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According to scientists who pioneered the field, and Gleick, who chronicles their discoveries, chaos science was revolutionary. Its focus on dynamic systems, nonlinearity, and theories that embrace the irregular distinguished its work from that of established science. Chaos questioned the foundations of Newtonian science and Euclidean geometry, as well as the rigid divisions between academic disciplines that had flourished for decades. Instead of breaking down a scientific or mathematical problem into its component parts, chaos scientists were looking for how whole systems worked, in particular dynamic systems whose defining qualities were complexity and motion. When Gleick was writing Chaos in the mid-1980s, this new science was already “reshaping the fabric of the scientific establishment” (4). Significantly, the contributions of chaos to the scientific community continue to be numerous and meaningful, challenging conventional notions of how the natural world and the universe function.
From the beginning, the author establishes that chaos science was something new: “Where chaos begins, classical science stops” (3). He reviews how scientists from several different fields began to examine “the irregular side of nature, the discontinuous and erratic side,” noting that previously “these have been puzzles to science, or worse, monstrosities” (3). In contrast, chaos theory welcomed these confounding puzzle pieces, partly because it was invested in examining entire phenomena rather than disparate elements. In addition, it investigated the material world—which humans readily recognize—as well as the theoretical plane; thus, it considered clouds as important as galaxies. Advocates of chaos science argued that after relativity and quantum physics, chaos constituted the “third great revolution” (6) in 20th-century scientific knowledge. Revolutions depend as much on defying a discipline’s foundations as establishing a new vision.
In the spirit of Thomas S. Kuhn, Gleick maintains that “[a] new science arises out of one that has reached a dead end” (37). The great failure within the scientific community that chaos scientists identified was “how tightly compartmentalized” it had become. This compartmentalization bred a narrow vision of how natural systems work: Looking only at cordoned-off parts of a system provides only a partial view of how that system functions. Both abstract mathematics and material physics are necessary to fully comprehend a dynamic system, for example. While this was revolutionary in the context of 20th-century science and academia, it echoed a wisdom that came out of the ancient maxim not to miss the forest for the trees. If looking too closely at the parts (the trees), one cannot grasp the nature of the whole (the forest). Chaos broadened the scientific view.
While chaos expanded the field of study, it refined some of the standard explanations of natural phenomena. Science does not develop, as the author emphasizes, along linear lines; it does not follow a clear teleological trajectory of discovery followed by progress. Chaos theory exemplified this trend: “The emergence of chaos as an entity unto itself was a story not only of new theories and new discoveries but also of the belated understanding of old ideas” (181). Chaos, like other revolutionary leaps in knowledge, emerged out of discoveries and mistakes, missteps and accidents, looping back on itself to clarify old ideas by using new technologies. Through its development across several disciplines, chaos began to change some of the “fundamental rule[s]” (226), as in Mandelbrot’s fractals. Basically, chaos changed the understanding of Euclidean geometry, while also relying on its foundations to make innovative intellectual leaps. It repeated this feat through its applications in various other fields.
Of course, as a new scientific field emerges, it experiences growing pains: The precepts of chaos were sometimes questioned; its methods were occasionally dismissed; and its ideas were not immediately accepted. The name itself inspired controversy. Even as Gleick wrote his book, after chaos had established itself as a specific discipline, “no one could quite agree on the word itself” (306). The scientists still working in earnest to legitimize the field worried that “chaos” could not express the fullness of their enterprise. The name stuck, however, and the author tries his best to define it in its entirety: “Physicist or biologist or mathematician, they believed that […] whatever their particular field, their task was to understand complexity itself” (307). It could even, as many chaos scientists believed, expand the understanding of the most complex idea in scientific history: the origins and evolution of life itself. As Norman Packard affirms, “Billions of years ago there were just blobs of protoplasm: now billions of years later here we are” (261). Out of chaos arises the most complex order of all.
Repeatedly, chaos theory has confirmed via mathematical conjecture and material experiment that order exists within apparent disorder. From the erratic patterns in the study of ecology, to the infinite number of fractals containing a finite area, to the complexity of the human body, chaos explains paradoxes that occur regularly (or irregularly) in nature and the universe. Contrary to conventional thinking, however, order in nature is not readily apparent or tidily organized; rather, it is embedded within nonlinear, dynamic systems that incorporate periods of randomness and bursts of chaos. Thus, natural systems embrace chaos as much as they create patterns; order and disorder are not mutually exclusive. Chaos science suggests not only that nature produces order within disorder but also that it prefers certain kinds of patterns, which repeat throughout the natural world.
As biologist Robert May collected data regarding the shifts in animal populations, he began to notice that patterns of order collapsed into chaos when parameters were pushed. However, within those periods of chaos, May discovered “an intricate structure—far more orderly than [he] could guess at first” (74). The disorder that appears at first glance obscures the underlying regularity that nature imposes. James Yorke confirmed this counterintuitive theory via mathematical standards: Everywhere scientists saw randomness, they found some kind of order within the dynamic system. His work ultimately reinforced the foundation of the entire discipline: “Chaos is ubiquitous; it is stable; it is structured” (76). The hallmark of nonlinear systems is chaos, but chaos contains stability and structure.
As Benoit Mandelbrot began reinventing standard geometry with his fractals, he discovered that “[w]ithin the most disorderly reams of data lived an unexpected kind of order” (86). Again, order lurked beneath the surface of what appeared to be disordered information. His work also revealed that “the degree of irregularity remains constant over different scales” (98). That is, not only does order exist within disorder but this kind of organization—structure within randomness—is embedded in universal ways throughout dynamic systems: “Over and over again, the world displays a regular irregularity” (98). One must grasp both concepts at once to understand fully the deep-seated paradox at the heart of chaos theory.
