If "you've seen photos and films of the Mandelbrot set...[if] you've seen that, then you see her. There she is. If you look at the Mandelbrot set and you turn it right side up, it's the Great Mother. There she is... “(OI, Allen, 138) “It's energy becoming energy becoming energy becoming energy."(OI, Nelson, xix)
This book is about many things, but it has its ultimate purpose in stimulating changes in education that will better serve our young and the future we deliver them into. And for this reason, it is fundamentally about many essential truths of human existence – some long neglected, others newly discovered - including the butterfly effects of ideas, the fractal growth of the mind, the self-organizing nestedness of the learning process, the dialectic relationship between our ways of knowing and our behavior, the emergence of understanding in a nonlinear reality, as well as the self-similarity of character and community development.
If all this sounds foreign to the ear, it is not because these words are so difficult to understand; indeed, the ideas they illuminate are so intuitive that a thoughtful child could grasp them – but rather because we have neglected talking about them for the three decades we might have been taking them to heart, which might have been enough to prevent the crisis we now face. Instead, discussion of these fascinating concepts has been confined to the upper echelons of academia, beyond the lights and language of those young minds we assume incapable of such understanding. But it’s not too late to take seriously the implications of what some call chaos theory or fractal geometry, among the most inspiring insights the human intellect has ever uncovered.
The principles of ecology, fractal geometry, chaos theory, and the dynamics of systems interactions could help illuminate how the mind works, how healthy lives, relationships, and communities might still develop, and to that end, how we ought to best educate our young.
One truly fascinating realm of human understanding that has only come into focus in recent decades (though an awareness of the phenomena itself had existed from the very beginning of human intellectual history) is that of ecological systems theory, including fractal geometry, chaos theory, and other complementary bodies of scholarship. It it took only a few courageous idealist to shed light on connections between these ideas, but many since have added to the conversation, and help us see what was was right in front of us all along.
Benoit Mandelbrot, a rebel mathematician and an IBM engineer who, in his off hours, wrote the book that illuminated what could turn out to be one of the greatest advances in human understanding. Mandelbrot compelled the modern world to see the practical implications of complex mathematics, and ultimately set into motion the butterfly effect of the insight that is fractal geometry by expressing in its fullest development what was sometimes only a glimmer of insight to others who came before him.
Following his love of geometry – the visual side of math – and seeking to understand the patterns of nature that had always been understood to be beyond the reach of classical Euclidean geometry, Mandelbrot dared to go where no mathematician had gone before Perhaps he remembered what so many have forgotten, that above the door at Plato’s Academy, the worlds first and still longest lasting institution of higher learning, there was inscribed the dictum, “Let no one ignorant of geometry enter here.” For, as he notes at the outset of his masterwork, The Republic, it is as if “all lines of discourse are lines converging on a common center.” So we can see why it is dialogue, not monologue, that is the art that he and Socrates tried to teach us…and that Mandelbrot build his own work on.
Idealism may not be considered practical in most academic circles, and the pressure against it may intimidate many, but--thank goodness--not all. Traveling through the Parnon range, the Tripolis road winds through the lush and fertile Eurotas valley toward Sparta, and I find myself thinking over the work of some others of those who have inspired my idealism by having maintained the courage of their own convictions. Rare--but real--role models. Patterns. Ideals. Gods?
The confidence it takes to stand up to convention and propose to change it toward its ideal is no less courageous in our world as it was when Socrates exercised his idealism twenty-five centuries ago. The personal and professional risks are sometimes enormous, and the gains accrued to us, their benefactors, are immeasurable. There are those cynics who rationalize the actions of such individuals, themselves persuaded that there is no such thing as genuine altruism, and that narrow self-interest dominates the motivation of even those who sacrifice themselves for the sake for the good. But the fact that some can manage to casually ignore these grand efforts by others gives the rest of us no reason to be so actively ignorant. It is a question of who we value and why.
