the “Examples of contextual instances of a simple pattern” (above) show a fundamental growth pattern so we might call this a dynamic archetype. The archetype of a circle is the perfect expression of the rule “the locus of all points that are equidistant from a central point” and might be called a transcendental archetype because it would take an infinite number of lines to make a perfect circle. The 5 Platonic solids (tetrahedron, cube, octahedron, dodecahedron, icosahedron) are static archetypes because they are defined by their faces and vertices only, not by any process. Jungian archetypes might be called character archetypes as they apply to the personification that tends to represent what Jung called a “primordial image”. This understanding led Jung to the ideas of anima/animus, the self, the shadow, and the persona but also shed light on the classic archetypes such as wise old man, the child, the mother, the maiden, etc. This was later expanded to Neo-Jungian archetypes such as caregiver, explorer, jester, rebel, citizen, hero, lover, sage, creator, innocent, magician, and sovereign. Not surprisingly, these twelve archetypes correspond to the twelve signs found in astrology. Whether Jung was familiar with and therefore incorporated concepts of astrology, or whether he independently discovered the same archetypes that astrologers identified thousands of years ago, remains an open question. What is clear is that Jung recognized archetypal patterns that appear across multiple ancient systems of understanding.

Everything, all of “that which is”, has an archetype that exists in the grand ontology of all archetypes. We understand the world through these archetypes even though they do not represent the reality of the instance of these archetypes, the things themselves. If I say “apple”, you understand what I mean, but “apple” says nothing about the reality of any individual apple. While this makes concepts easier to share and communicate about, it also hides much of the yet undiscovered reality of that concept. This is because we can only form concepts based on what we know, and what we know is always limited. It used to be common for things to have a “spirit”, which was a concept of a general archetype of a thing that included more than its observable qualities. It was not only the idea of a perfect instance of some thing but also the unique energy of that instance. While the concept of “spirit” still exists today, it would be rare to hear science refer to the spirit of the apple because “spirit” has been removed from the modern Western ontological vernacular; it no longer exists in the hierarchical spectrum of “all that is”, but only as a vague, undefined, poetic reference to a vague, undefined, poetic understanding of life. This is how language defines our perception of reality. A shaman may not know anything about the DNA of roses, but he may understand a lot about the spirit of roses. Who can claim to know more about the “truth” of the existence of roses? The scientist or the shaman? The answer depends on the context.

Tholonic instances are easier to understand when we look at isolated archetypes. It is easy to understand a square block is an expression of an archetypal cube, but what of a melting snowball? At what point does it stop being an expression of a sphere? From the tholonic perspective, never. The snowball came into existence as a result of many tholons (weather, terrain, gravity, etc.) cooperating and competing, exerting forces and limits in such a way that a snowball could form. The snowball changes form as these tholonic forces change due to waxing or waning circumstances that tend to reinforce some forces and diminish others. Each of these tholonic forces is an archetype because each tholon is an archetype. As these archetypal forces change, interact, negotiate, and compete, the resulting form will always be the most efficient expression of the state of those forces. In other words, everything that exists is as perfect an expression of its archetypes as is possible in the context of its existence. Everything that exists is made up of many branches of tholons or archetypes, so what we see is an amalgamation of countless archetypes that have managed to create a stable instance in a specific context.

The melted snowball is still an expression of a perfect sphere, but just a very diluted or weak expression given the strength of the other forces that have turned it into a puddle. One way to think about this is to imagine each archetype as having a field of influence (which they do, as will be explained later) similar to the way each planet has a gravitational field or how each electron has an electron field, both of which stretching to the edge of the universe. Right now, you are primarily under the influence of Earth’s gravitational field. You are also under the influence of Jupiter’s gravitational field, but it is too weak to have any observable effect. If you were to move closer to Jupiter, its effect would become more apparent. Similarly, the archetypal influence of a sphere is very strong when the water is in the form of a snowball, but very weak when it is a puddle.

Our snowball-turned-puddle is just less influenced by the “field” of the archetype of sphere and much more influenced by the “field” of the archetype of puddle (water in a low-energy state constrained by gravity). Each of these fields is defined by the archetype, which is a composite of the other archetypal forces that created it.

Some of these amalgamations of archetypes will become archetypes and parents of archetypes themselves. Perhaps the only pure, unamalgamated archetypes that exist are the concepts of somethingness and nothingness, or maybe 0 and 1.

So, when you see something that looks imperfect, think of it as perfect; it’s just that you are not aware of all the archetypal forces that are making it the way it is.

Key 66: Everything that exists must be perfect.

Examples of instances

Quarks

Here is another example of how we might discover tholonic structures in subatomic particles. Let’s look at a quark (which was initially named a parton by Richard Feynman to describe a hypothetical particle inside the atom’s nucleus).

Currently, we understand that protons have a charge of +1 and are composed of 2 up quarks, which have a charge of +2/3, and 1 down quark, which has a charge of -1/3, and neutrons have a charge of 0 and are composed of 1 up quark and 2 down quarks.

This is seen in a single complete tholon which consists of a real tholon (proton) and its virtual reflection tholon (neutron) as shown in Fig. q1 and Fig. q1a below. The upper trigram has a parent trigram at the top, which we can assign a value of -1/3, and the two children can be assigned a value of +2/3. The center child trigram, which is always a reflection trigram, has a value of 0. The opposite is true for the lower reflection trigram as well. With these values, the upper tholon has a charge of 1, like a proton, and its reflection tholon has a charge of 0, like a neutron. This also seems to indicate that a truly complete tholon requires two tholons; itself and its reflection tholon. It is worth noting that the simplest element, hydrogen, is the only stable element that does not have neutrons (heavy hydrogen, or deuterium, has 1 neutron and is stable, and the radioactive tritium has 2 neutrons).

What is remarkable here is that the tholonic structure naturally produces the exact charge pattern of a proton: The one value of -1/3 and two values of +2/3, which perfectly matches the charge distribution of 1 down quark (-1/3) and 2 up quarks (+2/3). This pattern emerges from the fundamental geometry of the tholon itself, where the parent trigram holds one value and the two child trigrams hold the other. Even more significant is that the negative charge of -1/3 appears at the top point, which is the parent Negotiation state directly sourced from the original N-state. The two children, representing Definition and Contribution, each carry the same equal positive charge of +2/3. Notably, the up quarks (children) are lighter than the down quark (parent), which aligns with the tholonic principle that child states are derivatives of the parent state. When these two children interact, they would create a middle point with a combined charge of +4/3, which would become a new N-child. However, since N-states carry a charge of -1/3, the total charge becomes -1/3 (parent) + 2/3 (D) + 2/3 (C) = +1, exactly matching a proton. This demonstrates that the charge distribution is not arbitrary but follows the fundamental N-D-C pattern of tholonic structure. Yes, this may simply be a “coincidence”, or a property of thirds, or the result of some as yet unknown relationship, such as how the spiraling of galaxies, the female-to-male population in bee colonies, and the branching of the sneezewort plant are based on the same ratio of 1.618 (phi). Still, it is more reasonable to start with the idea that the tetrahedron, the conceptual building block of reality, and quarks, the actual building blocks of reality, follow the same rules.

