17 Macro-, Micro-, and Nano-scale Engineering
3 Meccano Magazine, in 1928, printed a letter from Mr. A. H. Finlay of Holyrood, County Down, in Ireland (Fig. 1) in which a truncated icosahedral cage constructed from Meccano pieces (Meccano is known as Erector Set in the United States) was depicted.1 The legend suggested that the structure might be useful as a lampshade—but not much good as a football! A curious error,
4 ’Incidentally, I lay the blame for the dearth of engineers and scientists in the West fairly and
squarely on the fact that Lego has replaced Meccano as a ‘‘toy’’ of choice in many homes in the
developed world. I use the word ‘‘toy’’ advisedly, because Lego is a toy, whereas Meccano is not
only a toy but also an amazing introduction to the world of real engineering. It gives the
child a real understanding of how nuts and bolts should be put together. They learn
how to tighten a as this shape has subsequently become the standard pattern for the
construction of soccer balls. This letter also makes fascinating reading in light of the
development of Buckminster Fuller’s geodesic domes (Fig. 2), the discovery of C60,
buckminsterfullerene1
2
(Fig. 3). Jonathan Hare—who while working with me extracted C60 (essentially
simultaneously with the breakthrough of Kraetschmer, Lamb, Fostiropoulos, and
Huffman3
during some excitingly fraught weeks in September 1990—has pointed out that the
world is about 100 million times larger than a soccer ball and a soccer ball is about
100 million times larger than a C60 molecule—i.e., the buckyball (Fig. 4). The well-
known drawings of Haeckel of siliceous sea creatures, such as that of Aulonia hexagona
(Fig. 5), which appear in the wonderful book On Growth and form by D’Arcy
Thompson,4
led David Jones in 1967 to suggest that carbon might be coerced into forming graphite
balloons.5
Furthermore in 1970, while watching his son playing with a soccer ball, Eiji
Osawa6
came to the equally
12 Fig. 1. Page from Meccano Magazine, 1928
13 COURTESr OF SIR HAROLD W. KROTO
15 Fig. 2. Photograph from Graphics 132 of Buckminster Fuller's geodesic dome at Montreal
16 COURTESY OF THE BUCKMINSTER FULLER INSTITUTE
18
20 Fig. 4. Depiction of Hare's ratio—the last fundamental physical constant
21 Fig. 5. Drawing by Ernst Haeckel of Aulonia hexagona
22 FROM ON GROWTH AND FORM BY D'ARCY WENTWORTH THOMPSON. REPRINTED JONATHAN HARE
23 WITH THE PERMISSION OF CAMBRIDGE UNIVERSITY PRESS
25 imaginative conclusion that the carbon cage C60 molecule with the truncated soccer-ball structure that Bob Curl, Jim Heath, Yuan Liu, Sean O’Brien, Rick Smalley, and I discovered in 1985 7 would be stable—if it could be made. A year later, in 1971, Osawa, together with Yoshida,8 wrote about this molecule in a book on aromaticity in chemistry. As the geodesic dome images such as that in Fig. 2 were an important clue to the likely structure of C60,1 suggested that we name the molecule after Buckminster Fuller, and after a little struggle they agreed. If we also add to the potpourri the studies by artists such as Leonardo da Vinci and Piero della Francesca (Fig. 6), we see that this amazingly charismatic framework has been a geometric force underlying the creativity of a wide range of people as well as numerous natural and physical processes. As we enter the new millennium, it is worth throwing all these observations into a (think) tank, stirring them ah up together, and ruminating (hopefully imaginatively?) about the possible implications (hopefully beneficial!—this was, after all, the pattern of the charges used to ‘‘detonate’’ the atomic bomb) on the fact that the icosahedral structure has now surfaced as a ubiquitous unifying geometric ‘‘engineering’’ principle in the nanoscale world. Of course, the C60 molecule probably first formed on Earth when the forest fires started—though in minute amounts. The molecule has, of course, been around since time immemorial, since carbon atoms (mass 12)—now in our bodies—were synthesized by the curious triple-alpha process in stars. In this process gravitational attraction caused three He nuclei (mass 4; 3 x 4=12) to fuse together in carbon stars, which then exploded as red giants blasting carbon out into space as atoms, polyyne chain molecules, carbonaceous sootlike dust, and almost certainly also C60 as well as other fullerenes. C60 is, however, probably not in high enough abundance to be definitely detectable at this time. The C atoms and molecules then wafted around in space to end up by some ‘‘Umberto Eco-type’’ chance on our Earth—some in our bodies, yours and mine, and unfortunately also in the bodies of some others whose atoms should, in my opinion, still be waiting about in space.
