3: ORDER

On every scale of existence, order arises out of chaos and then returns to chaos. Each cycle of existence can take millennia or nanoseconds.

Synopsis: Numbers emerge as energetic concepts following the harmonic series, representing the distribution and balancing of energy. Order describes both the arrangement of things and the predictability of that arrangement, making it a function of perception and understanding. Chaos represents a spectrum from 0 to ∞, with order emerging from the interaction between these extremes at the balance point of maximum interaction. Sustainability results from the balance between internal and external forces. Laws operate within specific scopes (local and universal), with local laws affecting everything built upon them. Universal patterns (Fibonacci sequence, fractals, power laws, Benford’s law) appear across all scales of existence. Movement creates both order and chaos. David Bohm’s implicate/explicate theory illuminates how forms unfold into existence and enfold back into chaos, with the concept of dependent arising showing how instantiation depends on context and scope.

Keywords: energy, numbers, order, chaos, patterns, scope, laws, sustainability, perception

Everything that exists must follow the laws of existence. The penalty for not following those laws is non-existence. This is why we call them the Laws of Physics rather than the Highly Recommended Suggestions of Physics. These laws of physics can change between one state or scope of matter and another. Before we examine some of these laws, we must first understand the scopes within which these laws function and the concepts we use to understand them.

The Definition of Numbers

Numbers form the language of these laws, so we begin there. One way to think about numbers in general is to imagine value as a conceptual form of energy, and a particular value, like 1 or 2, as an instance of that concept. This should not be difficult, as this description finds agreement even between Platonists (“numbers are non-physical, non-sensible things that exist in an objective realm beyond time and space”) and Nominalists (“numbers don’t exist outside of abstract man-made concepts”). While this is not a new idea, it derives more from psychology and philosophy than mathematics¹. As concepts are energetic, they follow the laws of energy and exhibit stable and unstable patterns. The concept of numbers is one such stable pattern that emerged from the stable patterns we observe in nature and includes numerous sub-concepts, such as real, rational, whole, natural, irrational, and more, each with their own set of laws and definitions. From the tholonic perspective, whether the Platonist’s or Nominalist’s theories are correct does not matter. All that matters is that the concept of number exists and that these concepts represent instances of energy, because everything that exists, from things to ideas, are instances of energy.

We start with 0, nothingness, which, as explained earlier, also creates the concept of somethingness. We can represent all instances of somethingness with the non-numerical symbol ∞ or as the unity of the system that contains all somethingness, namely 1. This unity can be the unity of a bag filled with 12 oranges or the unity of the Universe. This is the first polarity, 0 and 1, nothingness and unity of all somethingness.

Energy always moves in one direction, the path of least resistance, the most efficient path, resulting in a more balanced state. Zero and 1 represent the most imbalanced state that can exist. How will this become more balanced? The next numerical concept after 1 is 2, which represents the first and simplest division of unity into parts. To create balance between absolute nothingness (0) and absolute unity (1), we need an intermediate state. This intermediate state is 1÷2, or ½, which from the perspective of parts counting wholes, we recognize as 2 parts. The concept of 2 also emerges from the duality of 0 and 1 itself; if there is 0 and there is 1, then there are two concepts.

With just the numbers 0 and 1, we can create 3 unique pairs with the values in proper order (0 precedes 1) and we can calculate their sums as :

(0+0)=0
(0+1)=1
(1+1)=2

We now have the value of 2 and the concept of 3, which makes 3 the next (and only) value that can be used to create further divisions

Now we have $\frac{1}{2}$ and $\frac{1}{3}$. Again, with [0,1,2,3] we have 10 combinations that produce 7 unique values [0,1,2,3,4,5,6], of which the smallest new value is 4, giving us $\frac{1}{4}$.

(0+0)=0, (0+1)=1, (0+2)=2, (0+3)=3
(1+1)=2, (1+2)=3, (1+3)=4
(2+2)=4, (2+3)=5
(3+3)=6

This pattern continues infinitely, and what we end up with is a series of values called the harmonic series, $0,1,\frac{1}{2},\frac{1}{3},\frac{1}{4},\frac{1}{5},\frac{1}{6},\frac{1}{7},\frac{1}{8}...$ (right image, left side).

