Seeing Past The Edge*
An Original Work of Non-fiction
By: David G. Yurth Copyright 1997
All Rights Reserved
Looking For Simple, Elegant Solutions
How Nature Works:
Self-Organizing Criticality in Complex Open Systems
Have you ever wondered why it is that all at once, without warning, while your life seems to be rolling smoothly along just as you planned it, out of nowhere something happens which catastrophically tips everything upside down? After the catastrophe has taken its toll and passed, do you re-run the film of those events in your mind, re-examining them, analyzing them, searching for a clue to something you may have missed along the way which might have made it possible to avoid or minimize the damage?
Unless you are somehow exempt from the rules which govern the rest of humanity, the human experience consists primarily of periods of relative calmness [getting up in the morning, going to work, doing our tasks, dealing with the up’s and down’s of everyday life, day in and day out], which flow without interruption in a generally consistent routine. Once in a while, however, something happens without warning which fundamentally alters the way we live.
Pilots have a saying which is illustrative. Flying, it is said, consists of hours and hours of endless tedium periodically interrupted by moments of stark terror. Try as we may, there seems to be nothing we can do to prevent or avoid these events. And we ask ourselves, “What does this mean? Why did this happen? Will it happen again? And if so, when? How can I avoid it next time?” In the emerging science of complexity, this phenomenon is called “punctuated equilibrium.”
A few years ago, after my marriage of twenty-nine years had ended badly, I traveled to the California coast to see some friends and get away from myself. After spending a day communing with the towering redwoods of the John Muir National Monument North of San Francisco, I decided to sit on the beach for awhile and watch the waves. As sometimes happens with me, I found myself completely fixated by the repetitive rhythmical undulation of the waves against the shore. I sat mesmerized for hours watching them ebb and flow. At some point in time, perhaps three o’clock in the morning, the sky cleared and the full moon began to illuminate the seascape.
The crests of the waves became visible all the way to the horizon, marching in an elegant, flowing ululation towards me. I was mesmerized by this Zen moment. Every now and again, I noticed that a rogue wave would flow across the prevailing pattern, coming from out of nowhere. The anomalous appearance of those waves really intrigued me. For hours, I tried to predict which direction the next one would come from. I tried to discern whether some pattern or subtle rhythm governed their direction and magnitude. But try as I might, I was forced by the time the sun came up to conclude that their origins and attributes were random and not related to the normal flow in any obvious way.
This experience was truly magical for me. As with other moments of powerful intuition in my life, I realized without understanding why that the waves I was watching were an analog of all of life and Nature. As I have reflected on my own life, I can see clearly that the momentous events which have had the most significant impact on me came from a direction I could not have anticipated and operated in ways that I could not predict. So it is, I believe, with all of Nature.
The Sand Pile Experiment
Part of the mystery which defines how Nature [big “N”] and the human experience work can be observed in something as simple as a pile of sand. This is an experiment anyone can perform. It goes like this: begin by accumulating a supply of dry sand. Start by placing one grain of sand on top of the next on any flat, level surface. The size of the grains of sand is not important. The experiment works as well with gravel and dried peas as it does with sand.
On top of the first grain of sand, place a second and then a third and so on.99 As the grains of sand are stacked progressively on top of each other, a most extraordinary thing begins to happen. As the mound of particles grows higher and higher, as the slope angle which defines it becomes steeper and steeper, the mound begins to manifest a prototypical behavior. At some point in the process, when a single grain is placed atop the mound, somewhere along the surface of the sand pile another grain, which is not directly connected by impact or proximity, will roll off the side towards the base. For reasons which are only now becoming evident, the information set represented by the placement of the single additional grain at the top of the pile is transmitted instantaneously throughout the pile to all the other grains. At this precise moment, the sand pile ceases to simply be a stack of units. Instead, it now exhibits all the characteristics of an open, complex, self-organizing system which has reached a state researchers call “criticality.”
If we continue to add grains of sand beyond this point, eventually
somewhere along the slope of the pile a catastrophic event will occur. In the language of complex systems, this event is referred to as an “avalanche.” We have all seen it before.
When we were kids, we used to play a game which capitalized on this phenomenon – after a pile of sand was built up to the point at which it was almost ready to collapse, we would shove a stick down into the apex of the mound. The objective of the game was to scoop away small sections of the mound until, at the very end, the removal of even a single grain would cause the stick to fall. The game was fun precisely because no one could predict which scoop of material would cause the stick to fall.100
We have all seen it before. At some point in time, an entire section of the sand pile will eventually collapse on its own if we continue to add material to the top.
