This blog is the fourth in a series of posts that focuses on Natures six organizing principles. The material in each of these posts has been condensed from the text of my new book entitled “Nature’s Patterns: Exploring Her Tangled Web“. The book will be published in both an Amazon Kindle edition and a soft cover edition in early June of 2014.
The previous blog posts are:
Blog #2: Everything Is Connected
Each species, including ourselves, is a link in many chains. The deer eats a hundred plants other than oak, and the cow a hundred plants other than corn. Both then, are links in a hundred chains. The pyramid is a tangle of chains so complex as to seem disorderly, yet the stability of the system proves it to be a highly organized structure. Its functioning depends on the cooperation and the competition of its diverse parts” – Aldo Leopold Sand County Almanac
Perhaps Nature’s greatest, and least understood, paradox is that she is both ordered and chaotic. This paradox represents the core reason why man cannot predict or control Nature.
A book is not just a collection of words. What makes a book different from random babbling is the ordered structure of the words placed there by the author and the rules of grammar. A symphony or a rock and roll piece consists of musical notes. But it is not just a collection of sound waves. It is distinguished from noise by musical principles that order the notes. A house consists of bricks and boards, but it is not a pile of random building materials. The difference is the architectural rules used to organize the material. In all three of these examples, energy must be used to achieve an ordered state.
Our universe is an elaborate ordered structure at many different levels. In Nature, energy is used to achieve and maintain an ordered state. Ordered structure and pattern are the conduits by which energy flows. Connectivity is the essential and intimate component of order.
Our forests are an important example of order in Nature. We depend upon the order in a forest’s interrelated ecosystem to convert the sun’s energy to forms that are useful to many creatures. Forests supply oxygen to the atmosphere and absorb carbon dioxide. Forests, like all other flora, are a basic food source for animals and insects.
It is quite easy for we humans to understand the basic order in Nature that has just been described. But, it is usually difficult or impossible for us to describe and define the irregular side of Nature which always lurks with the regularities that we observe. Things such as the changing shapes of clouds, a waterfall, waves crashing on a seashore, and the fluctuations of wildlife populations. Western science has faced a special challenge as it coped with its ignorance about these kinds of disorder in Nature which appear to be discontinuous and erratic.
As naturalists, it is important to have some understanding of both order and disorder in Nature. With that understanding we are better equipped to make sound ecological decisions that include knowing what we can and cannot do.
Over the past half century, scientists have come to realize that the complexity we see in Nature is both ordered and disordered. Chaos theory is about finding underlying patterns in systems that appear to be disordered. Author and scientist Douglas Hostadter once said,
“It turns out that an eerie type of chaos can lurk just behind a facade of order – and yet, deep inside the chaos lurks an even eerier type of order“.
There are forms of order among a lot of confusion and a many forms of confusion within order.
Take a moment to study this beautiful scene of a running stream. We see both order and disorder. The stream itself is ordered as it flows down the mountain following the basic and predictable laws of gravity. And parts of that stream appear ordered as water flows evenly. But, much of the stream is turbulent as it strikes the rocks. That turbulent flow is both ordered and disordered. Like the water, each rock has an ordered chemical composition that is easily definable. But, the rocks are randomly placed an an indefinable fashion. The rocks offer definable resistance forces to the water flow that follow the laws of physics. But, the result of these forces is not ordered or predictable. One can analyze this stream at any level of comprehension and find both order and disorder. No human being could precisely predict the exact stream flow through the maze of rocks.
“Determinism” means that, given an initial input, the subsequent output is uniquely and precisely defined. Determinism has historically been the hallmark of reductionism in Western science. Determinism has also been ingrained in the thinking of those who oversee and are stewards of Nature. Despite many results to the contrary when a human uses determinism to make some change to an ecosystem in the name of “management”, a certain specific result is expected. But, complexity science shows us that predictability is not possible within Nature’s ecosystems despite notions to the contrary.
Herein lies the paradox. Both professional and non-professional naturalists are conditioned to think in deterministic, cause and effect, terms. Yet, the actions of Nature cannot be defined as effects that are directly related to causes.
Chaos is the study of order within a system that exhibits apparent randomness. Chaos theory states that, under certain conditions, ordered, regular patterns can be seen to arise out of random, erratic and turbulent processes.