The harmonic series is a fundamental pattern in nature and music. This is undoubtedly the idea behind the Pythagorean concept that “Physical matter is music solidified,” or the Sanskrit Nada Brahma, “Existence is sound” (literally “god sound”), or the legends of Native Americans, Judeo-Christians, Hindu cosmology, Egyptian, Aboriginals, Mayans, Norse, and many other cultures that tell of sound shattering the void of nothingness. Conceiving the progression of numbers as the harmonic series $\frac{1}{1},\frac{1}{2},\frac{1}{3},\frac{1}{4}$, rather than the typical progression of 1,2,3,4 (which could also accurately be written as $\frac{1}{1},\frac{2}{1},\frac{3}{1},\frac{4}{1}$), remains consistent with concepts of how energy is distributed and conserved and shows numbers as an internal expansion of energy that begins with the initial all-encompassing concept of unity. In our numbers-as-energy thought experiment, the number 1 represents the largest value and contains within it all numbers. If there is a finite amount of energy in the Universe, then the entirety of that energy can be represented as 1 quantity, or 1 unit, of energy. This would then imply that the division of that 1 unit of energy accounts for creation. That division, or at least one fundamental pattern of that division, follows the natural harmonic patterns of energy as shown in the harmonic series, the music of the Universe, literally and figuratively. We find the harmonic series from $\frac{1}{1}$ to $\frac{1}{\infty}$ in the energy patterns of nature and the Universe because numbers do represent energy.

Key 10: Numbers represent energy and the number sequence represents the balancing of energy and the creation of all things.

We do not count in fractions. We count in whole numbers. The difference between whole numbers and fractions lies in how we compare unity with the parts of unity, $\frac{whole}{part}$ versus $\frac{part}{whole}$. If we want to know how much of the whole a part accounts for, we divide the whole by the part. If we want to know how much of the part the whole accounts for, we divide the part by the whole. As we humans, and all things, are parts of the whole of the Universe, we can only consider the parts, as we have no concept of the whole other than it is a whole, a unity, 1 existence, that all things have in common. Thus $\frac{2}{1},\frac{3}{1},\frac{4}{1}$ becomes 2,3,4.

Key 11: From a Universal perspective, numbers only get smaller. From an individual perspective, numbers only get larger.

The Definition of Order

Order describes both how things are arranged and the degree to which that arrangement is predictable. Predictability depends on the observer’s level of understanding. Those things can be objects, patterns, sequences, ideas, methods, or anything that can be defined. We typically think of order as some type of structured, organized pattern, but these represent only certain types of order. Many types exist, including random, chaotic, and linear patterns.

If we consider chaos to be a spectrum from 0 to ∞, where does order exist? Order emerges from the interaction between these two extremes. At 0, nothing exists to interact, making order impossible. At ∞, everything exists in undifferentiated totality, also making order impossible. Order becomes possible only in the middle regions of the spectrum where the forces of nothingness and somethingness interact productively. Maximum order occurs at the point of maximum interaction, the balance point between the extremes.

This reveals how chaos/order represents an instance of the archetype of nothingness/somethingness. The two primal opposites (0 and ∞) define the spectrum, and their interaction creates the conditions for order to manifest. Energy drives this interaction. Where energy creates stable patterns of interaction, we perceive order. The more balanced and sustained the interaction, the more order emerges.

Key 12: Everything that exists has energy and therefore has some type of order.

Key 13: Order emerges from and is sustained by the organizational patterns of energy.

We use the term “order” quite liberally, even to describe things that have no apparent or even provable order, such as “chaotic order” or “random order”. If everything has order, the word risks becoming meaningless. Traditionally, “order” refers to a discernible pattern, while the more post-modern view of “order” refers to “the way things are,” synonymous with “arrangement,” ordered or not.

