Sample Chapter

    Chapter 22



In Chapter 16 (The Principles of Creation), I introduced the term self-organization. This is an intrinsically mysterious process and it is easy to imagine how one might interpret self-organization as somewhat magical or perhaps even impossible. At first glance, it just doesn’t seem possible that an unconscious process could organize itself into complex systems. However, there are ways of thinking about self-organization that remove some of the mystery, and allows us to imagine how it could happen. The complexity in nature emerges from the accumulation of processes that obey local and simple rules. I will use the two terms local and simple interchangeably in order to best describe ways that nature self-organizes.

First let us not make the mistake of assuming that self-organization is a neat and flawless process. The term organization can give the impression of alignments and sequences that are precise and completely orderly. This is the organization we see when we open a new deck of cards, with all the suits and numbers in alignment, or an army of soldiers marching in unison. These examples are by design—this is the idea of organization I want to dispel. Nature dose not organize itself in the same manner.

Let’s begin with biological evolution, because it is the foundation for most of the organization we see in the living world. And also some of the same principles can be applied elsewhere. I have covered evolution earlier in the book so I will not go into great detail here, but instead, I will focus on only a few areas. Evolution by natural selection is a process that generally moves in a direction of greater complexity, where trial and error and enormous amounts of time are involved. Even though the end result is complex, the process is guided by simple rules. For example, one such rule is that nature selects species that are more successful at surviving and reproducing. In addition, the fact that there is no blueprint—no final goal that has to be realized—there are vast possible configurations or outcomes that could be considered organized. We could be presently living on a planet with completely different species and landscapes and it could still appear organized.

About 3.8 billion years ago simple life emerged on earth. We can only speculate how this happened, and what the environment was like at the time. Nevertheless, for life to self-organize and evolve, some life forms had to adapt to their local environments long enough to allow natural selection to work. Environments refer to a wide range of surroundings. For fish the environment is an ocean, river or lake; for land-dwelling animals it is the local landscape. And if we break it down to the microscopic level, for cells the environment can be inside an organism, and for molecules a cell can be its environment. The rules for fish are different from the rules for mammals or cells because their environments are different. Each component of life does its own thing blindly obeying local rules. As a consequence of local rules being repeated over and over again an overall organization appears.

Now, here is an important factor to consider: 3.8 billion years is a vast amount of time. The life we observe today—as organized as it may appear—has an untidy history. Nature does not organize itself like we might organize our filing cabinet. 3.8 billion years leaves a lot of room for trial and error; an unconscious process needs plenty of wiggle room. How much time is 3.8 billion years?  It would take over 100 years to count that high. Let’s say we could count one number every second, each day the total count would represent 86,400 years. That’s 86,400 X 365 X 100, more than enough years to sort things out.

Have you ever wondered why we have bodies that work most of the time, if we are lucky? Bodies with brains, hearts, lungs, arms and legs work in unison, and most of the processes are unconscious. All this is inherited from other creatures that have tested different body parts at different times in our evolutionary history. Successful arrangements of body parts are passed on to future generations and failed arrangements are discarded. Evolutionary self-organization allows for a huge failure rate—failures meaning discarded genes, as bodies that carry them are unable to survive and reproduce in their local environments. In bodies that work (survive and reproduce) the genes survive in the next generation. The bodies are then tested again and again with each ensuing generation. Our inherited bodies have survived test after test. That is why they work. Of course we shouldn’t perceive self-organization as a flawless process, because our bodies do fail us at times. However, when one considers all that can go wrong, our bodies are astoundingly efficient.

We can’t directly observe evolution (except for microbes such as viruses and bacteria), but we can observe the astonishing ways that some of nature’s creatures self-organize. Ants, bees and migratory birds come to mind. How is possible that without a plan that these creatures work together for what is seemingly a common goal? Presumably the traits necessary for their survival have been selected over evolutionary time, but I’ll leave that behind for now. If you have ever had the privilege of observing birds gathering in the fall for their long journey south, it is rather mesmerizing. As they move about they form patterns, but the patterns are constantly changing. These patterns are surely unplanned and merely a consequence of each bird following simple rules. Each bird stays in close contact, but at a safe distance from neighboring birds. The simple rule is, stay close to other birds, but keep a safe distance to avoid a collision. As a result of many birds following simple rules, complex patterns emerge.

Some patterns of self-organized systems comprise both living and inanimate structures. One such pattern is the fractal. The term was coined by Benoit Mandelbrot in 1975. Mandelbrot is largely responsible for advancing and popularizing fractal geometry. A fractal is a mathematical framework representing the shapes of nature. A fractal is an irregular geometric shape that is repeated in smaller and smaller shapes; each of which resembles the whole. Examples of fractals are the shapes of coastlines, mountain ranges, trees, rivers and their tributaries. These shapes are also present inside the human body in the form of blood vessels and the structure of our lungs. A fractal is just the kind of pattern one would expect to self-organize. It is a rough geometric shape that is repeated, however, it is not precise in the sense that there is no exact outcome that has to be achieved.

Patterns that appear in nature are not bound by precision; they are flexible in form and appearance. Take, for example, ocean waves and the patterns they form. Each wave arises and follows a predictable pattern to the shore. However, depending on the tides, ocean currents, wind speed and direction, the waves continuously vary. Sand dunes and snow banks also self-organize into patterns similar to ocean waves. The wind shapes the fine particles into banks. The patterns of the banks are an unconscious consequence of the wind, allowing for vast possible configurations. Ocean waves, sand dunes and snow banks self-organize by obeying simple rules (tides, wind speeds and direction…) and by not being bound by any precise outcome.