This became increasingly significant as chaos scientists began to observe the orderly disorder throughout dynamic systems that was intrinsic to the natural world. Experiments regarding strange attractors—which determine particular behaviors within a chaotic system—showed that nature was not random. Rather, “[n]ature was constrained. Disorder was channeled, it seemed, into patterns with some common underlying theme” (152). Thus, the initially observed chaos obeys a set of natural, perhaps universal, rules that organize, or at least inhibit, the chaotic behavior. Order and disorder coexist. As J. Doyne Farmer, a member of the Chaos Cabal, said, “Here was order, with randomness emerging, and then one step further away was randomness with its own underlying order” (252). As in deconstructionist theories about language, an idea cannot exist or be understood without its opposite. Just as the concept of bad cannot be fully understood without comprehending the concept of good, order and disorder are entangled.
This has profound impacts on how we understand nature. It’s not simply that we can discern patterns, counterintuitively, within apparently chaotic systems; it’s also that these patterns repeat throughout nature within its vast variety. As chaos science develops, it exposes an astonishing reality: “Of all the possible pathways of disorder, nature favors just a few” (267). This suggests that something universal—see Interconnectedness and Universality: Both the Part and the Whole—underlie these repeated findings of order within disorder, of structure within randomness, of pattern within chaos. Chaos science might even untangle some of the fundamental questions regarding the origin of life: “Pattern born amid formlessness: that is biology’s basic beauty and its basic mystery. Life sucks order from a sea of disorder” (299). Living matter, then, is perhaps best explained as the expression of a beautiful order derived from the swampy soup of universal chaos.
Interdisciplinary partnerships reveal the most insightful concepts and theories of chaos science. Mathematical abstraction and material experiment have both contributed meaningful work to the field, for example. The precepts of chaos have proven useful in numerous disciplines, including biology, ecology, physics, astronomy, and economics. This interdisciplinarity highlights basic conclusions of chaos: Seemingly opposing concepts, like order and disorder, are both necessary for understanding the universe; the part, no matter how miniscule, is integral to the workings of the whole; and an interconnectedness between natural systems and dynamic processes belies a set of potentially universal laws. The interdisciplinary applicability of the field reflects its vast and ambitious scope.
As the author acknowledges in the Prologue, these scientists were not looking for how the “constituent parts” of a system work: “They believe that they are looking for the whole” (5). As such, the frame of investigation must be wide enough to encompass many disciplines, and Gleick tracks these partnerships throughout the book. For example, “the study of chaos gave a strong impetus to theoretical biology, bringing biologists and physicists into scholarly partnerships that were inconceivable a few years before” (79). Additionally, as the author emphasizes the interdisciplinarity of chaos science, he mimics this characteristic within his own writing by including quotations from poetry and literature as epigraphs, citing poetic observations by Wallace Stevens and Christopher Marlow’s character, Dr. Faustus, as well as relevant comments from science historian Thomas S. Kuhn. These epigraphs imply that to understand the universe fully, one must absorb the ideas from literature and the imagination as well as from science and the experiment. Mary Shelley’s famous quotation from her introduction to Frankenstein—“Invention, it must be humbly admitted, does not consist in creating out of void, but out of chaos”—is here echoed by J. Doyne Farmer: “It [nonlinearity] seemed like something for nothing, or something out of nothing” (251). Either quotation could serve as a slogan for the field of chaos itself.
In addition, chaos science takes great interest in the interstitial happenings between two opposing concepts or within various transforming states. The notion that a dynamic system contains either order or disorder gives way to the realization that it always contains both order and disorder—especially when looking at a system holistically. Chaos science observed, from its very beginnings, that the part is inextricable from the whole, and vice versa. When economists tried to separate the short-term shocks to commodity prices from the long-term trends, for example, predictions about economic systems fell short: “[T]hat dichotomy had no place in the picture of reality” (85-86) that chaos science begins to explore. Indeed, dichotomies obscure the entanglement that exists between apparent opposites, the blurring that occurs at boundaries. Whether these boundaries are between phase transitions or between different physical materials (such as land and water), a pattern always appears within the dynamic chaos: “At the boundary, life blossoms” (198). That is, boundaries are the complicated sites of movement, fluidity, and dynamism—the motion that defines the liveliness of the natural world.
In studying Mandelbrot’s fractal geometry, chaos scientists began to understand the deeper implications of such holistic visions. Within every molecule were orders more of increasingly smaller molecules, “resembling the main set and yet not quite the same” (228). Each molecule spawned a new one, similar but different, whole in and of itself, yet part of the larger system: “[T]hose [molecules] would reveal molecules tinier still, always similar, never identical, fulfilling some mandate of infinite variety, a miracle of miniaturization in which every new detail was sure to be a universe of its own, diverse and entire” (229). This implies that the larger universe in which scientists study chaos could be part of a chain of universes, each similar but distinct, each entire and unique, which, in turn, has implications for the idea of interconnectedness and universality that chaos science expresses. Thus, chaos redefines the understanding of how the universe works: “Simple systems give rise to complex behavior. Complex systems give rise to simple behavior. And most important, the laws of complexity hold universally, caring not at all for the details of a system’s constituent atoms” (304). That is, the part cannot be fully separated from or fully integrated into the whole: Ultimately, the whole is more than the sum of its parts yet inextricably interconnected with them.
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