Fig. q1a, which is the folded 3D version of Fig. q1 is also the same shape as the quartz trans tridymite silicon oxide molecule, with the N-states holding the same position as the silicon atom. For those playing along, note that the trans tridymite structure contains 4 oxygen atoms (atomic number 8 each, totaling 32) and 2 silicon atoms (atomic number 14 each, totaling 28), resulting in a combined total of 60 protons.

Fig. q3 is from the previously referenced E8 Lattice research⁶,⁷ that explains the various models within the E8 crystal and describes this shape as “representing all 8 components of the electron”. This is not exactly the same as what we are saying here, but in a different order, which supports the overarching idea regarding tetrahedrons and subatomic particles.

Subatomics

To summarize, the foundation of all creation lies primarily in the 3 basic patterns created by the tholonic matrix, shown in the image to the right. All 3 patterns are redundant, but only one (the yellow hexagonal pattern in the center) is self-similar or fractal, and this is the only pattern that supports the N-states. For this reason, we assume that the yellow hex grid exists between the other two grids, and an N-state comes into existence between two poles.

You’ll notice that in Fig. h1 (from the previous chapter), the lines of succession from N-sources to N-states exist across all 3 directions. We also saw 6 N-states in a complete (virtual and real together) tholon. If our tholonic quark model is in the ballpark, we would expect to see 6 classes of quarks, and we do. They are called “flavors”, and they are: up, down, strange, charm, bottom, and top.

Neutrons do exist, which seems to go against the tholonic idea that the virtual tholons do not create anything, but remember, this thologram is a model of energy and relationships, not of form, so what we would expect to see is something that has zero net charge, like a neutron. In fact, the neutron has an internal charge distribution from its constituent quarks (1 up quark with +2/3 charge and 2 down quarks with -1/3 charge each), but these charges balance out to a net charge of 0. And what holds all these subatomic particles together? The strong nuclear force (mainly), which is the strongest force in the Universe (approximately 10³⁹ times more powerful than gravity at the subatomic scale) and the tholonic equivalent to, or represented by, the six integrated N-sources at the center of every hexagram.

In the thologram, all the NDC points are equidistantly separated from each other, meaning they all repel each other equally, except for the blue dots/N-states, which form strongly bonded clusters when forced together. We see this same quality in the strong nuclear force (SNF), which has a “weird” quality such that it gets stronger as like-particles are separated, pulling them back together like a rubber band. When these particles are very close to one another, however, the SNF becomes weaker and they behave as if they are nearly free! Physicists call this weirdness asymptotic freedom.

Most of what we have shown here involves how the movement of energy, in accordance with laws, brings form and, by extension, ideas, concepts, and archetypes into existence. Yet, almost nothing is said about the nature of the energy itself, other than that energy in its purest form is ultimately an expression of A&I. Here, we have 6 N-sources that hold the tholons together to form the center of creation. In the quantum world, there is a similar concept of an energy that holds everything together, called gluons. Gluons are massless, absorbed, and emitted by quarks, and hold quarks together using the SNF. 8 types of gluons form the connections between quarks to create a proton, just as 8 trigrams form a complete tholonic model of a proton (4 real trigrams from the upper parent tholon and 4 virtual trigrams from the lower reflection tholon).

Tholonically speaking, it is the laws described as geometry in the thologram that hold everything together. Is it reasonable to wonder if the other forces that hold things together, which are electromagnetism, the weak nuclear force, and gravity, are also represented geometrically somewhere in this infinite maze of tholonic patterns?

Understanding the tholonic nature of these forces may well give us an insight into the source of energy, which is to say, understanding the nature of the A&I that creates this reality.

But what about the electron? Where is that? Tholonically speaking, the electron is a product of the imbalance of the parent tholon, which instantiates as a proton and has a total charge of +1. Therefore, the parent tholon will naturally create an equal and opposite tholon that instantiates as an electron with a charge of -1. Where would this electron exist? At the opposite side of the N-sources across the scope or spectrum defined by the children C and D, which is where N-states manifest as stable expressions. In a 2D tholon map, this location is the outermost edge of the hexagram, and in a 3D tholon, it is the outermost exposed edges (image right).

As these N-states represent 0-dimensional archetypal concepts that instantiate as physical particles, we can understand why electrons, when instantiated, are unaffected by the SNF. The tholonic geometry shows that the N-child (which instantiates as the electron) emerges at a location that has no direct geometric connection to the six N-sources at the center (which instantiate as the SNF binding quarks). The geometry itself is the archetype that determines which instantiated particles will interact with which forces.

This may seem contradictory, as the electron does have a specific geometric location in the tholonic model (appearing somewhere along the spectrum between the Definition and Contribution points), yet we just said it has no geometric connection to the SNF. The key is that the electron’s geometric position (along the spectrum between the outer C and D points) is in a completely different scope from where the SNF operates (at the central 6 N-sources). These are two distinct geometric relationships within the same overall structure, operating at different scales and locations.

Neutrons and protons are hadrons, and all hadrons are made of quarks. A proton has 2 UP quarks and 1 DOWN quark, and a neutron has 1 UP quark and 2 DOWN quarks (note: DOWN quarks are heavier than UP quarks, which contributes to why neutrons weigh more than protons). In the image on the right, you can see both the proton and the neutron as their component quarks. Here we can see the same model applies but in a different context. An electron is not the product of a proton and neutron; elements are their product. It is more the product of a neutron, as neutrons decay into electrons, and in the model of the neutron, it would appear between the 2 DOWN quarks.

Applying the 2D tholon maps in the context of the SNF, we see that within a single proton or neutron, the SNF holds the three quarks together at the center. When protons and neutrons combine to form atomic nuclei, they interact through the residual strong force while maintaining their distinct identities. In the tholonic model, those 6 N-state clusters in the center of the hexagons would appear as 6 separate N-states

, rather than 6 joined N-states

, reflecting how nucleons remain distinct even while bound together. (What about the virtual tholons in this larger context? Do they instantiate as anti-matter?).

If the tholonic model repeats itself at every level, this means that everything that exists is somehow based on a self-similar trigram, conceptually at least. The underlying point is that the thologram, or any model of reality, is one perspective of a much greater multidimensional model. Being multidimensional, it can be perceived in many ways. All models, including those of our ancestors who lived in the wild and in a world dominated by spirits, plants, insects, predators, and gods, were built on the same concepts that were adapted to their context.

There’s another pattern that we see in the quarks that gives some insight into the nature of patterns.

There are 6 types of quarks, arbitrarily (for the most part) and whimsically named UP, DOWN, CHARM, STRANGE, TOP, and BOTTOM. While there is surely some pattern of the 6 quark types to the thologram, protons and neutrons are only composed of UP and DOWN quarks, so we will just look at these.

The 3 quarks that create a proton are UP-UP-DOWN, and the 3 that create a neutron are DOWN-DOWN-UP. While there are particles that are composed of 3 UP and 3 DOWN quarks (delta baryons), they are extremely unstable and imbalanced and only exist for ~5.63×10^-24 seconds. If we were to assign UP=0 and DOWN=1, we see that the 8 possible combinations of 3 quarks are 000, 001, 010, 011, 100, 101, 110, 111, which are also the binary values of the numbers 0, 1, 2, 3, 4, 5, 6, 7.