What do we really mean when we say something is ordered? The tholonic view of order, in practical terms, refers to how predictable something is, and this predictability results from our level of understanding. This makes order more a perception than a description. Guppies,² honeybees,³ hyenas,⁴ dogs,⁵ and numerous other animals demonstrate abilities to recognize order. A 10-month-old baby can recognize order among 3 items, and a crow’s ability to recognize the order of process equals that of a 7-year-old human. Yet none of them could solve a Rubik’s Cube because their understanding of order is limited. Order, then, also functions as a measure of understanding.

Key 14: Order is a measure of understanding and exists to the degree that it is perceivable, definable, and predictable.

Chaos precedes order and reclaims it, just as our lack of perception and understanding both precedes and eventually reclaims our perception and understanding. This remains difficult to dispute.

Key 15: Chaos precedes order and reclaims it.

This is not to say that chaos and order are defined solely by the limits of our perception, but rather that our definitions of them are. Nor does this claim that no such thing as chaos exists, only order yet to be perceived. We do claim that, as chaos precedes order, chaos represents the baseline of reality and creation. Chaos is the most energy-efficient, most sustainable state. Order must be one state or condition of chaos, as order is less sustainable than chaos. Order is, with respect to chaos, a temporary state.

What does “sustainable” mean?

Before we continue, we should clarify what sustainable means, as this concept appears throughout this work. Unfortunately, many different definitions exist for the word, especially with the growth of ecological awareness, which has come to dominate the term. Intuitively, the meaning of sustainability seems clear and obvious, but what does that mean technically? The simplest definition that applies to all contexts is “the state of a thing or process that coheres, disintegrates, or proves destructive to its environment or context”. This clearly applies to environmental concerns, but how does it apply to atoms, planets, and concepts? On a purely material level, sustainability depends on the fields of force that attract and repel. Things, from atoms to planets, are held together by their internal force fields, while any interaction they have results from the relationship created when these internal forces interact with external forces.

Key 16: Sustainability results from a balance between internal and external fields of force.

When we discuss systems within systems, which is how our reality is structured, we are also discussing the chaos and order within each of these systems. Every system has a scope, which can be its limits, range, reach, field, horizon, capacity, structure, or other terms used to indicate where that system begins and ends in various contexts. The scope of a container includes what it can contain, how much it can contain, how long it can contain it, and so on. The scope of water is anywhere water exists in any of its forms. The scope of the Sun is wherever the Sun’s energy reaches, how long it will last, and similar boundaries. In the world of quantum physics, everything we can know about a system is described by its wave function. This is called the wave-function postulate, and the wave function (symbolized as psi, ψ) of any system has limits. Those limits define the scope of a system.

The scope of a system is also defined by the order of a system, or rather, by where that order breaks down within the system. Newton’s laws of Motion work fine until things become too big, small, hot, cold, or fast. At those extremes, these laws begin to falter because the order of reality begins to change in those zones that lie at the outskirts of the order of reality we inhabit.

For example, imagine you are 1 mile tall. You can see perfectly ordered patches and circles of corn crops. As you shrink, that order becomes less visible, but you begin to see the order of rows of corn stalks. As you continue to shrink, you lose sight of the corn crops but begin to see the order of the plant, then the cells, then the molecules, then the atom, then the quarks, then the preons, then nothing, presumably, as preons are the 0-dimensional conceptual points that create quarks. The same applies to what you would see if you grew larger and larger, passing through the solar system, the galaxy, the multiverse, and finally… ?

Another example might be how we destroy the order of a tree to create the order of lumber. All that was part of the order of the tree comes to an end, and the order created by the lumber, such as a chair, comes into being. These are two scopes of order that do not overlap, but they are both children of an order that remains in both tree and lumber, such as the structure of wood (cellulose, hemicelluloses, and lignin). This tells us that the order of lumber and trees are subsets of, or dependent upon, or within, the structure of wood. When that wood burns, its order and the order of anything within its order, such as a desk or tree, disappears via pyrolysis, or thermal degradation, and the hydrocarbons are broken down to carbon dioxide, water vapor, and carbon (ash), each of which abides by the order within the scope it now inhabits.