Perhaps the best examples of their kind in modern times have been those individuals who, having the courage to look beyond the perimeters of what is already known, have in the last few decades uncovered what looks to be perhaps the greatest ever advance in human understanding which has cumulatively come to be called Chaos Theory.
Not surprisingly, Chaos was also the name of the original Greek god from which all the rest sprang in the course of time.
Chaos theory is, indeed, more in line with our ancient knowledge than our modern science, for in mythology as in chaos, "The universe is not a static creation... It is the result of growth and change, of progressive proliferation and differentiation away from an original unity."[1] The processes to which chaos gives insight reflect:
"the ancient themes of separation, succession, and conflict. First was Chaos-Void, whose origin we are not told. From Chaos-Void was produced...Eros-Desire, who drives the expanding creation...Night and Darkness, primal oppositions which generate Brightness and Day....and Gaea-Earth, the first proper being, female in nature"...who gives birth to the Sea and the Sky.[2]
To make a long and quite beautiful story of dramatic and complex paradigm shift as short and simple as possible, and probably as a consequent far less stunning than its real-world referent, allow me to summarize this evolution with one man’s ideas.:
Following his imagination like a child at play, Mandelbrot went against centuries of orthodoxy to bring our attention to those natural objects that, while they appear irregular and even unmeasurable on the surface, turn out to be surprisingly and even beautifully ordered, and even nested, when we look at them at different scales.
Seeing that the tools of Euclidean geometry we’d been using for thousands of years allowed only the study of smooth surfaces and human-made objects, Mandelbrot lamented that we could not understand the geometry of nature (a tree, for instance, or the length of a coastline, or any other of natures’ irregular creations) without a better understanding of the geometry of nature, what Aristotle called, ‘the mind inside nature,’ that illuminates how different scales of reality interact and are nested hierarchically, like Russian dolls.
As every middle-schooler knows, Euclidean geometry allows us to measure those dimensions visible at the human scale – height, width, and depth - but living things and natural phenomena reveals hidden dimensions that let us examine what is not readily available to the human eye.
Enter the new technology of computers, which gave us fresh eyes to see what had been in front of us all along
The problem that first fascinated Mandelbrot was that the length of a coastline was not fixed, as static maps might make it seem, but was in constant flux, largely depending on the yardstick with which one measured it. The shorter the yardstick one used, the longer the coastline revealed itself to be.
A complimentary insight to this had come to light years earlier in the form of Brownian motion – showing that what appears to be a straight line reveals itself, upon closer inspection, to be many highly irregular and tiny lines in random directions. From our human scale, a straight line appear to be just that, straight and relatively uniform, but the deeper one observes it, the more it could be seen that there was more going on than meets the eye.
To be sure, part of Mandelbrot’s good fortune was to be a free thinker in the right place at the right time. For just as, in centuries past, telescopes had extended our human vision outward into the world of the very large, and microscopes had extended it into the world of the very small, so in the twentieth century, computer technology brought us something we had had never seen before -- vision into the realm of infinity. With the power of unlimited iteration that computers make possible, we were able for the first time to go beyond the realm of human theorizing about infinity, and to actually see what happens visually when any data was repeated ad infinitum.
Mandelbrot saw – as many across disciplines would soon discover – that we could gain a better understanding of the dynamics of nature’s processes that had only been understood in static terms to that point. For when we can repeat a process thousands upon thousands, indeed, millions upon millions of times (using the result of one cycle, or iteration, as the starting point for the next), we can actually visualize the feedback dynamics that could only be speculate about when we had only the mind’s eye to work with.
Using this newfound technology to build on the work of those who came before him, Mandelbrot endeavored to show visually what all those numbers and equations really proved.
He began with the work of Georg Cantor, a 19th century mathematician who had discovered what were considered by his orthodox colleagues to be “math monsters.” What came to be called the Cantor Set is easy to create simply by removing the middle third of recurring lines, a process of self-similarity for which there is no end, and one which quickly takes us into unimaginable dimensions of the very small.
