THOLONIA 8.0.18

Everything up until now introduced the main concepts we will return to and depend on as we explore how simple dualities evolve into the complex structures that describe the reality we actually live in.

On a practical level, this complexity is no different from how we deal with the physical world in our everyday lives. When you hold a brick in your hand you are holding trillions of atomic particles, with countless interactions, fields, energy levels, and more, but you do not need to know that to build a house of bricks. When you drop the brick and it falls, you are not thinking about the nature of time, gravity, and warped space.

Likewise, to manage the “bricks” in the realm of Ideas, you also do not need to know all of the details, but it is helpful if you have an understanding of how they generally interact with each other so you do not try and build a “house” made of “bricks” and “oranges”.

That said, let us touch on one more concept that is fundamental to structure in general.

How Many Dimensions Are There?

Numerous, if we consider the extra dimensions that String theory requires or that extensions of Relativity such as Kaluza-Klein theory have proposed, but we will not be considering them here and will focus on the obvious dimensions.

The location of a thing relates it to its environment and assumes that the object being measured, the environment it exists in, and the measurer all share the same reality. It is well-established that material things are three-dimensional, and that our environment is also three-dimensional. Sure, there may be more than three dimensions, such as time, but there are at least three spatial dimensions that are well-established and very persistent.

The measurement of an instance of something, an object, is absolute within its own reference frame. A 1 cm³ sugar cube (and its measurer) traveling at near the speed of light will still measure 1 cm³ to the measurer. To a stationary bystander, that sugar cube would appear squashed flat like a thin wafer along its direction of motion, certainly not 1 cm³.

This occurs because of Relativity, but the point is simply that our 3D world appears consistent because we, the planet, and everything in our reality are all in the same space-time neighborhood.

Longitude, latitude, and altitude work perfectly well for geographical locations, as do right ascension, declination, and distance for celestial locations. 3D coordinates work because, and only when, all things are generally in the same neighborhood of space-time reality.

We ignore the differences in our own neighborhood because they are too small to be significant, but they exist. If you fall from 100 feet in the Arctic, you will hit the ground 16 milliseconds sooner than if you fall in Peru. The Arctic has more gravity than Peru, and that means time moves slower in the Arctic, but no one is going to notice or care.

Similarly, we do not notice that in every second of our life we are traveling at least 3,000 miles per second across various dimensions given the speed of the Earth, Sun, solar system, galaxy, and more. The point here is, location coordinates can only be relative to the local environment.

The classic explanation of a dimension goes something like “If something has only one dimension you only need one number to know its exact location”. In the case of one dimension, like in the number line below, if there is a dot at the number 6, along that dimension the dot is at 6.

This is true when, and only when, the position of the measurer and the thing being measured share the same context, as the value of 6 is only relative to that context.

If we wanted to give the absolute position of the dot, we would need to include the coordinates of where in the universe that dot exists. This would require coordinates in many dimensions: the three-dimensional position on the planet, the three-dimensional position of Earth in the solar system, the three-dimensional position of the solar system in the galaxy, the three-dimensional position of the galaxy in the universe (or multiverse), and the one-dimensional time coordinate, as they are all moving. Even then it would only be relative to the Universe as we know it.

So, even locating a simple one-dimensional dot requires many dimensional coordinates when measured from a broader context. The dot itself remains one-dimensional in its local space, but describing its absolute position demands a multi-dimensional coordinate system.

It is as if we have subjective dimensions, which are dimensions relative to the thing alone, and objective dimensions, which are the dimensions of the thing relative to all other things (the Universe), which seems ironic as this would equate subjective with absolute, and objective with relative.

Things

What can we say about what all things have in common? We can say at least the following:

This last statement might raise a few eyebrows. The claim here is not that any particular thing is the most efficient form of its perfect archetype, but rather the most efficient form for that particular thing under the conditions it exists in at any particular moment.

If these statements are true, then this would imply that the most primitive thing that can exist, the simplest and most efficient form possible, is the tetrahedron. It has three dimensions, but it is not made up of other things because when you remove any one point, it collapses to two dimensions, and no thing can be two-dimensional. Therefore, it must be the very first thing to come into existence, at least conceptually speaking.

It can be argued that it is the sphere, not the tetrahedron, that holds this title, and this is not incorrect. From the tholonic perspective, both forms are the same with a minor difference. Consider the simpler example of a two-dimensional triangle and a two-dimensional circle. In one sense, the circle is more fundamental because it can be created with simply one line, while a triangle requires three lines. However, if we accept that the path of least resistance is represented by the shortest distance between two points (all else being equal), then while a circle is easy to make, it is certainly not the most efficient. While a triangle is a polygon of three straight lines, a circle is a polygon of an infinite number of straight lines, each line being infinitely short. This then defines a two-dimensional circle as an infinite number of two-dimensional triangles.

The reason we consider the circle and the triangle (or tetrahedron and sphere) the same is because within the same dimension, the triangle is a single instance of the simplest two-dimensional form, and the circle is an infinite number of instances of that same two-dimensional form. Similarly, the tetrahedron is a single instance of the simplest three-dimensional form, and the sphere is an infinite number of instances of that same three-dimensional form. The only difference between the two forms is quantitative, not qualitative. The circle is the most efficient two-dimensional form that can be produced by the most efficient two-dimensional form of triangle, and the sphere is the most efficient three-dimensional form that can be produced by the most efficient three-dimensional form of tetrahedron. Very little in nature and reality can be described with only a single tetrahedron, but everything can be described as multiple tetrahedrons, and a sphere is just that. It is therefore the most efficient form in nature.

As a pattern of order, the tetrahedron (and the resulting sphere it creates) is one of the first, if not the first, to appear in nature. When we stack spheres on top of one another, they form a tetrahedron. If we stack other shapes, the structure will be altered depending on the geometry, but the tendency for connected things is to form tetrahedral structures to the degree their shape allows. As it is the tendency of all things to become spherical (thanks to gravity in the case of matter, and surface tension in the case of liquids), it is then also the tendency for things to form tetrahedral connections. Tetrahedrons are the first pattern of order and the archetype that represents the path of least resistance.

If the tetrahedron is the first thing that can be created, this would suggest also that every thing that exists can be reduced to a collection of tetrahedrons, and that they are the smallest thing that can exist (again, conceptually speaking). This might sound like a radical departure from our current thinking, but it is not that radical a departure as this is exactly what Emergence Theory: A Theory of Pixelated Spacetime¹ claims as well.

The tetrahedron possesses a unique property that distinguishes it from all other three-dimensional shapes. It is the only three-dimensional form that, when stacked, creates larger versions of itself while expanding in all three dimensions, and cannot be constructed from any more primitive shape. Other shapes that exhibit self-similar stacking properties, such as the octahedron or rhombic dodecahedron, can themselves be decomposed into tetrahedrons. In fact, any three-dimensional polyhedron can be triangulated into tetrahedrons, a fundamental principle in computational geometry known as tetrahedral decomposition. This means that the tetrahedron is not merely one fundamental building block among many, but rather the single irreducible primitive from which all three-dimensional forms can be constructed. It is the geometric atom of three-dimensional reality.

The tholonic model that this book describes suggests that the rules that apply to these 3D pixels that populate all of space extend beyond space to all of reality, including the invisible worlds of ideas, archetypes, and all forms and expressions of energy.

On the Small Side

Science has been grappling with the idea of tiny particles for some time. First, we had the grains of sand and dust, then atoms, then electrons, protons, and neutrons, then finally, quarks, which, so far, seem to be the most fundamental layer of matter. The problem is, quarks appear to be point particles with no measurable size, which creates conceptual challenges because science must work with measurable quantities. To address this, string theory proposes that reality is not made of particles, but rather tiny vibrating one-dimensional strings in 11 dimensions (and they thought this would be easier?). However, string theory remains highly theoretical, with no experimental evidence to date supporting its claims.

The quark remains the undefeated champion of tinyness. Current experiments can only place an upper bound on quark size at approximately 10^-19 meters, but they may be truly point-like. For comparison, early quark experiments suggested a scale of 10^-17 meters. Remember that number, 10^-17.

On the Big Side

Jumping to the other end of the scale we have some pretty big things in the Universe, the largest we know of being the Hercules-Corona Borealis Great Wall. This is a gravitationally bound galactic supercluster about 10 billion light-years wide. That is pretty, pretty big. What could be bigger than that? How about something with four dimensions? Would an extra dimension increase the size of something? Well, is a 2×2×2 cube bigger than a 2×2 sheet of paper, and is a 2×2×2×2 hyper-cube bigger than a 2×2×2 cube? What would a 2×2×2×2 cube look like? In the 3D world, from one perspective it would look like a regular cube, because we can only see three of the four dimensions, but turn it a little (in 4D space) and the 4D cube will appear as two 3D cubes, or a hexagonal prism, or rhombic dodecahedron, or a cuboid.