More importantly, it is interesting to note what does not happen. As we continue to add grains to the top, we do not observe another single grain sloughing off repeatedly as a consistent consequence. There is no one-to-one relationship at work in such a system. Trivial as this may seem, for the purposes of this discussion, this is a most important distinction. It is also important to observe that we cannot predict which grain of sand will trigger an avalanche, nor can we predict how catastrophic the avalanche will be when it occurs. We cannot predict where in the pile the avalanche will begin nor how far it will carry. This behavior is a hallmark of all complex, open, self-organizing systems.101
Dr. Per Bak and his colleagues at the Brookhaven National Laboratories in Long Island, New York, have developed a simple, elegant model which describes why the sand pile behaves as it does. In his book How Nature Works,102 Dr. Bak describes four elemental dynamics which characterize the behavior of all complex open systems. I highly recommend this book – it is extremely articulate and very readable.
Complex, Self-organizing Systems
For the purposes of this discussion, a complex, open, self-organizing system is defined as one which demonstrates the characteristics of the condition known as criticality. For purposes of illustration, at the grandest of scales, the Milky Way Galaxy is a complex, open self-organizing system103. The fact that this is universally acknowledged to be true presents some intriguing problems for astrophysics which cannot be accommodated by the Standard Model of physics currently in general use. Why this is so and what needs to be done to remedy this conundrum is one of the reasons we are engaged in this exercise.
The same is true of our solar system. In every sense, it demonstrates all the characteristics, attributes and behaviors associated with self-organizing systems.104 So does our planet. Taken by itself as a single comprehensive unit, the Earth and its sub-systems all demonstrate the attributes of self-organizing criticality at every scale, from the sub-quark to the Earth’s participation as a member of the solar system set105. All these systems operate in an integrated, indivisible aggregation of components which, in the final analysis, comprise a single overall system, just like our sand pile.
If we can sort out what causes the sand pile to behave as it does, perhaps we will be able to extend that insight to explain why a galaxy [as a macrocosm] and sub-quarks and other super-small sub-atomic particles [operating at the lower limits of the microcosm] operate as they do. Penetrating this level of insight into the dynamics of the processes which are universal to self-organizing systems, regardless of size, will take us well beyond the Edge and help us to understand human behaviors at all scales.
One more word before we begin. What we are attempting to do here is nothing less than create a fundamentally new approach to formulating a unified theory of the forces which govern the evolution of the Cosmos, in all its manifestations.
This is what Ken Wilber refers to as a Theory of Everything. One of the benchmarks of all reliable universal models is that they are simple106. In order to succeed in describing universal phenomena, a unified model must be comprised of rules, dynamics and attributes which are themselves easily describable and which manifest their attributes at all scales in every open, complex, self-organizing system. The model proposed by Dr. Bak provides us with several of the key components of the model we are in the process of developing here. As you read through his work, I hope you will be struck by a single overriding impression – as sophisticated as his mathematical models are, the rules he derives from his observations are the quintessence of elegance and simplicity.
Self organizing Criticality
It works like this: an open system does not become sufficiently complex to become self organizing until its level of organization breaches a threshold. In physics, this threshold is referred to as background noise, described by the
simple term I/*. In Darwinian terms, this means that in order for a system to begin to operate in a way that can be described as self organizing, the level of its organization, its volume, magnitude and complexity, must rise above a minimum, nominal level. This is consistent with everything we know about quantum mechanics – since the world we live in is a quantum world at every scale, this is also consistent with what we intuit and observe.107
A boulder does not move one micron [one millionth of a meter] until some outside force acts on it at some level which rises above the I/* threshold. You can push on a large boulder all day long, until you drop to the ground from exhaustion, but until you exert sufficient pressure to exceed the minimum force necessary to overcome inertia, the boulder will never move. However, once you have pushed hard enough to exceed the 1/* threshold, it will certainly move. It always does. That is the law and it applies universally in the macrocosm.108
In their seminal book Order Out of Chaos, Nobel laureates Ilya Prigogine and Isabelle Stengers109 provide a road map which defines the track for man’s new dialogue with nature. Their work broke totally new ground when it was published because it brought a simple, elegant order to our search for an answer to the question, “If the Universe operates in a perpetual state of chaos [which was what we believed before the book was published], why hasn’t it self- destructed long before now?”