Because there is no significance to the order of quarks, DUU is the same as UDU and UUD, and UDD is the same as DUD and DDU. We are only interested in the count of 1s and 0s in any triplet, not their order. This results in 4 types of groupings [000], [001,010,100], [011,101,110], [111]. In decimal value these are [0], [1,2,4], [3,5,6], [7]. As any member of each group can represent the entire group, we can use the smallest value of each group to represent that group, giving us 4 values of [0,1,3,7] to represent all possible groupings of 3 quarks.

0 and 7 represent the limits of this duality. In between 0 and 7 is where the protons [UUD, UDU, DUU] (numerically 1,2,4) and neutrons [UDD, DUD, DDU] (numerically 3,5,6) that make up our stable reality exist. Protons are amazingly stable, so stable they will theoretically far outlast the life of the Universe. Neutrons are only stable enough to last about 15 minutes on their own, which is respectable compared to the lifespan of most particles, but when bound to a proton, they can last billions of years.

Protons are clearly the dominant pattern not only because of their stability but because the members of the proton group follow a binary pattern of 1, 2, 4.

It is worth noting that our assignment of UP=0 and DOWN=1 is arbitrary and could be reversed. However, we chose to assign the value of 1 to the DOWN quark primarily because this assignment produces the pattern 1, 2, 4 for protons, which are the more stable particles. Additionally, because the proton is the dominant particle, and within that proton the DOWN quark occupies the N-state position (the parent Negotiation state at the top), this makes the DOWN quark the more dominant quark in our stable reality. Assigning 1 to the dominant quark reinforces the significance of this pattern.

This pattern of 1, 2, 4 represents powers of 2 (2⁰, 2¹, 2²), and would continue doubling forever for every new element added to the set. For example, if there were four binary values instead of three, the representative number would be 8, then 16, then 32, and so on, each doubling the previous value.

In contrast, the neutron values [3, 5, 6] are each the sum of pairs of powers of 2 (3=1+2, 5=1+4, 6=2+4), making them considerably less of a “cause” and more of an “effect” or derivative of the fundamental proton pattern.

Let’s look again at the image from the previous chapters that was used to explore the directions and shapes of the 3 most fundamental archetypal forms.

We can see the members of the groupings for protons (1,2,4) and neutrons (3,5,6) are identical to the values derived from the octahedron coordinates. This is a very fractal or self-similar pattern because the 8 sides of the octahedron match the 8 possible configurations of triquark particles (any particle composed of 3 quarks, such as protons and neutrons, plus a bunch more).

In the cube, the pattern 0, 2, 4, and 7 defines the 4 points of a tetrahedron, which are also 4 of the 8 points of a cube, and the neutron group of 3, 5, 6, and 1 defines another opposite tetrahedron that defines the remaining 4 points of the cube. Without knowing anything about protons and neutrons, the tholonic model would predict that the 0, 2, 4, 7 tetrahedron, or tholon, would instantiate as something much more on the somethingness side, the yang side, of the spectrum, and the 1, 3, 5, 6 would instantiate on the nothingness side, or yin side, of the spectrum.

This prediction is based on several factors: the [0,2,4,7] tetrahedron contains the two extremes (0 as pure potential and 7 as maximum manifestation of 111 in binary), includes the larger powers of 2 (2 and 4), and represents the boundaries of the system, making it more structurally dominant and active. In contrast, the [1,3,5,6] tetrahedron contains only the middle values, including all three composite numbers (3, 5, 6) which are sums of other values rather than fundamental powers of 2, making it more derivative and receptive in nature. We can see these characteristics clearly reflected in the physical properties of protons (stable, active, yang) and neutrons (unstable when isolated, receptive, yin).

If we identify which sides of the octahedron are values that match the proton group (red) and which match the neutron group (green), it will look like the image below.

At first glance, it would seem that the proton (+) and the electron (-) would be the fundamental duality, but this does not appear to be the case. It is worth noting that the positive and negative attributions to protons and electrons are completely arbitrary conventions; we could just as easily have reversed them. The duality is actually, and correctly, between somethingness (proton, +1) and nothingness (neutron, 0), within which a stable electron (-1) is formed.

Perhaps this is all “useless knowledge”, or maybe we can ignore these associations between quarks and geometry and write them off as the inevitable patterns of anything that has a pair of 3 polarities, such as 2 sets of 3 pennies or the additive/subtractive colors formed by the RGB and CMY, but it is precisely these patterns that we are interested in. Because of these patterns, we can relate quarks to shapes, shapes to colors, and quarks to colors. The latter example is the basis for quantum chromodynamics (QCD). QCD uses colors to explain how the 3 fundamental forces that govern the SNF interact, which happens to be similar to how the 3 primary colors interact.

When the idea of colors was introduced to explain this SNF interaction, it was met with skepticism. To quote the man who invented the concept of quark colors, University of Maryland physicist, professor O. W. “Wally” Greenberg:

And considerable it was, as today, quantum chromodynamics is fundamental to understanding how quarks, and reality, work.

Compare the current model of quarks as described using colors⁸ (Fig. v1, left) with the 2-dimensional tholon map of overlapping tholons showing 3 iterations (Fig. v2, right). There are several similarities. This is not to say the thologram is a new model of quantum physics, simply that we can find similar patterns. The tholonic argument is that the quantum model is an instance of the thologram in the context of the quantum world. Even the colors used to describe quarks are themselves a tholonic model in the context of frequencies of energies. In this case light, but the same applies to all frequencies of the electromagnetic spectrum.

For example, iron is imbalanced in that it has unpaired electrons that predominantly spin in the same direction, which is what causes it to be magnetic. In contrast, in most other elements, electrons pair up with opposite spins, balancing each other out. However, iron is also quite stable because the body-centered cubic crystal it forms at the atomic level provides stability regardless of the imbalance of the electron spin.

On a macro level, the more imbalance there is, the more structure is needed to compensate in order to remain sustainable. This tells us that stability extends the limits of tolerable imbalance - the more stable the structure, the more imbalance it can sustain. We also saw confirmation of this when it came to photosynthesis in plants (in Chapter 5, Reason).

Key 5: Stability extends the limits of sustainable imbalance.

How does the thologram tell us something about quarks and forces? The SNF is the strongest of all forces in existence, but only at the subatomic level. Outside of that context, it has no effect due to its extremely short range, just as 7 is the largest value only within the context and scope of values 0-7. The other apparent relationship is that in this example, the N-state must have the potential for 6 quarks (3 Up and 3 Down), representing the capacity to create either a proton (UUD) or a neutron (UDD). We see in the thologram that the residual strong force between nucleons only comes into play when there are 6 N-states

, that is, when two sets of 3 quarks (a proton and a neutron) interact.

Again, this is a good place to remind the reader that the tholonic model is not meant to be a model based on physics or even mechanics. It is a model that shows the patterns on which physics, mechanics, and everything else are based.

The 4 Fundamental Forces of Reality

We mentioned above that the first instance of matter would be tetrahedral, at least conceptually. The previous example of the quark model as two tetrahedrons demonstrates this: quarks form the hadrons from which all matter is composed, supporting the claim that tetrahedral structures underlie material reality.

We also stated that form, being an instantiation of the laws of form, would follow that model, meaning we should expect to see tetrahedral conceptual structures as a primary building block of reality. We can go all the way down to the four fundamental forces that govern the interactions of 6 quarks and 6 leptons (and their 12 corresponding anti-particles) that create all known matter and observable phenomena and see a tetrahedral relationship, where three forces interact to define or determine the properties of the fourth.