Here is what a hyper-cube (4D cube) looks like when it is rotated and projected onto a 2D space, like a shadow (orthographic projection).

What about something that is 5D, or 6D or 7D? Each one would be bigger by an order of magnitude. How about something that is 248D? That would be very, very big. If something was bigger than the Great Wall in 248D how small could it appear in 3D? About the size of a small travel bag! OK, you are probably thinking “248D!? That’s ridiculous!”

Crystal Power

So, there is this magic 248-dimensional crystal (actually, it is 8 dimensional with 248 not-necessarily-spatial, but not not-necessarily-spatial, dimensional symmetries, but as an algebraic expression it is considered to have 248 dimensions) called the E8 crystal. If E8 were a musical instrument, the 8 dimensions would be like the 8 basic notes, while the 248 dimensions would be all the possible chords, harmonies, and combinations you can play. This reality of ours is, presumably, the result of a number of 3D refractions of energy created by the various facets of this crystal that are cast upon the 3D canvas of the void that is our Universe from the higher dimensions of magic-crystal-land. As modern as this sounds, the E8 mathematical structure itself was first discovered in the late 1800s,³ but it was only recently, with the development of Emergence Theory and advances in computing power, that physicists began exploring how this abstract mathematical structure might actually describe the fabric of physical reality. This sounds pretty compatible with the Simulation Hypothesis. Maybe these two theories should get together for coffee sometime.

As crazy as this theory sounds, it is a real thing. Just do an Internet search for “emergence theory tetrahedron” and “The theory of everything quantum symmetry E8 lattice” and browse through the million-plus links that discuss it in painful detail, emphasis on the painful part, because most of the content is unintelligible to those not intimately familiar with the algebra of differentiable manifolds, quantum gravity and a bunch of other stuff I do not even know how to reference. However, that is not important to know for our purposes.

It should be stated that this theory is not accepted by all, and some scientists are definitely in the “swarming with worms of heretical perversity” camp regarding the magic crystal of reality. I do not have any opinion about the Emergence Theory (ET) other than it sounds fascinating, mainly because I am not qualified to have an opinion. The only reason it is being mentioned is because ET supports many of the claims that are made here, which were arrived at with no knowledge of ET.

This E8 lattice (that is its technical name, also called a quasicrystal, but magic crystal sounds much cooler) seems to be able to describe all sorts of things. These include space-time (both types, Minkowski and Kaluza-Klein versions. Yes, we have two types of space-time, because it is always better to have options), fermion particles, gravity, dark matter, quarks, positrons, neutrinos, Fibonacci relationships, and a bunch of other stuff. Neutrinos are particularly fascinating in this context because they have almost no mass, no charge, and barely interact with matter, earning them the nickname “ghost particles”. The cosmic neutrino background, created during the Big Bang approximately 13.8 billion years ago, still permeates the universe today. Does that not make them nearly pure patterns of information with almost no material substance?

Obviously, it is impossible to visualize such a crystal as it has countless patterns in the 3D world, but here are a few of these ways it can be perceived.

As you can see, the whole space-time part of the E8 lattice is just a small part of one of the 3D projections of an 8D slice of a 248D super-thing, leading one to wonder what other forms of reality it has the magic power to conjure up. Not surprisingly, this E8 lattice can be deconstructed to (or perhaps is constructed by) a series of tetrahedrons.⁴,⁵

A significant aspect of Emergence Theory (for us) is their claim that all of reality is made of information. What is information? Information is meaning conveyed by symbols. Languages and codes are groups of such symbols that convey meaning. The various possible arrangements of these symbols are governed by rules.⁶

Just as a fun comparison, check out the following cymatic patterns. With very little effort we can imagine how reality and the Universe are like a 248D drum filled with energy and vibrating in all frequencies.

The theories of quantum symmetry and emergence theory based on the E8 crystal hypothesize that all matter is a projection of countless “pixels” that are really, really small tetrahedrons⁷, each about 1.61 × 10^-35 meters in size. Remember the size of a quark, 10^-17? This is a lot smaller.

It might sound like this is mixing apples and multidimensional oranges, using definitions from emergence theory on one side of the scale, and definitions from quantum symmetry on the other side, but both of these theories integrate quantum mechanics, general and special relativity, the standard model and other mainstream physics theories to form a complete, fundamental picture of a Universe unfolding from the implicit to the explicit. The main difference between these two models is that the E8 Crystal describes the mechanics of creation, while emergence theory attempts to describe the syntax of its operation using the language of geometry.

Key 59: Geometry and mathematics are the language of archetypes.

Here we have a duality that encompasses the entire spectrum of 3D reality, at least. On one end, the alphahedron (the smallest structure theoretically possible), which is the tetrahedron, and on the other end, the omegahedron (the most complex structure in existence), which currently seems to be the 248D-ish magic crystal.

The Structure of Knowledge

Key 60: Just as subatomic particles are structured energy, atoms are structured particles, and molecules are structured atoms, information is structured data, knowledge is structured information, and ideas are structured knowledge.

Key 61: The concept of a thing and the thing itself are the same things on two different levels of order.

Both scopes of matter and ideas represent how a form of pure energy in its chaotic state is converted into order using the same laws as they apply to the relevant contexts of their scope. In one case, energy is ordered and expressed as matter and in the latter case as concepts. This is how it relates to holarchies, as holarchies can map not only the naturally occurring hierarchy of the concepts of reality (atoms, plants, people, etc.) but also the concept of concepts (domains of science, religions, culture, etc.).

If we applied our ideas regarding duality to the holarchy it would look something like this graph (above): We start with a concept XY₀, followed by its thesis Y₁, which creates its antithesis X₁. Within this duality of X_n and Y_n, or thesis and antithesis, arises the synthesis that acts as the seed for a new concept XY₁. The holarchy can only accommodate the central column of concepts as it has no model of a concept being born within a duality.

This graph only shows one instance per duality, but there could be many, many instances for each duality, the occurrence of which conform to the Bell curve as defined by the X_n and Y_n limits of each new pair.

Some readers might recognize this graph as looking very similar to the mystical Kabbalah, or the Tree of Life, as it is also called, which has its roots in ancient Sumer. There was no intention to arrive at such a comparison, but these similarities naturally arise whenever we are using reason to explain how reality works regardless of its understanding being scientific, mystical, or otherwise. Any system that has order will follow a pattern, and we can see these same patterns over and over again, from the electron to the galaxy, from flowers to computer networking. Our explanations of how realities work, whether we believe it was created by God in 6 days, or it is all a very sophisticated holographic projection, will have the same patterns of reasoning, albeit with different back-stories and interpretations of the significance of those patterns.

Knowledge by any other name

The image above is from a Neidan (Chinese inner alchemy) Taoist training manual of the 17^th century⁸ that comes from an oral tradition dating back to the 8^th century attributed to the legendary Chinese scholar Lü Dongbin of the Tang Dynasty. We can see the same pattern here in concept, but rather than the ordered, linear, “Cartesian” bifurcating diagrams above, it uses the classically Eastern artistic, poetic style to demonstrate a visualization technique of centering oneself in the middle of one’s 5 “shadow-geniuses” each of which has its own 5 “shadow-geniuses”, creating a self-similar pentafurcating tree. The purpose of this meditation is to “crystallize the spirit in the Elixir-field, the place of energy (solar plexus)”.

Note: “Shadow” here does not mean something negative, as in the Western concept. The description of these “shadow-geniuses” is “The pure and light energy rises upward and floats up to heaven and becomes the five-fold present shadow-genius”, suggesting that “shadow” is synonymous with “component of”, or what we would call a “parton”.

We tend to think that ancient ideas were not based in science, at least in the way we describe that word today. This is partly true, in that we had not yet discovered the laws of nature to the degree, or in the manner, we now have, but we can find incredibly sophisticated reasoning and logic in some ancient ideas.

Take two examples mentioned above, the Taoist I-Ching and the Kabbalah. Both have a tremendous body of impressive intellectual reasoning, and both are descriptions of the same larger concept of a reality that exists in a duality as seen through the contextual cultural lens of understanding. While the Kabbalah is a top-down model of creation that describes 32 archetypes made up of 10 archetypal states of existence with 22 archetypes of energy that connect these states (and based on the Hebrew alphabet of 22 characters and 10 numbers), the I-Ching is a fractally bifurcated whole of 10 pairs of balanced states and 22 pairs of imbalanced states that describe 32 pairs of archetypal states of the Tao.

The story of the I-Ching and Gottfried Wilhelm von Leibniz, the co-inventor (along with Newton) of differential and integral calculus, is a fascinating story that exemplifies this cultural lens. It is a bit of an aside, but it is relevant and worth the read.

