1 Return to Modelability
2"Comprehension of conceptual mathematics and the return to modelability are among the most critical factors governing humanity's epochal transition from bumblebee-like self's honey-seeking preoccupation into the realistic prospect of a spontaneously coordinate planetary society." (216.03) [My italics—A.E.]
3 Buckminster Fuller, Synergetics: Explorations in the Geometry of Thinking 1
4 Synergetic geometry is the product of a mind as comfortable with mathematical precision as with the intuitive leaps associated with visual and spatial conceptualizing. Buckminster Fuller was guided predominantly by intuition throughout his 87 years; nonetheless, he was entirely at ease with the painstaking exactitude of numerical calculation—such as that required in the development of the geodesic dome in the early 1940s. Years before the pocket calculator, he produced volumes of intricate trigonometric solutions, manipulating 8-digit numbers with the patience and precision of a monk. However, the peculiar language of Fuller's mathematical writings quickly betrays the intuitive influence and all but conceals that of the hard-nosed engineer. Buckminster Fuller was both the pragmatic Yankee mechanic and the enigmatic mystic, and synergetics is the product of that combination.
5 Above all, he was driven by curiosity—and found nature a far more compelling teacher than the textbooks in his Milton, Massachusetts, schoolhouse. Frustrated by the apparent lack of a connection between conventional mathematics and reality, young "Bucky" Fuller adopted his own approach. The resulting self-directed exploration into pattern and structure became the most powerful influence in his remarkable career as inventor, architect, engineer, and philosopher, and produced a geometrical system that is fascinating in its own right.
6 Synergetics is the discipline hiding behind Fuller's fantastic visions of a sustainable future. These reliable patterns were the source of his unshakable confidence in his design-science philosophy, which—in short—upholds that innovative application of the principles governing nature's behavior can insure ample life support for all humanity. While many people around the world have been exposed to Fuller's ideas and inventions, few have understood or even been aware of the mathematical principles underlying the elegant efficiency of [001/002]structures such as the Octet Truss and geodesic dome. Happily, these principles are easily accessible once you get into the spirit of Fuller's approach: synergetics is a "hands-on" branch of mathematics.
7 However, listening to one of Fuller's all-encompassing lectures, you might wonder when the "hands-on" part begins. Tangibility is not a prominent feature in his spell-binding discourse, the subject of which is no less than "humans in universe". He challenges, in the course of a few hours, age-old assumptions about our lives and institutions, asking us to reconsider the most commonplace aspects of experience. Some of his observations are stated so simply, you may find yourself wondering, "Why haven't I thought about that before"? For example: 2
8 How many of you have said to your children, 'darling, look at the beautiful sun going down'? [A show of many hands.] Well, we've known for 500 years that the sun isn't going down, and yet we consider it practical to keep on lying to our children!
9 Or:
10 When I was born in 1895, reality was everything you could see, smell, touch and hear. The world was thought to be absolutely self-evident. When I was 3 years old, the electron was discovered. That was the first invisible. It didn't get in any of the newspapers; (nobody thought that would be important!) Today 99.99% of everything that affects our lives cannot be detected by the human senses. We live in a world of invisibles.
11 And later, he takes his keys out of his pocket and carelessly tosses them in the air; gravity takes care of the landing.
12 Nature doesn't have to have department meetings to decide what to do with those keys (or how to grow a turnip). She knows just what to do. It must be that nature has only one department, one coordinating system.
13 These simple truths each relate to different aspects of synergetic geometry. But for all his lighter anecdotes, Fuller's underlying message could not have been more serious:
14 The fact that 99% of humanity does not understand nature is the prime reason for humanity's failure to exercise its option to attain universally sustainable physical success on this planet. The prime barrier to humanity's discovery and comprehension of nature is the obscurity of the mathematical language of science. Fortunately, however, nature is not using the strictly imaginary, awkward, and unrealistic coordinate system adopted by and taught by present-day academic science. (000.125b)
15 Nature is instead using the principles embodied in synergetics, which [002/003]thus provides the way to eradicate this "prime barrier" to our ability to understand science. Claiming to have discovered no less than the mathematical system that describes the coordination of physical and metaphysical phenomena alike—that is, of both energy and thought—Fuller was urgent in his insistence that we study these principles:
16 I am confident that humanity's survival depends on all of our willingness to comprehend feelingly the way nature works.