There may even be other relationships between the forces that could possibly be tested. In mechanics and structural engineering, a hyperstatic system is over-constrained, having more constraints than degrees of freedom, resulting in rigid, stable structures with limited possible configurations. Conversely, a hypostatic system is under-constrained, having fewer constraints than degrees of freedom, allowing movement, transformation, and many possible states. These concepts map directly to thermodynamic entropy: hyperstatic systems (over-constrained, ordered, few microstates) correspond to low entropy, while hypostatic systems (under-constrained, disordered, many microstates) correspond to high entropy.

When we map the four fundamental forces to the vertices of a tetrahedron, we can define three complementary axes: universal vs. atomic (scope of influence), strong vs. weak (relative coupling strength), and hyperstatic vs. hypostatic (constraint level and entropy). Gravity and the strong force are hyperstatic (binding, over-constraining, low entropy), while the weak force and electromagnetic force are hypostatic (transformative, under-constraining, high entropy).

According to the Standard Model, these forces emerged in a specific sequence during the early universe: first gravity separated (at the Planck epoch, ~10⁻⁴³ seconds after the Big Bang), then the strong force separated (~10⁻³⁶ seconds), and finally the electromagnetic and weak forces separated from the unified electroweak force (~10⁻¹² seconds). This temporal ordering may reflect a hierarchical relationship among the forces. The tetrahedral mapping that incorporates both this chronological sequence and the three complementary axes produces the structure shown in the images below.

What is most interesting with this order is how we see the N-source and the child N-state (blue dot and child blue/yellow dot) represented along the universal axis, connecting gravity to the electromagnetic force. Both of these forces dominate at the universal scale, and both can be described with the same mathematical formula pattern. Yes, EM has much more force than gravity at particle scales, but EM tends to balance itself out in mass, thereby neutralizing itself, while gravity has no negative force, making gravity far more influential than EM on the universal scale.

The blue-green vector connects gravity to the strong force, representing Definition and Limitation. Here we see an interesting contrast: while gravity and EM share the same mathematical formula pattern of

A=B\frac{Cc}{D^2}

(for gravitational force it is

F=G\frac{Mm}{r^2}

, and for EM force it is

F=k\frac{Qq}{r^2}

), the gravity-to-strong-force vector spans from universal to atomic scales, defining the limits of scope and manifestation. This is yet another example of self-similar patterns applied to different contexts.

We also see how the three axes that define the tetrahedral structure are mutually perpendicular (as opposite edges of the tetrahedron): the weak versus strong axis, the universal versus atomic axis, and the hyperstatic versus hypostatic axis. These three pairs of orthogonal vectors define the scope, context, and energy states of the structure.

This particular model suggests that gravity is the source of creation. This is consistent with the tholonic idea that gravity might be a material instance of consciousness, which is an instance of awareness, the source of all creation according to the tholonic model. In this framework, gravity is the first force because it was the first to come into existence, separating from the unified field at the Planck epoch. This also aligns with cosmological theories describing the Big Bang singularity as a point of infinite gravity, from which all space, time, matter, and energy emerged.

However, if we change the order based on some other reasoning, we get a very different set of relationships. Which one is the most accurate is anyone’s guess at this point, but I suspect they are all accurate from one or another perspective.

This tetrahedral model of the four fundamental forces can be viewed from multiple perspectives, each revealing different valid relationships. The specific arrangement of forces at the vertices can vary depending on which organizing principle we prioritize: chronological emergence, mathematical similarity, scope of influence, or functional properties. Each configuration remains internally consistent and reveals meaningful patterns.

For example, one arrangement might emphasize the chronological order in which forces separated during the Big Bang, while another might prioritize the mathematical similarity between gravity and electromagnetism (both following the inverse-square law). A third configuration might organize forces according to their scope (universal vs. atomic) or their thermodynamic properties (hyperstatic vs. hypostatic). These are not contradictory models, but rather different projections of the same underlying tetrahedral relationship.

This multiplicity of valid perspectives suggests that the tetrahedral structure itself may be more fundamental than any single arrangement of forces within it. The model demonstrates how the same four forces can be understood through different conceptual frameworks, all of which illuminate complementary aspects of physical reality. This aligns with the tholonic principle that patterns exist at multiple levels and can be accurately described from different contextual viewpoints.

The purpose of this analysis is to demonstrate how the tetrahedral pattern appears at every level and scale of creation. I feel I must stress this, as I can already hear physicists and engineers balking at these correlations. That being said, I will go further and propose that these three axes (the universal/atomic axis, the weak/strong axis, and the hyperstatic/hypostatic axis) which define scope, context, and energy states, correlate extremely well with the tholonic concepts of Definition/limitation, Contribution/Integration, and Negotiation/balance, respectively.

Molecules

The 1^st instance of matter in the Newtonian sense (vs. the quantum sense) is the elements. While all elements have some type of trigram structure, no element has a tetrahedral structure when it is isolated. The bonds between the atomic elements create the tetrahedral structure. This is a crucial observation: isolated elements exist conceptually as 2D instances, similar to how a triangle exists in a plane. It is only through the relationships between elements (through bonding) that the dimensional leap from 2D to 3D occurs, instantiating tetrahedral structures.

Elements are therefore acting like instances of 2D trigrams, even though they are expressions of a 3D tholon. This suggests that elements are literally the bridge between the 2D tholon map and the 3D tholon itself, the point where the map “folds” into dimensional reality through relationship and interaction.

In the tholonic model, when the 2D tholon map folds into 3D space, it creates the 1^st level of the thologram, which is a plane of tetrahedrons (both real tetrahedrons projecting outward and virtual tetrahedrons projecting inward). This 1^st level represents the fundamental pattern for the most basic building blocks of reality, regardless of scale.

Due to the fractal nature of the thologram, this tetrahedral pattern exhibits bidirectional self-similarity. Inward, the pattern self-replicates infinitely at ever-smaller scales (from atoms to subatomic particles, quarks, quantum fields, down to tetrahedral “pixels” at the Planck scale). Outward, the pattern builds through successive iterations at ever-larger scales (1^st Iteration, 2^nd Iteration, and beyond, forming molecules, compounds, and material structures).

At the material atomic scale, isolated elements are represented by individual tetrahedrons within this framework, each exhibiting tholonic properties such as form seeking the most stable state. Larger tetrahedral structures in matter emerge at the 1^st Iteration and beyond, when elements bond to form molecular structures like water and methane.

A single H₂O molecule, composed of 3 atoms, expresses itself as a trigram at the 2D level. When water molecules interact and bond with other molecules, they form larger 3D tetrahedral structures. This progression from 2D to 3D is analogous to how a 2D tholon map folds into a 3D tetrahedron when it creates children. In both cases, the dimensional leap from 2D to 3D occurs through relationship and interaction.