Cantor Set: A fractal in seven iterations
*
Cantor called this an “infinity of infinities,” but he was before his time in seeing the implications of this insight. In fact, he was highly criticized for this formulation, which pointed to the limits of mathematics as it had long been practiced, and is said to have suffered great depression for the rest of his life, in part due to the hostile attitudes of his colleagues and professional alienation he endured for having gone beyond the traditional paradigm in his explorations. But advances in understanding have always depended upon the courage of nonconformist to face the ridicule of more limited minds.
Another of the earliest human-made fractals came out of the work of Swedish mathematician, Helge von Koch. It is made by constructing an equilateral triangle, then adding another such triangle (1/3 the size) to each side of the first, and repeating this process over and over. With each successive iteration yet another scale is revealed, until what resembles a snowflake of potentially limitless complexity emerges. As it grows, the perimeters of the Koch curve, as it has come to be called, develop infinite length, even while its area remains finite.
Koch snowflake: A fractal in one, two, three, four, and seven iterations
*
In turn, French mathematician, Gaston Julia, had won critical acclaim and popular interest, along with prestigious awards, when his work on iterated functions early in the 20th century. Gaston had iterated simple equations in feedback loops, but the technology to process those iterations was still many decades away. So his work had all but been forgotten by the time Mandelbrot decided (in 1980) to plot Julia’s iterated functions onto a graph.
The results were images as astonishingly beautiful as the philosophical implications would be staggering. For these were not merely created, not pictures designed out of some wishful projection, but discovered idealizations of the fundamental shape reality. What they revealed was not merely a human-construct, but a pattern underlying the whole of reality that had existed, beyond our vision, for as long as the human mind had been at work in search of truth.
Julia sets can take many diverse, but self-similar, forms. Here are several examples:
Julia Sets:
*
When Mandelbrot combined the totality of the Julia sets into a sort of roadmap, what appeared seemed odd, at first, and even more deeply mysterious. But this magnificent image, which has come to be called the Mandelbrot set, has ultimately proved to be among the most practically beneficial discoveries ever made, revealing ever deeper dimensions of self-similarity that could only be intuited in times past. For they had long been assumed by ancient thinkers, including the Taoists, Plato, and Aristotle, who might be the first to recognized that Mandelbrot had uncovered the fundamental patterns of nature – following laws that had always existed, but had been invisible to us until now.
With the discovery of the Mandelbrot set, humanity got its first real glimpse of what infinity actually looks like – which is to say, the shape of the universe itself, and the flow of change within it. The implications would turn out to shatter what we thought we knew about ‘what is’ – which is perhaps why there has been such resistance to understanding this parsimonious theory (even as we’ve exploited its practical value in nearly all areas of human endeavor, including medicine, ecology, and technology).
Mandelbrot Set:
*
The philosophical implications of there being a self-similar pattern in nature that repeat at every scale, no matter how deep we zoom in or how far we zoom out, did not immediately move Mandelbrot’s colleagues in mathematics (most of whom still considered even Cantor’s set to be monstrous!), many of whom reacted with the same scorn the profession had shown his nonconforming predecessors. But while they turned against what they considered to be nothing more than pretty, but useless, pictures, the practical implications of what was now being called fractal geometry was soon realized by those outside his field.
That these iterations revealed the surprising order beneath the seeming chaos of reality would only become apparent to those in other arenas who were ultimately able to resolve a host of practical problems by way of these new fractal tools.
For instance, it was fractal antenna that made cell phones, as we know them today, possible (by way of a compact multi-scale design that maximizes space by way of a fractal helix that iterates two or more scales, making simultaneous reception of many different frequencies possible, something that could not earlier be accomplished by a single antenna).
In medicine, fractals have been used in the treatment of Parkinson’s, heart disease, and cancer. For instance, treatment advanced considerably when it was discovered that heart rhythms are not machine-like, as had earlier been assumed, but rather that a healthy heartbeat has chaotic fluctuations (indeed, heart attacks tend to occur when heartbeat is too regular and even). In the treatment of cancer, it was discovered that chaotic convergence of tiny blood vessels that preceded growth of tumors could be detected even before the tumor developed.