17 From Geometry to Geodesics: A Personal Perspective
18 What college student would not be overjoyed to receive an invitation to work on "ever-more relevant affairs" from a personal hero? That is precisely what I found in my mailbox in 1980 when Buckminster Fuller actually answered my letter, the timid plea of an undergraduate: "What can people do toward furthering your vision of making this planet work for everyone? And where can I apply the experience of having studied synergetics"? I was later to understand that Fuller's responding to an undergraduate's letter was not unusual but rather indicative of his profound trust in the integrity and capability of human beings—and especially of youth. His action was typical of his life and work, which relied heavily on intuition, with a powerful faith in the willingness of others to apply their minds as diligently and joyfully as he applied his. We have to take Fuller at his word when he claims to be not a genius but an "average healthy human being" who exercised his option to think. He embraced that potential in all of us.
19 I was introduced to the intricate discipline of geometry in a Harvard course "Synergetics: the structure of ordered space" taught by the editor of this series, Arthur L. Loeb and I had been fascinated by this material for a couple of years. Reconciled to its obscurity, I was enchanted by the perfection and complexity of this body of geometric knowledge, which was all but completely hidden from popular awareness. In those days Loeb's course was similarly hidden, a bizarre option within the 2-inch-thick course catalog, taught in a sequestered attic in Sever Hall where one would never wander accidentally. My peers had no doubt that there was a reason for that. In fact, my academic pursuits were perceived by most as an irreverent cross between kindergarten games and mathematical torture. My roommates, forever tripping over cardboard tetrahedra and unsuccessful tensegrity wheelbarrows while gingerly avoiding small deposits of Elmer's glue, [003/004]were tolerantly confused. I can't blame my classmates for their bemused head-shaking; I had trouble taking myself seriously. Mathematical elegance aside, I felt deep down that I had chosen an unbelievably fascinating road to nowhere, a choice that would limit my chance of meaningful participation in human affairs. But still I was trapped—like an addict immune from better judgment—in my polyhedral playpen.
20 Then one February evening, I heard Fuller speak at the Massachusetts Institute of Technology. It's easy to understand how pivotal the experience could be: in love with geometry but distressed by its nonapplicability, I heard Bucky Fuller that night spin out—in an omnidirectional web of ideas, predictions, and obscure but brilliantly juxtaposed facts—an unfamiliar version of world history in which synergetic geometry (and other aspects of "comprehensive thinking") somehow played a crucial role in rescuing humanity from its current crisis of squandering vast resources in an unwinnable arms race. We are suddenly at a turning point in history at which it is possible to provide adequate life support for everyone, declared Bucky. Malthus is obsolete. (He didn't know about alloys.)3 There is no such thing as a straight line, the sun does not go down, and it is time we updated our language.
21 A more mesmerizing discourse I have never heard. I walked—no, skipped—back home down Massachusetts Avenue: not that I could have told you exactly how it worked, this planetary success, but I was sold. My geometry had relevance!
22 I still can't explain exactly how synergetics is going to turn the world around, but I have found at least that I can explain synergetics. My hope is that if enough other people become aware of these principles, the missing pieces will ultimately come together. So far, this has been a valid working hypothesis. In teaching workshops to clarify Fuller's material, I have met people who found significant applications in their own work. Synergetics has provided both useful models to elucidate scientific phenomena and methods of solving structural problems. Examples of both aspects will be cited throughout the book; see especially the end of Chapter 15, "Case in Point: Donald Ingber" which can easily be read independently of the rest of the book.