The underlying phenomena which give rise to this question revolve around a condition described in mathematical circles as “entropy”. Entropy is a mathematical value which is used to describe the state of chaos which exists in a given system as the result of irreversible, externally imposed processes. In any system which has not reached a state of self-organizing criticality [the point at which creative and catastrophic events occur spontaneously within the system, without the intervention of outside forces], the rules of chaos and entropy operate with predictable consistency.
Here is a practical example. A wine glass is a highly organized closed system of crystals defined by a rigid crystalline structure. Its state of organization is arbitrarily defined and rigidly reinforced. Its level of entropy (disorganization) is said to be extremely low, since its state of coherent organization is very high. But if the wine glass is dropped on the floor and shattered into thousands of pieces, this becomes an irreversible, externally imposed event. The system’s state of coherence and organization are now entirely chaotic, and its entropy is said to be high. This applies to a wine glass, as it does with all closed systems, because the wine glass itself is not self-organizing.
One of the questions which has plagued scientists for hundreds of years has to do with why we observe both destructive, dissipative events and self- organizing events of creation occurring simultaneously in a single universe. Thanks to the vitality of modern scientific techniques and instruments of observation, we can look out into the heavens and witness both the formation of new solar systems and stars in the same firmament in which we find unmistakable evidence of catastrophic events of mass destruction. The universe we live in is in a constant state of both self destruction and self organization, which we now know operates at every scale of creation. How can this be? What primary forces are in operation to define these processes and control their behaviors?
Thanks to the work of Prigogine/Stengers, Bak and others, we have a new context within which to seek answers to these questions. If our new integrated model is to work, it must answer these and a number of other critical questions with elegance and simplicity. In order to maintain a sense of order and perspective about this subject, let’s first take a look at the four basic attributes of self-organizing systems provided by Dr. Bak. Then, after we have taken a moment to evaluate what they mean, we’ll attempt to relate them to the other elements or our model.
All open, complex, self-organizing systems demonstrate all four of the following attributes:
Punctuated Equilibrium: Between each catastrophic event or “avalanche” there are long periods of relative stasis which are punctuated from time to time by other “avalanches” of various magnitudes. These avalanches can be literal, as in the case of our sand pile or a snow covered slope, or they can take the form of mass extinctions, the rises and falls of the stock markets, the occurrence of solar flares, earthquakes, tornados, hurricanes or floods, wars, the Internet, etc.
Power Laws: The relationship between the magnitudes of avalanches and the frequency with which they occur can be expressed in terms of a simple exponential equation. There are no singular explanations for large events – the same forces which cause the Dow Jones Industrial Average to rise 5 points on one day also caused the crashes of 1929 and 1987. Wherever we find that a logarithmic relationship exists between a series of catastrophic events, we can be absolutely certain that the system which produced it is self-organizing.
Fractal Geometry: Discovered by Benoit Mandelbrot110 of IBM, fractal geometry is a mathematical construct which illustrates that where a complex, open, self-organizing system exists anywhere in our space-time continuum, it is self-similar at all scales. In fact, fractals are the natural record of the evolution of natural, open, complex, self-organizing systems. The insights provided by this tool are essential to our new model.
I/* Noise: When a complex system evolves to a state of self-organizing
criticality over a period of time, the record of its evolution can be described in terms which are also fractal. The shape of a river delta, the variegated slope of a mountain range, the shape of a coral reef, and the corrugated features of the human brain are all records of the evolution of self-organizing systems manifest in fractal form.
These properties are all so similar, when examined carefully, that we wonder if they are all manifestations of a single guiding principle. Is there a Newton’s Law [f=ma] of complex system behaviors? By the time we complete this discussion, it will become clear that self organized criticality, the spontaneous evolution of complex systems to a critical state, holds the key to understanding what these principles are and how they work.
So, let’s begin. “Punctuated equilibrium” is a scientific term which describes events we observe every day. It is illustrated in its simplest form by referring again to our sand pile. As we add grains of sand – the process of adding periodic increments is analogous to the evolution of the system over time – we realize that we cannot predict when an avalanche, large or small, will occur. Nor can we predict its magnitude or its location. What we can predict, however, is that eventually, at one moment or another, when the addition of the next single grain of sand takes the sand pile to a point of criticality, an avalanche will occur.
