Nature Creates Increasingly Complex Systems

Above — The highly complex Large Hadron Collider (LHC) lies underground across the Franco-Swiss border.
This LHC discovered theHiggs Particlein 2012. 


Nature Creates Increasingly Complex Systems 

The most fundamental process of Nature’s Continuing Creation is this:
      > When a steady flow of energy encounters a receptive environment, it can weave patterns and systems of increasing Complexity.
           > Example: When sunlight strikes the geology and chemistry of Earth, it evolves and sustains the complex patterns & systems of living things.

Complex Systems are the full flowering of Natural Continuing Creation here on Earth. Complex systems include crystalizing minerals, simmering water, tornadoes, a one-celled bacterium, bird flocks in flight, human bodies, the brain, bicycles with riders, money, governments, ecologies, religions, bodies of law, steel mills, computers, music, the Way of Nature’s Continuing Creation itself, and the entire universe that Nature continues to create.

           Remember — We define “Nature” and “Natural” to include humans and the inventions of humans!  

Why are Complex Systems vitally important to the Way of Nature’s Continuing Creation? One reason is because they show how NCC itself functions and evolves. Nature’s Continuing Creation: The Growing, Organizing, Direction of the Cosmos is itself a gigantic “System of All Complex Systems.”  It both describes and is described by all the principles and processes we will talk about in this key Essay.

This Essay is where we peer into the mechanics of the one and only miracle of the universe, which is Nature’s Continuing Creation. Understanding these natural processes dispels the need for us humans to weave fictional explanations involving magic and supernatural beings.

We’ll start by describing a few examples of complex systems – a living thing (or things) called the slime mold, mineral crystal formation, simmering water, tornadoes, ant colonies, and free-market economies. For each one, we will mention a number of its important system properties and processes. Then we’ll talk more about why such systems are important for the Flow of Continuing Natural Creation. We will go on to present additional examples of complex systems and discuss important general aspects of complexity in greater detail.

Bathtub Whirlpools & Hydro-electric Dams

The Third Law of Thermodynamics says that energy seeks to move from areas of high heat to low heat until a calm equilibrium of everything is attained.  Water at a high level will flow to a lower level whenever it can.  The force of gravity causes the water to move downward.  But often this movement builds a complex structure as it moves! For example, when we pull the plug on a bathtub full of water, it will form a spiraling whirlpool as the water leaves the tub.  Why?  Because the spiral structure of the whirlpool moves more water faster.  Similarly, on land, flowing water creates the structures of streams and rivers.  If a wooden waterwheel is built on one of these flows, it can power the grinding of grain between two millstones.  With a very large drop of a great deal of water, the energy released by the force of gravity can turn gigantic steel turbine blades, and that energy can be converted to electricity for human homes and industries.

In his excellent book, The Romance of Reality: How the Universe Organizes Itself to Create Life, Consciousness, and Cosmic Complexity, the neuroscientist Dr. Bobby Azarian tells us that energy flows also create chains of molecules, chemical structures, which are then further propelled to become the earliest forms of life.

He persuasively argues that in the right environments, Energy Flows always drive systems into forms of greater complexity.  This is what Dr. Azarian calls the “Fourth Law of Thermodynamics.”

Azarian argues that this is happening in the millions of Earth-like planets and moons in our Milky Way galaxy. Of those, Azarian argues that a good number will evolve consciousness and intelligence.  While we humans may so mis-manage our energy flows and resources that we kill off our biosphere here on Earth, hundreds of thousands of suitable planets and moons in the Milky Way alone may be more successful.  As all these planets and moons communicate with each other, the Universe itself is on track to “wake-up.”

The Beautiful, Orange-colored Slime Mold

The acclaimed science writer Steven Johnson begins his fascinating book, Emergence: The Connected Lives of Ants, Brains, Cities, and Software, with a portrait of a beautiful creature which is unfortunately called the slime mold. Typically growing on rotting bark and leaves in a forest, a common variety of slime mold looks like a patch of rust-orange lichen. It is actually a simple organism without intelligence or a central nervous system, closely related to the organisms collectively classified as fungus. 1

The Orange-colored Slime Mold

When food supply, temperature and humidity are favorable, the slime mold lives as separated, individual cells.  But when conditions are strained, these cells coalesce to form a single, larger organism.  Time lapse photography shows that the organism then crawls very slowly along the forest floor in a unified search for food.  When its environment improves, the cells separate and become solitary foragers once again!

Scientists have even shown that a unified slime mold patch can locate a food source by extending out “arms” to explore (through trial and error) and find (by a process of elimination) the shortest route through a laboratory maze. 2

The orange-colored slime mold is an excellent example of a Complex System. It demonstrates the key principle that simple parts interacting together can achieve the goal-seeking behavior without any direction from the central control of a brain. The slime mold does not even have central “pacemaker” cells.  3 Their cooperative behavior simply emerges, as cells pick up and follow scent-trails of the pheromone acrasin secreted on the ground by other cells that have already found good food. (The same thing happens with colonies of ants, termites, and bees, but in those cases the individual creatures do each have primitive central nervous systems.)

The formation of the larger slime mold is a prime example of emergence, and self-organization in complex systemsIt is a “bottom-up” (i.e., not centrally directed) creation of a new and different whole out of the interaction of simpler, identical parts. The self-organization process of the slime mold involves communication (via pheromone trails), just as exploring worker ants communicate as they mark out the way to a good food source for the columns of ants who follow after them.

Note:  A wonderful, recent short film called “The Insane Biology of: Slime Mold,” produced by Real Science, is now on YouTube. It presents a host on newly discovered capabilities of the Slime Mold.


What is Complexity ScienceIt is everything in all the circles below:

Complexity Science is the scientific study of complex systems, systems with many parts that interact to produce global behavior that cannot easily be explained in terms of interactions between the individual constituent elements.

Complexity Science also studies how complex systems interact with their environments. In doing so, the systems become elements in a larger complex system.  For example, a bullfrog is a complex system, and it is also part of the pond-ecology complex system where it lives.

            Note: For an excellent introduction to Complexity, see Rajesh R. Parwani’s book, Simplicity in Complexity: An Introduction to Complex Systems, Simplicity Research Institute, 2015. 

In the last half-century, Complexity Science has revealed many characteristics and features of complex systems, including hierarchy, feedback loops, triggers, cascades, self-organization, emergence, homeostasis, adaptation, and many others. We will describe these and many of the others in our Essay, taking link, bold, or italicize the name of each characteristic as we discuss it.

The Evolution of all living things, which we reserve for two Essays of their own, is a particular kind of Complex System. See our Essay, The Processes of Evolution & Their Meaning.

A Brief History of Complexity Science

The study of Complexity goes back quite far, but it hit a “eureka” moment in 1776 when Scottish economist Adam Smith described in his classic book, The Wealth of Nations, how a free-market economy’s “invisible hand” works to efficiently distribute goods and services without central government planning. A few pages farther on we will take a closer look at free markets as an example of complex systems.

Note: Today, 240 years after Adam Smith, the study of complex systems remains as much about political, social, economic, and cultural systems as it is about physical and biological systems.

Note: The year 1984 saw the founding of the first research institute focused on complex systems, The Santa Fe Institute. The Institute hosts visiting scholars and scientists who collaborate “to understand and unify the underlying, shared patterns in complex physical, biological, social, cultural, technological, and even possible astro-biological worlds.” Santa Fe Institute participants have included physics Nobel laureates Murray Gell-Mann and Philip Anderson, economics Nobel laureate Kenneth Arrow, and Manhattan Project scientists George Cowan and Herb Anderson. About thirty participants are in residence at any one time, with far more assembling for summer conferences.

In the last 30 years, complex systems have been modeled using mathematics, computer algorithms, statistical physics, information theory, and non-linear dynamics. We talk about how this happens in our Essay, Mathematics Evolves in Nature’s Continuing Creation.

Today, there are over 50 institutes and research centers focusing on the science of complex systems. Working in tandem, they have firmly established a set of principles that govern (with variations) all Complex Systems – cosmic, geologic, chemical, biological, cultural, and technological. “Complexity Labs” is an “online platform for the research, education, analysis, and design of complex systems. 4

Mineral Crystal Formation – Non-living Complex Systems

Although the slime mold and other living complex systems are colorful and amazing, it is important to begin with the complex systems of crystal formation and simmering water, because readers need to understand that the Principles of Complexity are very much present in millions of such nonliving systems.

Other Essays in this book, such as Mathematics Evolves in Continuing Creation, have discussed mineral crystalsAre crystals — of ice, quartz, diamond, etc. – themselves complex systems?  After all, their geometric shapes show large-scale order, and that order is interesting and beautiful. The answer is that crystals are only complex systems while they are being formed; that is, when energy and materials are being supplied by flow, heat, pressure and evaporation which work to add new molecules to the facets of the crystals. When the energy and materials stop flowing, the crystal becomes a static artifact of the dynamic complex system called crystallization.

“Crystal shapes are determined by the energy of the atoms (or molecules) in the material. Things always want to be in the lowest energy arrangement. Depending on the size, shape, and electronics of atoms or molecules, this leads to different patterns. Once a crystal pattern starts, it is almost always favorable for atoms (or molecules) to continue the pattern and grow into a crystal. Sometimes there are multiple patterns that give low energies, like in snowflakes, so there are multiple crystal shapes for a single material.”
— USCB Science Line, Materials Research Laboratory, University of Santa Barbara. 

Each prior layer of crystal acts as a scaffolding or template for the next layer. The templates provide a kind of “brainless memory” for non-living systems, because they permit the repetition of processes.

  • Scaffolding, or Templating is a common principle in the Processes of Complexity. A scaffolding depends on the position or arrangement of its parts. Position can also determine the very nature of a complex system. Arranged in layers, carbon atoms form graphite, which is soft and opaque.  Arranged in a crystal, carbon becomes a diamond – hard and transparent. Graphite and diamond are allotropes of carbon, i.e., they are both 100% carbon but with their atoms arranged in different patterns. Fullerenes and Carbon Nanotubes are also allotropes of carbon. (For more about graphite and diamonds, see Appendix A at the end of this Essay.)

— The importance of positioning is illustrated by the wild difference between Silver Fulminate (AgCNO) and Silver Cyanate (AgOCN) — two chemical compounds, made of the same elements, but arranged in different ways (and therefore called isomers). Silver fulminate is a primary explosive that has very little practical value due to its extreme sensitivity and instability. On the other hand, AgOCN is Silver Cyanate, which is used in the production of fertilizers. It does not explode and is completely stable.

The first protein molecule that ever replicated itself may have done so using the repetitive structure of crystallized clays, or the cellular structure of mineral froths, as a scaffold to support itself. 6

  • Crystal formation, like all complex systems, requires an in-flow of materials and a flow-through of energy. In the terminology of physics, every complex system must be an open system. The principle here is that complex systems are by definition dynamic, meaning that they change over time. They are processes: each one has a past, a present, and a (limited) future. Crystals emerge at the end-stage of the process: when heat energy is dissipated from a warm liquid, the material forms a cooler, solid crystal. 7
  • Crystals form when minerals dissolve in water, percolate through rock spaces, and precipitate out. Dissolving, percolating, and precipitating are all processes that take place within a number of complex geochemical systems.
  • Crystals grow over time because they will get larger if they have the room, the supply of dissolved materials, and a steady energy flow to drive the flow of the dissolved materials. Many other complex systems also grow, including hurricanes, bodies of law, technologies, plants and animals.
  • If some outside force or obstruction impinges on a growing crystal, it may change direction, lose some of its geometric regularity, or become stunted. All these limiting processes are also seen in living things, weather, and culture.
  • As we mentioned, when the energy and materials stop flowing to the worksite, the dynamic complex system of crystallization stops, leaving the crystal behind as its “static artifact.”

While the process of crystal formation is a complex system, it does not exhibit the fast and radical change, the metamorphosis, that other complex systems exhibit.  A classic example of metamorphosis is the transformation of many crawling insects into butterflies while they are in cocoons. (For more on the topic of crystals, see Appendix A at the end of this Essay.)

Seashells and other Animal “Artifacts”

Seashells are animal artifacts (namely, the exoskeletons) of the invertebrate sea-creatures (complex systems) that secreted them. Other examples of static artifacts left behind by dynamic complex systems include bird nests, the Greek Parthenon in Athens, and the Mona Lisa painting hanging in the Louvre. (The animal artifact known as the “Mona Lisapainting was created and left behind by the human animal known as “Leonardo Da Vinci.”)

