Patterns, Cycles, and Shapes

It might be strange at first to think of patterns, cycles, and shapes as hidden realities. After all, it is the human ability to detect patterns that helped organize human consciousness itself, it was the human perception of the cyclical passing of the seasons, the stars, and the moon that helped humans get their first real knowledge of how the world worked, and shapes are a pervasive feature of the human visual experience. But there are patterns too subtle for humans to perceive, or rather, there are patterns that elude us because many times they hide in plain sight. There are cycles that are too long in duration, or too geographically spread out for us to perceive, or which manifest themselves in ways not readily observable, or which are parts of reality not fully understood.  And there are shapes which hide worlds of functionality. Emerging from the basic physical, chemical, and/or biological laws, and even sometimes from human social and cultural reality, they are the unseen processes that unfold all around us, sometimes shaping us in definable ways, sometimes acting far beyond the scope of our limited lives.

Perceptible Patterns and Cycles

We need to start with the visible patterns and cycles of human life. The term pattern connotes two elements: repetition and consistency. A repeated series of shapes is suggestive to a human brain, as is a repeated series of events taking place in rapid succession. A single event in itself may be meaningless. The same kind of event, occurring in a number of different places within a relatively brief time, suggests a pattern. The consistent appearance of a particular kind of object under well-defined circumstances is instructive to a human brain, as is a consistent series of sounds or any other sensory information. In other words, in a human brain, the message from such phenomena is “This signal always means this; this object always does this; this thing always looks like this.” (It is the characteristic repetition of sounds and their consistent association with meaning that may be the basis of spoken language.) Individual visual elements that in isolation would suggest nothing can, when associated with other individual elements in the proper manner, help a pattern emerge.

Humans, even before they were aware of it, noted patterns in the natural world, such as the tendency of certain objects to present, assume, or suggest certain shapes or to arrange themselves in characteristic ways. There are patterns in the shapes of trees and other foliage, for example, such as the patterns apparent in the number of a flower’s petals or the spirals at the heart of flowers. (Strikingly enough, these floral characteristics often follow a mathematically discernible pattern known as a sequence of Fibonacci Numbers.) There are typical appearances of other natural phenomena, and it was the noting of these patterns of appearance that may have initiated the skill of categorization in humans. (See The Mathematical Mind in a subsequent volume.) Our ancestors found that animals in the wild seemed to behave in distinct patterns, exhibiting behaviors predictable enough that their human predators could track and kill them efficiently. Humans found an understanding of the characteristic patterns of behavior in domesticated animals to be absolutely necessary as well. Humans noted patterns of stars in the night sky, and it was from these patterns that the constellations were derived (although the members of different cultures discerned different objects in these starry patterns).

Patterns, therefore, form a major part of our reality. Patterns of weather in a given region over a calendar year comprise the region’s climate. Patterns of behavior and responses to external stimuli help define and shape a human personality. Patterns of human interaction form a society. Certain patterns or arrangements of shapes appeal to human aesthetic sensibilities. And, interestingly, humans often discern patterns in nature or on objects where none actually exist, a phenomenon known as pareidolia. (See Brain Tricks in Volume Two.)  Humans can also see false patterns in the behavior of others, assuming that events seemingly form a pattern, when in fact they do no such thing.

A cycle may be thought of as a pattern writ large, a sequence of events that manifest themselves over large periods of time and areas of space, a series of patterns that merge into larger, longer, and more dynamic entities. That last element, dynamism, is important in the understanding of cycles, because cycles don’t just sit there looking a certain way or doing certain things in isolation—they involve action and interaction, and many different cycles can be at work in a given environment. Moreover, cycles can be traced to an identifiable initial state (however arbitrarily the term “initial state” is defined) that is arrived at again and again in the life of the cycle itself. For humans, the most obvious cyclical event is the passing of the days, the endless succession of day and night (except in the far northern or far southern extremes of the world at or near the summer and winter solstices).  It is this procession of days that makes up the most common means by which humans measure and assess their experience.