In the short span of a single human life time, we all observe and are impacted by catastrophic events. They happen within and around us all the time, at an infinite number of levels, in all the sub-systems which comprise our physicality and the world we live in. These events are so much a part of our sensory experience that we become largely inured to all but the most catastrophic of them. What we notice and remember are the major catastrophic events of our lives. So it is with Nature. Changes occur in nature, not in a gradual way but as a consequence of major catastrophic events.111
On a broader scale, we can observe the record of a series of singularly catastrophic events which have occurred over periods spanning hundreds of millions of years. Mass extinctions, such as the collapse of the system which supported the dinosaurs, operate contemporaneously with a series of major geological events which continue to reconfigure the surface features of the planet.112
Power laws are expressions of a mathematical construct which describes the relationships between separate avalanche events. The simple exponential equations used to produce a graph of this information produce a straight line with a slope.113 The points along the line represent single occurrences, avalanches, of a measured or estimated magnitude. As with earthquake records, the occurrences of single events in any self-organizing system can be gauged in terms of their relative intensity.114
As we continue to build our sand pile, if we stay at it long enough, we will discover that for every event in which ten grains of sand slough off and tumble down the side [for example], there will be ten events in which only one grain of sand is liberated. For every event in which 100 grains of sand fall away in a single avalanche event, we will catalog ten events in which only 10 grains fall away.115 This phenomenon is an identifying characteristic of all self-organizing systems. It is reflected in graphs taken from historical records based on the Richter Scale116 of earthquake intensity and other historical records which catalogue events in systems which have not previously been recognized as self organizing.
When the record of earthquakes is taken as a whole, the logarithmic relationship between the individual events which occur within the system produces a single straight line with a slope. The slope angle characterizes the power relationships in self-organizing systems. The evidence is inescapable – the same power laws which apply to the behaviors of the sand pile apply with equal facility to earthquakes – the tectonic behavior of the earth’s crust is unmistakably that of a complex, self-organizing system.
Over the past thirty years, studies performed by more than 100 teams of scientists and researchers have demonstrated that the world we live in, in all its manifestations, is comprised of an inextricably interconnected aggregation of complex, open, self-organizing systems and sub-systems which operate according to these dynamics at all scales.117
The power laws identified by Dr. Bak apply with equal facility to the systemic behaviors demonstrated by records of mass extinctions118, all weather- related events,119 solar flares120 and cellular automata121. An analysis of the patterns demonstrated by periodic measurements of rush hour traffic and the distribution of human settlements around the globe produces the characteristic single line with a power slope122. Apparently, human behavior also produces test results which suggest that what we do and how we operate in human communities are also part of a complex, self-organizing system. When we evaluate the periodic recurrence of key words, phrases and themes in the collected works of Shakespeare123, Beethoven, Mozart124, the Christian Bible, the Quran of Islam, the Vedas of ancient India and other voluminous collections of literature, art, music, mathematics and other forms of human expression, we find the same pattern being repeated. Power laws which describe the relationships between the frequency and relative magnitude of “avalanches” in any self-organizing system operate universally, with equal consistency at all scales of the Cosmos.
This is a discovery of monumental importance. It demonstrates the universal applicability of a single, simple, elegant operational dynamic which is common to all of creation, at every level and in every complex self-organizing system, regardless of its size. Understanding how the functions described by this model operate will help us unravel one of the perpetual mysteries of the Universe. Even though we have access to a whole lexicon of high technology observation and data collection devices, we are still altogether unable to reliably predict such things as earthquakes, local weather [tornados, hurricanes, floods, droughts, etc.], volcanic eruptions, the fluctuations in the stock markets or the dynamics of the Internet with any degree of reliability or consistency.
Why this is true is key to our understanding of how the Cosmos works. This insight is also indispensable to the construction of our model of the Cosmos because it suggests, among other things, that Descartes was seriously mistaken- it is not possible to separate “physical stuff” from “spirit stuff” in any meaningful way without doing suicidal violence to our search for understanding.
The Role of Criticality
As we construct our sand pile, there comes a time when the sand pile can no longer be considered just a stack of single, unrelated grains. As the mound of sand reaches the point of criticality – that point at which the I/* threshold has been reached and the power laws become operative – the sand pile becomes a single integrated system. As soon as this happens, it is no longer possible to predict the magnitude, location or frequency of any single avalanche event. Even if we know everything there is to know about every single grain of sand comprising the pile simultaneously, the nature of open, complex and self- organizing systems is such that we would still not be able to improve the consistency, accuracy or reliability of our predictions.