Note:  When a human being looks at the Mona Lisa, a new and different complex system is created involving the reflected light, the painting, the viewer’s eyes and brain, and the prior education and experience of the viewer. 

Convection Cells in Simmering Water – An “Edge-of-Chaos” Complex System

In this Section, we’ll discuss convection cells — one of the common, but often un-noticed, edge-of-chaos systems.

A simple pot of water, brought to a simmer on a stove, presents a sudden structural change. When the water comes to a “simmer,” convection cells, also known as Benard cells, spontaneously emerge. Usually, we don’t see them, mostly because water is transparent.  However, we can see film-clips of this phenomenon online: click on Raleigh-Benard Convection.”

Benard Convection Cells

The convection cells are an edge-of-chaos system, which is a class of Complex Systems. Sitting on the edge of chaos, they can quickly change from calm, microscopic turbulence (i.e., still water), to patterned, organized, large-scale order, to violent turbulent chaos (the rolling boil), and then back to calm turbulence. Over and over, depending on the heat flow. 8

We are all aware of weather-related edge-of-chaos systems including whirlpools, tornadoes, and tropical cyclones (i.e., hurricanes). They all begin with the random, gentle turbulence of normal weather.  Relatively quickly (over a number of days), they gather strength form their characteristic structure – the funnel-shaped vortex. Paradoxically, while all these vortex structures can inflict chaos on trees, houses, and boats, the funnels themselves are not chaotic, they are organized. It is only when the vortexes decay and dissipate that the air or water resumes its calmly turbulent ebb and flow.

In 1984, Dr. Ilya Prigogine and Isabelle Stengers published their landmark book, Order Out of Chaos, in which they described a number of Complex Systems including our example of convection cells forming in simmering water and chemical clocks which by themselves change color and/or form self-same patterns at periodic intervals. (the Belousov-Zhabotinsky reaction).

Prigogine alternately called these systems “far from equilibrium systems,” “dissipative systems,” (both poor, confusing labels); or the now preferred “edge-of-chaos systems.” He won the 1977 Nobel Prize for Chemistry for his work on these systems. 9

Unfortunately, edge-of-chaos systems became known by the shorter label of chaotic systems. But these systems are only sometimes chaotic. This semantic subtlety created a confusion that persists today.  In our book, Nature’s Path of Continuing Creation, we will avoid confusion by always call these systems edge-of-chaos systems.

From our examples of convection cells and tornadoes, we can see a number of principles and processes common to all complex systems:

> Benard convection cells, tornadoes, and hurricanes are not alive. There are many complex systems in the universe that are not alive. While all living things are complex systems, not all complex systems are living things.

> The transition from one state of being to another is called by a number of different names in different areas of science and social science, including phase change, chain reaction, bifurcation, metamorphosis, political revolution, and paradigm shift.

> We note that every complex system, even a non-living one, has something akin to a “life.” It has a beginning; it has an existence during which it processes materials and energy to create and maintain structure, and it comes to an end.  In this sense, every complex system in the chemical and geological world is a model, a precursor, to living things. 

> Complex systems are all around us. At one end we have the non-living Convection Cells (see above), tornadoes, hurricanes, and whirlpools. At the other end, we have the complex systems called political revolutions. Political revolutions have happened repeatedly over the millennia, in countries all over the world.

> There is an energy flow moving through all complex systems. On Earth, all such energy ultimately comes from the sun. (When we burn coal or gasoline, we release energy originally created by and stored in green plants which have been compressed and heated under the Earth.) Systems that have such an open energy flow-through are called thermodynamically open systems.

> Earth’s undersea hydrothermal vents also flow-through heated, mineral rich seawater upward, supporting unique life forms around them without photosynthesis.  Many scientists believe that Earth’s first living organisms evolved there.

> The Benard Cells we mentioned earlier are amazing, but not magical. They are not so inexplicable that they require us to believe that a super-human “God” reaches down into every pot of water, worldwide, and causes the cells to form. Instead, the structures self-organize, according to the laws of physics.

— Similarly, ants and termites build their nests without any direction, not even from the queen. Studies show that when a sufficient number of termites are walking around, a critical mass is reached at which they begin nest-building activity. (However, each ant or termite does have a tiny bit of instinctual intelligence.)  In the case of Benard cells, there is no intelligence, no central direction whatsoever.

> Nature’s Continuing Creation says — If there is a super-human (e.g., godly) intelligence that intends the appearance of convection cells, it is acting only through its earlier creation of the laws of physics. Of course, we have no objective evidence that an external Godly intelligence exists. Because they self-organize, the Benard Cells, hurricanes, ant hills, and termite mounds, are all emergent phenomena.

> All Complex Systems must have boundaries. Energy flows in across that boundary, does work, and then flows out again. The Benard Cell system includes more than the water; it also has the boundary of the pot, and the heat under the pot. Benard Cells also appear in a shallow stone-bottomed thermal hot spring at Yellowstone Park, where no human has set them up.

— Each cell in the human body is also a complex system, and each one has a cell wall that separates it and protects it from outside threats. Similarly, each human being has a skin as its outer boundary, and which contains the person’s trillions of bodily cells.

> Even Systems that are at the Edge-of-Chaos,” i.e. about to lose their present organized structure, are still deterministic systems, meaning that if one knew the location of all the water molecules, all the exact dimensions of the pot, and all the exact degrees and flows of the heat, then one could, with a giant, yet to be engineered super-computer, model the exact pattern and pace of the Convection cell’s formation. But as a practical matter, predicting the exact shapes of the convection cells is (a) impossible, and (b) not worth knowing in such detail (because no one cares if one or two of the convection cells are not true hexagons, but only approximate hexagons).

> And if we are trying to predict the path of an even more complex system like an ecology through time, with billions of times more interacting parts than simmering water, prediction becomes inherently impossible. The only way to see the developmental outcome of an ecosystem is to let the system itself play out in the real world over real time.

> Benard Cells (a.k.a. Rayleigh-Benard Convection) and Storm Funnels (a.k.a. Funnel Clouds) are just two examples of non-living complex systems. In the world of modern physics, we find that Lasers, Spontaneous Magnetization, and Superconductivity are all examples of non-living, self-organizing, complex systems. In astronomy we find the formation of trillions more complex systems known as Galaxies, Stars, Planetary Systems, and Planets

Self-organization & Emergence

Every blade of grass, every bacterium, is a complex system. Yet, there is nothing living in any of the individual atoms that make up a human body. Life emerges, self-organizes, from the arrangement, the pattern of those atoms, and from the system’s throughput of energy.  In other words, living things are composed of non-living things; life emerges in assemblies of non-living elements. (See our Essay, Nature Creates Patterns of Information & Beauty.)


Self-organization occurs in a variety of physical, chemical, biological, robotic, social and cognitive systems. In addition to crystallization, and the formation of convection cells in a liquid heated from below, self-organization also happens in the rise of free market economies, and in the swarming/herding behaviors by groups of animals.

Our Practice of Continuing Natural Creation says: The evolution of complex order is inherent in our Universe. The evolution of complexity, in and of itself, is The Growing, Organizing, Direction of the Cosmos.

For our purposes in this book, the most important processes of Nature’s Continuing Creation are Open Energy Flow, Complexity, and Evolution.  Within Complexity, the most important sub-processes are Self-organization and Emergence.  We will discuss all four of these a great deal in this Essay. The terms are highly interrelated, and each of them contains a number of component sub-sub-processes.


Emergence is probably the most important phenomenon in Complex Systems.  It is as important to Complexity as Natural Selection is to Evolution.

Biology emerges on top of a foundation of chemistry, and chemistry emerges from a foundation of physics. Life, studied in biology, is an emergent property of interacting molecules as studied in chemistry, whose phenomena reflect interactions among elementary particles as modeled in particle physics. Consciousness and psychology are both Emergent from the biology of creatures’ brains.

Here is Wikipedia’s Definition of Self-organization:

Self-organization is:  “…a process where some form of overall order or coordination arises out of the local interactions between the components of an initially disordered system. This process is spontaneous: it is not necessarily directed or controlled by any agent or subsystem inside or outside of the system. It is often triggered by random fluctuations that are amplified by positive feedback. The resulting organization is wholly decentralized or distributed over all the components of the system. As such it is typically very robust and able to survive and self-repair substantial damage or perturbations.” 10

The Economist Jeffrey A. Goldstein defines Emergence as: “The arising of novel and coherent structures, patterns, and properties during the process of self-organization in complex systems.”
Dr. Goldstein writes that the five most Common Characteristics of Emergence are:

1. Radical novelty (we find features not previously observed in the systems),
2. Coherence or correlation (integrated wholes maintain themselves over some period of time),
3. A global or macro “level” (i.e., there is some property of “wholeness”),
4. The Emergence is the product of a dynamic process [i.e., propelled by moderated free energy, it evolves through time], and
5. The Emergence can be perceived or directly demonstrated. 11

Emergence happens when the simple, often identical components of a system create some new and more complex pattern simply through their interaction with each other. Whole Areas of Science Are Emergent, as is Life Itself.

The human body is made of tissues, which are made of cells, made of molecules, made of atoms, made of protons, neutrons and electrons.  Trees are also made of identical protons, neutrons and electrons.  But trees can grow leaves and humans can write poems — protons, neutrons, and electrons can do neither of those things.  The properties of humans and the properties of trees emerge from the way in which their components are organized — from the pattern in which their components are organized. 

Complex systems may exhibit both structures and behaviors that are emergent.  The behavior of an ecosystem is different than (but emergent from) the behaviors of the organisms living in it.

The structures of some systems are determined by their constituents (e.g., the liquidity of water, discussed in Appendix B to this Essay). But other systems will have properties that can only be studied at a higher level. For example, the termites in a mound have physiology, biochemistry and biological development that are at the one-termite level of analysis, but their social behavior and mound building is a property that emerges from the collection of termites and needs to be analyzed at a higher level. Thus, universities not only teach biology, but also psychology, sociology, economics, and political science.

Self-organization and Emergence May Be Inevitable in Open-Energy Systems

In his book, At Home in the Universe: The Search for the Laws of Self-organization and Complexity, Dr. Stuart Kauffman argues that the new laws of complexity show that the order is not accidental; it is spontaneous and inevitable. 12

In fact, Dr. Kaufman argues that the laws of complexity are more important than the laws of evolution, because complex systems often produce sudden revolutionary changes, while evolution comes along only later and selects from among the various complex systems already created. 13

For example, the laws of complexity are responsible for the sudden explosion of living forms in the Cambrian Geological Period, about 541 million years ago. TheCambrian Explosion” lasted about 25 million years, during which all of our modern animal phyla appeared, including Arthropods (e.g., spiders, insects, crabs), Mollusks (e.g., snails, mollusks, octopuses), Dinosaurs, Flowering Plants, Birds, and Mammals. Since then, natural selection and evolution have worked only to refine the forms. This is known as dual-phase evolution: In Phase One, the patterns of the new organisms form and grow. In Phase Two, those patterns are either refined… or removed. (For more examples, see our Essay, The Processes of Evolution & Their Meaning.) 14

Complex Systems Are Foundational for Nature‘s Continuing Creation

Having presented four examples of complex systems – slime molds, mineral crystals and convection cells in simmering water, and tornadoes (plus a bit about ants and termites) – let’s step aside and talk about why such systems are so very important to people who travel the Path of Nature’s Continuing Creation.

Complex Systems are vitally important to the Way of Nature’s Continuing Creation (NCC) because they are the natural, rational, and scientific inner-works by which NCC takes place. Continuing Natural Creation is itself a Complex System. It both describes and is described by all the principles and processes we will talk about in this Essay. Those principles are sufficient to establish The Growing, Organizing, Direction as we know it, and there is no reason to take a step “beyond” and imagine an external, eternal, and all-powerful personified super-being.