28 The term ‘‘engineering’’ tends to evoke the names of those giants of yesteryear who created the civil engineering structures that transformed our world—Isambard Kingdom Brunel and Richard Trevithick and James Watt and the Wright brothers. Today, however, the term embraces a far wider range and covers even more fascinating areas. It has expanded to cover architectural constructions such as the amazing Sagrada Familia of Antonio Gaudi, Frank Lloyd Wright’s Marin County Civic Center, and Norman Foster’s Hong
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49
53 COURTESY OF SIR HAROID W. KROTO
56 Fig. 7. A side elevational view of an elongated geodesic structure patented by Buckminster Fuller
57 COURTESY OF THE SUCKMINSTLR FUUCR INSTITUTE
58 Kong Shanghai Bank. Perhaps no other building combines the fundamentals of structural design and architecture more organically than does the geodesic dome of R. Buckminster Fuller. Perhaps it epitomizes Lloyd Wright’s axiom that ‘‘form and function are one’’ even more purely than any of Lloyd Wright’s creations. On top of all this we should not forget that, as we reach the end of the twentieth century, similar intellectual processes are involved in the creation of microchips—those tiny constructs that are revolutionizing our lives. Under the microscope they are seen to be elegant abstract mosaics, providing some of the most elegant art forms of the twentieth century.
59 For all its excitement, our discovery of C60 was most important because it showed that sheet materials on an atomic/molecular scale spontaneously form closed cages. Almost exactly five hundred years after 1492, we have come full circle and, just as Columbus explored a New ‘‘Round’’ World, we can now explore a new aspect of carbon chemistry only to discover a new round world of sheet materials. We should, however, have known about it much earlier—at least in the 1960s—as some clues were being uncovered by the combustion community, which had already recognized that some soots and carbon blacks consisted of graphene sheets organized in roughly concentric shells. What is more, some carbon fiber studies had revealed structures that were thought to be Swiss-role structures rather than the concentric carbon nanotubes (buckytubes) that we now recognize them to be today. These amazing new materials hark back to the patents of Buckminster Fuller9 in which the elongated geodesic structures diagrammed (Fig. 7) are essentially macroscopic prototypes of C?o and the buckytubes first recognized by Sumio'Iijima.10 These structures are not just restricted to carbon, as other multiple sheet materials such as molybedenum sulphide—as shown by Tenne and coworkers11—also can form related structures (Fig. 8).
60 ’R. B. Fuller, Inventions—The Patented Works of Buckminster Fuller (New York: St. Martin’s Press, 1983).
61 10S. lijima, Nature (London) 1991,354,58.
62 ’’R. Tenne, L. Margulis, M. Genut, G. Hodes, Nature, 1992, 360, 444.