Water is a particularly good substance for exploring tholonic structures because it is one of the first, if not the first, tetrahedral structures that all life on Earth depends upon. What makes water especially significant is its transformative nature: as an isolated H₂O molecule, it exists as a 3-atom trigram (a 2D conceptual form), but when water molecules bond together, they form tetrahedral structures (a 3D form). Water thus embodies both the 2D and 3D states, demonstrating the dimensional transformation central to the tholonic model. In contrast, methane (CH₄) is already tetrahedral as a single molecule, having 4 atoms arranged in tetrahedral geometry, already existing in its transformed 3D state. Methane is one of the first organic molecules and not just a building block of life on Earth, but quite possibly the basis for an entirely different form of life (such as the azotosome cell membrane pictured in the image at the beginning of this section) that we might discover on the Saturn moon of Titan.

It is worth noting an alternative cosmological perspective proposed by Nobel Prize-winning plasma physicist Hannes Alfvén,⁹ which suggests that the very original atom to come into existence was not hydrogen, but helium, with 2 protons, 2 neutrons, and 2 electrons. As helium is the 1^st noble gas, meaning it is perfectly balanced energetically, it would be less vulnerable to the wild energies present in the early universe. Helium also forms a hexagonal crystal, so the helium crystal could represent the original form to come into existence in the Universe (image right). Also significant in this model is that the 1^st creation of matter, as atoms, would have started with 2 protons, not 1.

Getting back to water, we saw that in the 1^st generation of a tholon, we have 4 trigrams, 3 of which are descending, or downward-pointing trigrams, and 1 is ascending, or upward-pointing trigram. (“Up” and “down” have only relative meaning here as it simply refers to the way the trigrams were drawn.) If we have 2 tholons, we also have a total of 8 trigrams made up of 6 descending and 2 ascending trigrams.

H₂O is composed of three atoms. One atom is oxygen, which has an atomic number of 8 as it has 8 protons in its nucleus, which defines its nuclear charge. Oxygen has 8 electrons total, with 6 in its outermost shell, but requires 8 electrons in its outer shell to achieve its most balanced state (the octet rule). The other two atoms are hydrogen, the archetype of all atoms. Hydrogen has an atomic number of 1 and has only 1 proton and 1 electron. Because oxygen has only 6 electrons in its outer shell but wants 8, it naturally forms a bond with two hydrogen atoms by sharing the one electron each hydrogen has to offer.

We can see a few similarities between the tholonic model of H₂O and its traditional chemical model. From a tholonic perspective, oxygen follows the pattern of 2 3^rd gen tholons from 1 face of a 2^nd gen tholon, which has 8 real tholons and 2 virtual tholons (Fig. v1 below, showing two 3^rd gen tholons). Hydrogen follows the pattern of a complete 2^nd gen tholon (Fig. v2, showing 2 complete 2^nd gen tholons). Combining these 3 tholons (Fig. v3) would represent a total of 10 tholons, with 8 externally-facing points (from the real tholons) of interaction and 2 internally facing points (from the virtual tholons) of non-interaction. When combined, the hydrogen tholons will attach to the empty or virtual tholons of oxygen.

This is just a hypothetical demonstration, as there may be a much better tholonic model for elements and compounds than this one. Still, this one is sufficient to show how we might be able to describe elements and compounds tholonically, which may give us new insights into their nature.

Can we see similar relationships with other compounds? Given that the basic archetypal shapes of molecules (shown above) can be represented within the thologram, perhaps this model can be applied to all compounds. We claim this might be possible, as there are virtually infinite configurations in the thologram. Instances of fundamental configurations, such as those that appear in the earlier stages of iterations and generations, like the Fibonacci sequence and the hexagon, would represent extremely stable patterns. Due to their recursive nature, these fundamental patterns exist across large scales and scopes, making them easily identifiable as they play a fundamental part in our reality (like water and methane).

Batteries

An example of how any system can be reduced to a tholon is presented in an insightful article on the effectiveness of batteries, titled “The Unfortunate Tetrahedron”¹⁰. This may seem fairly niche, but it turns out to be very relevant, which is not surprising considering that batteries are all about the movement and balancing of energy. From this perspective, a simple battery is a microcosm of the Universe from beginning to end. In this article, the author shows how the systems of a simple battery can be modeled as a tetrahedron and how these fundamental aspects of a system relate to one another. The author looks at the four aspects of batteries: energy density, power density, operating cost, and capital cost, where:

The article describes the relationship between E (energy density) and P (power density), which is equivalent to an N-source and a defining point that can be described in a Ragone Space. The Ragone plot (right) measures the performance comparison of various energy-storing devices. This chart is a perfect example of the axis of “laws, rules and limits” that connects an N-space with a defining point in the model of the tholon.

On the opposite side, between C (operating cost) and E (energy density), which is equivalent to a contributing point and an N-source, we have the tholonic axis of “service”, which is pretty clear: does the battery provide a service? Remember that the descriptions of “laws” and “service” were specifically meant to apply to concepts of Definition and Contribution in the context of our daily lives, given that the context of a battery is in the scope of “daily lives”.

According to the tholonic model, the only place where stable patterns capable of replication can occur is between the limitations of Definition and the integration of an instance (form) as Contribution, which here is D (capital cost) and C (operating cost). Across this spectrum of “cooperation or conflict” is where price and value come to terms with each other, as in “getting the most for your money”. In the battery world (and many other worlds as well), this is the juggling act between good, cheap, and fast, and the arena which produces all the various instances of batteries that can deliver power at a cost, most of the instances landing in the “middle”, representing the best product for the best price for a specific market. Here would appear instances like alkaline cell batteries (Duracell), lead-acid batteries (car batteries), nickel-cadmium batteries (rechargeable batteries), etc. Each of these new instances (stable patterns) can then go on to create their own tholonic archetypes.

Consciousness

The highly respected and published team of Donald David Hoffman (cognitive psychologist, author, and Professor in the Department of Cognitive Sciences at the University of California, Irvine) and Chetan Prakash (Ph.D. Mathematical Physics, Cornell University) developed the idea of a conscious agent, which is a dynamic process of consciousness. They argued that it is the interaction between various agents that produces measurable phenomena such as the position, momentum, and energy of objects. They further argue that these objects have no objective, absolute, or even preexisting properties and only exist in relation to consciousness via these conscious agents. This is a radical claim, but their arguments and evidence, as laid out in their paper “Objects of consciousness”¹¹, cannot be ignored. What also cannot be ignored is the striking similarity between their model and the tholonic model, as shown below. (I found this especially striking as I learned of their work long after the 1^st draft of this book. Of course, they do a far better job of explaining their idea technically, mathematically, and psychologically.)

Circuits and the “God Formula”

There are many examples of how concepts and processes follow the tholonic model:

Really, just about any ordered system can be seen from a tholonic perspective. The following are especially interesting and informative examples.

Electronic circuits are exciting and relevant to the tholonic model. One of the most common and essential circuits in electrical systems is the elementary resistor-capacitor circuit, or RC circuit. It is used to filter and control signals not only in manufactured electrical circuits but in natural electrical circuits, such as neurotransmission in the brain and throughout the entire nervous system of any living organism. The reader has undoubtedly seen such circuits as they exist in every computer system, alarm clock, microwave, and virtually all electronic devices.

Briefly, an electrical resistor is a component that can reduce the flow of current, adjust signal levels, divide voltages, and limit or control the current of a circuit in some way. A capacitor is a device that stores electrical energy in an electric field. In one way, a capacitor is like a battery in that it can store energy, but unlike a battery, it has no inherent charge of its own and must store a charge from an external source. Air alone acts like a capacitor and is often used in radio circuits.