An understanding of Complex Systems also permits us to firmly conclude that individual people do not have “souls” bestowed upon us by a super-human “God.” What we each really have is a consciousness, a personal identity, and a unique personality that emerge from the processes of Nature’s Continuing Creation. Your personal identity comes to you from your heredity and your environment, and nowhere else.  As we discuss more fully in our Essay, Dealing with Death on Our Nature-based Path of Creatingthe “soul” is really just one’s mind, self-consciousness, and personal identity. These things reside in the brain.  When the brain dies, these things turn completely off, never to return – just as they do in the very late stages of Alzheimer’s disease, even though the person’s body may well live on for months or even years.

Those are some of the important reasons why this Essay aims to impart a greater understanding of complex systems.

The Growing, Organizing, Direction Creates Patterns

What do the Processes of Nature’s Continuing Creation create?  Fundamentally, NCC creates patterns, across both space and time. When two simple things are combined to create a new thing, the new thing has a pattern.  Hydrogen and oxygen atoms combine to form water molecules, and when they do so, they join in a definite and important pattern. (See our Essay, Patterns in Continuing Creation.)  Systems, including Complex Systems, are patterns in motion. They are dynamic patterns, under “command” of energy (e.g., heat, light, kinetic push, electric current, etc.) For example, flowers form in brightly colored patterns, in order to attract pollinating insects. Modern entrepreneurs often join together to create corporations, including a hierarchical pattern of ranks, from executives, to supervisors, to workers. Other common patterns found in complex social systems are branching, tribal, collegial, hub-and-spoke, network, and bureaucratic patterns, all of which are studied in anthropology and sociology.

Complex systems also frequently display self-similarity,” where patterns at lower (or earlier) levels of the system are repeated at higher (or later) levels. For example, tree trunks divide into main branches, and those branches divide into smaller branches, which then divide into twigs. Coastlines are jagged whether we look at 1000 miles or one yard. We will say more about self-similarity later in this Essay.

Knowing the “Mind of God”

The Old Religions tell us that humans can’t know the “mind of God,” or that “God works in mysterious ways” that have to be taken on faith.  As the Old Testament Book of Isaiah says,

“As the heavens are higher than the Earth,
 So are my ways higher than your ways
 And my thoughts than your thoughts.”
       — Isaiah, 55:9; New International Version

But today, we do know quite a bit about how the so-called “Mind of God” works. More exactly, we know a lot about how the Organizing Energy and Information flow of the Cosmos works (although we certainly do not know all, and we may never know all). Today, Nature’s Continuing Creation (NCC) is a largely understandable process which works according to laws of science that we increasingly comprehend. “God” was miraculous and mysterious; but NCC is wondrous, natural, and increasingly understandable. The Processes of NCC happen all around us, all the time. The fact that we are increasingly able to explain this process makes it more wondrous, not less! Therefore, we participants in Nature’s Continuing Creation hold that “God” does not reach down into our individual lives, granting some favors and withholding others.  Instead, we see and know that NCC works through the Processes of Complexity that we talk about in this Essay.

A good understanding of Complexity is vital for Co-creators of Our Way, because Nature’s Continuing Creation: The Growing, Organizing, Direction of the Cosmos is itself a Complex Adaptive Systemthe largest one of all — and learning about it is itself a spiritual activity. To know Continuing Natural Creation is to participate in Continuing Natural Creation. 

More Examples of Emergence and Self-organization

Here are some further examples of emergence in complex systems, both non-living and living:

Friction, Temperature, and Other Emergent Macro-Phenomena

The qualities of large-scale assemblies of matter are emergent. Friction, for example, is an emergent quality, because friction is created when things rub together. Since friction requires more than article or component, it is by definition a macroscopic behavior. Friction, in turn, generates heat, which gives us the further emergent phenomena of temperature, with its phase-transitions, including melting, gasification, and (under extreme heat), becoming a plasma. Other emergent macro-phenomena of large-scale assemblies (such as concrete, steel and wood), include viscosity, elasticity, and tensile strength.

The Color Yellow is an Emergent Phenomenon

The color yellow, and all the other colors that humans see, are emergent phenomena.  A spectrometer doesn’t see “yellow.” It senses colors, but displays them as wavelengths, as sine curves on a cathode ray tube. Wavelengths of a certain height are seen as yellow, but only by the eyes plus brains of certain animals, including humans. Therefore, the phenomenon of “yellow” emerges from the entrance of a certain light wavelength into the eyes and brains of certain animals. The phenomenon of the color “yellow” is the unique product of our complex human perception system in action — it is a true emergent phenomenon.

Money Is an Emergent Phenomenon

Money, in all its forms, is a clear example of Emergence, one we can all relate to.  If we think about it, we realize that money is not a physical thing. Physically, a dollar bill is not money, it is a piece of printed paper. A gold coin is not money, it is a disk of yellow metal.  And a bank account is physically not money, it is numbers and words on a computer screen.  15 Money is an emergent, abstract concept that can take many physical forms — gold, printed bills, numbers in a bank account.  Because money is also a useful artifact of human culture, we are correct to say that it both emerged and was invented.  And since money was invented in many different cultures at many different times, it is also possible to argue that money was discovered. 16

Among the earliest humans, things were bartered – a club was traded for an animal pelt. Both the club and the animal pelt are directly useful to their receivers. But clubs and pelts can be cumbersome to carry around, and the specific people you meet might not need them.  So, a “medium of exchange” emerged to fill the need for easier, more fluid trading.  Arrowheads are easy to carry, durable, and hard to make. They are valuable because all hunting societies need them. If you want to trade a club for a pelt but the person you meet at the campfire doesn’t have a pelt, you could sell him the club for, say, two arrowheads, and readily use the arrowheads later to buy a pelt elsewhere. Thus – arrowheads can become (emerge) as a form of money.

Over time, a rich person might accumulate more arrowheads than she needs, just so she can use them as money later. After hundreds of years and the discovery of gold, gold coins would replace arrowheads as the dominant form of money.  Gold is small, durable, and prized by all people, hunters and farmers alike.

Accumulated money held for later use is called capital. If the society eventually became developed enough for law and commercial trust to emerge, a rich person (such as a duke or a “banker”) would no longer need to use her coins, she could just write and sign I.O.U.’s – “Notes” – and those slips of paper would themselves evolve to become “money.” The gold coins themselves could be kept in a strongroom below the castle, “supporting” the slips of paper.  Over time, large stable governments like the United States would abandon the “gold standard,” meaning that they would print paper money backed not by gold in a strongroom, but by the “full faith and credit” of the nation.

In today’s world, paper money is being replaced by electronic credit-card blips and credit/debit entries made on computerized ledgers.

Traffic Roundabouts Emerge in Complex Systems

Emergent processes or behaviors can be seen in many social arenas, such as tribal governance, traffic patterns, and the evolution of cities. City planners usually do not design all the streets of a city. Instead, they initially make use of ancient pathways and dirt roads that are already in place. For example, Broadway in downtown Manhattan was originally an old Native American trail hacked through the forest. 17

Traffic roundabouts (traffic circles) are a good example of emergent “self-organization,” happening all around us. Long before there were traffic engineers, horse-drawn wagon drivers spontaneously and collectively figured out that the easiest way to get across the public square was to travel around it, everyone going in the same direction – either clockwise or counter-clockwise. (Interestingly, countries that drive on the right side of the road always form counterclockwise traffic circles, while countries driving on the left-hand side of the road form clockwise traffic circles.)

Roundabouts make for less engine idling time, less slowing and accelerating, and less noise than a stoplight intersection. The ancient roundabout system has proved so effective that modern cities are replacing stoplights at problem intersections with traffic circles and getting better results. 18

Emergent Structures in Chemistry

There are many complex systems in chemistry, including reaction-diffusion systems which emerge when certain chemicals are mixed. The mixtures begin to form changing patterns, e.g., concentric circles which impinge on and flow into each other. Sophisticated mathematics have been developed to model these systems. 19

A particularly remarkable reaction-diffusion system is the Belousov–Zhabotinsky reaction, which was studied by Dr. Ilya Prigogine, one of the founders of Complexity Science. We referred to it earlier in this Essay.

Also, Autocatalysis takes place in many chemical reactions.  A catalyst is a chemical that speeds up the reaction of two other different chemicals. It acts as a kind of “marriage broker” between the other chemicals. Autocatalysis happens when one of the two interacting chemicals itself speeds up the interaction. The analogy would be a rapid seduction rather than a brokered marriage.

Phase Transitions in Chemistry and Biology

Although we described religious conversion as a phase transition elsewhere in this book, that term is usually reserved for chemical and biochemical processes.  As children, we dissolved more and more sugar in a glass of water, until the water could absorb no more. Then, sugar crystals would precipitate out onto a piece of string we had hung in the center of the glass. (That piece of string is akin to the “initial singularity,” because it is imperfection in the consistency of the sugar-water solution that triggers the formation of the solid crystals.)

The “Iodine Clock,” an example of chemical solutions known as chemical oscillators, will remain clear for a significant time after the components are mixed together. Then, the mix will suddenly change to a uniform blue.

Biological phase transitions happen in protein folding, in gel-to-liquid changes by biological membranes, and in the awakening or lighting up of neural networks in the brain.

Note: For an excellent article about how to overcome personal cognitive biases, see Robert B. Cialdini, “The Science of Anti-science Thinking,” in Scientific American, July, 2018, pp. 37-41. 

Near-synonyms for “phase transition” include “the straw that breaks the camel’s back,” “crystallization,” “sudden religious conversion experience (in Evangelical Christianity, being “born again,”) “tipping point,” “breakthrough,” “chain reaction,” and “paradigm shift.”

Language and Culture Are Clearly Emergent

Culture, including language and music, is clearly emergent from human brains in concert with human experience.

Culture, for example, the English language, does not depend on any one human brain or on any one life experience. Instead, it resided in the generations of human brains that lived down through hundreds of years; and it resides now in the English-speaking generation that lives today.

Each generational set of interacting brains modifies its usage of English, causing the language to evolve over time.  Modern English is very different from the Middle English of Chaucer’s TheCanterbury Tales (14th century), which in turn is very different from the Old English of Beowulf, a poem written down in the mid-10th century. Here are the first four lines of The Canterbury Tales, in the original Middle English, with a translation to modern English at the right:

“Whan that Aprill, with his shoures soote                    (When April, with its sweet rain showers)
The droghte of March hath perced to the roote           (Has pierced the drought of March to its root) 
And bathed every veyne in swich licour,                      (And bathed every vine in sweet liquor, i.e., in water,)
Of which vertu engendred is the flour…”                      (Whose sustenance gives birth to the flower)

We could say that language, literature, and music have evolving “lives of their own,” and that living human minds are simply their temporary hosts… as are essays, books, and sheet music.

Within the overall arena of culture, there are sub-cultures and “schools of art” which are themselves complex (and evolved) systems. One such emergent system is Hip Hop Culture. Readers are encouraged to click on the Wikipedia link for Hip Hop Music and read the extensive and scholarly essay there.  That essay almost certainly continues to explore the historical antecedents of Hip Hop, documented with over three hundred footnotes as of 6-273-18.

Every artistic and cultural movement – Impressionism, Jazz, Transcendentalism, the Tea Party Movement, the Underground Railroad, Mormonism, Scientology, etc. – has a similar evolutionary history of its own, with many different creators and antecedent trends coming together to create something new and different.

“Open-source Software” Emerges in the Complex System of the Internet

Open-source Software, as well as Wikipedia Research Projects form two compelling illustrations of Self-organization. Wikipedia articles are written by an army of mostly unpaid volunteers who cooperate to write and edit the hundreds of thousands of Wikipedia topics. Today, Artificial Intelligence (AI) is able to answer queries and write responses on its own, without human writers.

An Oak Tree is an Emergent Complex System

An oak tree as an example of a complex system where humans are not directing anything. An oak tree emerges from a seed, an acorn.  Well, the tree really emerges from the acorn and the ground the acorn is planted in.  And, if we know basic biology, the tree also emerges (we say “grows”) from the water it “drinks,” the air (carbon dioxide) it “breathes,” and the sunshine it uses for photosynthesis.

Since the acorn contained DNA passed down from a chain of more primitive plants that lived hundreds of thousands of years ago, the oak tree emerged from those ancestors as well. The components of earth, water, air, sunlight and encoded DNA instructions self-assemble, coming together to create the oak tree. They combine to make a Whole that is more than – and utterly different from — the sum of its parts.