23 After Fuller's lecture, the next step was clear: read Synergetics. If I expected easy answers, I was in for a surprise. Fuller's ambiguous writing called for considerable interpretation. With the patient guidance of Arthur Loeb, I struggled through Fuller's massive text [004/005]and learned that truth was far more elusive than he had made it sound that night at MIT. But the geometry was no less seductive, and ultimately I decided to risk a 13-cent stamp.
24 And then his unexpected letter arrived—in response to my earnest but decidedly indirect questions. Even a photocopied list of organizations would have been received with glee. How it was that my letter filtered through the procedural maze that lay between Buckminster Fuller and the formidable stack of mail that was opened and sorted by various trusted assistants every day, I'll never know.
25 The signature was real:
26 Dear Amy Edmondson:
27 …I would like to take advantage of your offer to come and work with me.…I am busier and busier with ever more relevant affairs.
28 Warmly, Faithfully,
Buckminster Fuller
29 Ever more relevant affairs! A college student's dream and—she is convinced after 3 years of first-hand acquaintance—an accurate description of Fuller's experience. Even with a healthy dose of skepticism about some aspects of his philosophy, one could not help being stunned by his tireless enthusiasm for work. At four times my age, he was awake and working before I arrived and long after I had crept home to bed exhausted. The secret of this energy was his conviction that humanity had a viable option of designing an unprecedentedly successful environment aboard "Spaceship Earth"4, and that his work just might play an important part in that. I found that the more deeply involved in the actual work I became (in my case, calculations and drawings for Fuller's geodesic dome projects), the more impressed I was by the scope of his vision.
30 Bucky was extraordinarily generous with his time—perhaps due to an uncontrollable urge to teach—and treated every listener as an intellectual equal. This might be called a skillful teaching strategy, except that it was utterly spontaneous. One of the most important lessons of my 3-year experience was the difference between Bucky on the other side of his desk—spontaneously lapsing into simple clear explanations as a result of the catalyst of a pair of expectant human eyes which would cloud into a worried frown when lost—and Buckminster Fuller's dense polysyllabic prose in the 800 pages of Synergetics. I became accustomed to translating [005/006]the Fullerese into lay English for various befuddled readers who went so far as to call the office for help.
31 This is not a book about those 3 years; it is about synergetic geometry. Here I have only tried to give you some of the background that has led me to attempt to explain what is in many ways unexplainable, for no one can speak for Bucky Fuller but himself. The goal of this volume is to help readers get through the barriers imposed by Fuller's idiosyncratic use of language, and to introduce the major concepts of synergetics in an accessible format. The next steps are up to all of us.
32 Operational Mathematics
33 We can imagine the young Bucky, an enthusiastic misfit sensing that he is alone in his skepticism about the fundamental premises of geometry. ("Does no one see what I see? Does no one else sense the terrible problems that lie ahead if we follow these absurd premises to their logical ends?") While his grade-school classmates were apparently content to go right along with the teacher's strange games, Bucky was astonished by the implausible new concepts.
34 Bucky would tell us that he tried, constantly, to accept the rules—be a good student, make his family proud, submit to and even excel at the illogical activities—but somehow his efforts at model behavior were always thwarted. He just couldn't help pointing out that the teacher's "straight line" was not at all straight, but rather slightly curved and definitely fragmented. Perplexed by her lack of accuracy, Bucky saw a trail of powdery chalk dust left on the blackboard, a trace of the motion of her hand, and it seemed quite unlike her words.
35 Bucky was virtually blind until he got his first eyeglasses at the age of 5, so he had truly experienced life without this primary sense. Now he was insatiably curious about the visual patterns around him. An "infinite straight line"? He would turn toward the window, thoughtfully pondering where that "infinite line" stopped. "Out the window and over the hill and on and on it goes"; it didn't seem right somehow. Bucky, childishly earnest even in his eighties, would tell this story, explaining that he didn't mean to be "fresh", he just couldn't help wondering if that teacher really knew what she was talking about.[006/007]
36 Much later, fascinated by Eddington's 5 definition of science as the systematic attempt to set in order the facts of experience, Fuller had a plan. It must be possible to develop a mathematical system consistent with experience. He concluded that humanity had been on the wrong track all these years.