63 Fig. 8. Molybedenum sulphide buckytube
64 COURTESY OF HUMBERTO TERRONES
66 So now we have the tantalizing glimpse of a new material, which could revolutionize civil and electronic engineering much as steel and aluminum did in earlier times. The buckytube discovery promises a material some fifty to one hundred times stronger than steel at about one-sixth the weight, a material which could provide nanometer-diameter, low-resistance wires to interconnect the nanoscale components on the molecular computer chips that appear to be just over the horizon. However, to harness the exceptional tensile strengths as well as the electronic and magnetic properties of these molecular structures, advances in synthetic technology that rival the ingenuity breakthroughs of the past will be required. We need molecular engineering with a precision as yet well beyond us. It will require us to leap forward from the past approach in which chess-type logic was used to outmaneuver entropy and create new, ever more complex molecules. This was the board on which such wizards of synthetic chemistry as Robert Burns Woodward, Robert Robinson, and John Cornforth played and on which their heirs such as Jean Marie Lehn, K. T. Nicolau, and Fraser Stoddart are playing today.
67 Perhaps we should take a leaf out of the Natural World’s book and attempt to create the nanoscale jigs that will allow us to hold in place the components of the nanoscale (pure carbon) Meccano components we have discovered, so that we can build truly complex, exactly specified giant molecules. To achieve its aims, ‘‘Life’’ has invented proteinaceous enzymes which are effectively gantries much like scaffolding we use to build the skyscrapers of today. A particularly delightful example, which exists in our bodies, is the amazing enzyme ATP synthase (Fig. 9) of Paul Boyer (UCLA) and John Walker (MRC Cambridge), who were awarded the 1997 Nobel Chemistry Prize for elucidating its structure and mode of action.12 It seems, at least to me, to be a portent of fascinating chemistry of the future. The advance has similarities with the breakthrough made by Max Perutz, who discovered that deoxyhemoglobin (another favorite of mine) had developed the knack of readjusting its structure on oxygen uptake in order to facilitate further oxygen uptake (up to four molecules). This is really unusual, as in general one would expect oxygen uptake to get harder as successive molecules are added—as in the case of when one blows up a balloon which gets more and more difficult. Boyer and Walker found that there are tiny biological electric motors in our bodies which are essentially molecular machines consisting of a segmented pumpkinshaped protein structure with an axial central shaft. As an asymmetric rotor in the shaft turns, driven by a flow of H ions through a disc at its base, it distorts cavities in the walls of three of the segments. The motion enables this amazing molecular machine to drive the addition of phosphate (P) to adenosine diphosphate (ADP) to form adenosine triphosphate (ATP) in the cavi-
68 UD. Voet, J. G. Voet, C. W. Pratt, Fundamentals of Biochemistry (New York, Wiley, 1999) 514-517.
71 Fig. 9. The enzyme ATP synthase
73 ties.13 In muscle tissue the ATP can revert back to ADP + P, and the energy stored in ATP is released, enabling us to move our arms and legs. What an amazing delight it is to discover that our muscles are powered by myriads of microscopic electric motors. We turn over at least half our body weight of ATP each day. The more we learn about nature, the more we seem to find that we are reinventing the wheel—or in this case the armature.
74 Perhaps a new age of chemistry—truly nanometer-scale molecular engineering—is on the horizon, an age in which we will start by modifying existing enzymes to make new molecules perfectly. New advances in genetic engineering will be required. Perhaps in the next stage we will learn how to build our own enzyme-like gantries—perhaps mainly out of carbon—and how to perfect a synthetic chemistry technology capable of rivaling the staggering efficiency of DNA replication (error rate of l:109). Any higher error rate than l:109 for DNA would be too high for us to exist for long enough! Such synthetic strategies seem a far cry from our present capabilities. Hopefully, however, now that we know what is achievable, the young geniuses of the new millennium will develop such techniques, spurred on by aesthetic visions of the novel molecular architecture which nature has created.
75 Acknowledgments: I wish to thank my colleagues Jonathon Hare, Humberto Terrones, and David Walton for their help with this article.
76 13Voet, Voet, Pratt, op. cit.