There are few (if any) perfectly symmetrical shapes or straight lines in nature. The only straight line that I can think of in nature is the horizon of the ocean. And in actuality it is curved, but it appears straight to an observer. Everything we look at, whether it appears organized or not, is actually irregular in shape, even if it appears regular. The entire planet is comprised of diverse landscapes, such as oceans, deserts, forests, prairies and mountain ranges. There is no blueprint for how our planet should be, which is what you would expect to find as a result of self-organizing systems. This principle also applies to solar systems and galaxies. Contrary to the precision that most people assume exists in outer space, there is a huge amount of freedom in the heavens. Galaxies are different from each other, ranging both in the number of stars and in the shapes that galaxies take. The configurations of solar systems also vary widely. Some stars have no planets orbiting them, while other stars have planets of various composition, location and size. Each solar system and galaxy is unique. Again there is no blueprint for how a solar system or a galaxy should be. Also, there are vast regions in space, though containing matter, that have not organized into solar systems and galaxies.

This brings me to an important point. For the most part people like order, so it is easy to find. I am not suggesting that we see order where it isn’t—it’s there. However, we tend to overlook the disorder which is every bit as present. For nature to self-organize it requires room for error, which one could call disorder. For order to emerge from an unconscious process, a certain amount of disorder is guaranteed. Both order and disorder are essentially a result of the same process. It is easy to imagine how disorder could exist without order, but I can’t formulate an idea for how order could come about without disorder as a byproduct. Or maybe order is a byproduct of disorder—it all depends how you look at it. Perhaps we should keep these thoughts in mind as we try to organize our lives. A continual state of order is most likely impossible to achieve, so it’s okay to let things go from time to time.

Perhaps the most mysterious part of nature is that its essence is an unconscious process. It’s easy to fall into the trap of believing that it takes a conscious act to create something constructive. We are conscious beings, and thus we tend to overrate consciousness and overlook unconsciousness. In all of nature, consciousness is only a tiny fraction of the process—the tip of the iceberg. We only need to reflect on our own bodies to appreciate this fact. We are able to make decisions and use our bodies in conscious ways. The unconscious part, however, is extensively more complex and influential to our overall well-being. Trillions of cells self-organize into all the components that make up you and me. Each day of our lives, it is the unconscious processes that keeps us going, and for the most part we take it for granted.

Now let’s get down to the nuts and bolts of self-organization—the atom. Everything we see, touch and experience is composed of elementary matter: particles that managed to self-organize, giving the world its structure. How did this happen? This is most likely impossible to answer in totality, but it may be understandable in principle. Organized matter did not just magically appear. In the early universe the temperature was too hot for atoms to form. Electrons moved about freely for roughly the first 400,000 years until the universe cooled sufficiently for electrons to join atomic nuclei. However, the simplest elements did appear a few minutes after the big bang (absent of electrons). The simple light elements (hydrogen, helium, and lithium) appeared first, and were later followed by the heavier more complex elements via stars. It is interesting to note that the origins of matter followed a progression where the atoms increased in complexity over the passage of time. And that is just what you would expect to happen in a self-organizing system. How else can a complex system be built, other than step by step?

The patterns and order that we see in nature emerge from diverse local environments, which obey their own set of simple rules. Similar to fractals, where intricate forms are made up of simple shapes that are repeated, the whole appears to be greater than the sum of its parts. When nature is broken down into finer ingredients, the functioning of the parts can be somewhat understood with relatively simple explanations, as compared to trying to understand the whole picture. Although self-organization is still a mysterious process, if we closely observe nature, we see it happen over and over again. The fact that matter managed to organize into stars, planets and galaxies—and even more remarkable, life—is one of the most astounding facts anyone can ever contemplate. However, the simple fact that I am here and writing about it, means that it did.


One response to “Sample Chapter

  1. prof dr mircea orasanu

    these are very important and essential for simple chapter of mathematics supposed prof dr mircea orasanu and prof drd horia orasanu and followed that must to present to the history of hyperbolic geometry. Euclid, Gauss, Felix Klein and Henri Poincare all made major contribution to the field. We will discuss some of their influences in the following sections, starting with Euclid and his postulates that defined geometry. Then we will look at the effect of Gauss’s thoughts on Euclid’s parallel postulate through noneuclidean geometry. Later, Klein settled any doubt of noneuclidean consistency. Lastly, Poincare makes some notable contributions to solidifying hyperbolic geometry as an area of academic study.This essay is an introduction Euclid’s Postulates
    Euclidean geometry came from Euclid’s five postulates. It is the most intuitive geometry in that it is the way humans naturally think about the world. Nonetheless, there are a few other lesser-known, but equally important, geometries that also have many applications in the world and the universe. These “other” geometries come from Euclid’s fifth postulate: “If a straight line falling on two straight lines makes the interior angles on the same side less than two right angles the two straight lines if produced indefinitely meet on that side on which the angles [are] less than two right angles” [6]. See Figure 1(A) below for an illustration of this. An equivalent way to express this is that the angle sum of a triangle is two right angles.


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