You can easily imagine the never-ending series of chaos → order → chaos → order → chaos → order …

For this reason we also claim:

Key 17: Order precedes chaos.

True random events may be the exception, as a truly random event follows no rule, pattern, or reason. By this definition, nothing in nature (again, in the macro Newtonian scope of our daily reality) is likely truly random, but it remains safe to say that apparent random events exist that do follow currently unknown rules, patterns, and reason. This makes it impossible to prove anything is random, even if we ignore Gödel’s incompleteness theorem, which proves that proving any absolute truth is impossible. We can only establish truths based on unprovable assumptions. For this reason, we avoid the concept of randomness for the most part in this book, but we can say that:

Key 18: Randomness can create chaos, but chaos cannot create randomness.

The Scope of Order

Some laws are universal, and some are local. However, what we call universal may well be local within a much larger context that lies beyond our perception.

An example of a local law might be the Standard Model of particle physics, which describes the relationship between three of the four fundamental forces and the elementary particles that make up the matter in our universe. This represents a set of laws and constants that apply to particle physics. We do not see this model replicated in larger systems because the model only makes sense when dealing with the reality of sub-atomic particles. Likewise, Oort constants only apply to the rotational properties of the Milky Way.

Science calls the scope of our everyday Newtonian reality Macrorealism⁶ or Local Realism, and the subatomic scope is called Quantum Mechanics. Understanding how different laws operate in different scopes represents an area of intense research and has led to landmark experiments such as:

• Bell’s inequalities: The mathematics that enables the distinction between two different views of reality, typically the relativistic view versus the quantum view.

• Einstein-Podolsky-Rosen paradox: The speculation that every particle in the Universe knows the state of every other particle in the Universe at all times and that no two particles in the Universe have the same state.

• Leggett-Garg inequality: The claim that in the quantum world something can exist in two states simultaneously, which is impossible for the macroscopic world.

These represent only a few examples.

Key 19: Local laws and constants are valid only within the context of their scope.

An example of universal laws or patterns that span many scopes might be the Fibonacci sequence (0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377…) and its constant ratio of Phi (φ), also called the Golden Ratio (1:1.618). This ratio appears not only in galaxies and sea shells but, according to some evolutionary and chemical scientists,⁷ represents the ratio that keeps all of existence in order and defines the shape of space-time itself.

Another universal law might be simple fractal math formulas that have a form like f(x)= x²-1, which can be found across all forms of existence,⁸ suggesting that self-similarity is a universal property. Power laws explain how a relative change in one measurement can result in a proportional relative change in another (such as logarithmic or exponential relationships), and we observe these across all levels of existence.

An example of proportional relative change can be demonstrated with a line, which we will call L, that is 1 inch long. Doubling its length gives us a line that is 2 inches long, or L × 2, or L × 2¹. When the line defines a square, doubling its length creates an area that is L × 4, or L × 2². In a cube, the volume becomes L × 8, or L × 2³. If the line defined something that was 4-dimensional, like a hyper-cube, then the “volume” of that hyper-cube would be L × 16, or L × 2⁴. By doubling the defining element of a line, we see exponential growth in the size of whatever the line is describing. This is “how a relative change in one measurement can result in a proportional relative change in another measurement.”

These universal laws can be found in astronomy, physics, biology, meteorology, cosmology, mathematics, economics, and many other areas, including society, wealth and work distribution, competition, media exposure, and much more.

Another universal law is Benford’s law, which describes the pattern of first digits in naturally occurring numbers, such as lengths of rivers, populations, and numbers printed on the first page of a newspaper. This might sound odd, as simple logic would suggest that the chances of, say, the number 1 being the first digit in a series of numbers would be 1 in 9, but that is not the case. About 150 years ago, it was discovered that the number 1 is the first digit 30% of the time, while the number 9 appears as the first digit only about 5% of the time. In the two images below, we can see this law in action when we plot the populations of every county in the U.S. and then count the first digit of each of those populations.