The tree is more than the sum of its atoms. What has been added?  Not the atoms, they have just changed their positions. Not energy, although energy certainly has to flow through the oak to create it and sustain it. What has been added is the pattern and organization of all the atoms. And the organization features specialization of tree tissues and cooperation among the cells and tissues.

Spiritual Implications of the “Oak Tree System”

Today, we know a very great deal about how oak trees function. We know about the morphogenesis, photosynthesis, genetic reproduction, capillary action, and a host of other scientific sub-processes that together “explain” the oak tree. We know the oak’s ecology, the underlying biology, the more-underlying chemistry, and the still-more-underlying physics of the mighty oak. And the detail of our knowledge increases with each passing year.

Our step-by-step knowledge of the oak tree’s heredity and growth has terrifically reduced the mystery of the oak tree’s role in the Story of Continuing Creation.  But that our knowledge has not decreased, but rather increased the wonder and the spectacle of this repeating and evolving Creation.  The mighty oak tree is a fitting symbol for all of Life, and for the entire Creative Flow of The Growing, Organizing, Direction of the Cosmos.

The Gaia Hypothesis Argues that Earth is a Single Living Complex System

The Gaia hypothesis holds that Earth’s biosphere s fundamentally organized in a way that is broadly conducive to life.  If so, this would be an instance of Emergence & Self-organization on a very large scale. 

The Concept of a Supernatural God Is an Emergent Phenomenon!

We Gardeners in Nature’s Continuing Creation hold that the very idea and concept of God is also an emergent phenomenon.  It emerges from the evolved complex system that is the interaction of human beings and their environment.  It arises from five early human traits (indeed, pre-human traits) whose evolution goes back tens of thousands of years:

  1. Humans evolved a very early built-in tendency to see patterns everywhere we look. For example, when we look at cloud formations, we see the shapes of ships, towers, people’s faces. We also tend to see patterns (real and imagined) in events, and we love to tell stories about those events.
  2. We evolved a high anticipation of danger, so we see danger and threat at every turn. 
  3. We perceived causation behind every event. Everything happened because it was caused to happen by something or someone. If we were pummeled by an earthquake, that quake must have been caused by something or someone. (“Everything happens for a reason.”)
  4. Since the greatest danger to an individual usually came from animal predators or other humans or (enemies, rivals), we tended to personify all the sources of the danger or evil. So, ancient humans thought a hailstorm was caused by a person, (or a person-like demon), not by the natural forces of air temperature and wind. Early humans didn’t understand “natural” or “impersonal” forces.
  5. We tended to impute a reason for the personified agent to send the hailstorm. “Maybe we didn’t sacrifice enough lambs to Yahweh.”

We discuss these five traits at greater length in our Essays that evaluate the great world religions (and also modern cults): Evaluating Taoism and Zen, Evaluating Jesus’ Teaching, Medieval Roman Catholicism to the Protestant Reformation, Evaluating Buddhism, Evaluating Hinduism, Evaluating Islam, and Smaller Religions & Modern Cults.

Ant Colonies Are Complex Adaptive Systems

Let’s look at additional examples of Complex Systems and also introduce Complex Adaptive Systems. As their environments change, adaptive systems are able to change themselves in an effort to survive and prosper.

An ant colony is a good example of a Complex Adaptive System.  Each ant in a colony is an autonomous unit that reacts depending only on its local environment and the genetically encoded rules for its species of ant. Despite the lack of centralized decision making, ant colonies exhibit complex behavior and have even been able to demonstrate the ability to solve geometric problems. For example, colonies routinely find the maximum distance from all colony entrances to dispose of dead bodies. 20

All complex systems require a favorable environment in which to work.  For example, complex systems in physics and chemistry must have the right pressure, temperature, and energy flow.  But complex adaptive systems, (in particular, evolutionary systems), are able to change themselves (through mutation and natural selection) to better fit their changed surroundings. For more discussion, see our Essay, The Processes of Evolution and Their Meaning.

Many adaptive systems accomplish this self-change with no central control. The queen ant does not give direct orders and does not tell the worker-ants what to do. Instead, each ant reacts to stimuli in the form of chemical scent from larvae, other ants, intruders, food and from the build-up of waste, and leaves behind a chemical trail, which, in turn, provides a stimulus to other ants.

All living things are complex adaptive systems, because they each evolved, and the process of evolution is a process of adaptation. Living organisms follow the laws of evolution in addition to the laws of complexity. Specifically, they are subject to the instructions of their DNA. And when that DNA mutates, it can lead to variations in the organisms’ capabilities. The organisms with the new capabilities then compete against the “older models” that do not have the new features. The process of natural selectionchooses” which set of living things (which set of each one’s capabilities) has the best chance to survive and reproduce a new generation. This is accomplished when the organisms having less-than-best capabilities do not survive and/or do not reproduce a new generation. (See our Essay, The Processes of Evolution and Their Meaning.)

Ants Suddenly “Go to Work” Building a New Nest

Ants also provide a fine example of sudden and swift emergence. The late Harvard biologist E.O. Wilson tells us that a solitary ant placed on strange ground will wander around aimlessly.  Add a few more of her sister ants from the same colony, and the aimlessness continues.  But when a sufficient number of ants have added their pheromones to the ground, a critical mass or tipping-point is reached at which the ants start to spontaneously cooperate in nest-building behaviors. As each ant travels, it leaves behind a chemical pheromone trail on the ground.  As more ants move along one trail or in one direction, they leave behind a build-up of the pheromones.  When the build-up is great enough, they begin nest-building. Thus, the ants have undergone a phase transition from disorganized individuals to a semi-organized “proto-colony,” even though their queen is not present to direct them. Clearly, this is bottom-up, self-organizing, system behavior.

In complex systems, even in ones made up of intelligent humans, the elements may be ignorant of the behavior of the system as a whole, responding only to the information or physical stimuli available to them locally.  No one ant has an overall understanding of the colony. Truck drivers who deliver newspapers do not understand the organization and financing of The Washington Post.

People Experience Sudden Religious Conversions

A human’s religious life can also be a complex adaptive system. When wandering ants get a sufficiently fulsome the pheromonal message to start building a nest, it’s as if they suddenly get religion.” A person’s sudden religious conversion is to the ants’ sudden nest-building. Both of them are examples of a sudden phase transition (in a thermodynamic system) or a bifurcation (in systems being described mathematically.  In chemistry, it’s like dissolving more and more sugar into a glass of water, and then seeing the super-saturated solution precipitate a sugar crystal.

A person’s sudden religious conversion begins when a potential convert absorbs more and more of the doctrines, customs, and fellowship of a new faith. His or her brain is busy processing and integrating all this on both the conscious and subconscious level. Suddenly, at a tipping point, when some final straw is added to the mix that triggers a cascade of “meaning” that jells everything together in the individual’s mind. They accept much or often all of what they have been taught.

People who experience this are said to have had an epiphany, or a great awakening.” In evangelical Christianity, it is called being “born again.”  However, Participants in Nature’s Way of Continuing Creation hold that this sudden “religious” conversion process is natural, not divine.  In fact, people can also be mentally programmed to join cults or political parties, and then later de-programmedout of them.

A number of sudden conversion processes are described in the acclaimed book, Varieties of Religious Experience, written in 1902 by Harvard psychologist and philosopher, William James

Self-similarity and Multi-level Competition in Adaptive Complex Systems

In many Complex Adaptive Systems, both the individual elements of the system and the system as a whole are adaptive.  Such systems are often self-similar as well, in that similar behaviors take place at different levels of the system. For example, there is Multi-level Natural Selection: the individuals in a native tribe compete for survival and reproductive rights; while at the same time,
the tribe as-a-whole competes with other tribes for survival and/or for greater “presence,” i.e., they compete for increase in population, land, wealth, and influence.

System Organization Helps Overcome Negative Feedback, Being Swamped, and Dying Out

It is not just the sheer number of connections between components which encourages emergence; it is also how these connections are organized.  Many complex adaptive systems evolve partial control systems that make the system more effective, stable, and adaptable.

A hierarchical organization is one example that can generate emergent behavior, but so can decentralized organizational structures, such as a marketplace or a network. In some cases, the system has to reach a combined threshold of diversity, organization, and connectivity before emergent behavior appears. A good example of this is nest-building among ants, which requires a sufficient number or ants laying down a sufficient number of pheromone trails to “convince everyone” that critical mass has been attained.  21

Other important properties of many (but not all) complex adaptive systems:

Many of these features can be found on all levels of complex adaptive systems. Cells specialize, adapt and reproduce themselves just like larger organisms do. Communication and cooperation take place on all levels, from the individual agent level to the system level. The forces driving co-operation between agents in such a system, in some cases, can be analyzed with Game Theory. (We talked more about Game Theory in our Essay, Mathematics Evolves in Nature’s Continuing Creation.

More Examples of Complex Adaptive Systems:

The World Wide Web (the Internet) – Another Complex Adaptive System

The World Wide Web is huge, modern example of a decentralized complex adaptive system exhibiting emergent properties. There is no central organization rationing the number of links, yet the number of links pointing to each page follows a power law in which a few pages are linked to many times and most pages are seldom linked to. A related property of the network of links in the World Wide Web is that almost any pair of pages can be connected to each other through a relatively short chain of links. Although relatively well known now, this property was initially unexpected in an unregulated network. Open-source software, such as Wikipedia and Wikivoyage, are also impressive examples of emergence. 22

Note: The so-called “Zeroeth Law of Wikipedia” is cited by Wikipedia editors to highlight its apparently surprising and unpredictable quality of the system, given its wide range of multiple writers and links. As editor Gareth Owen quips, “The problem with Wikipedia is that it only works in practice. In theory, it’s a total disaster.” — Gareth Owen.  23

Free Market Economies Are Complex Adaptive Systems

The Benard Cell phenomenon we talked about earlier in this Essay, is a complex system made out of pure physics and chemistry, and the slime mold is composed of individual living cells. Now let’s look at a complex system that is itself made up of thinking human beings and organizations of human beings – a free-market economy. A free-market economy is made up of complex systems that are themselves made up of complex systems.

In fact, Complexity Science got its start in the study of free-market economies. The earliest precursor to modern complex systems theory can be found in the classical economics of Adam Smith (1723-1790) who wrote in his 1776 book, The Wealth of Nations, that the self-interested actions of competing buyers and sellers in a free market brings about a distribution of goods so orderly that it was as if the results were accomplished by an invisible hand.” 24

The earliest free markets were utterly without central control. The earliest organization was likely the Saturday “farmers’ market,” followed by having a fixed market location within a town, followed by regional fairs. (“Are you going to Scarborough Fair? Parsley, sage, rosemary, and thyme.”)

In a free market, individual humans, each pursuing their own self-interest, spontaneously cooperate to produce functional economies that feature efficient allocation of resources, economies of scale, and specialization of labor. The international stock market is an example of emergence on a grand scale. As a whole, it precisely regulates the relative security prices of companies across the world; yet it has no leader.

A century after Adam Smith, Economist and Nobel Laureate Friedrich Hayek (1899-2992) also wrote about emergence in free markets, law and politics. Hayek argued that these structures were not the conscious creations of a rational agent (be it God, the Sovereign, or the English Parliament). According to Hayek, the most important social structures, including laws (which he called the “nomos”) are emergent. 25

When no central planning is in place, there is no one entity which controls the workings of the entire market. Investors, participating buyers and sellers must base their decisions on limited knowledge.

  • Over time, however, market economies can evolve a degree of centralized control. Business leaders, local lords, and eventually, kings would build roads to connect the trading centers.
  • Money – a complex system in itself – was invented as a way to communicate and transmit value, replacing cumbersome barter.
  • Lenders and financiers evolved, partially centralizing major decisions about industries, technologies, and locations.