We have 2 essential elements in this circuit: an element that limits and divides and an element that collects and stores. These concepts are perfectly in line with the basic concepts of Definition/limitation and Contribution/integration as shown in the Alternate View above.

This time constant is then used to calculate V and I using the formulas V(τ)=V_B(1-e^-τ/RC) and I(τ)=I₀(e^-τ/RC). The point here is not to get into the math but to show not only that V and I relate to each other via R and C, and by extension, D and C, but that they do so across a field that in the world of electronics is defined by e, or 2.71828, the base of the natural logarithm. This is especially interesting when applying the properties of this RC field to that of the DC field of the tholon because e is one of the most profound and fascinating numbers in nature!

Historical note: The value of e was discovered by Jacob Bernoulli around 1683 while studying compound interest. The symbol e first appeared in Leonhard Euler’s work around 1727-1728.

It is similar to pi in its significance, but where pi is the ratio between circumference and diameter shared by all circles, e is the base rate of growth shared by all continually growing processes. It has also been called the epitome of universal growth. This growth can be anything: population, radioactive decay, interest calculations, even jagged or unpredictable systems that do not grow smoothly. Anything that has continuous growth can be modeled with e. e is to growth what pi is to circles.

e and the Natural Log, or ln(), are two sides of the same concept. They are inverse functions of one another, so ln(e)=1. e describes growth, and the Natural Log describes time. For example:

If you remember back in chapter 3, it was shown how logarithms were the natural way nature understands scale or scope, and while common logs are based on 10, the natural log uses e as its base. It is called “natural” because e emerges naturally from continuous growth processes, making it the unique number where the rate of growth equals the value itself (the derivative of e^x is e^x).

Considering that the tholon is a growth model, it seems particularly applicable that e would define the field from which new N-states emerge to spawn new tholons.

There is one more significance to e that is purely tholonic and will no doubt annoy math purists but is added here not only because of its symmetry but because the concepts that these values describe do exist in the tholonic model, even if this particular form may not be the exact way they are best represented.

As was just shown, the spectrum between Definition and Contribution is, in this context, defined by the value of e. Referring back to how it was described that 1 point creates 2 points and 2 points create 3 points, when we created the 2^nd point, we had a 1D line from Negotiation to Definition. However, we also had a center and a radius, thereby defining a circle. In this way, the 1^st and 2^nd points imply a circular relationship, which is characterized by π, so if we were to assign a value to that 1D line, π would be the best candidate. It was earlier suggested how the 3^rd point represented complex numbers. If N = -1, then the CN line could reasonably be seen as i, the imaginary value for √(-1).

There are two perspectives on how these values relate to the tholonic structure. In the 2D trigram representation, the values (e, π, i) can be assigned to the edges or vectors, describing the relationships and processes between points. In the 3D tetrahedral representation, these same values can be assigned to the vertices themselves, describing instantiated points in “conceptual space”. The first perspective emphasizes how things relate, where values represent dynamic connections. The second perspective emphasizes where things exist in this “conceptual space” and how these archetypes are defined and positioned. The reader may find one or both of these perspectives applicable depending on the context being examined.

If this tholonic trigram represents the three values of e, π, and i, we can construct Euler’s Formula, or what has been called the most elegant formula in mathematics, e^iπ + 1 = 0. This formula integrates all the dynamic connections between the points and the originating point into a beautiful concept. In addition, as e represents time and π represents space, we have the two dimensions of time and space, plus the concept that describes the reality of cycles, that being complex numbers (which are necessary to add cycles that are different, for example).

What would be the value of the 4^th point, the white dot? Given that e is already a measurement of time, and considering that the time constant τ = RC defines the field between Definition and Contribution in the RC circuit, perhaps τ itself could represent this 4^th point, but this remains speculative.

This beautiful formula is fundamental to the continuous exchange of energy that we perceive as time (where 0 equals the present moment) and numerous other fundamental aspects of reality. This formula is so fundamental it has not only been called the God Formula, it has been presented as empirical proof of the existence of god. We are not that ambitious, pious, or learned and simply call it a fundamental archetypal pattern.

If e^iπ = -1, then ln(-1) = πi. When we apply the concepts of e and ln() as described above, πi equates to time, and the spectrum of e represents the growth. Does this also suggest that the originating energy of everything, including the Universe, started with a negative movement (the -1 of e^iπ)? There is more evidence to suggest that is the case, and later it is shown why and what that really means.

There is yet another supporting argument for e, which we can see when we map the original formula for e that was discovered by Bernoulli in the 17^th century (right) to the tholonic trigram, which shows a remarkably compatible pattern.

The image shows the three vertices: 1 at the top (N-state), x on the left (Contribution), and 1/x on the right (Definition), with e as the base. If we go in the forward direction using these three values, applying the formula e = (1 + 1/x)^x, we arrive at e, the value of growth. If we go in the reverse direction using 1 = (1 - x)^(1/x), we arrive at 1, the value of unity (and no growth). What is so interesting about this is that the N-state is 1, as in not 0, not nothing, representative of something. The Definition point (1/x) is the point of resistance and limitation, or low entropy chaos, representing something that is limited. The Contribution point (x) is the point of integration, the final state of balance, high entropy chaos. We could easily translate the math to say:

This formula reveals a profound distinction in the tholonic model. The first tholon, the primordial origin, begins with an N-state of 0, representing absolute nothingness, pure potential, the void before existence. This 0 → 1 transition represents the creation event itself, the emergence of something from nothing, unique and non-repeatable. However, once existence has begun, all subsequent child tholons can no longer start from 0, for they are born within an already-existing reality. All child tholons therefore begin with an N-state of 1, representing unity, something, existence itself. This is why Bernoulli’s formula starts with 1, not 0. It describes growth and evolution within existence, not creation from nothing. The formula e = (1 + 1/x)^x models the “something-to-something” processes of ongoing reality, the fractal replication and growth that occurs after the singular creation event. In this view, the first tholon with N-state = 0 is absolutely unique in all of reality, marking the boundary between nothingness and existence, while every subsequent structure builds upon the foundation of that initial 1.

The Bigger Picture

It may look like our math has taken some “liberties” using more exotic values to support the argument that there is a natural and fundamental pattern of order that can be seen in the tetrahedron, and there are probably a lot of patterns that can be applied with various numbers that make the same “sense”. That would be partly true, as the tetrahedron contains all kinds of patterns that can be seen in nature and math, but some are more “in your face” than others.

For example, when we use the numbers 6, 2, and 3 for our trigram corner points, we can see a pattern of division (Fig. g1) and a pattern of multiplication (Fig. g2). It is worth remembering that the pattern of 2 × 3 = 6 is the most fundamental pattern of relationships that all interactions of matter are based on, as previously demonstrated. These are the same patterns for + and - as well. When we use e, i, and π, we can see a pattern of multiplication and exponents (Fig. g3).

Each of these patterns represents different ways energy moves in a tholon and requires different types of values to function properly. The values of 6, 2, and 3 work with patterns g1 and g2, but not in the same manner with pattern g3, which works with values e, i, and π, but they support each other.