Leibniz

When the Jesuits, reputed to be the intellectuals among Christian missionaries, traveled to China, they were so fascinated by the I-Ching that they brought it back to Europe in the late 1600s. It was here that Leibniz saw the I-Ching and claimed it to be sent to him by God.⁹

Prior to seeing the I-Ching, Leibniz had been developing (discovering?) a number system since 1679 that he considered sacred and which he described in his 1703 article, Explication de l’Arithmétique Binaire. It was the binary system of 0s and 1s, much like the Yin/Yang of the I-Ching. It was of no real practical use to anyone at the time, but that was not why he developed it. Leibniz, a very pious man, thought that if all values could be expressed in terms of only something and nothing, on and off, yes and no, positive and negative, and more, then truly, this would be the language of life. As he thought, God the Creator was represented as 1, while the void was represented as 0.

Leibniz’s principal work on this topic was his ideas on monism, as he called it. In short, he describes how each substance is programmed to act in a predetermined way and is integrated with all other substances according to a preexisting archetypal harmony. The most, and only essential substance was the simplest, which he described as “that which is one, has no parts and is therefore indivisible” and from which all other substances emerged, that is, God.

At the same time he was inventing this divine math meant to explore the hidden secrets of reality, he was also inventing the first mechanical calculator suitable not only for addition and subtraction but for multiplication as well. His dream was to make a logical thinking device.¹⁰

Leibniz was creating tools for exoteric and esoteric understanding, both based on the same logic, but within two very different contexts. Leibniz’s sacred math was lost to obscurity, until it was (coincidentally) resuscitated some 300 years later at the pre-dawn of the digital computer.

To synopsize the entire digital revolution into one paragraph, imagine one of these digital pioneers saying this. “I have got an idea. Let us develop a component that will act as a conductor when a certain amount of voltage is passed through it, and an insulator when no voltage is passed through it. We will call this component a ‘gate’. Because this gate can only respond to one of two states, high or low voltage, yes or no, so to speak, which represents the most basic principles of reasoning, we will call it a ‘logic gate’. Any problem that can be reduced into so many yes-or-no conditions can be calculated by these logic gates. We can use the numbers 1 and 0 to represent these states as digits. Because the heart of these electronic machines will be made up of these yes-or-no circuits, we will call them ‘digital circuits’”. And thus, the digital computer as we know it today was invented.

If Leibniz was alive today to see his sacred binary math of 1s and 0s being used as the language of his ‘thinking machine’, ushering in the greatest transformation of knowledge ever known to Man, he would recognize it as both a tool of practical use as well as a tool of great esoteric potential, a key to the secret knowledge he was looking for.

The Source of Ideas

We like to think we come up with ideas, but perhaps this is no truer than a flower “deciding” to change colors when exposed to different light, or a river “deciding” to change course because the wolf population has increased.¹¹

Although currently not a mainstream theory, the understanding that Ideas are more like expressions of living intelligences that we have a symbiotic relationship with is currently alive and well, and has been around for thousands of years. Traditionally, these forms of intelligence and intention were anthropomorphized into deities, angels, demons, spirits, and more, and it was understood that we use them for our purposes, noble and otherwise, and they use us for their purposes, noble or otherwise. Today we have new evidenced-based hypotheses of this same concept in the forms of panpsychism, morphic fields, collective (un)consciousness, Universal mind, and more. From this perspective, all forms of life are simply instances of various Ideas and concepts that have instantiated themselves.

One of the fundamental differences in how similar concepts evolve over time is in what and how structure is applied to the idea. Take, for example, the idea of the biblical creation story vs. reality-as-a-simulation hypothesis. We can see by their similarity that they are clearly the same concept, but one filtered and defined through the belief structures of Judeo-Christian doctrine and the other through the structured reasoning of modern science.

The above was a somewhat circuitous route to get to this point of looking at knowledge as a form of structured information and how it is not only the basis of reason but the basis of existence as well. It was stated before that the tetrahedron is the most fundamental concept of form. We are going a step further here and also claiming that the tetrahedron is also the structure that information takes when it forms knowledge.

How would we begin to test such an idea? We can start in the same way we would test the idea of a tetrahedron, by deconstructing it into its even more basic component, the triangle, and if we can discover a triad of information, we can form a tetrahedron of knowledge. We have already seen one fundamental pattern (Newton’s 2^nd law) that discovers a 4^th point from any 3 points, so perhaps we can learn something more from just a triangle.

What follows are some examples of how we might identify conceptual trinities in a wide variety of systems of knowledge and/or information.

Language

In the realm of ideas, the most important tool that man has deployed has been language. Language transmits the reasoning behind ideas. It is how ideas evolve, how they are destroyed and how they defend themselves, which, according to Dawkins, they do, as he explains in his book “The Selfish Gene”. As such, we would expect to see language embedded with the same structure as that of ideas, concepts, and forms.

Humans are sort of stuck with the language we have been using for thousands of years, and if we were to (and when we do) invent a new language it would look radically different, but it would probably function similarly because all naturally evolved languages follow a law based on mathematical statistics that also approximate the same laws of science. This amazing pattern of language was discovered in the 19^th century and is called Zipf’s law (which when normalized is called the Riemann Zeta Function) and is fundamental to everything from the diffraction of light to the size of craters on the moon. This is another topic, but the point here is that language evolves according to, and limited by, the same forces that drive all evolution, growth and change.

This applies to intentionally designed languages as well. In 1968, Aristid Lindenmayer, a Hungarian theoretical biologist and botanist at the University of Utrecht, designed a symbolic language called L-system that incorporated various symbols that were bound by a set of rules. He developed this language as a way to model and describe the behavior of plants and a variety of other organisms¹². The philosophy and architecture of the language were based on the observed logic of growth, that is, life. Not coincidentally, this language describes self-similar systems. This is the language of the future, but sadly, only for our digital offspring, at least not until we do some major gray matter rewiring upstairs.

Granted, L-System language is mainly used as a modeling language, but has an alphabet, grammatical roots, and rules, like human language¹³. This is brought up to show that organically evolved systems that have survived the challenges of sustainability, such as human language, exhibit similar characteristics to the highly ordered, structured, and hierarchical systems that describe life itself.

Although human language is surprisingly efficient and operates with the same structure that naturally exists in ideas and concepts, its efficiency is greatly due to our brain’s ability to apply context and instantly run through many interpretations of words and sentence structure until it finds the most contextually applicable interpretation. This is entropy in action, as each possible interpretation is a microstate that the brain has to instantly field-test. Take the sentences:

Say the first sentence 5 times, each time putting the stress on a different word. This sentence has the equivalent of 5 microstates, and depending on the context of who/what/where/when/why, the brain will calculate the highest probability of its intended meaning. Likewise, the second sentence has potentially 16 microstates, as there are 8 different interpretations based on stress, and 2 possible meanings as to whether the man had a stick or a stick was or was not used, to hit him with. Applying the concept of entropy in this scenario, finding meaning in the sentence equates to the balancing of energy between two states. But what is imbalanced that needs balancing? The imbalance is one of knowledge, as the information provided by each interpretation is quite different, and that information might be important to know. To get the answers, the brain has a built-in intention-drive, which is the neurology that makes one need to, or desire to find answers. This is not a well-understood process, but it is being studied¹⁴. The brain’s built-in intention-drive is wired specifically for the purpose of discerning significance and increasing knowledge, which it has learned is a critical competitive and survival skill. Even when there is no actual information to discern, the brain can create significance. I suspect that delusional disorders are somehow related to a hyperactive intention-drive.

How does this cognitive wiring and processing work? While the physiological details of the wiring are not known, it is an educated guess that the intention-drive is a result of, and proportional to, the electrical charge in the ions that create neural signals. One clue is to look at the processing involved.

The meanings of words, their order, the context of who is speaking and where they are, along with many other details, come into play to turn that sentence into structured information, or knowledge, in our head. It is our brain’s language processing ability that converts the often messy structure of words into meaningfulness. Were language more structured we might say this sentence as:

Although we do not speak this way, this is more or less how the brain re-patterns the concepts to discern meaning.

There is such a language which was developed to specifically optimize the transmissions of concepts. It is called Ithkuil¹⁵. In Ithkuil, you can say “On the contrary, I think it may turn out that this rugged mountain range trails off at some point”, in the following manner:

I doubt we will be adopting these any time soon, but they are still fascinating. Given what we know about the parallels between language, neurology, and the nature of growth and evolution, such new languages may provide insight into the creation of patterned information systems (which includes reality), especially with regard to our own neurology.

Regardless of the language, they all depend on semantics, which is what makes any language work. Semantics is also a structure that the brain’s wiring can most easily process, which is why language is structured the way it is.

Semantics

Semantics is the branch of linguistics and logic concerned with meaning, but there are two kinds of meaning, according to the Theory of Meaning¹⁶. The first kind is the more common definition of semantics.