Human societies progressively organized series of days into weeks and months. The cycles of the Moon were used initially to measure time. The Babylonians and the ancient Greeks, among others, tried to calculate the year through the lunar cycle, but found it necessary to occasionally insert months into the year to keep the dates of the onset of the seasons reasonably consistent. (Jewish, Christian, and Muslim religious calendars are still deeply affected by the cycles of the Moon.)¹ As skill in calendar making grew in various human cultures, it was understood that every 365 days or so the Sun and the stars would be in the same position they had been in at the start of their cycle of movement. (It would take some time before it was ascertained that the true year was closer to 365¼ days, and even longer to determine the exact solar year.)  We now know that the Earth orbits the Sun at a speed of 29.78 kilometers per second, or an average of 939,800,765 kilometers per year (leap years excepted), a huge cycle of which all of us are a part.² It was a surprise, as we have seen, when it was ascertained that the year was indeed the story of our planet’s journey—not the Sun’s.

Days, weeks, months, and years measured the passage of time, and with it the cycle of human birth, growth, maturation, aging, and death, the most intimately important of human cycles. The seasons, manifested by obvious changes in the weather in the temperate and continental climate zones of the Earth and less obvious ones in the tropical and polar regions, were an obvious way in which the year could be subdivided. Seasons could be marked by significant shifts in weather, such as pronounced changes in temperature, or the coming and going of precipitation (often in the form of torrential rain). Seasons were also marked in many areas by the migrations of animals or their characteristic breeding periods. Changes in plant life were often observed, and this, as we will see later in this work, had significant consequences in certain regions. (See The Plant World and Religion and Its Origins in subsequent volumes.) 

Patterns and Cycles Not Readily Seen or Comprehended

Patterns, as we noted earlier, are a fundamental element of self-organization and complexity. The build up of simple patterns makes a complex phenomenon. Seen in one way, physical reality is simply a series of simple patterns (both in structure and repetitive behavior) overlaid one on the other, interconnected and interacting, building up sufficient complexity to allow higher levels of organization to emerge. This process is so pervasive that most people don’t see it, until it’s pointed out to them that things seem to be working this way. Into this process natural selection insinuated an ever-growing consciousness, the possessors of which deal with the process’s consequences, attempt to comprehend the workings of the process itself, and try, with uneven success, to direct and manipulate the process.

The subatomic world organizes patterns of activity, such as electron exchange, into the atoms and molecules from which the macroscopic world arises. Much of this activity forms rough patterns. The idea of a rough pattern or cycle is important. Events in a pattern or cycle fall into a range of possibilities, which play out in varying ways as the pattern manifests itself or the cycle unfolds.

As we saw in our examination of self-organization, there are objects that accumulate or interact with each other in such a way as to form patterns which bring order out of chaos. Pattern formation seems to be a fundamental feature of the Universe, one so common and operating at such a diversity of spatial and temporal levels that it is often overlooked. All around us, in a process largely unseen until its results are too big to ignore, patterns of energy-matter are self-organizing to create innumerable physical structures—sand dunes, river deltas, glaciers, clouds, and all the other structures that define the features of the non-human world.

Additionally, all around us in the physical world, elements and molecules are continuously circulating through various reservoirs (the Earth itself, living things, the ocean and other bodies of water, the atmosphere), being utilized in a variety of ways, and taking various forms, in cycles that intersect and interconnect with each other to form an overarching system that encompasses the entire world. Key among these are…