Chaos theory helps us to understand Nature’s systems. It has been used to model biological systems, which are some of the most chaotic systems imaginable. Chaotic patterns show up everywhere in Nature, including the mountain stream we’ve just described, cloud patterns, the currents of the ocean, the effects of air turbulence, the flow of blood through fractal blood vessels, the branches of trees, astronomy, epidemiology, ecosystems, and human society. In all of these examples, we see forms of order amongst a lot of disorder.
Complex systems are characterized by unpredictability and complexity. They all behave, in many ways, in a non-deterministic or apparently random manner. But yet, their parts are sometimes deterministic. This is characteristic of chaotic systems — they are deterministic but behave as if they are not.
So, why can determinism produce a seeming lack of determinism ? The answer lies in the nature of cause and effect relationships between elements within the controlling feedback mechanisms of any complex system. To understand chaos, we need to understand the ideas of non-linearity and feedback.
The concept of linear relationship suggests that two quantities are related to each other by a constant proportion. Doubling a quantity causes its related quantity to double as well. If I put 10 pounds of fertilizer on my bean field, my yield will go up by 2 bushels. If I put on 20 pounds, my bean crop will increase by 4 bushels. If I put on 30 pounds, my crop will yield an increase of 6 bushels. The constant multiplying factor for our bean crop yield increase is 2. A linear relationship between two elements in a system can be drawn on a graph with a straight line. It’s a relationship with constant proportionality between cause and effect. The dynamics of a linear system can be reconstructed simply by summing up the individual causes acting on a single component. We can say that a linear system is defined by the sum of its parts. Small initial errors in prediction or from a random measurement grow linearly over time. Linear systems are rare in Nature.
A nonlinear relationship is one where the cause does not produce a constant proportional effect. If we were to plot a curve for a nonlinear event, we would see a smooth curve, wiggles, an abrupt cutoff, or any number of different types of lines .We can say that a nonlinear system is more than the sum of its parts. Small initial errors in prediction or from a random measurement grow exponentially over time. This means that, over time, huge unpredictable effects can take place from small initial changes. Nonlinear systems are ubiquitous in Nature.
Those of us who consider ourselves experienced naturalists know that wildlife population growth is nonlinear. In our bean field, the number of baby rabbits is not defined by some arbitrary constant. Instead, the baby rabbit population will depend upon a number of factors. We know that food availability affects how many rabbits are born. We know that the level of predation by coyotes and other predators affects how many rabbits die. In turn, food availability depends on climate and on food consumption by other creatures. Rabbit death depends on disease and on the population levels of predators. Predator populations such as coyotes could soar or drop off deeply due to weather, the presence of apex predators like wolves, or the current supply of rabbits. Food sources for the rabbits could be heavily affected by weather systems that started half way around the world. These factors are all interrelationships that are highly variable, not proportional, and non-linear.
When one combines all of these factors, next year’s population of rabbits becomes unknowable because we cannot possibly predict next year’s weather, food supply, or predator levels. Mathematicians call this process “nonlinear”. Science calls this scenario “chaos”.
The concept of nonlinearity is vitally important to a steward of Nature because nonlinearities in Nature prevent the naturalist from predicting the outcome of an event or action. Nonlinearities confound our expectations about the relationship between our actions and expected responses in Nature. Nature’s feedback mechanisms are why nonlinearity prevents human predictability in Nature.
Feedback is a concept that is central to all complex systems. Feedback provides both self-control and chaos within a system. A feedback loop is a mechanism by which change in a variable results in either an amplification (positive feedback) or a dampening (negative feedback) of that change.
Most life processes are dynamic and dependent, They move from one moment to the next depending upon or using the previous state in order to create the next state.
The thermo-regulation process in warm blooded animals is an example of a simple feedback loop. The blood, at a given temperature, enters the body’s feedback loop that regulates body temperature. A physiological sensor detects the blood temperature. The feedback mechanism provides some sort of a warming or a cooling effect as needed. The blood exits the feedback loop and reenters as an input for further temperature processing as needed. Within a certain ambient temperature range, an animal’s feedback system safely maintains an internal temperature range in which its metabolism can operate. Within that temperature range, the feedback control mechanism responds in an approximately linear fashion.
However, linear feedback rarely happens in Nature. Far more often, we see varying and unpredictable inputs and environmental factors. The results are non-linear, highly unpredictable, chaotic outputs. The current size of a rabbit population is dependent upon the previous population as well as external factors that control the process as it proceeds to the next state. Weather, food supply, and predator activity are external factors that could affect the birth rate in the next generation of rabbits.