An example of this type of objective description might be the following bifurcating graph of a simple sentence.

The semantic web is the term used to apply semantic concepts to digital information in an attempt to define what information “is” in a manner that is structured so that computers can read data and know if it is information and, more importantly, why it is information. It does this by creating a relationship between two things.

To a human, this is information because we know how to parse this sentence into meaning. That is what learning to speak is all about. To a computer, however, it is just a meaningless collection of 1s and 0s, specifically:

_{010000100110111101100010001000000110100101110011001000000110100101101110011101000110010101110010011001010111001101110100011001010110010000100000011010010110111000100000011101000110100001100101001000000100110101101111011011100110000100100000010011000110100101110011011000010010111000001010}

If we break this sentence up into three parts and define each part in a way that software can understand, then a computer can attempt to find meaning in it. For example, we can tell the computer that we have two things, “Bob” and”Mona Lisa”, and one relationship, “is interested in”.

With these three data points, three “atoms” of data, we have the simplest form of information, an information “molecule”, so to speak. The “things” are the objects, and the “relationship” is the predicate. Together they are called a triplet. We may have some other triplets about Bob, such as, he is a person, he is a friend of Alice, and more, and we can bind these triplets together quite naturally.

Predicates can be just about anything including “lives in”, “has a”, “enjoys”, and more. Objects, however, are part of a much larger, more structured hierarchies, much like the holarchies described above. Using predicates and objects we can now graph our sentence (above right).

How does a computer know what “is interested in” or what a “person” is? It does not “know” the way you or I know, but it does know that a person is a type of agent, has a family name, a first name and that a person knows things. So, as far as a computer is concerned, a person is just a data-set with a bunch of specific properties and relationships to other data-sets.¹⁷ These definitions and relationships are defined hierarchically into the “that which is” ontology maps.

There are thousands of these ontologies of definitions run by corporations, governments, individuals, schools, the military, and more, that cover an incredible array of data in areas of geography, life sciences, linguistics, media, social networking, medicine, catfish, diseases, road-maps, accommodations in Tuscany, and more, and they can all talk to each other by linking triplets together.¹⁸

As you can imagine, a computer can create millions of connections between triplets with little effort and in a very short time. With all these connections, we can ask the computer typical questions like “How many romantic comedy Hollywood movies are directed by a person who is born in a city that has an average temperature above 15°?” Of course, social media companies, who have their own ontologies that they aggressively build from their user-base, can ask questions like “Give me a list of all the boys who are eligible to vote in the next election, and who listen to Seattle grunge bands, are politically left-wing, and have friends and family that are politically progressive.” More worrying are the queries of the near future, such as “Tell me all the names of people that are likely to commit a crime in the next week.” That may sound like paranoia about a dystopian future, but AI systems in China have an 80% success rate in predicting who is a criminal just by looking at them. At Stanford University they have developed an AI system that has a 91% accuracy rate of determining if someone is gay or straight¹⁹, and that is just the beginning.

Language is based on rules of nature and can be deconstructed into triplets, and we can see these same rules applied to both the physiology required to support language, and the language itself. In fact, the bifurcated structure of linguistic syntax maps remarkably onto the bifurcated structure of tubulin proteins in microtubules. Stuart Hameroff, the American doctor and professor at the University of Arizona known for his studies relating consciousness and quantum mechanics, has extensively studied how microtubules may function as information processing structures in neurons, revealing these striking structural parallels between language formation and neurological architecture.

It is also quite fascinating, though not surprising, that this information encoding is the result of the bifurcated tree structure of tubulin proteins interacting with hexagonal structures called Ca2+/calmodulin-dependent protein kinase II, or CaMKII. The significance of binary trees and hexagonal structures will become increasingly apparent as we go deeper into the mechanics of awareness.

Supply Chain

Here is another real-world example of a current project that is being developed with economists, world leaders, and investors, that attempts to model the supply chain in a holistic manner in order to show how environmentally sustainable solutions can be more profitable than unsustainable solutions over the long term, and how small details along the chain can have global consequences.

The project started out with reams of data from every sector of the economy, every mode of transport and delivery, distribution, allocations, and more. It was little more than a random pile of data in the form of spreadsheets, various databases, government and industry reports. The researchers sifted through this data looking for patterns, relationships, and dependencies. What eventually emerged were sets of conceptual “triplets” with their corresponding instances and the relationships and rules that existed between them. The researchers had no knowledge of holarchies, yet what they developed was quite similar.

Here are some (somewhat simplified) graphs taken from this project that describes the relationship between resources, location, and sector using the instances of water, Argentina, and agriculture.

When modeling all elements of the supply chain, they ended up with the following visual representation of the model, with each color representing one of the three concepts that define each context or level (image below). The left image shows the set of three circles that represent resources ↔︎ location ↔︎ sector level, with a real-world data-set of water ↔︎ Argentina ↔︎ agriculture. Within one of the inner circles, such as agriculture, is information about product ↔︎ production ↔︎ transport, such as tomatoes ↔︎ kilos/yr ↔︎ import/export. In the end, they were able to calculate the environmental, economic, and social impact that one potato had at every stage of its journey from a spud on an Argentine farm to the garbage bin at a restaurant in Paris. It is not a coincidence that this structure is identical to the structure of the neural wiring that connects a synapse, or transmission point, to a dendrite, a reception point, in the brain.

You can clearly see the triplet and holarchic design of this representation of the supply chain in the image above (left). This would be expected if you considered a supply chain as a large-scale version of a living system. The image on the right seems to confirm this, or at least suggest that the brain and the central nervous system is an organic living instance of a real-time supply chain of three levels of embedded interdependency.

Law of Laws

Earlier, we used Newton’s 2^nd law of motion as an example to show how one law has many contexts, but Newton’s 2^nd is only one of the three laws of Newton’s laws of Motion. These Laws are:

These are not simply three isolated laws, but rather three attributes of a greater phenomenon that describes all matter.

(Later we show why these laws should be in the order of #3 first, followed by #1 and then #2).

While Newton discovered these laws of physics in 1666, the principles behind them were well established as least as far back as 1494 when the Venetian magician, mathematician and monk, Luca Pacioli invented double entry accounting, which is still the most common form of accounting used to this day.

Pacioli’s underlying principle to his accounting system evolved from his metaphysical and cosmological view that everything comes from nothing, and reality is simply an imbalance of that nothing. Therefore, the sum of all things must equal nothing. To apply this to accounting, wherever there is a negative entry there must also be an equal and opposite positive entry. A $10 reduction in the “petty cash” account due to the purchase of paperclips automatically creates a $10 increase in the value of “office supplies” account. Totaling the sums of all the different accounts must therefore equal 0, otherwise the account is not balanced.

In other words, for every transaction there is an equal and opposite transaction.

That works for the balance part of the 3 laws, but what of inertia and force? Is inertia equivalent to cash-flow? Is entropy equivalent to depreciation or amortization? Is force equivalent to income or revenue? Playing around with applying Newton’s laws to finance is complicated, given the countless ways value is used and defined, but some of the results look very interesting.

There is no doubt that Newton was quite aware of Pacioli’s work, and given both were students of the mystical and arcane, they probably shared many of the same beliefs, so it is probably safe to say that Pacioli’s ideas had some effect on Newton’s theories. How much, we can only speculate.

We can see this trinity of concepts in any structured system. Here are some examples.

Music

The relationship of music to trigrams is so profound that it deserves a book unto itself, and many have been written, so I will only share that entire theories of music are modeled on the trigram, such as the Tonnetz (German for tone-network) model, which is a conceptual lattice diagram representing tonal space first described by Swiss mathematician, physicist, astronomer, geographer, logician and engineer, and one of the greatest thinkers of modern history, Leonhard Euler, in 1739. Modern music theorists take it a step further, that of a two-dimensional map of trigrams mapped to a spinning torus. Note: This model of music is also referenced in chapter 12, “Predeterminism”.

Drama

Around 335 B.C., Aristotle described the dramatic structure of a story as having a beginning, a middle, and an end. Eight hundred years later, the Roman grammarian Aelius Donatus expanded that to a three-part structure of the protasis (introduction), epitasis (main action), and catastrophe (resolution, which, in those days, was inevitably catastrophic). Finally, German playwright and novelist Gustav Freytag turned the three-part structure into a five-part structure with the Freytag Pyramid.

The Freytag Pyramid can easily be defined as a trigram (below right) showing the five-part structure of incitement, rising actions (inflation), climax, falling action (deflation), and resolution. Leading up to these five parts is exposition, which describes the baseline of the story, the characters, set and setting, and more. After the five parts, there is the denouement, or the returning to the baseline of the natural order. It is easy to see how the Freytag Pyramid is the classic three-part structure of incitement (beginning), climax (middle), and resolution (end) with the additional dynamics of inflation and deflation. While it is called a five-part structure, there is obviously the sixth part, that of the baseline, the condition before and after the action described by the five parts.