The Biogeochemical Cycles

All of the same elements out of which living bodies are composed cycle and recycle between the world of the living and the world of the non-living.  The nitrogen cycle circulates nitrogen through various organisms and organic matter, and is particularly important for plant life. Plants can only use nitrogen in solid forms, despite the huge amount of nitrogen in the atmosphere. The oxygen cycle moves oxygen between and within the atmosphere, biosphere, and lithosphere (the Earth’s crust). Photosynthesis is the chief (but not exclusive) source of oxygen on this planet. The oxygen cycle is closely related to the carbon cycle, inasmuch as the carbon dioxide emitted from animals is used in the photosynthetic processes of plants. Carbon is the crucial element in living things since it links with other atoms so readily. (See page 87.) Carbon is found in both living and dead organisms; its decay in dead organisms, from ¹⁴C to ¹⁴N, is one of the most reliable radioactive “clocks” we possess. In the biosphere, therefore, carbon is part of organic molecules. It is found in the atmosphere, although comprising a relatively small percentage of the atmosphere’s composition. In the lithosphere it is found in fossil fuels and other minerals. In the hydrosphere, it is found in the shells of marine animals and as dissolved atmospheric carbon dioxide. The other major biogeochemical cycles are the phosphorus cycle and the sulphur cycle. The intimately related nutrient cycle encompasses the actions of the water, carbon, nitrogen, potassium, and phosphate cycles in more specialized processes to maintain life on the planet.  

The hydrological cycle circulates water through all the systems that interact on the Earth’s outer crust, through evaporation, precipitation, and run-off. Water is continuously being circulated through the atmosphere, drawing from the world’s bodies of liquid water, deposited once more as rain (doing so in certain areas of the world in a predictable seasonal form known as the monsoon), snow, sleet, or hail in patterns across the Earth’s surface, and channeled in countless ways, from the tiniest rivulets to the longest rivers. As we have seen, all the biogeochemical cycles are interconnected with it.

The cycles of nature demonstrate, in one sense, the transitory nature of form and the changeable character of being itself. The same atom can be a part of several different entities in succession, assuming different roles, a part of several different combinations, transiting between the worlds of life and non-life. We are composed of such stuff ourselves, and our deaths simply release the elements out of which are composed back into the non-human world, a process we ludicrously try to avoid through such practices as embalming.

Other Significant, Largely Unobserved Cycles and Patterns

The Sun (and with it, of course, the whole solar system) actually orbits around the center of the Milky Way Galaxy. It takes the Sun between about 200 million to about 226 million years to make one orbit (according to different sources), and in the course of the Sun’s existence, it is somewhere between its 21^st to 23^rd orbit. This is the greatest cycle of which we have become aware, although there are some cosmologists who are convinced that the Universe itself is created, exists, dies, and is created anew over and over in an endless cycle.

The Earth seems to be going through a 100,000 year climate cycle affected by variances in the Sun’s magnetic activity. Other cycles of solar activity appear to be implicated in the Earth’s climate. (See The Atmosphere; The Variations of Climate in a later volume.) Monitoring the Sun’s sunspot activity has become increasingly important as human communications technology has grown more electronics-dependent.

On our home planet, currents circulate through the entire world ocean in long cycles, rising and falling, varying in temperature, salinity, and volume, profoundly affecting the world’s climate, influencing the entire hydrological cycle, and interacting with the biogeochemical cycles in a constant fashion. Human mariners ignore the power of ocean currents at their peril. Patterns of the wind, driven by the Sun and interacting with the Earth’s surface, form an invisible yet detectable feature of everyday life. The fact of the wind is obvious; the cause of the wind is much less so, and has taken centuries of effort to elucidate. Humans have only recently begun to understand that the local winds they experience are part of a larger, integrated whole. And the tides rise and fall, under the influence of both the Moon and the Sun, in a cyclical pattern, a phenomenon suspected in the pre-Common Era and confirmed by modern astronomy.