Free-market economies exhibit many of the principles of complex systems that we have already listed. Here are some additional features that were not present in the convection cells of boiling water:

  • Free market economies oscillate, often between the cycles of “boom and bust.” Even without the intervention of real events, the momentum of optimism can carry economic activity and prices too high. Then, a momentum of pessimism can carry the market too low. Similarly, in chemistry there are mixtures that oscillate between two states, with each state having a different color. All such chemical systems are Complex Processes.  Examples include the Belousov-Zhabotinsky (BZ) reaction, the Briggs-Rauscher reaction, and the Bray-Liebhafsky reaction.
  • The swings in market sentiment are often caused by feedback loops.  For example, say that a charismatic salesperson can convince buyers to buy tulip bulbs. Those buyers communicate their excitement to other buyers in a loop of positive reinforcement resulting in more and more tulip sales. Then, at some point, countervailing opinions gain a foothold and they “talk prices back down.” In Holland, from 1623-1637, there was a famous “tulip mania” during which the price of tulip bulbs skyrocketed, and then crashed back down.  More familiar is the speculative stock market rise of the 1920’s, ending in the great Wall Street Crash of 1929.
  • Similarly, the human body heats up during exercise, the sweat glands secrete water onto the skin, which cools the body back down as it evaporates, but this cycle is usually not as dramatic or as newsworthy as the stock market Crash of 1929.  (The efficient and prolific ability to sweat is one of the things which allows humans to walk or run at a good speed for longer and farther than any other mammal.) 

Human Brains Are Complex Adaptive Systems

The daily working of a normal human brain is a complex adaptive system, because the brain is able to learn. The evolution of a human brain was (and still is) a complex adaptive system, as evidenced by the very large cerebral cortex on top of the mammalian brain from which it evolved. 26

“The evolution of animal brains was the result of a complex adaptive system. In the human cortex, our billions of neurons are each connected by thousands of fine filaments going in all directions. We see dense local connectivity and a few very long axon projections between regions inside the cortex and to other brain regions. But there is also structure: there are neuron “highways,” central “switching stations” and “managing editors” in the brain.”  Every year more is discovered about how the human brain works, and new books are published all the time.                   — Partha Mitra, (“The Brain’s Highways: Mapping the Last Frontier,” in Scientific American, May 22, 2012.) 

Where is a thought located in our brain? Is it in a specific neuron?  No. Is a piece of it in a whole bunch of neurons?  Not really. The thought emerges from the interaction of a whole bunch of neurons.

  • Complex systems may be nested a smaller/minor system lying inside a larger/major system. In other words, the components of a complex system may themselves be complex systems. For example, an economy is made up of organizations, which are made up of people, who are made up of cells — all of which are complex systems. 27
  • The partial control structures in a free market economy, or in the brain, show them to be examples of hierarchical organization. Both “hierarchy” andindirect control” are often characteristics of complex systems. In the example of Benard Convection Cells, we saw that there was no hierarchy, but the presence and shape of the pot surface at the bottom of the simmering water provided a kind of indirect control — an unconfined heated fluid that’s open on all sides no would not form convection cells.

Simple Rules Can Lead to Complex Behavior

We’ve seen complex systems, often having suddenly emerging structures, can form out of simple parts. Individual ants cooperate to create ant societies and ant hills. Individual plant cells combine to form a stalk of corn. Wind, heat, and atmospheric moisture combine to form hurricanes. Under the agency of the human brain, letters are combined to form words, words to form sentences, and sentences to form the Essay you are now reading.

Now we want to show that simple rules can lead to complex system behaviors as well. Examples include flocks of birds in flight, schools of fish, The Game of Life, algorithms, and computer programs.

Flocks of Birds in Flight – “Swarming”

When flocks of birds fly, or when schools of fish swim, they often move together in close formation. Their patterns of motion over time are both coordinated (they move together, almost simultaneously), and chaotic (there is no telling which way they might go next).  In bird flocks, the complex movement pattern is called a “murmuration.” When flying insects gather together, it is called swarming, and groups of cattle or horses engage in herding. Groups of fish move in “schools.” Clearly, the beautiful movement patterns of these animals (especially the birds and fish) are excellent examples of emergence in complex systems.  One important purpose of swarming and herding it to provide warnings about and protection from predators. 

Researchers, including John Naughton (a senior research fellow at Cambridge University), have studied this phenomenon, and have found that this ever-changing and beautiful behavior results from the birds’ (or fish) following and balancing just three simple “rules of the game:”

  1. Maintain Separation (don’t crowd your neighbors),
  2. Maintain Alignment (steer toward the average heading of your neighbors), and
  3. Maintain Cohesion (steer toward the average position of your neighbors).” 28

For example, a particular bird in the middle of the flock may see that the bird ahead of her, steady at our bird’s “two o’clock” position. And our bird also sees that the flyer bird at her “three o’clock” has just turned about 5 degrees to the left. And so, our bird learns that her companions on her left side have opened up a bit of room. So, our bird decides to change her course maybe 3 degrees left.  Go to YouTube and search on “Starlings Mumuration” for a video of Starlings in coordinated flight. In this way, the simple parts (the birds) can form beautiful ever-changing flow patterns when directed by very simple marching orders.

  • Herds, flocks, and schools achieve greater safety because they can look for predators in all directions, and signal danger to each other. In herds, stronger animals can patrol the edge of the herd, protecting the females and young that are in the middle. When birds fly in flocks and fish swim in schools, they confuse some predators, who have difficulty distinguishing the individual animals and/or deciding which individuals to attack.
  • Of course, swarming creatures build other emergent structures, (mostly nests) for safety, reproduction, and food distribution. Colonies of ants build anthills, termites build mounds, swarms of bees make honeycombs,
  • Swarming groups also clearly communicate. The birds and fish use tiny gestures, as we saw in the YouTube video of starlings.
  • Ants communicate (in part) by leaving pheromone trails in the air and on the ground as they walk. First the complex system (i.e., the entire ant colony) explores by having a few ants go wandering around, each leaving a pheromone trail behind. If an ant finds good food, she comes back and now she leaves a trail with a different (or stronger) “Food This Way” scent. 29
  • Humans exhibit herd behavior when they riot or demonstrate as a leaderless (or near-leaderless) crowd. This also happens during warfare, when command, control, and organization break down in the extremis of battle.

When just a few homeless (“nest-less”) ants move aimlessly around, they do not start building an anthill. But when experimenters add more ants to the site, leaving more trails, the ants reach a tipping point where the random ant behavior coalesces into purposeful building activity: yes, they forage; but they also start to build a nest.  An ant-colony system coalesces around nest building and nest habitation. Economist Adam Smith would have said that an invisible hand produces a functional “ant economy,” because he used that expression to explain how an undirected market economy manages to efficiently allocate resources. 30

“Look to the ant [colony], you sluggard;
 Consider its ways and be wise!
It has no commander, no overseer or ruler,

 Yet stores its provisions in summer
 And gathers its food at harvest.”
       –Proverbs 6:6-8

Today, there are artificially intelligent computer systems which use similar “group-trial-and-error” applications for artificial learning and for film and television animations. One example is the Boids” algorithm (or game), which mimics the swarming behavior of birds.

Swarming mechanical drones have been successfully developed which can fly in flocks to more effectively search for lost people, track developing forest fires, or seek and attack incoming enemy missiles. 31

We can illustrate this by looking at two of the easy parlor games mathematicians and computer scientists have developed to prove this very point. The two best-known games are called Conway’s Game of Life and Langton’s ant. These games or simulations are fun to play (or “run”) online, after just a few minutes spent studying the rules.

Cellular Automatons

The two games mentioned above are essentially abstract mathematical models of all real-world complex systems. They show how mathematics aids and formalizes yet another area of science. (See our Essay, Mathematics and Continuing Creation.)

These games are formally called cellular automatons, also known as Turing machines.” The second name is a tribute to Alan Turing (1912-1954), who invented the early mathematics of algorithms, and the cellular automaton name was bestowed in 1970 by its creator, the British mathematician and game theorist, John Conway (1937-2020). Boids is another artificial life program, developed by Craig Reynolds in 1986, which simulates the flocking behavior of birds.

— A cellular automaton is defined as “a set of units in a mathematical model that have simple rules governing their replication and destruction. They are used to model complex systems composed of simple units such as living things or parallel processors.

— A Turing machine is defined as “a mathematical model of a hypothetical computing machine that can use a predefined set of rules to determine a result from a set of input variables.”

These definitions are helpful, but the best way to understand these games is to “play” or “run” one of them.  Readers can “play” or “run” all these games online.  Below, we will describe one of them – Conway’s Game of Life.  (We refer the reader to the internet to find out more about the game, Langton’s Ant.)

“Conway’s Game of Life

Emergence in this deceptively simple simulation is very dramatic, and the Reader can see it happen in real time on the Web by clicking, “Conway’s Game of Life.” Amazing patterns or structures emerge from this game’s simple rules and simple parts. One of the important things we see is how easily this Creation of patterns or structures takes place.  (See also the Wikipedia entry for “Game of Life.”)

The rules are simple: “Conway’s Game of Lifeis played on a grid of square cells — like a chess board but extending infinitely in every direction. A cell can be alive or dead. A live cell is shown by putting a marker on its square. A dead cell is shown by leaving the square empty. Each cell in the grid has a neighborhood consisting of the eight cells in every direction including diagonals. The Game of Life teaches us that complexity can arise from simple components following simple rules below:

To apply Step-one of the Conway Game-Of-Life rules, we count the number of live neighbors for each cell.
What happens next depends on this number of live neighbors:

      • A dead cell with exactly three live neighbors becomes a live cell (birth).
      • A live cell with two or three live neighbors stays alive (survival).
      • In all other cases, a cell dies or remains dead (overcrowding or loneliness).
      • All the changes in all the cells are done simultaneously.
      • Then Step-two repeats the same rules to the new picture.
      • Then Step-three, four, and so on repeatedly.

A good way to get started in “Conway’s Game of Life is to try out different starting patterns and see what happens. We can pick as many alive cells as we want and place them anywhere on the grid we want.

Then, this Game’s simple decision rules are applied to each of the live cells, causing them to change or not change, and resulting in a new “second round” pattern of live cells. Then the decision rules are applied again, resulting in a third pattern. And so on.

After a number of rounds or iterations, also called “generations,” the Game often settles down into patterns called Still Life Objects (known asattractors in mathematics), which can remain the same with no further change in their pattern. No live cells die, and no new cells are born. Some of the most common “Still-Life” Attractors are called the “beehive,” “boat,” “ship” and the “loaf,” because they resemble those real-life things.

An attractor, a.k.a., strange attractor, is the evocative name given in mathematical Chaos Theory to patterns that often (or even always) turn up regardless of the starting positions/conditions of the system. An example in real life would be the whirlwind shape of hurricanes, which sooner or later repeatedly emerge over the Caribbean and Gulf of Mexico.

With different starting positions, the Game of Life’s patterns can change a great deal over time. For example, the Game of Life can evolve to produce “oscillators — objects (patterns) that change from round to round, but eventually repeat themselves.

More rare are “Gliders” – patterns in systems such as Conway’s Game of Life that move (glider) across the grid with successive rounds of the game.

Visual representation of an Attractor, a.k.a. Strange Attractor

Most rare are the eerily life-like Complex Patterns. For example, The Queen Bee Shuttle first moves to the right, but after a few steps, it produces the still life called a “beehive” and turns back to the left. Then it produces another beehive to its left and turns right again. Such complex patterns may persist for a long time, and then disappear.

New Patterns Are Still Being Discovered – An article written by Siobahn Roberts for the New York Times (12-28-20) tells us that “The Game of Life motivated the use of cellular automata in the rich field of complexity science, with simulations modeling everything from ants to traffic, clouds to galaxies. More trivially, the game attracted a cult of ‘Lifenthusiasts,’ programmers who spent a lot of time hacking Life — that is, constructing patterns in hopes of spotting new ‘Life-forms…’ In 2018, there was a much-celebrated discovery of a special kind of ‘spaceship’…named ‘Sir Robin.’ Made of hundreds of cells, it moves two cells forward and one sideways every six generations. It was discovered by Adam P. Goucher, a British algorithmist, building on an earlier partial find by Tomas Rokicki… In September, Pavel Grankovskiy, of Russia, discovered the ‘Speed Demonoid Spaceship’ pattern…and In December, John Winston Garth, of Alabama, discovered the ‘Doo-dah Spaceship.’ Both are contenders for pattern of the year, in what has been a good year for new Game of Life discoveries.”

Conway’s Game of Life shows that complexity – elaborate structures and movements — can arise from the simplest of rules applied to individual parts that are all alike. This is another piece of evidence showing that Continuing Creation (including our own individual lives) functions just fine without the micro-managing intervention of a supernatural Creator. 