In the study of ecology, we began to understand the relation between mass and energy in living systems, including how big animals use energy more efficiently than small ones, important since natural selection chooses the most efficient design. And perhaps the most astonishing of all, we learned that the distribution of different size trees in a forest turn out to have the same self-similar relationship as the relation of branches on a tree, which is to say, small trees bear the same relationship to large trees in the forest in the same way that daughter branches resemble mother branches on a single tree. And big to small has the same pattern on trees in a forest as in the forest as a whole.
Meteorologist Edward Lorenz added his insights to this dialogue after his 1961 discovery of what came to be called the butterfly effect. As the story goes, Lorenz was running weather predictions using a numerical computer model, when a glitch in a sequence moved him to abbreviate the decimal. 506127 to simply .506. Leaving the room to get a cup of coffee, he returned to discover that the tiny shortcut had resulted in an entirely different weather scenario.
The technical name for this phenomena is “sensitive dependence on initial conditions,” the idea being that even a very small variation in initial conditions (i.e. a butterfly flapping its wings in one part of the world) could create very big changes in outcomes (such as altering, delaying, accelerating or even preventing a tornado in some distant place at some later time).
In 1890, Henri Poincaré postulated that this could be a common phenomena. And Ray Bradbury put forth the idea that one butterfly could have far-reaching effects on historic events in his 1952 short story about time travel, A Sound of Thunder.
As acclaimed science writer, James Gleick wrote in his 1988 book, CHAOS: Making a New Science,
"It completely changes what it means to know something."[3] "[S]omething was philosophically out of joint. The practical import could be staggering."[4]
Until then, “The microscopic pieces were perfectly clear; the macroscopic behavior remained a mystery. The tradition of looking at systems locally--isolating the mechanisms and then adding them together--was beginning to break down. For pendulums, for fluids, for electronic circuits, for lasers, knowledge of the fundamental equations no longer seemed to be the right kind of knowledge at all."[5]
"There was always one small compromise, so small that working scientists usually forgot it was there, lurking in a corner of their philosophies like an unpaid bill. Measurement could never be perfect. ... Given an approximate knowledge of a system's initial conditions and an understanding of natural law, one can calculate the approximate behavior of the system. This assumption lay at the philosophical heart of science...[that] arbitrarily small influences don't blow up to have arbitrarily large effects.'"[6]Now they could see, "[S]mall errors proved catastrophic."[7]
"In science as in life, it is well known that a chain of events can have a point of crisis that could magnify small changes,”[8]as the ancients learned from feedback loops in nature.
“But chaos meant that such points were everywhere. They were pervasive. In [nonlinear] systems like the weather, sensitive dependence on initial conditions was an inescapable consequence of the way small scales intertwined with large." [9]
"Implicitly, the mission of many twentieth-century scientists--biologists, neurologists, economists--has been to break their universes down into the simplest atoms that will obey scientific rules. In all these sciences, a kind of Newtonian determinism has been brought to bear."[10]
Now we could see that "[A]ny physical system that behaved nonperiodically would be unpredictable."[11] "[T]he spaces between the sensors will hide fluctuations that the computer will not know about, tiny deviations from the average."[12] "The Butterfly Effect was no accident; it was necessary." [13]
Revealing this nonlinear complexity of nature showed us not only that fractals are everywhere, but that small variables, such as human choice, can make huge differences. For just "as a growing snowflake falls to earth, typically floating in the wind for an hour or more, the choices made by the branching tips at any instant depend sensitively on such things as temperature, the humidity, and the presence of impurities in the atmosphere...[thus], any pair of snowflakes will experience very different paths...[and] the final flake records the history of all the changing weather conditions it has experienced, and the combinations may well be infinite."[Gleick, p. 311] Likewise, the choices made by a growing human at any instant depend sensitively on many things, and thus, any pair of human beings, even those who share quite similar initial conditions, will experience very different paths. The final person records the history of all the changing conditions it has experienced, and the combinations may well be infinite.