The anatomy and physiology of the human body reflect a long evolutionary inheritance, across both time and space, in which patterns of organization, evident in the systems that comprise a human body, and the structures of the organs within those systems (such as the substructures of the brain) act in conjunction with repeated patterns of activity and energy exchange (such as respiration and metabolism) to keep a human alive (for a while, at least). Patterns of neuronal interaction in a human brain form a consciousness. The patterns and cycles within sleep are yet another example of the influence of certain regular actions on the human experience. In the human body, blood courses through us in a continuous cycle. Oxygen and carbon dioxide are exchanged in a constant cycle. Our bodies tear themselves down cell-by-cell, the different systems doing this with different frequencies and over different durations, (sometimes depending on the need to make repairs in a given organ), most often in a cyclical way. Most of these processes were not known or understood until recently. 

The routine so often required in ordinary life is a pattern, one that affects all other activities in a human life. Although there are individual variations in these routines—after all, humans are not robotic—there are enough consistencies in them that we can say that a rough pattern, a cycle of behavior, has been established. Individuals often develop many rough behavioral patterns in their internal lives as well, often exhibiting remarkable consistency in their private thoughts and actions.

Non-human animals often arrange themselves in herds (on land), in flocks (in the air), or in schools (in the water), forming patterns in which both movement through the particular medium and interaction are unconsciously self-regulated. The human observation of such patterns may have contributed to the evolution of advanced human intelligence.

Purported Cycles and Patterns That Do Not Exist

I emphatically reject the notion of historical cycles. Certain misguided thinkers and writers have, in my view, attempted to superimpose their own biases and preferences on the telling of the story of human history through the assertion—backed up by deliberately selective or twisted “evidence”—that human life has unfolded in discernible, repetitive patterns. By the very nature of historical processes themselves, by the very nature of the randomness that permeates human life, by the very unpredictability of specific human behaviors, and by the very ceaseless processes of change found throughout the Universe, the planet Earth, and the human community, such schemes are rendered nonsensical and fraudulent. They are attempts to simplify that which cannot be simplified—the story of the most complicated beings on the planet. Like all ideological systems, they are vulnerable to that most dangerous of intellectual temptations: the desire to make the evidence fit the scheme or system, rather than shaping the scheme or system around the evidence.

Humans are surrounded by, confronted with, immersed in, affected by, and interactively involved with myriad patterns and cycles within nature. But the human response to these patterns and cycles occurs in a context in which humans are also responding to each other. Since the human response to other people is based, as we will see in greater detail elsewhere, on inherently flawed, incomplete, and limited communication processes, that response is deeply unpredictable. Since humans launch and are affected by innumerable chains of unexpected consequences, the reality shaped by such chains is also deeply unpredictable. Since, as we will soon see, the world can be regarded, in one perspective, as a non-equilibrium system, that is to say one which is in a continuous state of transformation, that means that this world is never the same entity from century to century, year to year, day to day, or even moment to moment. To believe, therefore, that history “repeats itself” and that there are “great cycles” of history is to believe in the absurd.

Similarly, the assertions by certain people who misleadingly call themselves social scientists that “generations” follow patterns and emerge in a cyclical fashion is based on “research” that is completely specious. The whole question of “generational cycles” would hardly be worth even considering were it not for the widespread belief in this tiresome nonsense. Human life is simply too complicated to be summed up in such neat little schema. There are no boundaries on these so-called “generations”, and they have no universally accepted characteristics. The actions of the cast of characters in the human drama are not arranged for our convenience or easy understanding, however much we want them to be. [See Errors Many People Make in Thinking About History (Specifically) and Reality (Generally) in a subsequent volume.]

Others have made claims that there exist cycles of economic activity that make it possible to predict periods of boom and bust. In my view, the jury is still out on these claims, which we will examine in greater detail elsewhere, but I have serious doubts about them.

The Nature and Function of Shapes

Shape is one of the inherent and obvious properties of tangible objects, but we often overlook a fundamental fact about it: the shape of an object is very often intimately related to its function. The shape of an object, or a configuration of small objects that form an overall shape, can be extraordinarily significant. (There is in fact an entire discipline that studies shapes as they are found in nature, morphology, and there is a term for how naturally occurring shapes are generated, morphogenesis.) The most common shape in the macroscopic world is the sphere (or its close approximation). Gravity takes swirling, rotating materials of all kinds and forms them into stars, planets, and moons in their sextillions, all (with the exception of some of the moons) in the shape of a sphere.