77 Definition: Universe from Synergetics 2; Further
78 Explorations in the Geometry of Thinking
7980 304.00 Our definition of Universe provides for the undiscovered and for the yet-to-be discovered. Do not worry about that farthermost star which is yet to be consciously apprehended by any human being. Do not think we have not provided for those physical or chemical phenomena as yet not observed and recorded by human or mechanical sensing devices. The existence of such phenomena may not have even been postulated, but they can all be accommodated by our definition of Universe. Because we start with whole Universe we have left out nothing: There is no multiplication by amplification of, or addition to, eternally regenerative Universe; there is only multiplication by division. The farthermost star and the most unfamiliar physical phenomena are all accommodated by further arithmetical subdividing of our aggregate of overlapping experiences. Nothing could have been left out when you start with whole Universe. (See Secs. 522.32, 537.31, 540.03, and 1050.13.)
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81 Odd BallIn synergetics we find the difference of exactly one whole integer frequently manifest in our geometrical interrelationship explorations. Beyond the one additional proton and one additional electron that progressively characterize the hierarchy of the already- discovered family of 92 regenerative chemical elements and their short-lived transuranium manifestability by high-energy physics experiments, we find time and again a single integer to be associated with the positive-negative energetic pulsations in Universe. Because the energetic-synergetic relationships are usually generalized relationships independent of size, these single rational integer differentials are frequently found to characterize the limit magnitudes of asymmetric deviations from the zerophrase vector equilibrium. (See Sec. 1043.)The minor aberrations of otherwise elegantly matching phenomena of nature, such as the microweight aberrations of the 92 regenerative chemical elements in respect to their atomic numbers, were not explained until isotopes and their neutrons were discovered a few decades ago. Such discoveries numerically elucidate the whole-integer rationalization of the unique isotopal system’s structural-proclivity agglomeratings.There is a phenomenon that we might describe as the eternal disquietude of the Odd Ball promulgating eternal reorderings, realignments, and inexorable transformings to accommodate the eternal regeneration integrity of intellectually differentiable Universe. This suggests philosophically that the individual metaphysical human viewpoint—the individual ego of the human—is indeed an essential function of the eternally regenerative integrity of complex law-governed Universe.Possibly this mathematical Odd-Ball-oneness inherently regenerates the ever-reborn ego. Just when you think you are negative, you find you are positively so. This is the eternal wellspring of positive-negative regeneration of acceleratingly heating entropy and cooling-off syntropy, which is synergetically interoperative between the inherently terminal physical differentiating and the inherently eternal metaphysical integration.Humans as Ultimate Complexities•[311.10-311.18 Complex Humans Scenario]
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82 Synergetics presents a picture of the multioptioned operational field of cosmic favorabilities, intertransformabilities, and complementary interaccommodations within which each human individual, his life, his world, is always one alternately elective, complex-integrity way Universe could have evolved.No man or woman can ever prove when they wake up in the morning that they are the same person who they think they remember went to sleep. They may dream that they had other dreams, but there is now no way to prove that there are not a great many alternate ‘‘me’s,’’ and that one of them may have awakened under one set of alternate possibilities while the others may have awakened under other circumstances, and that each of them thinks that it is the only ‘‘me.’’Let’s assume that you have the realistically imaginative capability to invent a Universe wherein there are no substantive ‘‘things,’’ a Universe wherein there are only events. Life is first of all awareness. No otherness: no awareness. Much otherness is difference-from-me-ness. Events are cognizable and re-cognizable only through awareness of the occurrence of interrelationship differences in sequentially observed conditions. Your Universe would have to be a Universe of ever-changing events, differentially adding here, subtracting there, multiplying, and dividing, reaching out or coming in, differentially including and integratingly refining, either locally gaining or losing, while continually and complexedly transforming at a plurality of rates and magnitudes. Within this Universe you also invent all the 92 regenerative chemical elements and their respectively unique, repulsive or associative behaviors compounding to form billions of unique substances while catalytically disassociating such substances to form all the chemical-element isotopal ag- glomeratings. You may go on to invent all the generalized principles of synergetic mass-interattractiveness