37 Experimental Evidence
38 It seemed to Fuller that mathematicians arbitrarily invent impossible concepts, decide rules for their interaction, and then memorize the whole game. But what did he propose as an alternative?
39 Starting from scratch. Mathematical principles must be derived from experience. Start with real things, observe, record, and then deduce. Working with demonstrable (as opposed to impossible) concepts, the resulting generalizations would reflect and apply to the world in which we live. It seemed highly likely that such an experimental approach would lead to a comprehensive and rational set of principles that represented actual phenomena. Furthermore, Bucky suspected that such an inventory would relate to metaphysical as well as physical structure.
40 Fuller decided that to begin this process of rethinking mathematics he had to ask some very basic questions. What does exist? What are the characteristics of existence? He proposed that science's understanding of reality should be incorporated into new models to replace the no longer appropriate cubes and other "solids" that had kept mathematicians deliberately divorced from reality since the days of ancient Greece.
41 To begin with, there are no "solids"; matter consists exclusively of energy. "Things" are actually events—transient arrangements of frenetically vibrating atomic motion. It's almost unthinkable, but perhaps if we get our vocabulary and models to be more consistent with an energy-event reality, children can become comfortable with the "invisible" discoveries of science. In short, simplifies Fuller, we have the option to tell children the truth about nature in the first place.
42 What if we do go along with the rule that mathematics should not depend upon a concept that cannot be demonstrated; where does that leave us? Fuller saw inconsistencies even in the notion of an "imaginary straight line", for imagination relies on experience ("image ination" he would say) to construct its images. Therefore [007/008]an "operational mathematics" must rely on concepts that correspond to reality.
43 Bucky pulls us back into the turn-of-the-century schoolhouse of his childhood.
44 The teacher stood at the blackboard, made a little dot, and said, 'This is a point; it doesn't exist'. (So she wiped that out.) Then she drew a whole string of them and called it a 'line'. Having no thickness, it couldn't exist either. Next she made a raft out of these lines and came up with a 'plane'. I'm sorry to say it didn't exist either, sighs Bucky. She then stacked them together and got a 'cube', and suddenly that existed.
45 Telling the story, Bucky scratches his head as if still puzzled 70 years later:
46 I couldn't believe it; how did she get existence out of nonexistence to the fourth power? So I asked, 'How old is it'? She said, 'don't be naughty.'… It was an absolute ghost cube. (EIK video) 6
47 Instead of a dimensionless "point", Fuller proposes the widely applicable "energy event". Every identifiable experience is an energy event, he summarizes, and many are small enough to be considered "points", such as a small deposit of chalk dust. An aggregate of events too distant to be differentiated from one another can also be treated as a point. Consider for example a plastic bag of oranges carried by a pedestrian and viewed from the top of the Empire State Building, or a star—consisting of immense numbers of speeding particles—appearing as a tiny dot of negligible size despite having an actual diameter far greater than that of the Earth. 7
48 The mathematician's "straight line", defined as having length but no width, simply cannot be demonstrated. All physical "lines" upon closer inspection are actually wavelike or fragmented trajectories: even a "line of sight" is a wave phenomenon, insists Fuller; "physics has found no straight lines".2 But forces exist, and they pull or push in a line, which can be modeled by a vector, so Bucky proposes that we replace the word "line" with "vector". Finally, the "continuous plane" with no thickness must be replaced by a mesh of energy events interrelated by fine networks of tiny vectors. To Fuller, these adjustments were crucial, for mathematicians' games with continuous planes and sizeless points were ultimately irrelevant diversions; however enticing the intellectual pursuit might be, they do not help us understand how nature works.
49 The essential nature of the above revolution is semantic and can easily seem trivial. The difficulty in evaluating the impact of such changes lies in the subtlety of the effect of words and the images they produce. Only through experimenting with Fuller's substitutions for [008/009]some period of time can we judge the merits of mathematical terminology that reflects science's new understanding of reality.