Practitioners of Continuing Creation also say — that both real life and Conway’s Game of Life are “non-zero-sum games.” Because while the total energy and matter in the universe always remains fixed, within the more limited boundaries of open systems, such as our Earth, the pass-through of energy can and does build order, structure, and information content. 

  • A zero-sum game is any game where the winners can only gain what the losers lose. A non-zero-sum game is one where all “players,” (or most players, or the average of all players) win something.

A “non-zero” result is exactly what we see when we consider that the initial sea of undifferentiated quarks and leptons were combined at the Big Bang — under the four fundamental forces of physics — to make the elements hydrogen and helium, and then again combined inside stars to make all 94 of the naturally occurring elements of the universe.

Complex Systems Are Dynamical

The history of a complex system are usually important. Because complex systems are dynamical systems, meaning they change over time, and prior states may have an influence on present states.
systems can evolve into spontaneous recovery and failure, i.e., it may build a structure that later collapses, and then recover to build again – in the same way or in a similar but different (evolved) way.

Feedback Loops

Dynamic Systems often contain feedback loops. Both negative (damping) and positive (amplifying) feedback are almost always found in complex systems. The effects of an element’s behavior are fed back into its system in such a way that the element itself is altered.

Self-similarity in Complex Systems

One of the results from the mathematics of (near) chaos theory is a deeper understanding of “self-similarity.” 

Self-similarity is so common in Nature that it must be seen as a feature of all evolution: Trees exhibit self-similarity because the branching pattern of their large limbs is repeated in their smaller limbs, and again in their twigs. The splits are never identical, but they are highly similar. The same is true for biological systems such as the branching of the circulatory and bronchial systems. Branching systems are excellent for “bottom-up” gathering of materials, and for “top-down” distributing and, in hierarchical systems, for collecting information and issuing directives.

The Tree of Life, which illustrates the evolution of all living species, itself displays a self-similar branching pattern.

Recursive Patterns

Self-similar patterns occur when a construction template or ruleset is recursive, and it is used over and over at different scales. So, a number of connected elements may form a shape that is derived from the shape of an individual element. 32

Networks of Networks

Networks can merge and become a network-of-networks. A large traffic pattern consists of many smaller traffic patterns. Cells merge to make organs, organs make bodies. Sentences are collections of words; paragraphs are collections of sentences. The internet is a famous network-of-networks. 

Fractal Patterns

Long coastlines are made up short coastlines. A coastline has promontories and bays.  Within every bay are smaller promontories and small inlets.  And within every inlet are still smaller inlets… and so on.

In 1967, the French-American polymath and mathematician, Benoit Mandelbrot published “How Long is the Coast of Britain? Statistical Self-similarity and Fractional Dimension,” showing that a coastline’s length varies with the scale of the measuring instrument, resembles itself at all scales, and is infinite in length for an infinitesimally small measuring device. The term fractal was first used by Mandelbrot in 1975. He based it on the Latin frāctus, meaning “broken” or “fractured,” and used it to extend the concept of theoretical fractional dimensions to geometric patterns in nature. 33

The “Koch Snowflake” Fractal Pattern

Self-same fractal patterns like a coastline and the endless outer rim of the Koch Snowflake,can now be modeled by mathematicians. You can model (draw) a mathematical “coastline” yourself – or you can see it being done online — by reading the Wikipedia entry for theKoch snowflake,(also called the Koch curve) which is infinitely long yet encloses a finite space!

Other Systems exhibiting self-similarity have fractal patterns. Sea sponges are self-similar. If someone gave us a photo of a random sponge cross-section, we could not tell if it was a large-scale cross-section or a very small-scale cross-section, because the pattern is the same at all scalesA “fractal” that is a mathematical representation of a sponge, named the Menger sponge, can be seen online. 34

Even economic markets (which are complex systems created by economic evolution) exhibit fractal patterns: The swings of cotton prices and stock prices are fractal, not random:  Over ten years, they tend to go up for a while (said to have upward momentum), then the trend “breaks,” and they go down for a while (said to have “downward momentum”). If you look at a smaller scale, say over one year, you see the same pattern.  If you look over one week, you see the same pattern.

Note: Because no element can be coerced to follow a specific path of assembly, no large number of elements will display the exact same pattern as another group. Patterns caused by large numbers of elements are alike, but never the same. Hence, all snowflakes look alike, and the cross-sections of all sponges of one species look alike but no two are exactly identical.  It is impossible to predict exact self-similar patterns, because the variables are too many and their interactions are too random.

Complex Systems Were Never Designed… Until Humans Began Designing Them

Let’s take a further look at the implications of complex systems for people who are interested in following Nature’s Continuing Creation: The Growing, Organizing, Direction of the Cosmos.

Until the evolution of human consciousness and tool-making ability, the complex things created by the Processes of Nature’s Continuing Creation were clearly not created “by design.” No all-powerful Designer planned and executed the pattern of the Milky Way or the organization of the human body. How do we know this?

  • First, as we have been explaining, bottom-up processes work just fine to create complexity.
  • Second, because all the products of creation are flawed.

Take the human body, for example. The three problems bullet-pointed below are from a longer list of things that are wrong (“sub-optimal”) in the human body, cited in the article “If Humans Were Built to Last,” by S. Jay Olshansky, Bruce A. Carnes and Robert N. Butler, Scientific American, 2003, updated from March 2001: 

For us humans, “a number of the debilitating and even some of the fatal disorders of aging stem in part from bipedal locomotion and an upright posture — ironically, the same features that have enabled the human species to flourish.

      • “Every step we take places extraordinary pressure on our feet, ankles, knees and back— structures that support the weight of the whole body above them.
      • “Over the course of just a single day, disks in the lower back are subjected to pressures equivalent to several tons per square inch.
      • “Humans, like most mammals, use the same tube for eating that we use for breathing. This makes it relatively easy for humans to choke, and even die, on their own food.”

A Human designed by a loving God “would have additional ribs to hold organs in place better, thicker, stronger bones and thicker spinal discs, knees that bend backward, leg veins with more check valves, larger hamstrings and tendons, larger outer ears and more plentiful ear hairs, a urethra that runs along the outside of the prostate not through it, and a stronger sphincter valve on the bladder.” 

To these “engineering” defects, we might add that we are vulnerable to disease, including osteoarthritis, dementia, cancer, multiple sclerosis, and heart disease, just to name a few. Some diseases are caused by the wear and tear of age, some by bacteria or viruses, and some by disabilities and pre-dispositions inherited at birth. (For our deeper, more spiritual discussion of Suffering, see our Essays, Answering Evolution’s Critics, Suffering and Evil – Causes & Responses, and Dealing with Death on Our Path of Creating.)

Our big human brains require painful birth, smaller jaws, early birth with long childhoods. Yet birds cram a lot more functionality into their tinier brains. Why wasn’t our species designed to do that?  And If God wanted us to be less perfect than Himself, why couldn’t he choose human imperfections that are less comic and less painful?

Therefore, We Can Conclude that Humans Were Not Designed by a Loving God  

Humans are hardly the only “poorly designed” creatures on Earth.  Many other animals (and also plants) are also “sub-optimal,” including halibut, elk, and peacocks:

  • Sole, halibut, and their relatives are bony fish, originally tall and narrow. Attracted by the food supply and opportunities for concealment on the ocean bottom, they flopped over on to one of their sides, and then adapted from there.
  • To paraphrase the evolutionary biologist Richard Dawkins’ classic work, The Blind Watchmaker: Why the Evidence of Evolution Reveals a Universe without Design, “A problem [with sole and halibut] was that one eye was always looking down into the sand. So, through successive mutations, the downward eye moved around to the top side, under natural selection, to where it could serve a useful purpose. But the end result is very ungainly – and clearly not the product of thought-through design. No sensible designer would have conceived such a monstrosity if given a free hand to create a flatfish on a clean drawing board…. But evolution never starts from a clean drawing board.” Instead, it begins with the organism that is available, and ‘tinkers’ with it. The resulting new generation, ‘creature 2.0,’ will likely not work very well, but maybe it will.” 35
  • Natural selection leads to huge antlers on male (bull) elk, to attract females. But it makes it very hard for bull elk to survive if cornered in a dense wood by wolves. This sub-optimal outcome is due to female preference gone overboard.
  • Bull elephant seals are enormously outsized. In the elephant seal community, 8% of the males father 80% of the pups, thus “wasting” the reproductive existence of the other males who are the great majority that loses the competition for females. (A similar outcome happens in the Human practice of polygamy).
  • Male Peacocks have evolved enormous tail-feather “trains” because they attract females, who “think” grandiose male displays imply greater strength, longer life, and/or better reproductive power. Even if the giant trains are correlated with those traits, do they have to be so large that the males have trouble getting around? No, but apparently once the sexual-selection algorithm is in place, it can be hard to curtail (pardon the pun).

The above four examples from the animal kingdom show that Evolution itself (a natural complex process of Nature’s Continuing Creation) can lead to inefficiencies; and that competition between individuals can lead to excesses, self-defeating features that increase danger from predators, wasted energy, simple ungainliness… all of which proves the falsity of so-calledIntelligent Design.”

Other Characteristics of Complex Systems

The Complexity Process of Continuing Creation is Bottom-Up, not Top-Down

In other Essays, we’ve said that the earliest processes of Continuing Creation accomplished differentiation.  The Four Fundamental Forces – gravity, the strong nuclear force, weak nuclear force, and electromagnetism – separated from or “froze out” of the one grand unified force that composed the Initial Singularity. At nearly the same time, the laws of physics and possibly also mathematics “froze out,” and then the first matter, in the form of sub-atomic particles, also differentiated out. Perhaps this very early differentiation could be seen as “top-down” Creation. We may never know if the first “splitting out” was planned and directed by “God.”

Since that time, Continuing Creation has been happening through combination, which is a bottom-up process. Small atoms combine to create complex chemical compounds. Later, small cells combine to make large and complex organisms; some of which combine to make societies. Small units of technology are combined to make structures and machines. Units of culture called “memes” combine to make law and culture. Since all these new wholes are usually unique, the processes of combination also achieve further differentiation!

Entropy Versus Open-Energy Systems

What powers Nature’s Continuing Creation of Pattern?  Especially in the case of a dynamical system?

Systems which construct some kind of new order, which add information and grow, must be Open-Energy Systems. Open-energy systems (also called “open systems”) are systems that continually take in energy from an outside source and use it to build new pattern, new organization. Some of the energy becomes locked up in the new created thing, and the rest dissipates (usually as heat) or is excreted out.  During their lives, all living things are open-energy systems.

In a contrasting Closed System, (also called “isolated systems”) no new energy enters the system.  Whatever energy the system has works in the system for a time and then “runs out.”  A wind-up pocket watch is a good example of a closed system. Once the watch spring unwinds, delivering its energy to the hands tick by tick, the watch stops.  Similarly, once a car runs out of gasoline, it stops.

The Second Law of Thermodynamics, also called the Law of Entropy, says that eventually, everything runs down. Complete Entropy means complete disorder, lack of all pattern and structure, and lack of energy to create or repair pattern and structure.

“The Second Law of Thermodynamics states that as energy is transferred or transformed, more and more of it is wasted. The Second Law also states that there is a natural tendency of any system that is isolated from an energy source to degenerate into a more disordered state.” In thermodynamics, increasing disorder is called increasing entropy. 36

Some scientists say that even the universe will dissipate all its heat-energy and die out. Inside our present universe, however, gravity has so far worked to coalesce matter into balls large enough to ignite into stars, and this is expected to continue for billions of years.

If everything is running down, how are things ever created? How can systems grow; and how can they become more complex?  How can Continuing Creation take place?  The answer is that continuing Creation can only take place when there is a steady, “moderate” flow of energy into and through system.  For example, all living things must take in energy, deploy that energy, and excrete it out. 

Each new star begins a new localized output of energy. Certain planets having the right composition and the right distances from these suns can use their energy flow-through to build new complex systems. Some of those systems may come alive, as they have here on Earth.

Here’s a very compact description of The Growing, Organizing, Direction of the Cosmos: 

  • Energy passes through.
  • Matter comes in and eventually goes out.
  • Organized Information increases; and can last the longest.

Imperfection and Instability

In physics, symmetry breaking is a phenomenon in which (infinitesimally) small fluctuations acting on a system crossing a critical point decide the system’s fate, by determining which branch of a bifurcation is taken. To an outside observer unaware of the fluctuations (or “noise”), the choice will appear arbitrary.