This, like all info-trigrams, is self-similar, with the ascending and descending elements being more “atomic”, and the trigrams being more “molecular”. The substance of a story is typically made of many “molecules”. While there may be many types of Freytag contexts, most stories are one of, or a mixture of, the following 6. The image above shows this in an analysis of “Harry Potter and the Deathly Hallows”, by J. K. Rowling.

Reduction

The overarching idea here is that every model can be described by a self-similar set of three axes. This is not arbitrary, as we claim that any system can be reduced to, and described by, a collection of information primitives (triplets or trigrams). From these essentially two-dimensional information primitives (in that they can be described with only three points) we can build knowledge primitives that are tetrahedral in concept.

Furthermore, we hope to demonstrate that these three axes are essentially three different perspectives of one state. An example of this is how electrical energy is expressed through three different properties: voltage (volts), current (amps), and resistance (ohms), forming a trigram, which are then capable of describing a 4^th property of power, forming a tetrahedron. We go even further and claim that the 3+1 dimensions of our reality (X, Y, Z, + time), is itself the most fundamental expression of this same model.

We will return to more in-depth examples after some exploration into these concepts.

Info-atoms

If our premise is that the smallest element of knowledge must conform to the same laws as the smallest elements of form, conceptually speaking, then we need to show how these 2D models, such as the holarchy, fit into not just a 3D model, but specifically tetrahedral structures that represent “knowledge molecules” with an ordered self-similar hierarchy where each holon is represented as a tetrahedron of information.

Our revised model of hierarchical tetrahedrons will surely look and act differently than a holarchy. To avoid confusion, we will refer to these tetrahedron holons as tholons (for obvious reasons), and the holarchy of tholons as the thologram.

Key 62: Every tholon is an archetype.

We are working from the premise that everything that exists is a product of a stable pattern existing between different states. The simplest concept of such a duality is that of something and nothing. Not much can be said about nothing, but as for something, we do not need to imagine something that represents everything at once. Such a conception is not only beyond our ability, but given that everything has yet to come into existence (or if it has, it has not yet come into our context), it is impossible. On the contrary, we only need to imagine the simplest form of something, for example, a singular dot. A simple dot on a blank page is a diagram of the model on which this reality, and all knowledge, is based. If we conceive of an infinite void of nothingness within which exists a single point, then that point alone represents the totality of everything that exists. This single dot is often called the singularity. In the cosmological sense, the singularity is the point at which the known laws of physics break down, where space and time cease to exist as distinct entities and merge into an undefined state.

These singularities were predicted by Relativity and theoretically have zero volume and infinite density (and therefore infinite gravity). The cosmological singularity was the initial state of the Big Bang, and similar singularities are predicted (though not observable) at the centers of black holes.

There is another significance to the concept of singularity, and that is the technological singularity. This is the point in time when technological growth becomes uncontrollable and irreversible, that is, technology has the ability to design and build itself, creating exponential advancement that results in a super-intelligence. Futurist Ray Kurzweil, Google’s Director of Engineering, predicts this moment will happen in 2045.

For our purposes, we only need to consider that the singularity that created this Universe is a 0-dimensional dot. This simplest of concepts can explain the holarchy, tetrahedrons, magic crystals, all the laws of physics and every form of intelligence in existence.

Geometry I

The most effective way to describe this process of emergence from a dot to everything in existence is with the language of geometry.

We are taught that the progression from point to tetrahedron follows a very clear and simple path of point → line → trigram → tetrahedron.

From the tholonic perspective, this is a very incomplete description because it considers any point to be just like any other point, but they are not the same, as each point has very different qualitative attributes. If we ignore those attributes, we are blind to what geometry can show us about so much more than shapes. Order is the most significant difference between these points, which is described below.

(Unfortunately, if you are reading this on a black and white eBook reader, these color patterns are meaningless. See Appendix A, “About This Book” to test the gray scale of the primary colors on your e-reader.)

We start with a 0-dimensional dot represented by a blue dot in the middle of nothing (Fig. c1). Because it is 0 dimensions and surrounded by nothing, it only exists as a concept. It has no form, no spatial dimensions, no measurable properties other than the concept that it exists. But where does it exist? It cannot be measured, seen, or interacted with in any way, so how can we say it even exists? We can only say it exists because of the awareness of its existence. The only difference between pure nothingness and nothingness containing an imaginary point is the idea itself. Without the awareness of its existence, nothingness would simply remain nothingness. This is our first duality, that of nothingness and the concept of somethingness, and also the first condition of imbalance.

This next step requires some philosophical conjecture because we have to ask why or how does a 2^nd (green) dot appear (Fig. c2).

If we accept the premise that everything that is created has the attributes of, and limitations of, whatever created it, then the answer is clear and simple. This lone imaginary dot in the middle of infinite nothingness exists only as an awareness of the concept of a point. Therefore, the one attribute this point must inherit is awareness itself, as that is what it was created from. Having inherited this attribute of awareness, the first dot now possesses the same creative capacity as the awareness that created it. Just as the original awareness created the first dot, the first dot’s awareness creates the second dot in precisely the same manner. And what was this awareness? We can only presume that it was the most fundamental form of awareness, that being the awareness of existing (which is not the same as the meta-awareness of being aware that one is aware). This primal first instance of awareness is therefore the archetype of all awareness that will ever come into being. Additionally, being the only awareness that exists, it is virtually unlimited awareness, and possibly infinite awareness as well if we consider “infinite” to mean the totality of all.

One might reasonably object: “How can a 0-dimensional point possess awareness?” From our three-dimensional perspective, a 0-dimensional point appears to have no properties whatsoever. However, we have already established that reality exists within a multi-dimensional framework, as evidenced by the E8 crystal structure with its 248 dimensions and the projections from higher dimensions into our observable 3D space. Just as the vast complexity of the E8 crystal can manifest as simple tetrahedral projections in three dimensions, this apparently simple 0-dimensional point could be a projection or manifestation of something far more complex when viewed from higher-dimensional reality. Therefore, it is entirely reasonable to propose that this point can indeed possess and inherit the properties of its creator, including awareness, even though it appears dimensionless from our limited three-dimensional perspective. Indeed, awareness itself, especially in its archetypal form, may reasonably be considered the ultimate multi-dimensional existence, far more complex and encompassing than our current three-dimensional understanding allows us to perceive.

There is one more, far less obvious attribute to consider as well, and that is intention. The very fact that the 0-dimensional point exists as an idea demonstrates that there must have been the intention to conceive of it. Ideas do not spontaneously appear without intentionality. So, our point in the middle of infinite nothingness has two inseparable attributes: Awareness and Intention. The nature of that intention is addressed further on.

Key 63: Awareness and Intention (A&I) is the source of existence.

We see this same concept, that of creation being the result of A&I, in the spiritual texts of every major belief system. For example, in the Abrahamic (Jewish, Christian, and Islamic) lore²⁰, when God spoke to Moses, God was quite specific about its name. God told Moses its name was “I Am (Who/Which/That) I Am” (

) and also informed Moses that the voice he was hearing was (or was sent by) “I AM” (

The phrase “I Am” is especially relevant to the fundamental forms of Awareness and Intention as “I” is the simplest concept of Awareness that can be communicated. The infinitive verb “to be” is inherently a statement of intention to exist, with its present tense form being “Am”. Quite literally, “I Am” means “Awareness and Intention”.

Key 63: “I Am” literally means the present form of “Awareness and Intention”.

Buddhists appear to have cut out the middleman (or perhaps “middle-god”) as they do not have the concept of a divine creator being, but they do have the concept of a primal “I Am” awareness, as suggested in a Buddhist teaching: A person asked Buddha, “Are you a God?” Buddha replied, “No.” “Are you an Angel?” “No.” “Then what are you?” “I am awake.”

We can also see the concepts of A&I in the context of physics. Take the example of energy, mass, and light, as we briefly addressed earlier. Light has no mass, and in its archetypal state, it exists as the concept of a 0-dimensional point with zero energy. Just as a magnetic field can exist with a value of zero (an established scientific axiom), a photon can exist as an archetype with zero energy. We cannot measure such a photon, but the archetype exists as a concept. This conceptual point, a result of awareness, only gains measurable properties when intention manifests as movement (speed, frequency, amplitude). This movement is not an intention of the photon’s own creation, but rather an instance of the archetypal Intention that originated from the very first primal point. Movement requires energy, therefore the movement of energy itself is an instantiation of primal Intention, making light (or any form of radiation) a primal expression of A&I. It suggests that awareness may be the purest form of energy, but it is intention that makes it manifest through movement. Awareness and Intention always exist as two inseparable aspects of the primal archetype, similar to how electric and magnetic fields exist as inseparable aspects of an electromagnetic field, each able to be zero yet still existing as concepts.