50 Back to the starting point! Nothing can be accepted as self-evident; a new mathematics must be derived though "operational" procedure. Fuller decided that through sufficient observation of both naturally occurring and experimentally derived phenomena without reference to a specific framework, nature's own coordinate system might emerge. He sought a body of generalizations describing the way patterns are organized and able to cohere over time. We shall see how these principles can be discerned both in deliberate experiments with various materials and by recording existing natural patterns.
51 Bucky's grade-school skepticism was thus the beginning of a lifelong search for "nature's coordinate system". After rejecting traditional academia through his dramatic departure from Harvard's freshman class in 1914,8 he began an independent exploration of mathematics which he was to pursue for the rest of his life. A sort of philosophical geometry gradually began to take shape, consisting of a rich body of facts and principles, some new and others newly considered. Synergetic geometry is tied together as one cohesive system by the unmistakable presence of Bucky Fuller in conventional and bizarre observations alike. Including expositions called "Tetrahedron Discovers Itself and Universe", "Life", "Cosmic Hierarchy", "Complex of Jitterbugs", and the more conventional "Closest Packing of Spheres", Synergetics does not fall neatly into any preconceived category. This volume will attempt to clarify these multifaceted (or polyhedral) observations, which together constitute synergetic geometry.
52 Nature's Coordinate System
53 What accounts for the shape similarities among unrelated phenomena, radically different in both scale and material? Or, more fundamentally, what accounts for nature's magnificent orderliness itself? Whether honeycomb or conch shell or virus, time after time individual structures turn out true to form. The fundamental hypothesis behind synergetics—and the work of many other pioneers exploring the science of form—is that nature's structuring occurs according to the requirements of minimum energy, itself a function of the interplay between physical forces and spatial constraints.[009/010]
54 Wait. The role of physical forces (gravity, magnetism, electrical and chemical attractions) is clearly important, but what are "spatial constraints"?
55 We are so used to thinking of "space" as empty nothingness that the idea of its having specific properties seems absurd. However, as will become increasingly clear from the examples throughout this book, space has shape.
56 The idea is concisely expressed by Arthur Loeb in his introduction to Space Structures: "Space is not a passive vacuum, but has properties that impose powerful constraints on any structure that inhabits it. These constraints are independent of specific interactive forces, hence geometrical in nature." 9
57 A simple example is the fact that to enclose space with only four polygons, these polygons must all be triangles. Nothing else will work, no matter how hard you try. The limitation is a function of neither material nor size but rather of the nature of space. Fuller alludes to this active role when he says "natural is what nature permits".
58 When Bucky points out that nature doesn't have to stop everything she's doing and gather the physics, chemistry, biology, and mathematics departments to decide how to grow a turnip (or build a virus), he is calling our attention to the self-organization of natural phenomena. Structuring in nature occurs automatically.
59 "Nature has only one department", declares Bucky, "one comprehensive coordinating system".
60 How does this self-structuring occur? In the most general terms, according to the path of least resistance, or, as stated above, according to the "requirements of minimum energy". In short, natural systems automatically find comfortable arrangements, which are necessarily a result of the balance between specific forces and inherent spatial properties. When Fuller set out to inventory possible configurations and thereby formulate generalizations, his exploration was destined to be "geometrical in nature" because of the nature of systems, as we shall learn in Chapter 3. "Nature's coordinate system" is thus a geometry of most economical relationships which govern all structuring. In Fuller's more long-winded words,
61 "a geometry composed of a system of interrelated vectors may be discovered that represents the complete family of potential forces, proclivities, and proportional morphosis…" (215.02).
62 We shall see how "operational procedure" produced a geometry of vectors and look at the specific shape of this diagram of potentials in Chapter 7 "Vector Equilibrium", and Chapter 9 "Isotropic Vector Matrix". The most notable characteristic of these models is the absence of perpendicularity. We thus shall explore Fuller's statement that nature is never operating in perpendicular and parallel directions [010/011]but rather convergently and divergently in radial growth patterns.