In Cosmic Evolution, the Great Singularity (Big Bang) is usually seen as an instability – a weakness, flaw, or variance — from perfect system equilibrium.

As we discussed just above, the human body is cursed with painful and often debilitating imperfections, while other creatures have evolved mate-attraction structures that are excessive.

Also, the story of evolution is replete with organisms that evolved, lived for a time, and then went extinct. So, while they may have been well-suited for their early environments, they were poorly suited to later conditions.

Almost no crystal found in nature is perfect. Usually, there is a break, a change of direction, a new slant to the crystal’s axis, etc. These are caused by random changes in the crystal’s environment: by a change in the concentration of the mineral solution, in its rate of flow, by some random piece becoming an occlusion.  It’s as if the crystal had a sudden, random mutation which leads it in a new, but still recognizable direction.

Even diamonds – crystallized carbon — almost always contain imperfections. Snowflakes – crystalized water – are usually based on a tiny dust particle, the “seed particle,” around which the snowflake can form. Such a particle is analogous to an “imperfection.”

> The only perfect things we know of are mathematical truths.  While all the circles that have ever been drawn are imperfect, an ideal circle can be precisely defined as “a set of all points on a flat surface that are equidistant from a given (center) point.” However, even in mathematics it turns out no mathematical system can ever completely describe all the truth all the time. For example, if we assume that space itself is curved, as Einstein proved, a completely different geometry is true. (See our Essay, Mathematics Evolves in Nature’s Continuing Creation for a further discussion, including discussion of Kurt Goedel’s Incompleteness Theorem.)

> There is a deep connection between imperfection and change itself. In biological evolution, a species never changes without first having a mutation – a genetic copying error — in the DNA of an individual organism. Usually, a plant or animal with a mutation has a “birth defect” causing it to compete poorly with others of the same species. But sometimes a mutation gives an individual a competitive advantage – e.g., it makes him or her stronger, faster, or more efficient. In those cases, the mutated organism lives to reproduce and pass its gene set down to the next generation. 37

In physics, Quantum Mechanics (Quantum Theory) argues that imperfection is inherent in the fundamental structure of the universe.  If that theory is true, then imperfection is natural. If so, then perhaps imperfection/error in the processes of Nature’s Continuing Creation (such as growth and evolution) are also natural; and maybe even inevitable as Stuart Kauffman has argued.  (For more detail, see our yet-to-be-written Essay on Physics and Continuing Creation.)

In other Essays, we said that the Initial singularity itself was inherently unstable, due to natural quantum fluctuations. Thus, “instability” may be the first principle of Nature’s Creative Evolution.  Instability leads to change — the emergence of differences.

“Physicists have countless examples of natural instability, in which energy is released to power change from simplicity to complexity.  One of the most common is that cooling water vapor below the freezing point produces snowflakes, no two alike and all complex and beautiful’…physicists call these changes “phase transitions” and the “Nobel Prize in 1992 was awarded for understanding the mathematics of their common features.” The Big Bang itself was one of these instabilities.” — John C. Mather 38


Once a self-organizing system is up and running, small perturbations of the system will usually not change it. Once the ants are engaged in nest-building activity, removing a few of them will not change the pattern of the activity. The system is said to exhibit stability, or homeostasis – it has the ability of self-preservation. 39 In humans, belief systems are like that. Once a religion has been adopted and practiced, it is very difficult for a person to change his or her beliefs. 40

On the other hand, when enough countering influences accumulate in the system and a last, sudden triggering event causes the system to undergo a major transformation or phase change… or to collapse altogether.


A surprising characteristic of Edge-of-Chaos complex systems is that they are very unpredictable.  For example, it is impossible to predict the emergence of a cyclone, because the factors involved – temperature, winds, moisture, — are themselves rapidly changing every minute. 41

  • Instability and imperfection in a complex system can easily make the system unpredictable.
  • Feedback Loops can increase systems unpredictability. Positive feedback promotes change, often with exponential speed, allowing local variations to grow into global patterns.
  • On the other hand, negative feedback can dampen out an emerging pattern. Sometimes a large number of interactions may cancel each other out or create so much noise that the emerging pattern or behavior is swamped.

We can Explain Complex Systems, but We Can’t Predict their Outcomes

As P.W. Anderson, the Nobel laureate in physics known for his work in symmetry breaking, superconductivity, and emergence, has written: “The ability to reduce everything to simple fundamental laws does not imply the ability to start from those laws and reconstruct the universe.  At each level of complexity entirely new properties appear. Psychology is not applied biology, nor is biology applied chemistry. We can now see that the whole becomes not merely more, but very different from the sum of its parts.” 42

More Variables Mean Greater Unpredictability

One reason why emergent behavior is hard to predict is that when the number of components in a system increases, the number of combinations of those components increases much faster.  For example, the possible interactions between groups of molecules grows enormously with the number of molecules such that it is impossible for a computer to even list the arrangements for a system as small as 20 molecules.

If we were standing on earth in the age when the only living things were single-celled microbes, and if we knew everything there is to know about the Earth, physics, chemistry, and those microbes, could we predict the evolution of human beings (homo sapiens)?  No, we could not – if the gigantic meteor that wiped out the dinosaurs had not crashed into the Earth, dinosaurs might still be the capstone form of life on Earth.

And given the emergence of dinosaurs, there is nothing in their biology or history that would allow us to predict their extinction; or to predict the subsequent emergence of mammals, including humankind.  The trend toward greater complexity would likely have continued, but in a different (random) direction.  Perhaps the Velociraptors in Michael Crichton’s “Jurassic Park” really would have evolved a brain and intelligence equal to that of humans.

To paraphrase the renowned Harvard biologist E.O. Wilson, “No individual path of evolution of any kind can be predicted, either at the beginning or even toward the end of its trajectory…The possible evolution of a species can be visualized as a journey through a maze”… with every turn sending the species in an unforeseen direction or bottling it up at a dead-end.” 43

Dr. Kauffman’s Analysis of Unpredictability

Dr. Stuart Kauffman, a medical doctor, theoretical biologist, and author of five books on the Science of Complexity, writes that we cannot predict the end result of an edge-of-chaos complex system for at least three reasons, as follows: 44

  1. Quantum Unpredictability”

The first reason is that quantum mechanics ensures a fundamental indeterminism at the sub-atomic level. Since that indeterminism has macroscopic consequences – for example, a random quantum event can cause a mutation in DNA molecules – “we appear to be fundamentally forbidden from deriving detailed specific predictions about all molecular and supra-molecular events.”

  1. The “Butterfly Effect”

Dr. Kaufmann’s second reason comes from edge-of-chaos theory: The Butterfly Effect, i.e., extreme sensitivity to initial conditions. Any tiny change in a chaotic system can have large and amplifying effects. After the small trigger event, the consequences are non-linear. One reason is that energy can be fed back into the system by positive feedback loops. In practical terms, non-linearity means that a small triggering perturbation may cause a large effect. (In linear systems, on the other hand, the effect is always directly proportional to cause.)

An early pioneer of (Near) Chaos Theory was the meteorologist Edward Lorenz who, in 1961, was using a computer to predict weather. By accident, he changed one of the many variables in his model from 0.506127 to a rounded-off 0.506. This difference is tiny and was expected to have had practically no effect. However, Lorenz discovered that this small change in initial conditions produced a very large changes in the long-term outcome. Lorenz’s discovery showed that even detailed atmospheric modeling cannot in general make long-term weather predictions. Weather is usually predictable only about a week ahead. 45

Similarly, A small mutation in just one gene can trigger a major change in evolution. If that change leads to sharper teeth, a more poisonous venom, a greater resistance to disease, better camouflage, or other competitive advantage it could lead to the birth of a new species. Provided, of course, that conditions in the environment (other creatures, foodstuffs, climate) are positioned favorably to the advance of the new species.

  1. Incompressibility

The third reason is because living systems are open-energy complex systems. Like computer programs, once an open-energy system is started, it inevitably moves and changes.  It proceeds to a new form (or forms) different from its beginning configuration. The programs that run on computers are algorithms – a set of steps that leads to a computed answer for a given input.  A proven theorem of the theory of computation says that “There exists no shorter means to predict what an algorithm will do than to fully execute it, observing [the entire] succession of actions and states as they unfold.” 46

Thus, the algorithm, the steps of the system, are said to be incompressible. So, the shortest way to definitively model the birth of an actual hurricane can only be to replay the entire life of that particular hurricane, including all the flapping butterfly wings that helped cause it, and this could never be possible. 47

Information Can Live Longer than Things

In non-living systems, like crystals, matter and information are wedded together. The hexagonal shape of a crystal closely derives from the template of the atoms or molecules that compose it.

Over the centuries, however, information has become increasingly abstracted from matter. Money, as we saw, evolved from gold coins to computer blips. Our minds, along with the switches and computers created by them, are able to process information as information. The medium becomes secondary:  A folk tale can reside equally well in a mind, an oral tradition, a book, a movie, or a webpage.

In another example from economics, as civilization progresses, “Land becomes territory. When granted to citizens, territory becomes property that is owned.  Property can be represented by a deed, and the deed can be mortgaged. The mortgage can be bought, then itself becomes an investment.” 48

A building may last only a few hundred years, but the blueprints for that building can last for thousands of years, first in paper form, and then as digital images in a computer memory.  When the computer wears out, the design of the building can be passed to a newer computer.  In this way, technology and culture can far outlive the people who created it.

Creative Destruction

In the physical world of matter – of things — there is often no change without total or partial destruction. This is true even for rocks; even for geography.  A plain must be destroyed in order for a canyon to be formed. A tree must die in order for new plants and insects to grow from its nutrients. When hydrogen joins oxygen to form water, they both lose their characteristics as gases at Earth-surface temperature and pressure. This general process is called creative destruction.

In the world of information, however, new things can be created without destroying the old. Algebra can be created without the destruction of geometry. (In fact, they complement each other – many mathematical truths can be described and even proven using either one of them.)

In systems involving both physical structure and information, both construction and destruction can happen together. When an individual joins a tribe, she loses some of her individuality and independence.  On the other hand, membership in the group can leverage and expand that individual’s powers. She might, for example, become the medicine-woman of the tribe.  Even lowly hydrogen, when it combines with oxygen to form water, can become the biological basis for all of life.

Can the Properties of Water Be Predicted?

Hurricanes can be explained, but they can’t be predicted. How about the emergent qualities of water?  For a long time, it was thought that even if we knew everything there is to know about hydrogen and oxygen, we could not predict the emergent properties of water. Today, the picture is less clearly defined.

If we were to know everything there is to know about oxygen (O) and hydrogen (H), could we predict the other properties of water (H2O) Its liquidity? Its transparency? Its ability to dissolve things? Its surface-tension?  According to chemistry professor Pier Luigi Luisi, the answer is that yes, we could predict those things, but science does not yet have the knowledge to predict all of them. 49 (For a more detailed treatment of this topic, see APPENDIX B at the end of this Essay.)

Our Human Role as Observer…  and Participant

We also know that the full animal experience of water’s liquidity depends on the senses and mind of water’s observer.  Mammalian bodies, including humans, can move through water, drink water, and likely see that it is colorless. But some animals do not drink water – they absorb it. Animals who are blind cannot see that water is clear, nor that is it transparent. Humans cannot smell water, but perhaps other creatures can. So, many emergent qualities of water depend on what sensory equipment the observer brings to the arena.

The Whole is Still More than the Sum of Its Parts  

Most importantly for Participants in Nature’s Continuing Creation – Whether we can or cannot predict things like the liquidity and transparency of water, the whole is still different than its parts, and still more than the sum of Its parts. Water is still utterly different than either the oxygen or hydrogen that compose it. The Practice of Nature’s Continuing Creation says: If we were to know everything there is to know about O and H, and we also had fully known and experienced water itself, could we then predict that it would become the medium for life on Earth?  Would we foresee that it will react with many chemicals and will also dissolve many things easily and carry them from place to place when the water is pumped by a heart?  Perhaps — but this prediction would not be so easy for intelligent creatures or intelligent machines who have no blood and hearts of their own. 