In a nutshell, chaos theory reminds us of what we have long known:
"Nature forms patterns. Some are orderly in space but disorderly in time, others orderly in time but disorderly in space. Some patterns are fractal, exhibiting structures self-similar in scale... The dynamics seem so basic--shapes changing in space and time--yet only now are the tools available to understand them."[James Gleick, CHAOS: Making a New Science (Penguin Books: New York) p. 311] [14]
"Chaos has created special techniques of using computers and special kinds of graphics images, pictures that capture a fantastic and delicate structure underlying complexity. The new science has spawned its own language, an elegant shop talk of fractals and bifurcations, intermittences and periodicities, folded-towel diffeomorphisms and smooth noodle maps. These are the new elements of motion, just as, in traditional physics, quarks and gluons are the new elements of matter. To some physicists chaos is a science of process rather than state, of becoming rather than being." [15]
"Few laymen realized how tightly compartmentalized the scientific community had become, a battleship with bulkheads sealed against leaks."[16] "Each scientist had a private constellation of intellectual parents. Each had his own picture of the landscape of ideas, and each picture was limited in its own way. Knowledge was imperfect. Scientists were biased by the customs of their disciplines or by the accidental paths of their own educations. The scientific world can be surprisingly finite."[17] "Graduate students were warned that their careers could be jeopardized if they wrote theses in an untested discipline."[18]
Thank goodness, not all were daunted by this taboo.
"No committee of scientists pushed history into a new channel--a handful of individuals did it, with individual perceptions and individual goals."[19] "A few freethinkers working alone, unable to explain where they are heading, afraid even to tell their colleagues what they are doing ..."[20]
For this reason;
"Chaos breaks across the lines that separate scientific disciplines. Because it is a science of the global nature of systems, it has brought together thinkers from fields that had been widely separated. ... Chaos poses problems that defy accepted ways of working in science. It makes strong claims about the universal behavior of complexity. ... Believers in chaos--and they sometimes call themselves believers, or converts, or evangelists - speculate about determinism and free will, about evolution, about the nature of conscious intelligence. They feel that they are turning back a trend in science toward reductionism, the analysis of systems in terms of their constituent parts: quarks, chromosomes, or neurons. They believe that they are looking for the whole."
For the voices that advance this argument further, we have to look into yet other disciplines. The Welch-born and dyslexic botanist and systems theorist, Timothy Allen (among the best teachers the University of Wisconsin-Madison, and notably ILS, could boast) offered up his perfectly brilliant insights long before fractals and chaos in what he then called Hierarchy Theory, which illuminate the nature of nestedness better than any before or since, by my lights.
“The notion of hierarchical arrangement is central to biology and even has an Aristotelian origin… A nested hierarchy is one where the holon at the apex of the hierarchy contains and is composed of all lower holons.”(p.38) Examples: Populations, individuals, organs, cells… or families, genera, species…(Hierarchy: Perspectives for Ecological Complexity, by T.F.H. Allen and Thomas B. Starr (University of Chicago Press, Chicago /London)
“Hierarchies can be profitably viewed as systems of constraint. Any holon higher in the hierarchy exerts some constraint on all lower holons with which it communicates,”(p.11) just as a general exerts constraint over troops under him, or the milky way exerts over our solar system, and it over our planet and moon.
“The power to constrain gives the burden of responsibility, whereas being constrained gives freedom from those pressures.”(p.15) Showing the parent/child nature of our power on all levels.