This may sound like we are teetering on the edge of mysticism, but this is not our goal. We simply are following the most reasonable path that our ability to understand our reality allows. The fact that it suggests that all of existence is a form of A&I is not mysticism, it is a hypothesis of reality. Science is slowly beginning to consider that there might be a relationship between awareness and reality, but the tholonic position is that awareness is not only the fabric of reality, but that the intention of that awareness is the energy that drives all of creation and the only energy in existence. Just as the term “electrical current” implies a magnetic component, the word “awareness”, as we use it here, implies an intention component, as Awareness and Intention always coexist. In the reality we exist in, there is no Awareness without Intention, nor Intention without Awareness.

We have seen how mass is a form of energy, and how they both follow the same rules applicable to their context. Because of this, we can speculate that mass and energy are two different instances of the same archetype of pure energy but instantiated within two different scopes or contexts. We will take one step further and say that awareness itself (as we currently understand that concept) is an instance of that same archetype but in an even “finer” context, that is, before there was mass, there was energy, and before there was energy there was A&I. Were this the case, it would shed light on why and how awareness and intention is an integral part of reality, which could provide answers to the quantum mystery of how and why awareness itself is required for reality to exist, because in this scenario, everything that exists must have some instance of awareness. We accept that reality is a result of the interaction between two instances of energy: radiation and mass. But what if A&I itself is a third, even more fundamental state from which energy (as we understand it) emerges?

It would be very convenient if awareness and/or intention was somehow mapable to one of the missing formulas in our hexagonal model of Newton’s 2^nd, because then we could see that mass, energy, and force were connected to awareness and intention, suggesting that nothing can come into existence without A&I. We might then also be able to calculate the field and force of awareness. To be clear, I am not claiming this is the case, just that it would be convenient if it was. One potential avenue of exploration might be to consider force as an expression of Intention (I), since force causes movement and change, while mass could represent Awareness (A) as the substrate or being that exists. Acceleration would then represent the manifestation (M) or result of Intention acting upon Awareness. In this hypothetical mapping, Newton’s equation F = ma could translate conceptually to:

I=A\times M

, or rearranged,

M=\frac{I}{A}

. While this remains highly speculative, such a framework might provide a mathematical language for describing how A&I manifests in physical reality, potentially bridging metaphysics and physics in ways currently unexplored.

Restating this fundamental principle: our first dot has the two attributes of A&I, and the limitation of 0-dimensions. This dot, then, is itself a form of awareness and intention, and being so, there is now an awareness of dotness, not its dotness, just dotness, as that is all there is to be aware of, but it is an awareness of dotness with intention. Just as the first dot is the effect of intentional awareness, that same intentional awareness in the newly created (blue) dot will be the cause of a new effect, a new conceptual (green) dot. Perhaps this is what Nietzsche was referring to when he wrote in “Beyond Good and Evil”:

The new dot, and all dots that will ever come into being, have the same qualities of awareness and intention, as that is what created them, so as soon as the first dot was created, a never-ending cause-effect chain reaction of dots creating dots was initiated, like a kind of conceptual Big Bang. With these first 2 conceptual, 0-dimensional dots, the first relationship was created: the line. It is worth noting that even before we have a geometric triangle, we now have our first semantic triplet: two objects (the two dots) connected by a predicate (the line representing their relationship). This is the archetypal structure of all semantic triplets, the fundamental pattern by which information is organized and communicated. In this way, the structure of information itself emerges simultaneously with the first relationship, demonstrating that information and existence are inseparable.

There are now 2 states of dotness: the blue dot and the green dot. This is the birth of the concepts “I” vs. “Other than I”, and “Me” vs. “You”. Where before there could only exist unlimited A&I as there was nothing other than dotness, now there is an instance of awareness that is limited by, and defined by, another instance of awareness. This results in 2 types of awareness: the subjective, which is the awareness of one’s existence, and which is infinite by nature, and the objective, the awareness of another’s existence, which is finite by nature. Both of these states, the subjective and the objective, exist in each dot, so now there are 2 forms of awareness in 2 dots. In this way, 1 dot creates 2 dots which creates 4 perspectives (this will soon be a very significant detail).

With two dots in existence, each has its own center with the other defining its limits. Where these 2 instances meet, where subjective meets objective, where the infinite meets the finite, a pair of new (red) dots emerges (Fig. c3), each created from the merging of these polar opposites.

At this stage we have all 3 types of dots: blue, green and red. Each of these dots came into being due to a unique cause and each had a unique effect.

Our ever-expanding conceptual model, however, faces a fundamental limitation: it is imprisoned in the 2D world. Even though it can generate an infinite number of dots within the 2D plane, it cannot produce a new dot that transcends into the 3D plane. Why cannot the same process that created 2D from 1D be used to create 3D from 2D?

The reason is geometric: three dot types are necessary and sufficient for defining any 2D area. Multiple instances of red, green, and blue dots can describe any 2D geometry. A 4^th type constrained to 2D would be redundant, offering no dimensional expansion. We need a completely new type of dot that transcends this 2D limitation while remaining compatible with all 3 existing types.

Not surprisingly, the trigrams have already given us the answer with two clues. The 1^st clue: the creation of one trigram implies the creation of three additional trigrams, each connected to a side of the center trigram. The 2^nd clue: for each of these new trigrams, another dot is created. These 3 additional dots at the outer tips are each of a different color. Here is the key insight: every trigram must be composed of 3 unique dots (R, G, and B). A new type of dot capable of creating a 3D tetrahedron would automatically create 3 new trigrams. This new dot would have to act as a red dot to the blue-green pair of the original trigram, a blue dot to the green-red pair, and a green dot to the red-blue pair.

The RGB dot

, or what we will refer to as the white dot

, represents the combination of all three primary dots. This dot can add 1 dimension to 2-dimensions and defines volume as a result of the union of the 3 unique trigrams that extend from the center trigram. Such a dot is created when the 3 outer trigrams fold until their points meet. The folding occurs naturally because it represents the most balanced and efficient interaction between a set of four unique dots (R, G, B, W). Energy minimization drives this configuration to emerge as the most stable state.

Note: This same concept is also explained in a mathematical manner in the chapter “How Creation Works” in the book “The Tholonic I-Ching”, which examines the I-Ching from a tholonic perspective.

Holons to Tholons

Let us back up and apply some of the semantic concepts to the holarchy as it will shed more light on the nature of information and how a holarchy forms a network of trinities in the way these holons interact with one another.

According to the creators of the holarchy model, each holon has three functions:

These attributes hold up quite well when compared to our real-world example of a supply chain, as there is a contributing supply, a demanding market for that supply, and the negotiations, cooperation, and competition that connect the two.

Here is where we turn a holon into a tholon: by rearranging the order, while keeping all the relationships the same, and then presenting that order in a different format.

This is much more than a cosmetic change, for by changing the focus and the pattern we can see a lot more information. For example, we naturally want to imagine how to connect these three attributes. If we create connecting lines (demonstrated below) and color them to match the dots they emerge from, we can visualize the relationships between attributes: a red line emerging from the red dot of Contribution shows the relationship between Contribution and Negotiation (the blue dot); a green line emerging from the green dot of Definition shows the relationship between Definition and Contribution (the red dot); and a blue line emerging from the blue dot of Negotiation shows the relationship between Negotiation and Definition (the green dot). The colors we are using, red, green, and blue, are the simplest representations. However, using different colors for lines and dots, such as complementary colors, can create very clear patterns that are more complex and symmetrical and support the model just as well.

There is still a piece missing from the holarchic model. If we apply the holarchic model to the archetype concepts of town, state, and country, it shows only hierarchical interactions: between state and country and between town and state. It shows no direct connection between town and country. The tholonic model, however, does show this direct connection (the yellow line in the diagram). Note that in this diagram we are using additive color mixing: each line’s color is generated by combining the colors of the two points it connects (yellow = red town + green country, cyan = blue state + green country, magenta = blue state + red town). If the concept of state is stable, then a new state will naturally appear across this direct town-country connection simply because it can, and if it can, it must. For example, the three towns (that is, colonies) that existed near the Delaware Bay in the newly declared United States of America eventually became the State of Delaware, the first state in the United States.

The tholonic model therefore creates a new instance of state, which means there are now two instances of state. It may seem redundant to have two instances of state, but in fact, they are not the same. The originating concept of state is that of any social structure that exists between country and town, but a state that exists between town and country is specific to that town and country. For example, the abstract concepts of town, state, and country may instantiate as Woodstock, New York, USA, or Navarro, Buenos Aires, Argentina, two radically different instances of the same town/state/country tholonic archetype. But this is not the most important difference between these two states. As described earlier, the blue Negotiated point is the only point from which children can emerge, therefore, a new negotiated point must exist for there to be any instances. That point, in this example, is the negotiated balance between town and country. Specifically, a state is Defined (limited, constrained) by its country and Contributes (allows for creation of) its towns. So, this new point of state between town and country would be an instance of the concept of a state, for example, the state of California. Now, California is itself a concept that has within it its own California-based instances of economy, politics, culture, terrain, weather, and more.