We can predict only what the power laws permit. The importance of this insight cannot be overstated. It means, among other things, that in spite of all the best technology we will ever devise, we will never, under any circumstances be able to reliably predict the magnitude, location or timing of any events which occur as part of any self-organizing system125. This includes earthquakes126, solar flares, stock market behaviors, mass extinctions, meteor strikes, weather, geologic events or the behaviors of the Internet. If our way of thinking about the world we live in could be brought into alignment with the way the Cosmos really works, our approach to living would be altered in ways that are largely unimaginable.
One feature of the dynamic we call “criticality” flies in the face of the long- held notion about how the world has geologically evolved. For many decades, it was taken as gospel in the geological sciences that the geology of the planet evolved gradually, by slow, minimal, irresistible events. It is now unarguably clear that this notion was terribly mistaken127. The geology of the Grand Canyon, the appearance of the Rocky Mountains, the emergence of the Hawaiian Islands, the creation of the Gulf of Mexico are now known to be the results of catastrophic geological events.
In the human experience, we witness the same phenomenon. A phrase originating in the Middle East says it best: “The straw that broke the camel’s back” illustrates what happens with our emotional state when we reach a state of criticality. A single insignificant event, perhaps unrelated to anything which has occurred in our recent past, often triggers a violent, seemingly senseless overreaction. This event, the triggering of violent emotional reactions which far outweigh in their magnitude the significance of the event which occasions them, is an avalanche of the purest sort, a catastrophic event which occurs out of all proportion to the causative event. Indeed, we are walking, talking, self- organizing systems, poised on the brink of catastrophic behavior all the time.128 Criticality is mathematically defined as the state of highest efficiency in a complex system.129 At the point of criticality, catastrophic events happen in a big way, all at once, and not by gradual degrees. This is as true of rush hour traffic jams as it is of mass extinctions and major weather events. When we understand this aspect of complex systems, we also begin to understand something fundamental about the way Nature works.
The World Wide Web
One of my favorite examples of self-organizing criticality is the emergence of the World Wide Web and Internet over the past thirty years. The history of the Internet illustrates in a most dramatic and present way every aspect of self- organizing behavior in complex human systems. Before the system could manifest itself, a number of intermediate foundational steps had to occur first. In relative terms, the system has emerged as a series of clearly identifiable quantum events, none of which were predictable in advance, and all of which demonstrate strict adherence to the rules which govern self-organizing systems. Once the infrastructure had been defined by a small number of original participants [government sponsored laboratories and university-based research groups], the system limped along in a state of stasis for nearly a decade before a single event of any significance occurred to alter its “shape.” During this period, the Web was the almost exclusive province of a few researchers and scientists whose primary objective was to share and distribute research data.130
In the early 80’s, a significant and altogether unanticipated series of “avalanches” occurred. With the emergence of (1) the personal computer and (2) the development of advanced telephony connectivity technologies, which enabled personal computers to talk to one another via conventional residential telephone lines, the stage was set for an explosive, catastrophic avalanche of new innovations which has fundamentally altered the global landscape of commerce and communications.
Within the past ten years, personal computers and the manner in which they facilitate access to ever-evolving kinds and volumes of information via the World Wide Web and the Internet have brought us to a point of criticality once again.
The economic consequences of this series of catastrophic events have always been fundamentally unpredictable. The cascade effect produced by the emergence of the Web and the Internet, as a generally distributed and universally available means of producing, transmitting and accessing information, has been documented by a number of prominent research organizations. Care to guess what the data accumulated by these groups looks like when plotted over time?131 What is most fascinating about this social phenomenon is that the Internet as a system is evolving as it has because its practitioners recognize that everything is information.
By definition, the Internet traffics in a single commodity – information. It is likely that the long term effect of the emergence of the Internet will be to significantly reorient our thinking about how the world works, in all aspects of life on this planet, in the same way and perhaps to the same extent that a single catastrophic event caused the extermination of dinosaurs. If it continues to operate as it has in the past [and there is no assurance that it will], the predictions made by Arthur C. Clarke in 1984 could eventually come to pass.132 The emergence of the Internet and the recent catastrophic collapse of the dot-com stocks on the world’s publicly traded stock markets demonstrate perhaps more clearly and powerfully than any other current phenomena how self-organizing systems operate in the human community. This insight is compelling because it takes us to a point of consideration not previously explored in this context. Does human behavior, taken as a whole without respect to individual behaviors, correspond to the rules which define self-organizing criticality in complex, open systems?