Pattee (1978) distinction between laws and rules… “we can never alter or evade laws of nature; we can always evade and change rules.”(p.42)
“We do not mean to imply that reality, independent of our cognizance, is in its nature hierarchical… What we are trying to say is that somewhere between the world behind our observations and human understanding, hierarchies enter into the scheme of things.”(p.6) As Aristotle himself had suggested, “hierarchical structure is a consequence of human observations.”(p.6) “Discrete levels need to be recognized as convenience, not truth.”(p.6) “We suggest that it is more profitable to view the discreteness of levels as a product of human perception.”(p.11) The level we single out is useful for our purposes, but the question of ‘what is real?’ must include all of them.
“For instance, the level of organization that defines the whole human individual is a helpful level for many models,” but it is no more or less ‘real’ than the level of organization that constitutes a human dyad, or a group, or a group of groups.
Some objects of our knowledge may be more difficult to see, but we are talking conceptually, and we must see concepts through the minds eye…conceptual objects are no less ‘real’ or even ‘objective’ than chairs and rocks – it’s just a question of where we focus on the lens of our minds eye.
nested hierarchies/surfaces (p.121)
“Structural boundaries are more readily observed and so understood than functional boundaries. The latter cannot be assigned to a continuous part of physical space.”(p.70)
“In this sense an ecosystem or social system is just as ‘real’ as an individual plant, animal or human.”(p.69)
“biology has physics envy”[Cohen, 1971](p.65)
“A difficulty commonly experienced by the holistic scientist is that of showing the utility of this point of view in the face of the abundant success of the presently dominant mode in biology, mechanistic reductionism.”(p.46)
“Mechanistic models are undeniably powerful…” and “perhaps the main body of predictive biology is readily couched in mechanistic terms, precisely because mechanisms are all that are sought. If there are phenomena that are not susceptible to mechanistic explanations, then the prevalent investigative strategy will not find them. This book is in part a plea for a suspension of judgment on the necessary superiority of mechanism as a model, so that alternate searches may be made.”(p.46)
“Clearly a dual reductionist-holist strategy is optimal.” “But the unified model is only a paradigm, and we gain much by…embracing complementarity as a modeling paradigm.”(p.43)
“The principle of complementarity drives through paradox by recognizing that formal incompatibilities are necessary between dual modes of description, both of which are required for a complete account of phenomenon.”
“The complementarity principle is quite central to our thesis and should perhaps have been introduced at the very outset so that its importance could have been seen throughout. The reason we have held it back until now is that it is a principle quite out of step with most…[contemporary] practice…” Hierarchy: Perspectives for Ecological Complexity, by T.F.H. Allen and Thomas B. Starr (University of Chicago Press, Chicago /London)
Complementarity – between mechanism/organism, reductionism/holism, materialism/idealism, modern methods of knowledge utilize on the former, while ancient methods utilize the latter…but we need both if the whole truth is our goal.
Two senses of idealism, one meaning ideas to things (idealism/materialism), the other meaning potentialities to actualities (idealism/realism)… The first is about what is more ‘real’ (abstract or concrete objects, ideas or rocks), while the latter is about seeing what could be (ideals), and how to move what is toward it (realize potentials).
“Idealism and reductionism” exist on a continuum… they are ways of knowing, and both equally essential to holism, or wholism. A well developed mind learns to see both dialectically… “dialectical materialism” (p.10) Some objects may be easier to ‘see’ at our human scale, but are not more objective because of this, just more tangible or concrete.
“There is a better way than stringing together 500 differential equations: a perspective which is cognizant of the intrusion of the humanity of the scientist into his observations.”
“…The scientist must remember his humanity, or suffer delusions of objectivity.”(p.29)
Like it or not, “The scientist becomes part of the phenomenon. R.D. Laing in Politics of Experience, takes note that the psychiatrist cannot observe the patient: he can only observe the patient being observed by the doctor, and that is different.”(p.29)
“Both scientists and artists are conscious of the human scale, but the artist celebrates it while the scientist tries to eliminate its effects.”(p.26)
“In the final analysis, the scientist must translate back to the human understanding, and it is there that the scientist and the artist share moments of creative insight.”(p.29)
Thus, what we have here is both an ancient and a revolutionary method of knowing -- but only revolutionary because we have nearly forgotten so much ancient wisdom. This method provides a way of understanding the universe, indeed, the multiverse, even human beings themselves, as interconnected in nested systems, constrained but not determined by their contexts.