Notice in the diagram the small blue N dot that appears at the center of the yellow line connecting Contribution (red) and Definition (green). This represents a new instantiated state of Negotiation that emerges between these two poles. Since Definition is analogous to low entropy chaos (limitation) and Contribution is analogous to high entropy chaos (dispersion), the yellow line connecting them forms a spectrum along which a sustainable state of order naturally emerges. This is the instantiated Negotiation point—a balanced state that appears wherever the conditions allow it, following the principle that if a stable pattern can exist, it must exist.

In our illustrations, we will often use the two-dimensional representation of the thologram rather than the three-dimensional because it is simply easier to visualize. As you can see in the representation above, the two-dimensional thologram has four points but is limited to two-dimensional space. When we extend this model into three-dimensional space, that fourth point lifts out of the plane and creates the three-dimensional tetrahedron from what was a triangle. The 3-dimensional model is far more complex, which we get into later.

Before we continue, we must clarify some points on vocabulary, particularly the word negotiate and its various forms. Words can be confusing, and sentences even more so. Consider the grammatically correct sentence shown above, invented by Professor William J. Rapaport in 1972:

The confusion comes from the fact that the word buffalo has a number of meanings: as an animal, a place in New York, and a synonym for bullying.

In the English language, verbs have different forms to indicate various aspects of action. The progressive form indicates ongoing action, the perfect form indicates a completed action, and the perfect progressive form indicates the transition between the two (that is, ongoing action that will be completed at some definite point). All these forms also have past, present, and future tenses.

Can verbs also function as nouns? Yes, in some cases, as with the word balance. The noun balance is defined as “a state of equilibrium”, and that same definition applies to the achieved state when we use balance as a verb. This is not the case with words like run or drive, as there is no present state to achieve, no final condition that driving or running results in, only a past state of ran or drove.

In some cases, even the pronunciation determines the function. The word “perfect”, when pronounced PER-fect, is a noun, and when pronounced per-FECT, it is a verb.

Given these complexities of language, let us be very clear on how we are defining the word negotiate.

First, understand that in this hierarchy of energy, everything is happening all the time, so when we refer to these energies we refer to them in the present (unless otherwise noted).

In the tholonic model, the three points of a tholon can be referred to by different names depending on whether we are emphasizing their dynamic processes or their stable states. These three points are:

As Actions (verb-like): When emphasizing the ongoing processes, we use terms like Negotiate, Define, and Contribute. These describe dynamic interactions occurring continuously: forces are negotiating or balancing with each other, boundaries are defining or limiting possibilities, and elements are contributing or integrating to larger patterns.

As States (noun-like): When emphasizing the stable conditions that have been achieved, we use terms like Balance, Limitation, and Integration. A Balanced or Negotiated state represents the sustainable equilibrium that emerges from negotiation, a Limited or Defined state represents the established boundaries or constraints, and an Integrated or Contributed state represents what has been incorporated into the system.

The Thologram

The primary reason why the properties of movement and energy are the key points in a thologram rather than the instantiated elements, as in the holarchy, is that these properties remain consistent at every level of creation. There may be millions of instances of different types of elements within the holarchy, from subatomic elements to universal elements, and everything in between, but the properties of movement and energy are always the same, even though they are expressed differently for each context. Therefore, it is the properties of movement and energy that define the structure of the hierarchy, not the instances of elements.

To further illustrate this point, we can use the previous semantic example of “Alice is a friend of Bob”. The tholonic model looks at “is a friend of” as the energetic force that defines Alice and Bob, at least within this narrow context of friendship. Without relationships, Alice and Bob would not even exist, as relationships define every interaction at every level of existence.

Consider the sentence Bob is a farmer that grows corn and eats meat. This sentence contains three semantic triplets. We can look at the relationship of the three objects (nouns): Bob, corn, meat, which describes Bob’s specific context. Or we can look at the relationship of the three predicates (verbs): is a, grows, eats, which applies to all organisms that practice agriculture or cultivation (like Leaf Cutter ants farming fungus, Fijian ants herding aphids, damselfish cultivating algae, yeti crabs farming bacteria, and humans).

These properties direct energy, energy has movement, and movement has direction. In this example, the direction is clear. However, this direction could change under different circumstances as we will see later.

The idea of modeling reality on the movement of energy rather than the things themselves is not a new idea. The Reciprocal System theory is built on the same premise and provides the best explanation of why we are using the movement of energy in the relationships and not the contexts of where that energy is coming from or going to.

Like every theory, it has its fans, but also its critics. In any case, it applies perfectly here.

Newton’s laws of Motion are similar in this regard, as the laws of motion describe the energy that relates to mass, not any particular instance of mass. Because of this, we can show a direct relationship between these tholonic concepts and Newton’s laws.

The order of the laws assigned by Newton shows the concept of balancing (verb) following the concepts of Definition (mass, inertia) and Contribution (force). In the tholonic model, the First Cause, the top of the hierarchy, begins with a stable point of Negotiated Balance (noun), from which Definition and Contribution emerge as the result of the movement of energy. For this reason, the tholonic order of Newton’s laws would be the following:

Key 64: Relationships define the function and purpose of any instance

Now that we have mapped the three properties of Negotiation, Definition, and Contribution onto a trigram, we can see and label a new class of attributes that result from these properties interacting with each other. What would we expect to see across the spectrums between these points?

This trigram of relationships is present in every instance of creation and will be expressed according to the context and scope of its instantiation.

In the context of society, we have laws (Negotiation/Definition), cooperation and conflict (Definition/Contribution), and service and supply (Contribution/Negotiation). Social theory, such as Adam Smith’s Theory of the Invisible Hand²², is predicated on the idea of cooperation based on voluntary exchange that benefits both parties as well as society.

In the context of the atomic world, the same three spectrums appear. Laws would refer to the limits that an atom must exist within. Cooperation and conflict could describe how the atom’s negative and positive forces work with and against each other, or how atoms fuse in nuclear fusion or break apart in nuclear fission. Service and supply describes the aspects of an atom that contribute to or enable the properties of its parent tholon, the realm from which it was created. In the tholonic view, this would be the realm of subatomic particles such as electrons, protons, and neutrons. How useful would subatomic particles be if there were no atoms?

Key 65: Stable patterns and instances form dynamic relationships and movement of energy, which form stable patterns and instances.

Simple Instance

What would be the simplest instance of this trigram? The simplest would be an element that contains only a single proton (Definition or D) and a single electron (Contribution or C), which exactly describes the first instance of matter, hydrogen. The proton defines what the atom fundamentally is, establishing its identity as hydrogen (atomic number = 1), an unchangeable constraint that cannot be altered without transforming it into a different element. The electron contributes to how the atom interacts with the world, enabling it to participate in chemical bonds, form molecules, and integrate into larger structures.

What is especially relevant is that hydrogen does not contain a neutron. From the tholonic perspective, this is precisely what we would expect, as the Negotiated Balance state, being a 0-dimensional point, does not actually exist physically (other than as a concept). Hydrogen with a neutron does exist and is called deuterium, representing a more stable, balanced version of the element. However, the fact that the most basic, fundamental, and abundant element in existence, and the element from which all other elements are created, lacks this physical manifestation of the Balance point strongly supports the tholonic model.

On the biological level, this same pattern appears in sexual reproduction. The maternal DNA provides one set of genetic information (Definition), establishing half of the constraints and limitations that define what the offspring can be. The paternal DNA provides the complementary set (Contribution), contributing the other half and enabling new genetic combinations through recombination. The offspring (Negotiated Balance) represents a unique individual that emerges from the interaction of these two sources, possessing traits that did not exist in exactly this combination in either parent. Just as hydrogen combines a proton and electron to form the first element, sexual reproduction combines two distinct genetic sources to create a new life that is neither parent, yet draws from both.

In the realm of philosophy, this same pattern appears in the historical development of epistemology. Rationalism, exemplified by Descartes and Leibniz, argued that knowledge is defined by reason and innate ideas (Definition), establishing the constraint that true knowledge must be derived through logical deduction. Empiricism, championed by Locke and Hume, argued that sensory experience contributes all knowledge (Contribution), asserting that the mind begins as a blank slate filled only through observation. Kant’s Critical Philosophy emerged as a Negotiated Balance between these opposing positions, demonstrating that both reason and experience are necessary for knowledge, that neither alone is sufficient, and that their interaction produces our understanding of reality. This synthesis created a new philosophical framework that transcended both rationalism and empiricism while incorporating essential elements of each.