63 Another important aspect of "nature's coordinate system" is the existence of rules governing the coherence of structures. What holds its shape? If nothing is self-evident, we can no longer take "solids", or reliable structures, for granted. Chapter 5 examines Fuller's investigation into structure and the resulting principles governing the stability of systems.
64 All of this takes a while to sink in. The idea that space has shape is profoundly reorienting; we are so used to conceiving of space as passive emptiness on which we impose desired configurations that an entirely new perception cannot be adopted overnight. Nonetheless, upon further study, this premise begins to feel quite comfortable and necessary—an all-embracing somethingness influencing structural phenomena. As more specifics are uncovered, this conception, which is at once so elusive and so ordinary, begins to seem more and more the latter.
65 Universe
66 The ultimate manifestation of nature's coordinate system is "Universe". Fuller deliberately omits the article, for "the universe" implies the possible existence of more than one—just as we do not say "the God" but rather simply "God". Fuller capitalizes "Universe" for the same reason: Universe is everything; it's all there is. (Or, more poetically,
67 "Universe is all that isn't me and me".(EIK video)
68 But Fuller would never leave it at that; he is indefatigably thorough.
69 Einstein revolutionized our understanding of Universe, explains Fuller; prior to his relativity theory, we could think in terms of a single-frame (simultaneously complete) picture, unimaginably vast, but still simultaneous at any given moment. This understanding must now be replaced by a "scenario" concept:
70 301.10 Universe is the aggregate of all humanity's consciously apprehended and communicated nonsimultaneous and only partially overlapping experiences.
71 He willingly dissects his own long-winded definition.
72 To Fuller, aggregate implies a complex that cannot be comprehended in totality at only one moment:
73 "Consciousness means awareness of otherness." (302.00)
74 To be apprehended, information must first be within the range of human perception and then actually be noticed.
75 "Communicated means informing self or others. Nonsimultaneous means not occurring at the same time" (302.00)
76 Events of Universe [011/012]are instead "partially overlapping"—like generations. My lifetime overlaps my grandmother's and hers overlaps the life of her grandmother, but I was born long after the death of both my great- and great-great-grandmothers. Such are the events of Universe; every experience overlaps some but not all other experiences.
77 Another facet of the "scenario" concept centers on the misconception of the environment as a static whole. For instance, looking out at a distant star it is all too easy to think we are "seeing" it just as it is at that moment, while in reality that particular star is so far away that its light takes 100 years to reach us. What we are actually looking at is a "live show" taking place 100 years ago. We are seeing an event that occurred before we were born. Universe is the integral (or sum total) of all experience. It cannot be unitarily conceived, but as thus defined it is all inclusive.
78 "You cannot get out of Universe" (321.02).
79 Fuller's definition avoids imparting a sense of thingness—part of his effort to encourage us to think in terms of "pure principle". Universe is energy and thought all knotted together by incredibly complicated webs of relationships. It is ultimately impossible to separate the physical and metaphysical; both are "experience". The scientific principles that govern the interactions of energy events—as timeless statements of truth—are themselves metaphysical. The line therefore becomes ever more difficult to draw. This is why Fuller's definition depends upon consciousness. Our awareness of energy events defines their existence; we cannot go beyond the limits set by our understanding.
80 Finally, Fuller assures us that the definition is complete:
81 People say to me, "I think you have left something out of your definition of Universe". That statement becomes part of my experience. But never will anyone disprove my working hypothesis because it will take experimental proof to satisfy me, and the experiment will always be part of the experience of my definition, ergo included. (306.01)
82 He elaborates in a 1975 videotaped lecture entitled Everything I Know.
83 "Someone might ask 'what about dreams? I think you left that out,' and I reply, 'no, for that is part of your experience.'" (EIK video)
84 (He seems to have all the angles covered!)