Complex patterns can be generated from feedback mechanisms even when the input processes are understood. Many times, Nature’s systems are not predictable because the effect of Nature’s feedback loops is non-linear. These non-linear relationships result from the systems feedback mechanisms which are, in turn, usually driven by unpredictable influences external to the organism being affected. In our rabbit population example, we have a scenario where the feedback output is unpredictable. We have multiple input controlling factors such as weather, food supply, and predation all of which are nonlinear and unpredictable. The sudden appearance of a predator is an unpredictable event which will cause an organism’s feedback system to respond in a non-linear fashion. In doing so, individuals would react to the seemingly random and varying position of the predator. Feedback systems that respond to a number of different unpredictable influences result in the complexity and unpredictability that we see in Nature’s ecosystems and their organisms. This is a classic scenario for Nature’s chaotic systems.
Chaos is, by definition, a non-linear mixture of order and disorder. It has also been shown that, within chaotic systems, a small perturbation in an input value (sometimes referred to as an initial condition) could result in a large perturbation at some future time and/or at some distance. This non-linear phenomenon takes place because of feedback.
Feedback is a driving force in evolution. In Nature’s changing dance driven by natural selection, species survive or fail as their feedback systems respond to the changing environment in which they live. The result is more complexity over time without thought, design, or a leader.
Nature’s feedback systems produce resilience in ecosystems. Resilience is a measure of a system’s ability to survive and persist within a variable environment. The opposite of resilience is brittleness or rigidity. Resilience arises from a rich structure of many feedback loops that can work in different ways to restore a system even after a large perturbation. It is common to call this richness of feedback loops “diversity” or “biodiversity”. Ecosystems with much biodiversity are resilient because they contain many complex feedback systems that serve to correct for outside perturbations. As part of being careful not to break interconnections in Nature, the naturalist must be careful to preserve an ecosystem’s resilience when considering an ecological issue.
Sensitive dependence on initial conditions is the hallmark of chaotic dynamics. If we can’t accurately define or predict an initial state or position, we are then incapable of determining or predicting an outcome. This is the fallacy of the “linear” cause and effect approach to “resource management”. Naturalists are unable to precisely and accurately define the initial conditions of the system to which they are about to make a change. And, they are unable to predict the results of their actions. The legalized killing of of wolves is an excellent example of mankind changing an initial condition in a complex system without considering the non-linear relationships. Over the years, with the loss of their wolf predators, elk and deer herds flourished. In turn, with growing elk and deer populations foraging stream side aspen, cottonwood, and willow trees, the plants became stunted. This resulted in stream erosion which resulted in the reduction of beaver, fish, and bird habitats that were damaged or destroyed.
It is now accepted that weather forecasts, which are chaotic systems, can be accurate only in the short-term, and that long-term forecasts, even made with the most sophisticated computer methods imaginable, will always be no better than guesses. Thus the presence of chaotic systems in Nature seems to place a limit on our ability to either apply deterministic physical laws or our own best judgment to predict motions or patterns with any degree of certainty.
So, what do weather forecasts and ecosystems have in common? They are both complex systems that, down deep inside, are created using simple rules and are highly sensitive to the effect of initial conditions. Their sometimes non-linear rules operate within the feedback loops which we mentioned earlier. With each cycle in a feedback loop, small non-linear changes within a system get amplified. The resulting system’s patterns are both chaotic and ordered because both regularity and irregularity are generated. There is no way we humans can predict how these small amplifications will affect the activity of a system over time.
Order and chaos within Nature are deeply linked. The result is unexpected relationships. Patterns are never quite regular. They never seem to repeat exactly. The proof that a relationship between chaos and order exists is in these irregularities.
Chaos theory has made a valuable contribution to the naturalist. From this research, there are two important messages that are sent to those who are stewards of Nature.
2) Even small changes by humanity within Nature’s ecosystems can result in huge and/or unexpected effects over time.
The key to how a complex system operates is the connectivity between its components. Consequently, the use of network theory has become an important part of the study of how complex systems work and how individual members in a system connect with each other. In the next blog, Organizing Principle #4, we will discuss these energy transport and transportation networks.
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My name is Bill Graham. As a Marine Biologist who has worked in the US and Mexico for 30 years, I am a student of Nature, a teacher, a researcher, and a nature photographer. Through my work, I have acquired an ever growing passion for how everything in Nature is connected. Today, I travel extensively contemplating about, writing about, and photographing Nature’s connections. I also work with conservation projects in the USA and Mexico and mentor talented youth.