This occurs because, while we may count in a linear fashion (1,2,3,4… etc.), nature distributes itself in a logarithmic fashion. For example, consider three naturally occurring scales: 0 to 10, 10 to 100, and 100 to 1000. With each new scale, we simply add a 0. There are 10 numbers in the first scale, 90 in the second scale, and 900 in the third scale, but as far as nature is concerned, each scale has an infinite number of divisions, so they are effectively the same from nature’s perspective. This is how we discovered (or why we invented) logarithms: to replicate the natural way numbers work (and why we call them natural logarithms). The image below shows these two scales.

Logarithms allow us to multiply simply by adding. For example, the log of 10 equals 1, and the log of 100 equals 2, so instead of multiplying 10×100 to get 1000, we can just add 1+2. This gives us 3, and because we are using the normal base 10 system, we convert these log values back to normal values with 10³, which equals 1000.

Once upon a time, before the invention of digital calculators, and after its invention in 1859 by a French artillery officer, every engineer had a slide rule, which allowed them to perform this multiplication-by-adding (and more) simply by sliding rulers back and forth.

How does this apply to 30% of all our numbers beginning with a 1? The occurrence of any number as the first digit equals the log of the next number minus the log of the number. The chances that the value of 1 will be the first value in a random list of numbers is log(2)-log(1)=0.30, or 30%. For the value of 9, the chances are log(10)-log(9)=0.045, or 4.5%.

The point here is not to delve into the mathematics but to show that nature’s concept of scale, or scope, is invariant, meaning nature treats all the scopes or scales the same. We would therefore expect to find laws in one scale equally applied to all scales.

Appearance of Order

A good visual example of how these laws (in this case, oscillation and entropy, which is discussed at length in the next chapter) affect our perception and understanding of chaos and order exists in the distribution of the energy that fills every corner of the Universe. This is known as cosmic microwave background radiation (CMBR). The left image (of the right chart) shows the CMBR filling the known Universe with ~2.64 K of heat (-269.51°C, about 4°C above absolute zero). The energy is widely dispersed, has no pattern, and provides a perfect example of chaos. It may actually be perfect chaos, which is why some scientists are proposing to use CMBR as a natural source of random numbers⁹ (as true random numbers are extremely difficult to generate). However, to see this natural chaos, a major correction had to be applied to adjust for red-shifted and blue-shifted effects due to our galaxy hurtling through the Universe at approximately 1,497,600 miles per hour. This velocity makes anything we are heading toward appear more blue, and everything we are heading away from appear more red (due to the compression and expansion of the wavelengths of light). The way we actually see this omnipresent chaos is shown in the right image. The only factor that accounts for the difference between the appearance of chaos and order is the movement of our galaxy. It is through this movement that chaos appears as order.

Can we say that if something appears to have order then it has order? In this case, the chaos remains chaos, and the apparent order results from the laws of interaction of energy. We can say that about anything, as where there is no movement, there is no energy, and where there is no energy, there is the chaos of nothingness.

Key 20: Movement creates order.

The CMBR is considered the smoking-gun evidence of the Big Bang,¹⁰ which is the scientific explanation of when the chaos of somethingness met the chaos of nothingness.

Key 21: Movement creates chaos.

Order of Laws

Even though there are many classes of laws, for this writing, we are only going to use these two general scopes of laws, the local and the universal, because no matter what laws may exist, they will fall into one of these two scopes (or children of these scopes).

Local laws may be local, but they can affect everything that is built upon them. Everything is made of atoms, and atoms are the size they are because of Planck’s constant, which describes the relationship between the mass and the frequency of the particles that make up an atom. If that constant were to change, the entire Universe would be radically different, if it even existed at all. If Planck’s constant were to increase by only 2.5%, the size of Earth, its spin, gravity, and the density of the atmosphere would all increase. If it were 2.5% less, Earth would shrink by 20%, its rotation would increase, gravity would lessen, and much of the atmosphere would disappear. If Planck’s constant changed from 6.2618×10^-34 to 6.2618×10^-20, the radius of an atom would go from being microscopically small to being 100 times the distance to the nearest star.