The double helical structure of DNA is an example of the crucial importance of shape. It is through the interactions made possible by its “twisted ladder” shape that DNA functions. And in proteins, the shape protein chains assume is usually the key to the way in which they will function. In general, therefore, shape formation in nature is not random (in the sense of following no rules). Living things are shaped as they are because it is conducive in some way to their survival, or at the very least, not a hindrance to that survival.

In considering the role of shape in living things, Philip Ball makes an important distinction between pattern and form:

Form is a more individual affair. I would define it loosely as the characteristic shape of a class of objects. Like the elements of a pattern… objects with the same form do not have to be identical, or even similar in size; they simply have to share certain features that we can recognize as typical. Shells of sea creatures are like this. The shells of organisms of the same species all tend to have a certain form that can be recognized and identified even by a relatively untrained eye, despite the fact that no two shells are identical. The same is true of flowers, and of the shapes of mineral crystals. The true form of these objects is that which remains after we have averaged away all the slight and inevitable variations between individuals. Patterns, then are typically extended in space, while forms are bounded and finite. (But take this as a guideline, not a rule.)³

So natural shapes and forms are usually similar to others of their kind without being identical. As patterns show a range of possibilities, so shapes exhibit a range of appearances that form the boundaries of the categories into which they fall. The perfectly uniform and defined shapes of geometry are human inventions. Even the spheres formed by gravity are not always completely spherical. Our own Earth is an example, being somewhat flatter at the poles than elsewhere, making its shape (technically) one of an oblate spheroid.

The late mathematician Benoit Mandelbrot identified a property in nature that appears to be extremely common: self-similarity, the tendency of things within categories to be roughly similar in appearance regardless of their scale. This tendency is at the heart of fractal phenomena. Such patterns of self-similarity can be seen throughout the natural world. For example, tree branches follow roughly the same form whether they are huge or tiny. Blood vessels appear similar to each other regardless of their size. A river and its tributaries, seen from above, show striking fractal-like properties. The repetitions of shapes at different scales is called iteration. It is by this simple process of repeating, in different sizes, the same basic shapes that complex visible patterns emerge.

Fractal forms are an example of phenomena that are ubiquitous, and often seen, but not interpreted or identified until someone notices them and points them out. Once noticed and brought to the attention of others, those people “see” what they have unconsciously seen many times but not truly perceived. On one level, nature itself can be seen as a collection of iterated shapes that form an overall pattern.

Humans, naturally, have manipulated shapes and created patterns for both functional and aesthetic reasons ever since our genus evolved. Humans seem to have a great attraction to perceived visual symmetries in nature (visual elements which “balance” or reflect each other, or images that form regular shapes such as spirals or repeated crystallization patterns) and they have employed symmetry in the arts with great regularity. Those shapes which are most widely used in a given culture often reflect a long aesthetic history, and form much of the visual backdrop which those raised in such cultures come to think of as “normal”. Further, humans often like tessellations, repeated shapes arranged on a geometric plane, shapes that interlock and leave no overlapping or blank areas. They are very widespread in the human world.

The cycles that are repeating all around us would, if audible, be a strange, dissonant symphony of music played at different tempos and in different keys. The patterns that surround us, if they were entirely visible to us, would look like an especially dense abstract art piece, one that was moving and changing constantly, forming a picture the appearance of which was in constant transition. And the shapes of nature, if seen in their true light, would appear to us to be emblematic of the forces which brought about the natural world itself. We not only live in a world of such phenomena, we ourselves are examples of such phenomena. We are the repeated and evolving patterns called humans. We are along for the ride in the greatest and most ancient cycle of them all.