    • Even if an emergent phenomenon can be fully explained by scientific knowledge of the properties and interactions of its parts, the emergent phenomenon itself is still very real.                Water’s liquidity is very real.
    • While the beautiful patterns made by flocks of flying birds can be explained by the behaviors of the individual birds, the patterns of the flock are still very real, and                                    different-looking from the flight on one bird.
    • Every year we learn more about how individual ants interact to create a colony – but the colony itself is still real, still different from its component parts, and in important ways                        very different than the ants that make it up.


APPENDIX A — More About Graphite and Diamonds

In the mineral and chemical worlds, we can often fully and logically explain how the characteristics of a substance’s atoms produce the structure of the chemical or mineral.

Information can be created by the mere positioning of the atoms in a single element.  The element Carbon is a prime example.  Pure Carbon naturally occurs as amorphous carbon, graphite, or diamond, depending on how the individual carbon atoms are positioned and linked.  These various forms are called allotropes of carbon.  A new man-made allotrope is the carbon nanotube.

In graphite (the main ingredient of pencil “lead”), the carbon atoms are joined in flat layers one-atom thick.  These layers easily slide across each other under light pressure. Graphite is used to make pencil lead because its layers rub off and leave a mark when a pencil is moved across a piece of paper.  (A similar “sliding quality” makes water wet and liquid.)

In a diamond, the carbon atoms are joined together on all sides (in a face-centered cubic crystal) by enormous pressure and temperatures inside the Earth, making the Diamond the hardest natural element on Earth.

Carbon atoms arranged one way are called graphite.  Arranged another way – they are called diamonds.  But it’s the same stuff!  Only the arrangement of the carbon atoms – only their pattern is different.

Looking at the 2 patterns, could we predict that one is dull, soft and black, while the other is supremely hard and utterly transparent?   Yes, we can.  Diamond and graphite are both made up of carbon atoms, except they have different physical form and properties, due to the nature of bonds formed between the carbon atoms.  Diamonds are the hardest natural substance in the world, while graphite, the key component of pencils, is soft and easy to crumble.

In the most prevalent form of carbon, there are 6 protons and 6 neutrons in the nucleus.  The 6 positive protons are balanced by a total of 6 negative electrons — 2 orbiting in the first (inner) shell, and 4 orbiting in the second (outer) shell.

Carbon atoms in graphite are bonded in layers with only weak covalent bonds holding the layers together. When we write with a pencil some of the layers detach from the pencil lead and attach to the paper.  Also, one of the four electrons in a graphite atom is weakly bound to all the three neighboring carbon atoms, and is free to move around, giving graphite its electric conductivity.  Each layer of graphite is quite strong, but as a whole the substance is not.

But the outer shell of all carbon atoms can hold as many as eight electrons.  One way this can happens is if two adjacent carbon atoms share two electrons – one from each atom.  The shared electrons take turns cycling around each of the two nuclei.  This sharing pulls the two atoms very close together – it sort of “welds” them tightly together.  When millions of adjacent carbon atoms all do this with all of their adjacent partners – the carbon takes the form of a diamond.

Carbon atoms in diamond are bonded in a stronger three-dimensional tetrahedron pattern – there are no layers.  The crystal structure ensures that diamond is brittle with very sharply defined cleavage planes.  The nearness of the adjacent carbon atoms in the tetrahedron, along with the covalent bonds between them (i.e., they share their electrons) gives the diamond its tremendous strength.  (See

The carbon allotropes display a very wide range of extremes characteristics, all of which increase the total amount of Information existing in our world.

Graphite is one of the softest materials known.Synthetic nanocrystalline diamond is the hardest material known.
Graphite is a very good lubricant, displaying superlubricity.Diamond is the ultimate abrasive.
Graphite is a conductor of electricity.Diamond is an excellent electrical insulator, and has the highest breakdown electric field of any known material.
Some forms of graphite are used for thermal insulation (i.e. firebreaks and heat shields), but some other forms are good thermal conductors.Diamond is the best known naturally occurring thermal conductor
Graphite is opaque.Diamond is highly transparent.
Graphite crystallizes in the hexagonal system.Diamond crystallizes in the cubic system.
Amorphous carbon is completely isotropic.Carbon nanotubes are among the most anisotropic materials known.

Note: The above Graphite versus Diamond Table is from, accessed 7-24-18, along with the following sources:

  • Irifune, Tetsuo; Kurio, Ayako; Sakamoto, Shizue; Inoue, Toru; Sumiya, Hitoshi (2003). “Materials: Ultrahard polycrystalline diamond from graphite”. Nature. 421 (6923): 599–600. Bibcode:2003Natur.421..599I. doi:10.1038/421599b. PMID 12571587.
  • Dienwiebel, Martin; Verhoeven, Gertjan; Pradeep, Namboodiri; Frenken, Joost; Heimberg, Jennifer; Zandbergen, Henny (2004). “Superlubricity of Graphite” (PDF). Physical Review Letters. 92 (12). Bibcode:2004PhRvL..92l6101D. doi:10.1103/PhysRevLett.92.126101. Archived (PDF) from the original on 2011-09-17.
  • Deprez, N.; McLachan, D. S. (1988). “The analysis of the electrical conductivity of graphite conductivity of graphite powders during compaction”. Journal of Physics D: Applied Physics. Institute of Physics. 21 (1): 101–107. Bibcode:1988JPhD…21..101D. doi:10.1088/0022-3727/21/1/015.
  • Collins, A. T. (1993). “The Optical and Electronic Properties of Semiconducting Diamond”. Philosophical Transactions of the Royal Society A. 342 (1664): 233–244. Bibcode:1993RSPTA.342..233C. doi:10.1098/rsta.1993.0017.
  • Delhaes, P. (2001). Graphite and Precursors. CRC Press. ISBN 90-5699-228-7.
  • Unwin, Peter. “Fullerenes (An Overview)”. Archived from the original on 2007-12-01. Retrieved 2007-12-08.


APPENDIX B – More About the Qualities of Water:  Can We Predict Them?

Hurricanes can be explained, but they can’t be predicted. How about the emergent qualities of water?  For a long time, it was thought that even if we knew everything there is to know about hydrogen and oxygen, we could not predict the emergent properties of water. Today, the picture is less clearly defined.

We now seem to be able to explain why water is a liquid at room temperature at the surface pressure of the Earth:  Water gets a lot of properties from the position (pattern again) of the H’s relative to the O’s.  The two H’s (Hydrogen atoms) are where the ears would be on the single “O” (oxygen atom) of Mickey Mouse’s face. So, the positive H’s are on the upper side of “Mickey’s head,” leaving the lower part of the face to be negative.

In water, the H’s and O’s are joined to each other by strong covalent bonds, i.e., the H and the O share their electrons.  Each water molecule is therefore dipolar – it can attract negative molecules toward the top of its face, and positive molecules toward the bottom of its face.  This makes all water molecules very attracted to each other, and each one can attract four others.

Once assembled, each water molecule wants to stay assembled. But the bonds between the water molecules are not covalent – they are weak and can only hold for fractions of a second.  Once the bond breaks, the polarity of the molecule makes it spin and tumble about until it finds an adjacent water molecule to join once again.

This serial and momentary holding makes the water a liquid. It is this combination of attraction, brief bonding, release, spin, and brief bonding again and again that makes water a liquid and not a solid – the molecules are constantly connecting and disconnecting, tumbling and “flowing” around each other.  If there were no H-bonds at all between the water molecules, they would fly around as steam, which is water in gaseous form. (A similar weak bonding makes graphite molecules slide off each other, enabling us to write on paper with graphite (“lead”) pencils. (See Appendix A to this Essay for more about graphite and its cousins, diamonds.)

But wait a minute. We have explained why water is a liquid (at standard temperature and pressure), but would a scientist who has never experienced water be able to predict it?

Maybe not, because one might well expect water to be a gas at room temperature and pressure due to its low molecular weight!

In fact, both Oxygen O2 and Nitrogen N2 have higher molecular weights (masses) than water, and these are gases at room temperature.

If we look at the hydrocarbon series, methane is lighter than water, while ethane, propane and butane molecules are all larger and heavier than water molecules; but all of them are gasses at room temperature. More amazing still is that H2S (hydrogen sulfide) which is very much heavier than water, yet H2S is a gas at room temperature.

If we were to know everything there is to know about O and H, could we predict the other properties of water? Its liquidity? Its transparency? Its ability to dissolve things? Its surface-tension?  The answer is that yes, we could predict those things, but according to Pier Luigi Luisi 50 science does not yet have the knowledge to do that.

If we were to know everything there is to know about O and H, could we predict that water would become the basis, the chemical medium, for life on Earth?  Maybe – because water can dissolve, and therefore transport – so many things in its flow. But given that, could we even begin to visualize all the varied and weird plants and animals which water becomes part of?   No, we could not.

(For more detail, see

“If we were to know everything there is to know about Oxygen and Hydrogen, and we also had fully known and experienced water itself, could we then predict that water would become the medium for life on Earth? Would we foresee that it will react with many chemicals and will also dissolve many things easily and carry them from place to place when the water is pumped by a heart?  Perhaps… but such a prediction would not be so easy for intelligent creatures or intelligent machines who have no blood and hearts of their own, nor any history of them in their pasts.”
— J.X. Mason

  1. Steven Johnson, Emergence: The Connected Lives of Ants, Brains, Cities, and Software, 2001, Scribner, pp. 11-23.
  2. Steven Johnson, Ibid., pp. 11-17.
  3. Steven Johnson, Ibid., 17-21.
  4. See
  5. Posted April 2004
  6. Robert M. Hazen, The Story of Earth: The First 4.5 Billion Years, from Stardust to Living Planet, 2012, Penguin Books, pp. 140-1. See also Donald E. Ingber, “The Origin of Cellular Life,” BioEssays 22.1160, 2000, John Wiley & Sons.
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  12. Stuart Kauffman, At Home in the Universe: The Search for the Laws of Self-organization and Complexity, 1995, Oxford University Press, pp. 71-92.
  13. Stuart Kauffman, Ibid., p. 8.
  14. Stuart Kauffman, Ibid., p. 199-201.
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  33. Benoit B. Mandelbrot, 5 May, 1967. “How Long Is the Coast of Britain? Statistical Self-similarity and Fractional Dimension,” Science, New Series. 156 (3775), pp, 636–638.
  34. James Gleick, Chaos: Making a New Science,1987, Viking, p. 101.
  35. Richard Dawkins, The Blind Watchmaker: Why the Evidence of Evolution Reveals a Universe Without Design, 1986, W.W. Norton, p. 92.
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  38. John C. Mather, “Cosmic Complexity,” in This Explains Everything, John Brockman editor, 2013, Harper Collins, pp. 239-41.
  39. Simon A. Levin, “Ecosystems and the Biosphere as Complex Adaptive Systems,” Ecosystems, May 1998.
  40. William James, The Varieties of Religious Experience, Lectures at the University of Edinburgh, 1901 and 1902. Available online in PDF format:
  41. James Gleick, Ibid,, pp 44, 253, 258, 261.
  42. P.W. Anderson, “More is Different: Broken Symmetry and the Nature of the Hierarchical Structure of Science”, 1972, Science, 177 (4047): pp. 393–96.
  43. E.O. Wilson, The Social Conquest of Earth, 2012, Liveright Publishing, pp. 21-22.
  44. Stuart Kauffman, At Home in the Universe: The Search for the Laws of Self-Organization and Complexity, 1995, Oxford University Press, pp. 17-23.
  45. Edward N. Lorenz, “Deterministic Nonperiodic Flow,” Journal of the Atmospheric Sciences, March 1963. 20 (2): pp. 130–141.
  46. Stuart Kauffman, Ibid., p. 22.
  47. Brian Eno, “The Limits of Intuition”, in This Explains Everything, John Brockman, editor, 2013, Harper Collins, pp. 210-11.
  48. Douglas Rushkoff, “The Precession of the Simulacra,” in This Explains Everything, John Brockman, Editor, 2013, Harper Collins, p. 315.
  49. Pier Luigi Luisi, “Emergence in Chemistry: Chemistry as the Embodiment of Emergence,” Foundations of Chemistry, 4:183-200, 2002. Accessed online by searching for “Why is water liquid.”
  50. Pier Luigi Luisi, “Emergence in Chemistry: Chemistry as the Embodiment of Emergence,” Foundations of Chemistry 4:183-200, 2002.

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