More generally, this pattern reflects the Hegelian Dialectic of thesis, antithesis, and synthesis. In fact, for any tholonic concept to exist as a potentially viable and sustainable expression, it must satisfy this form, supporting a thesis (D), antithesis (C), and synthesis (N) that emerges from the interaction of D and C.

In chemistry, this pattern appears in the pH scale, which measures the concentration of hydrogen ions in a solution. Acids (Definition) represent one extreme, with high concentrations of hydrogen ions that constrain and limit what chemical reactions can occur (pH 0-6). Bases or alkalies (Contribution) represent the opposing extreme, with low hydrogen ion concentrations that enable different sets of reactions (pH 8-14). Neutral solutions (Negotiated Balance) exist at pH 7, where the concentration of hydrogen ions equals the concentration of hydroxide ions, creating a balanced state. Water, the foundation of most life, exists at this balanced point of pH 7. The more complex the life-form, the more precisely it requires this balanced pH, as deviation in either direction limits the range of biochemical processes that can occur. When acids and bases are combined, they interact to find a stable negotiated balance, releasing energy in the process as they move toward neutrality.

There are countless instances of nature and reality following this most fundamental of all patterns.

One detail is important before moving on. The initial 0-dimensional blue dot, which we call the N-source (Negotiation source), is the originating point and the only point able to replicate itself. Why this is so will be explained shortly.

The N-source operates in two modes: as an active process seeking equilibrium, or as a stable achieved state that serves as a template for generating new patterns. When actively negotiating, it has dimensional form and contextual instance. When balanced, it becomes a 0-dimensional concept that can propagate across scales.

When an N-source creates the Definition (D) and Contribution (C) points, these two points interact with each other along the spectrum between them. From this interaction, a new negotiated state emerges, which we call an N-child. The N-child appears on the line connecting D and C (as shown in earlier diagrams by the small blue dot on the yellow line). This N-child represents a new instance of balance specific to that particular D-C interaction. When the N-child becomes stable enough, it can mature into a full N-source capable of generating its own D and C points, continuing the pattern across scales. This is how the tholonic structure replicates and propagates throughout reality.

House of Mirrors

Within the trigram, there is energy, and therefore movement, and therefore patterns and oscillations. From these dynamics, stable states arise that are sustainable enough to become new N-children, which can mature into full N-sources. Even though one particular N-child will exist at one specific point on the spectrum between C and D, all possible states collectively cover the entire range between C and D. We can generally predict where along this spectrum various states will arise by applying a Bell curve distribution.

The image on the right shows a Bell curve within the trigram to illustrate where along the CD spectrum stable instances will most likely occur. The yellow line connecting C and D represents the field of interactions between these two points. This is where new N-children emerge from the negotiation between Definition and Contribution. When an N-child becomes stable enough, it can mature into a full N-source capable of generating its own patterns.

We can now describe the three fundamental points of a tholonic trigram more clearly:

By these descriptions, we can describe a general process that defines creation as something like:

At the most abstract levels, this describes the Big Bang, biological reproduction, the laws of physics, philosophy, and anything else that exists within a duality.

“Quantum Gravity Research”. Quantum Gravity Research, https://www.quantumgravityresearch.org.↩︎
“Emergence Theory Overview.” Quantum Gravity Research. Accessed August 07, 2020. https://quantumgravityresearch.org/lay-person-overview.↩︎
The E8 Lie group was discovered and classified by German mathematician Wilhelm Killing between 1888-1890, and further developed by French mathematician Élie Cartan in 1894. At that time, E8 was purely an abstract mathematical structure, one of the five exceptional simple Lie groups. It had no known physical application and existed only as a fascinating symmetry pattern in higher-dimensional algebra. The breakthrough came over a century later when physicists began exploring whether E8 could describe fundamental physics. In 2007, physicist Garrett Lisi proposed his controversial “Exceptionally Simple Theory of Everything” using E8 to unify all fundamental forces and particles. Around the same time, Quantum Gravity Research developed Emergence Theory, which proposes that physical reality emerges from an E8 lattice structure, with spacetime itself being a 3D projection of this higher-dimensional crystal. Both theories use the same E8 mathematical structure discovered in the 1890s, but they apply it in radically different ways than its discoverers ever imagined. The name “E8” remains because it refers to the specific 248-dimensional symmetry group, regardless of whether it describes abstract algebra or the fabric of reality itself.↩︎
Smith, F. D. (n.d.). E8 Root Vectors from 8D to 3D - Valdosta, Georgia. http://www.valdostamuseum.com/hamsmith/E8to4Dand3D.pdf ↩︎
Jgmoxness. (n.d.). Visualizing a Theory of Everything! http://theoryofeverything.org/theToE/tags/e8 ↩︎
What is Reality? Emergence Theory Tries to Explain. (2017, March 11). http://www.deepstuff.org/what-is-reality-emergence-theory-tries-to-explain ↩︎
Amazing description of how the E8 crystal can be defined as tetrahedrals. https://quantumgravityresearch.org/portfolio/a-deep-link-between-3d-and-8d ↩︎
“T’ai-I Chin-hua Tsung-chih (Teaching of the Golden Flower of the Supreme One)”. Translated by Richard Wilhelm; Translated from German by Cary F. Baynes; Published by Kegan Paul, Trench and Trubner (1931); Routledge and Kegan Paul Ltd (1965); ISBN 0 7100 2095 (c); ISBN 0 7100 7485 9 (p). https://www.lifeforcebooks.com/wp-content/uploads/2018/10/SecretGoldenFlower.pdf↩︎
Gottfried Wilhelm Leibniz. (n.d.). http://www.wikiwand.com/en/Gottfried_Wilhelm_Leibniz, Leibniz and the I-Ching. (n.d.). http://www.wikiwand.com/en/Binary_number#/Leibniz_and_the_I_Ching ↩︎
Gottfried Leibniz. (n.d.). Retrieved from http://history-computer.com/Dreamers/Leibniz.html ↩︎
Abrantes, R. (2018, November 19). How Wolves Change Rivers | Ethology Institute | Read and Watch Now. Retrieved from https://ethology.eu/how-wolves-change-rivers ↩︎
Grzegorz Rozenberg and Arto Salomaa. The mathematical theory of L systems (Academic Press, New York, 1980). ISBN 0-12-597140-0↩︎
In that it applies the syntactic features of natural languages. This is mentioned in the book: Prusinkiewicz, Przemyslaw, et al. The Algorithmic Beauty of Plants. Springer, 1996. This book is also available online. The relevant chapter is http://algorithmicbotany.org/papers/abop/abop-ch1.pdf. This site in general is an excellent resource for algorithms of nature.↩︎
Kidd, C., & Hayden, B. Y. (2015). The Psychology and Neuroscience of Curiosity. Neuron, 88(3), 449–460. https://doi.org/10.1016/j.neuron.2015.09.010, https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4635443/pdf/nihms722442.pdf↩︎
Quijada, John. A Grammar of the Ithkuil Language. John Quijada, 2011.↩︎
Speaks, Jeff. “Theories of Meaning”. Stanford Encyclopedia of Philosophy, Stanford University, 27 June 2019,https://plato.stanford.edu/entries/meaning ↩︎
Example of a “person” as defined by the semantic web: http://xmlns.com/foaf/spec/#term_Person ↩︎
McCrae, J. P. (n.d.). The Linked Open Data Cloud. https://www.lod-cloud.net ↩︎
Wang, Y., & Kosinski, M. (in press). “Deep neural networks are more accurate than humans at detecting sexual orientation from facial images”. Journal of Personality and Social Psychology; Newspaper article on this research: Levin, Sam. “New AI Can Work out Whether You’re Gay or Straight from a Photograph”. The Guardian, Guardian News and Media, 7 Sept. 2017, http://www.theguardian.com/technology/2017/sep/07/new-artificial-intelligence-can-tell-whether-youre-gay-or-straight-from-a-photograph ↩︎
Exodus 3:14 “And God said to Moses, ‘Ehyeh-Asher-Ehyeh,’ (‘Ehyeh-Asher-Ehyeh’ Meaning of Heb. uncertain; variously translated: ”I Am That I Am”; ”I Am Who I Am”; ”I Will Be What I Will Be”; and more.) ‘Thus shall you say to the Israelites, ’Ehyeh (“Ehyeh” meaning “I Am” or “I Will Be.”) sent me to you.’”, ↩︎
“Reciprocal Theory” RationalWiki, https://rationalwiki.org/wiki/Reciprocal_Theory.↩︎
Adam Smith, “An Inquiry into the Nature and Causes of the Wealth of Nations”, 1776, London↩︎

Part II

7: STRUCTURE

Knowledge and information, like form, have structures that follow the same rules as form.

Keywords: tetrahedron, E8 crystal, N-source, tholonic trigram, dimensions, holarchy, Emergence Theory