So why didn’t we see this before? The truth is, we did! The reality of such relationships have been with us throughout history – we just didn’t have the technology and astonishing pictures to illuminate the metaphor. Certainly an argument can be made that artists have always been attuned to the ubiquity of fractal reality. And while I may not the best person to make the case, I am prepared to argue that the ideas behind these dynamics have informed the intuitions of philosophers since antiquity.
Socrates, Aristotle, Confucius, and the Taoists long ago gave us logical evidence of this 'nestedness' of being, but it has apparently taken until now to discover the empirical evidence for it – at least by our scientific lights.
Still, we should not be surprising that even thousands of years after ancient philosophers offered us their insights about the organic systems (Plato) and the “mind inside nature” (Aristotle), that we should rediscover the fundamental 'nestedness' of complex reality with the recognition and proliferation of what is widely called 'chaos theory', which is perhaps better called chaos/order theory, for this reason.
Fractal geometry is the geometry of movement and growth, the physics of flow. The ideal form of motion is seen in the complex circular flow of matter through time, contained but infinite, ever-deeper in its nestedness. But motion is contrast with movement in interaction where consciousness is involved.[Laban] Our potential for growth is subject to many interacting forces which change human potentials into their actualized forms by the woven effects of the interacting causes in the course of the life-process. The parts played by attention and intention in such a process are critical variables which steer us by ever finer choices inherent within life-plans and policies. It is a principle similar to that of the half way to the door paradox, in which it seems as if one can never really get out the room because one always has to go half-way first; time is the force perpendicular to the space between us and the door which changes as we choose to move toward the door, thus changing our conditions such that the choice is ever new, and always in need of reevaluation. The geometry of deep psychological reality and growth is non-linear, and as it is an emergent reality, understanding it calls for a sort of psychological travel or penetration of the generic human subject/object to be known. Such that that persons under consideration become subject to the psychologist when they can empathize, inside-looking-out. When we are able to get beyond objectivity in the human sciences, and see from inside the systems we wish to know, our method is no longer observation, but consideration, and what's evident from this view is often something we have long known.
This is an insight that can help us answer many an ancient question, including those involving free-will, determination, and social conditioning -- and it is especially important for the light that it sheds on the importance of choice in the process. A snowflake may 'choose' in a different sense than a community or a culture 'chooses,' and all of these differently than an individual human being makes a choice. But the role of self-determination of an individual system within the context of other systems is made far more comprehensive within the context of this world-view that we have remembered...at last. And this insight has the potential to help us through a true paradigm shift, back to what the ancients understood all those millennia ago.
What could better support the humble ideal of Socratic ignorance, after all, than the discovery that there actually are an infinite number of points of view from which any object of knowledge might be viewed? What better to keep us remembering how little we know and much we still have left to learn? We are compelled then to reiterate the key Socratic question, what does it mean, after all, to 'know' something -- most especially something fundamental and primary; something objective, not constructed; something of the natural world, not the artificial?
Thomas Kuhn’s defines the notion of a scientific ‘paradigm’ as ‘a constellation of achievements -- concepts, values, techniques, etc. -- shared by a scientific community and used by that community to define legitimate problems and solutions.”[Kuhn (1962).] And with a paradigm shift comes “[A] new language for understanding the complex, highly integrative systems of life has indeed emerged,” Fritjov Capra argues, one that could uplift our understanding of how the mind works.
“Different scientists call it by different names -- ‘dynamical systems theory,’ ‘the theory of complexity,’ ‘nonlinear dynamics,’ ‘network dynamics,’ and...chaotic attractors, fractals, dissipative structures, self-organization, and autopoietic networks are some of its key concepts.”[Capra (1996), p.xviii.]