On a more realistic level, consider a bridge made of bricks. If the laws that bind molecules together change such that they have a lesser negative charge, then the bridge would melt on a warm day. The (relatively) universal Newtonian laws did not change. Only the local laws changed on the particle level.

The laws of particle physics logically affect everything that exists because everything is made of particles, but that does not make the laws of particle physics universal in scope. Rather, that which is made of particles is dependent on the laws that operate in the local particle scope, thereby making the effects of local laws farther reaching than their domain.

Key 22: Local laws can alter everything that descends from or depends on them.

The State of Order

These laws create order out of chaos and chaos out of order. That order exists between the two states of zero-energy chaos and total-energy chaos, but even within the chaos, we can find clues of order as neither a zero nor a total state of chaos is possible in the material domain, only closest-to-zero and closest-to-total states.

One theory that sheds light on new thinking about chaos and order is David Bohm’s Implicate Explicate theory. In short, Bohm describes this theory by stating the following:

In the enfolded (or implicate) order, space and time are no longer the dominant factors determining the relationships of dependence or independence of different elements. Rather, an entirely different sort of basic connection of elements is possible, from which our ordinary notions of space and time, along with those of separately existent material particles, are abstracted as forms derived from the deeper order. These ordinary notions, in fact, appear in what is called the “explicate” or “unfolded” order, which is a special and distinguished form contained within the general totality of all the implicate orders. ~Bohm, “Wholeness and the Implicate Order”

To demonstrate this concept, we can use an ink droplet analogy. In this demonstration, we place three drops of ink into a cylinder of glycerin. The cylinders are then turned, which mixes the ink droplets together. Reversing the spin of the cylinders then reconstructs the ink drops. When the ink droplets are in their original form, at the beginning and the end of the spinning, they are explicitly ink droplets and have the order of ink drops. When they are mixed up together, they are implicitly ink droplets only, and their order would be considered more chaotic. The order of the ink drops has been destroyed, but the information of that order exists as a virtual ink-drop, an archetype only, within the chaos of their mixed state.¹¹

In practical terms, this theory says that when something exists in the physical world, it is in an explicit, or unfolded state. To exist in this state, it must conform to a set of rules that define the archetype(s) of the form it will take. When it does not conform to these rules, it still exists, but only in an implicit or enfolded state, a state we cannot see or interact with (under normal circumstances). This sounds similar to the “sea” of potential or unmanifest wave functions that collapse into form. This state has its own rules as well, but they are a super-set of the explicit rules, making a thing, or physical reality as we know it, just one sub-state of a thing, or reality, it can be in.

These local and universal laws cause form to unfold, to explicate itself, self-organize, form patterns, and move in accordance with these laws. By the same token, these laws will also enfold or implicate these forms, causing them to return to an unrecognizable state, but even in that unrecognizable state, they are contributing to or affecting other yet-to-coalesce implicate patterns. Depending on the form and the medium, and under certain conditions, one can imagine how the past (that which is enfolding) and the future (that which is unfolding) can affect each other in both directions.

A second example better illustrates the idea. Below are four pages that started out as identical. To each page were added some random dots, but within a narrow region of a circular line. However, none of those dots stood out from the page’s original random dots and were in no way identifiable as special dots. As we merge the pages, the randomness gets denser and denser until all four pages are perfectly aligned, and those extra random dots can easily be seen as a circular line.

The circle is implicit in the random dots of each separate page and explicit when the pages line up together in the proper manner. In this example, the local pattern would be the random pattern on each page, which represents the scope, and the universal pattern would be the parts of the circle as it exists on every page.

All of this addresses the relationship between instantiation and context. How something comes into existence and how it is expressed depends in the context and scope of where it is being expressed. This concept is not only technical or scientific but also philosophical. We can see it in Buddhism as the principle of Pratītyasamutpāda, which means dependent arising, and which states that all phenomena (dharma) arise in dependence upon other phenomena (dharmas). More than that, it also implies that the significance of something is defined by its environment. An obvious example of this is how the same wooden ball falls in the air, is motionless on the ground, and rises in the water.