For example, if we only use values of i for pattern g1, using the values of i¹, i², i³, we get values of i, -1, -i, which perfectly comply with pattern g1 as i/(-1) = -i, i/(-i) = -1, and i × -1 = -i. But this is a tetrahedron, so we need that 4^th white dot point that needs to be a value that is fundamental to, and compatible with, all the other values. That would be i⁰, which is 1 and the value that all these values are derived from. And with that, all the formulas work.

If we continued with i⁵, i⁶, and so on, we would get the same values because no matter how many multiples of i are used, it can only result in 1, i, -1, or -i, which is yet more validation of the tetrahedron model. This pattern also tells us that the cardinal values of the points on a trigram are the exponential values of 1 (at the top), then 2 and 3, with the 4^th point as 0 after the tholonic trigram has created its 3 children and folded into a tetrahedron. So, while the instances of the pattern are different, the pattern shows how different types of functions are grouped by the base and side trigrams.

Back to Basics

Let’s now map Newton’s 2^nd law (in the form of Ohm’s law) to the tholon, which fits nicely.

To apply Ohm’s law, we have to correlate the N, D, and C values to V, I, and R, like so:

We’ve taken a big leap here by applying math to such abstract concepts and expecting to see something meaningful, but if we look at these definitions as abstractions, they seem quite reasonable, just as they did to the founders of mathematics.

The (lost) Meaning of Math

To look closer, we need to make sure we’re all on the same page regarding how the trigram can describe the math functions of Ohm’s law, and to do that, we need to clarify some elementary concepts, such as what the math symbols mean in this context.

Addition and subtraction are easy concepts to grasp. We take some number of things and add or remove some number of things. But depending on the context, even simple addition and subtraction requires some extra thought. A good example of this is how addition and subtraction affect colors. It is not intuitive to most people that violet - cyan = blue, for example, but once shown, it makes sense.

What about multiplication and division? In this context, we will describe division as the definition of one value by the units of another value.

For example, in division, such as 3 = 12/4, we are stating that 3 is what we get when we measure an existing value of 12 by a unit of 4. In multiplication, such as 12 = 3 × 4, we are determining a new value of 12 by combining 3 of these units-of-4.

The 4, as the divisor or multiplier, is the unit of measurement, and the 3 is the number of units. Every kid knows what was just stated, but when we apply those same simple rules and concepts to a non-math context, they become very significant.

(For highly speculative thoughts on the meaning of squares and square roots, see Meaning of Squares and Square Roots in Appendix C, “Tholonic Math”)

As mentioned above, we would expect to see the same laws expressed in different ways across all the scopes that the laws apply to, so we would expect to see an example of Newton’s 2^nd law in the tholonic realms of society, or planets, or organisms, and we do. For comparison, we also show how the attributes of the tholon would appear using the same laws.

For example, if we claim that a society is based on its ethics and we also posit that ethics are to be measured by laws, we can say society = ethics ÷ laws, and likewise, ethics = laws × society. Suppose we measure the power of a society by its ability to function or “work”, and the measure of a society by its sustainability, then, according to these formulas. In that case, a society with a lot of laws and very little ethics will work less and be less sustainable. On the other hand, a society that has a lot of ethics and very few laws will be far more sustainable and produce even more work.

Here, we interpret “laws” as limiting factors with regard to its members. Those limits could even be limits on limits, e.g., The 1^st amendment of the U.S. Constitution guaranteeing the right to free speech is a law, but it is a limitation on a limitation in that it limits the State from limiting an individual’s right. For context, an example of a society with a lot of limiting laws and very little ethics would be North Korea or Syria. An example of a society with fewer limiting laws and higher ethics would be Norway or Sweden. Note: These rankings are according to institutions that rank countries ¹³and not necessarily the examples I would personally choose.

If we claim that individuals interacting with each other (commerce, culture, aid, community) represents the strength of a society, and we use the concept of society to represent this strength of social interaction, then we might say this interaction correlates with current. If ethics represents the arena in which individuals operate, then we could correlate ethics with voltage. Laws, which define limits, would then reasonably be correlated to resistance. Altogether, individuals, ethics, and laws form a society.

These are numbers that work with Newton’s and Ohm’s law, but in this context, the quantitative value of these numbers is not important. We are using the numbers to show relationships. The number itself is merely a concept of measure. Power, which is the transference of energy over time, would then correlate to how much “work” this society could generate. Perhaps this would be seen in their social achievement, productivity, or levels of cooperation, but it could also represent a “work product” of oppression, taxation, or enslavement if that is the goal of the society.

How these assignments were arrived at is not critical because they may differ depending on how one chooses to correlate, so this detail does not matter for the point being made.

With these assignments, society = ethics/laws follows the same reasoning as the formula 3 = 6/2. To demonstrate how these relationships work, let us examine three different hypothetical scenarios that show what happens when we change the values of ethics and laws:

Case 1 (Baseline scenario): - Ethics = 6, Laws = 2 - Society = ethics/laws = 6/2 = 3 - Work = ethics × society = 6 × 3 = 18

Case 2 (Doubled ethics, same laws): - Ethics = 12 (doubled), Laws = 2 (unchanged) - Society = ethics/laws = 12/2 = 6 (society doubles) - Work = ethics × society = 12 × 6 = 72 (work quadruples!)

Case 3 (Same ethics, doubled laws): - Ethics = 6 (unchanged), Laws = 4 (doubled) - Society = ethics/laws = 6/4 = 1.5 (society reduced by half) - Work = ethics × society = 6 × 1.5 = 9 (work cut in half)

When we analyze these three scenarios for work efficiency (work produced per unit of total input), we can rank them as follows:

If this premise has any validity, this would suggest that a lot of laws and little ethics, or perhaps where the ethics are enforced by law rather than conscience, leads to an inefficient society. In contrast, a society with few laws and lots of ethics leads to a productive society.

How would we calculate sustainability then? Here is one way, perhaps, but this is totally outside the context of the law as we currently use it, so it will probably make no sense from an engineering perspective. In short, we simply take the product of all the unit-counts of society and measure it by the product of the unit-measures of society:

society = I = V/R or P/V or √(P/R) ∴ unit count/unit measure ∴ (V × P × √P)/(R × V × √R)

Case 1 (Baseline): - Formula: 6/2 or 18/6 or √(18/2) - Calculation: (6 × 18 × √18)/(2 × 6 × √2) = 458.2/16.9 - Sustainability = 27.1

Case 2 (Doubled ethics): - Formula: 12/2 or 72/12 or √(72/2) - Calculation: (12 × 72 × √72)/(2 × 12 × √2) = 7331.3/33.9 - Sustainability = 216.3 (8× more sustainable than baseline!)

Case 3 (Doubled laws): - Formula: 6/4 or 9/6 or √(9/4) - Calculation: (6 × 9 × √9)/(4 × 6 × √4) = 162/48 - Sustainability = 3.4 (8× less sustainable than baseline)

How these translate to the real world is only speculative, as it is up to the reader to decide if laws, society, ethics, and work are the best concepts to use here. If so, how are the social equivalents of power, ethics, laws, work, and sustainability measured, and what is the significance of squares and square-roots?

How would this look if we used concepts such as natural rights, privileges and responsibilities?

This can apply to any properly defined trigram. For example, suppose we applied this same exercise to the cognitive behavioral trigram we mentioned previously. In that case, we might claim that behavior is a product of thoughts (one’s own or those one is exposed to) and that thoughts are to be measured by feelings.