85 Generalized Principles
86 The principle of leverage is a scientific generalization. It makes no difference of what material either the fulcrum or the lever consists…. Nor do the special-case sizes of the lever and fulcrum…in any way alter either the principle or the mathematical regularity of the ratios of physical work advantage….[012/013]
87 Mind is the…uniquely human faculty that surveys the ever larger inventory of special-case experiences stored in the brain bank…from time to time discovers one of the rare scientifically generalizable principles running consistently through all the relevant experience set. (Synergetics, p. xxvi)
88 Fuller spoke frequently and ponderously on the "generalized principles": those statements—be they verbal or in the shorthand of mathematical equations—that have been proven to always hold true. In other words, generalized principles are rules with no exceptions. From the simple (the mechanical advantage allowed by leverage) to the highly profound (E = mc ², equating matter with energy and quantifying the rate of exchange), these principles, taken all together, describe Universe. Applying a generalized principle in a novel way is called invention. In the broadest sense, synergetics is the search for generalized principles. ("Design science" is the application, as will be discussed in Chapter 16).
89 Fuller placed enormous stock in these principles, and saw humanity's role in Universe as discoverer and utilizer of the progressively uncovered truths. Endowed with "minds" (as distinct from "brains", which merely coordinate sensory input), humans are uniquely able to survey successive experiences and detect reliable patterns, thereby discovering over time such subtle workings of Universe as gravity. Utterly invisible and unpredicted by the investigation of separate objects, gravitational force represents a profound discovery and is certainly without exception. More remarkable still, human mind was able to express the magnitude of this force in precise terms: F = GMm/r². 10 A fantastic leap beyond sensory-based information, this discovery places tiny humans in contact with great Universal motions.
90 That the human mind is able to detect eternal truths amidst "special-case" experiences, explains Fuller, is the wealth of humanity and our hope for the future. Many of these Universal laws are widely known and applied, as for example the principle of leverage, but other equally reliable truths are all but completely unfamiliar, such as the geometric discoveries described in this book. Fuller, convinced that an inventory of yet to be explored applications had the potential to solve humanity's problems, was the ardent champion of unfamiliar principles.
91 Universe is thus the total web spun by all generalized principles and their interaction. As rules without exception, they are necessarily "interaccommodative". Fuller's terminology takes some getting used to: "eternally regenerative Universe" is an ongoing event governed by "the omni-interaccommodative complex of unique and eternal generalized principles". The principle of synergy, described in [013/014]Chapter 3, accounts for the incalculable complexity of the whole web despite thorough comprehension of many of the separate parts. And finally, "God is the unknowable totality of generalized principles".
92 Return to Modelability
93 Synergetics is a product of Fuller's passionate concern with models. Concerned that society's ignorance of science is seriously destructive, he devoted years of thought to ways of alleviating this ignorance. In the 20th century, we suddenly find ourselves confronted with an "invisible" atomic reality in which the average person understands very little about how things work. Although confronted daily with "incredible technology", which to Fuller includes the natural phenomena of Universe as well as the ever-expanding inventory of human invention, the vast majority assume such phenomena to be out of their reach. Fuller attributes this widespread discomfort to both the "invisibility" of science and the devastatingly complicated mathematics without which, scientists claim, their findings cannot be described. The dangerous chasm between scientists and lay people, with the truth guarded by an elite few and the rest resigned to ignorance, thus seems inevitable.
94 The origin of this troubled state of affairs? An incorrect mathematical system! Long ago human beings surveyed this environment and, seeing a never-ending flat Earth, decided upon cubes and orthogonal planes as the appropriate measuring system. Today, says Fuller, we're still stuck with that uninformed early guess, and as a result, nature's behavior has seemed irrational, perverse, and difficult to describe because we're using the wrong kind of yardstick. With accurate models, he claims, this gap can be closed. The purpose of synergetics is to make the invisible events and transformations of Universe visible, through tangible models that elucidate the principles behind our energy-event Universe. Human beings will thereby be able to "coordinate their senses" with a new understanding of reality.
95 Synergetics is full of tantalizing models; the difficulty comes in assigning them to aspects of physical reality. However, a number of notable examples, in which a newly discovered scientific phenomenon is described by one of Fuller's previously developed models, suggest that there may be many more such successes to come. The immediate goal therefore is to unravel and study the geometric system itself.[014/015]