Capra expands Kuhn’s conception of a scientific paradigm to that of a “social paradigm” which he defines as “a constellation of concepts, values, perceptions, and practices shared by a community, which forms a particular vision of reality that is the basis of the way the community organizes itself.”[Capra (1986, 1996), p.6.]
In the old paradigm, “physics has been the model and source of metaphors for all other sciences.”[Capra (1996), p.13.] Rene Descartes wrote, “All philosophy is like a tree. The roots are metaphysics, the trunk is physics, and the branches are all other sciences.”[Quoted in Capra (1982), p.55.] Today, science is overcoming that Cartesian metaphor. “The paradigm shift in science, at its depest level,” Capra writes, “implies a shift from physics to the life sciences.... However, this is still not generally recognized today.”[Capra (1996), p.13.]
Shifts in paradigms occur in discontinuous, sometimes revolutionary, breaks. For instance, ever since the scientific revolution in the seventeenth century, when “values were separated from facts...we have tended to believe that scientific facts are independent of what we do and are therefore independent of our values.”[Capra (1996),p.11.] With the discovery of the new physics, however, we have come to recognize that what we value we attend to, what we attend to we observe, and what we observe we change. [*put observation has power...] Therefore, we now recognize that, “In reality, scientific facts emerge out of an entire constellation of human perceptions, values, and actions -- in a word, out of a paradigm -- from which they cannot be separated.”[Capra (1996), p.11.] “Scientists, therefore, are responsible for their research not only intellectually but also morally.”[Capra (1996), p.11.]
Deep Ecology, as we’ve said, is a school of thought that “recognizes the fundamental interdependence of all phenomena...and the intrinsic value of all living beings,” with humans representing just one of many life forms in a complex web of nested networks.[Capra (1996), p.6-7.] Consistent with the philosophy of many spiritual traditions, including many strands of Christian, Buddhist and Native American thought. Another way of characterizing deep ecology was put forth by Arne Naess: “The essense of deep ecology,” he says, “is to ask deeper questions,”[Devall and Sessions (1985), p. 74.]
And this, Capra argues, “is also the essence of a paradigm shift.”[Capra (1996).]
Deep ecology gives rise to the recognition of a psychological connection between self and nature, from which moral consideration naturally and necessarily follows. According to Arne Naess, “Care flows naturally if the ‘self’ is widened and deepened so that protection of free Nature is felt and conceived as protection of ourselves...[and] just as we need no morals to make us breathe...[so] if your ‘self’ in the wider sense embraces another being, you need no moral exhortation to show care.... You care for yourself without feeling any moral pressure to do it....If reality is like it is experienced by the ecological self, our behavior naturally and beautifully follows norms of strict environmental ethics.”[Arne Naess, quoted in Capra (1996), p.12.]
Capra gives us direction, and reaffirms the ancients in the process, in his claim that “neither is intrinsically good or bad. What is good, or healthy, is a dynamic balance; what is bad, or unhealthy, is imbalance -- overemphasis of one tendency and neglect of the other.”[Capra (1996), p.9.] [connect w/different ways of knowing]
“Power, in the sense of domination over others.” And “there is another kind of power, one that is more appropriate for the new paradigm -- power as influence of others.”[Capra (1996), p.11.]
[1]Powell, p.75.
[2]Powell, p.75.
[3]Gleick, p.175.
[4]Gleick, p. 17.
[5]Gleick, p. 44.
[6]Gleick, p. 15.
[7]Gleick, p. 17.
[8] Gleick, p. 23.
[9]Gleick, p. 23.
[10]James Gleick, Chaos: The Making of a New Science (New York: Penguine, 1988), p. 14.
[11]Gleick, p. 18.
[12]Gleick, p. 21.
[13]Gleick, p. 22.
[14]Gleick, p. 311.
[15]Gleick, p. 5.
[16]Gleick, p.31.
[17]Gleick, p.182.
[18]Gleick, p. 37.
[19]Gleick, p.182.
[20]Gleick, p. 37.
[21]Gleick, p. 5.