Using this mapping, we would have behavior = thoughts ÷ feelings and thoughts = behavior × feelings.

This would suggest that high thought with low feeling results in higher behavior and higher power (whatever that means in this context - intention? beliefs? desires? will?). Conversely, low thought and high feelings results in much lower power and even lower behavior.

I suspect it would take quite a bit of discussion and research to find the best values. The point of this is to suggest that these equations would produce meaningful results with the correct values. However, someone who acts out of emotions with very little thought is bound to have a less sustainable lifestyle than one who tempers their emotions with thought, so these mappings may not be too far off.

In any case, the twelve formulas of Newton’s 2^nd law show some potential when applied to other contexts and may offer a new perspective on the dynamics of culture and society that, if nothing else, raises some worthwhile questions. As it applies here, it shows how the tholon can describe everything from atoms to culture as long as we know what data to apply. Because the math involved in a tholon can be more than the reader might be interested in, more of this subject is covered in Appendix C, “Tholonic Math”.

Because our 4D (3D+time) reality maps neatly into the 4D tetrahedron, especially when using the synergetic 4D quadray coordinate system based on the tetrahedron, we may be able to correlate radically different contexts, such as space-time, psychology, and electricity, to name a few.

With this in mind, let’s reexamine the previous claims that began this thread:

The definition of something is its boundaries, limits, abilities, attributes, properties, and resources. These details are the results of the scope and context of that thing’s instance. It could be environmental factors, genetic attributes, or physical limitations, such as the size and weight of a thing, energy levels, etc.

It is the nature of energy to expand (i.e., disperse due to entropy) in every way possible. That expansion is the contribution, but the resistance from these factors determines what expansions get the opportunity to be expressed and what expansions are thwarted. That battle between the force of expansion and the force of resistance is the negotiation (see Negotiation = Contribution × Definition).

As Definition is Negotiation ÷ Contribution, we can say that Definition is measured by that which is Contributed, or the Definition of something is determined by what it can (sustainably) Contribute.

What a thing can Contribute is measured by its Definition, but the degree to which it can contribute is determined by its environment and how it interacts with that environment. That interaction is a result of Negotiation. A thing must provide something that something in its environment needs; otherwise, what it has to contribute is useless and unintegratable.

A thing’s ability to find a stable and sustainable position within its environment and scope is determined by the degree to which it can contribute with its current resources. A thing may have a Definition that gives it a lot of A and a little of B, but if its environment needs a lot of B and very little A, then it is B that the thing must Contribute to ensure its existence in that environment, or it needs to find another environment, or change its environment so that A is in more demand.

Applying different values and concepts can result in new data. We experiment with this a little, but given it is outside the central theme of this book, we have put that section under “New data?” in Appendix C, “Tholonic Math”

The shape of knowledge

The point of all this is to show one way that the tholon can be used and viewed. There are many new ways of looking at energy in all its forms when viewed tholonically.

We showed examples of quarks and molecules, but in higher orders, such as DNA, we also see some striking similarities that, with a bit of investigation, would likely expose some significant relationships.

DNA and how it is both tholonic and binary in nature is examined in the companion book “The Tholonic I-Ching”.

DNA’s relationship with tetrahedrons is particularly unique given the creation of tetrahedrally structured DNA (a.k.a. TDN). TDN is the cutting edge of DNA nanotechnology and has various applications such as drug delivery, inhibiting certain gene expressions, and interfacing with bio-sensors. These TDNs assemble themselves from scratch and offer greater strength and stability than traditional dual-strand DNA. Given that there is little accessible information on TDNs for the layperson, there is not much more that can be said here other than they represent a significant advancement and will most likely play a role in future biotechnology, including potential applications in TDN-interfacing AI and DNA-integrated quantum computers.

Our simple trigrams of relationships, such as Newton’s 2^nd law, form conceptual tetrahedrons or tholons of relationships. Whereas before, it was stated that every piece of knowledge could be deconstructed into a trigram, by the same token, every piece of knowledge forms a tetrahedron. With this more expanded tetrahedral model in mind, let’s briefly jump back to the examples of deconstruction mentioned earlier.

Abbott, Edwin A. (1884). “Flatland: A Romance in Many Dimensions”. New York: Dover Thrift Edition (1992 unabridged). p. ii., https://en.wikipedia.org/wiki/Flatland↩︎
Fuller, R. Buckminster, and E. J. Applewhite. “Synergetics. Explorations in the Geometry of Thinking”. Macmillan, 1975. The entire book can be found online at http://synergetics.info ↩︎
References to the above come from http://synergetics.info/s02/p0000.html ↩︎
McGovern, Jim; “What Have Space-time, Shape and Symmetry to Do with Thermodynamics? ”, ECOS 2007, Proceedings of the 20th International Conference on Efficiency, Cost, Optimization, Simulation and Environmental Impact of Energy Systems, Ed. Alberto Mirandola, Ozer Arnas, Andrea Lazzaretto, pp. 349-356, June 25-28, 2007, Padova, Italy, arXiv:0710.1242, Available at: https://arxiv.org/pdf/0710.1242.pdf↩︎
Trigg, Charles W. “Gardner’s Three-Square Problem: 54 Solutions”, Journal of Recreational Mathematics, Vol. 4, 1971. Also cited in The Fibonacci Quarterly, Dec. 1973.↩︎
Smith, F. D. (n.d.). E8 Root Vectors from 8D to 3D - Valdosta, Georgia. http://www.valdostamuseum.com/hamsmith/E8to4Dand3D.pdf ↩︎
Amazing description of how the E8 crystal can be defined as tetrahedrals. https://quantumgravityresearch.org/portfolio/a-deep-link-between-3d-and-8d ↩︎
Greenberg, O. W. “The Origin of Quark Color.” Physics Today. American Institute of PhysicsAIP, January 1, 2015. https://physicstoday.scitation.org/doi/10.1063/PT.3.2655.↩︎
Alfvén, H. (1986). “Cosmology: Myth or Science?” IEEE Transactions on Plasma Science, Vol. 14, No. 6.↩︎
Steingart, Dan. “The Unfortunate Tetrahedron.” Medium. The unfortunate tetrahedron, May 30, 2017. https://medium.com/the-unfortunate-tetrahedron/the-unfortunate-tetrahedron-ce1e44d0b961.↩︎
Hoffman DD, Prakash C. “Objects of consciousness.” Front Psychol. 2014;5 577. doi:10.3389/fpsyg.2014.00577. PMID: 24987382; PMCID: PMC4060643.↩︎
Institute, Santa Fe. “Economic Complexity: A Different Way to Look at the Economy.” Medium. November 03, 2014. Accessed August 02, 2020. https://medium.com/sfi-30-foundations-frontiers/economic-complexity-a-different-way-to-look-at-the-economy-eae5fa2341cd.↩︎
“Freedom in the World” (2018), published by Freedom House, Democracy Index (2017), published by The Economist Intelligence Unit, V-Dem Annual Democracy Report (2018), published by the V-Dem Institute↩︎

9: INSTANCES

Examples of how tholonic archetypes instantiate

Keywords: archetypes, dimensional progression, geometric instantiation, fractal self-similarity, conceptual-material transformation, tholonic relationships, mathematical patterns, archetypal manifestation, N-D-C dynamics

Archetypes