and entropic radiation, as well as the latter’s reflectivity and refractivity. And you will have to invent precession and all the unique frequencies of the chemical elements as well as each and all cyclic events. Then you start playing your game of Universe. You have all the stars and galaxies of stars entropically exporting energy and planets syntropically importing energies that, when they reach critical mass, become new stars as fragments of the exploded old stars become cores for the beginning of new planets. As you invent, you arrive at more and more intertransformative complexities and timing problems; the whole game gets more and more complicated. Quite clearly experiences must multiply, so the complexity of your invented Universe multiplies exponentially at a fourth-power rate in respect to the arithmetical progression of time. And since every event is always accomplished with six equieconomical, four-dimensionally directioned moves—the four dimensions being (1) inwardly, (2) outwardly, (3) circumferentially and equatorially around (axial spinning), and (4) polarized, involutionally- evolutionally, inside-outingly around—by means of the alternative, equimax- imally economical optional move events you might find by the close of each event that you are six, five, four, three, or two radial zones outwardly in any direction from where you started—or right back where you started—and you soon come to the complex invention of thus-far-discovered billions of galaxies consisting of approximately 100 billion stars of the macrocosm and multibillions of invisible-to-naked-human-eye, microcosmic, associating and disassociating behavioral identities, altogether camouflaged beneath the blanket of make-believe ‘‘reality’’ of exclusively terrestrial politics and economic me-firstings, whose nonsensical preoccupation we call ‘‘today.’’ It is doubtful that the million-light-year-distanced Andromeda nebula has any interest in Republicans or Democrats, communists or capitalists, or any other terrestrial partisanships.So it could be that human beings, wherever they occur in Universe, may be introduced as a means of coping metaphysically with the most complex kinds of local Universe problems, so that each one of us is where the problem-solving of Universe is being transacted. If we were to think of ourselves as things—as china dolls, as kinds of china dolls that would just get smashed up or would just get worn or eroded away—that wouldn’t be very good thinking. It would be much closer to actual Universe to think of ourselves as an absolutely continuous complex process. We are quite possibly the most complex of the problem-solving challenges of the invention that is eternally regenerative Scenario Universe. In this way each of us might be a department of the mind of what we might call god.It is reasonable to suppose that there must be an overall physical- metaphysical cosmic accounting system that is always omniconsiderately integrative of all the a priori set of generalized interrelationship principles that we have found scientifically to be unfailingly operative in Universe. It may well be that each of us humans is an important function in sustaining the eternally regenerative integrity of Universe. The invention of the game of limited and terminal local awareness that we call ‘‘life’’ is in contradistinction to the concept of eternally total cosmic knowledge, intellect, and wisdom, whose totality of comprehensive comprehension would answeringly cancel out all questions and all problems, which would result in the eternally timeless, sublime 0=0 equation of absolute perfection.Local life in Universe involves the invention of time. Time involves nonsimultaneity and limited information—ergo, only partial equatability. By introducing time and the myriad differential of interevent lags consequent to the exponentially multiplying, reinterpositioning distance variables inherent in the six alternative moves for each of the myriad of differentially frequenced, never-simultaneous events, the exponentially multiplying complexity of interevent lags accounts for both the micronuclear and macroastronomical progressive range of distance differentials of experience-limited, local-Universe human observing. Since each of the only-mathematically-statable, scientifically generalized laws of physical Universe constitutes a statement of truth, and since science has discovered a plurality of observable and ever redemon- strably operative truths—all of which are always omniinteraccommodative—it may be said that truth is complex. It is mathematically hypothesizable that all of the truths are potentially integratable and that the resulting integral truth constitutes the cosmic that humans intuitively sense to be in governance of Universe and speak of to one another with the inadequate soundword god.We can thus invent a hypothetical Universe with a limited game of individual human participation in only-locally-occurring, time-distance mor- phation awareness conceptualizations integratingly cognizant, as the sequential reality of human realization, of the complexedly interacting plurality of omniinteraccommodative cosmic laws that altogether enact events in pure principle, so reliably pure as to be sensorially apprehended by human brains and partially comprehended by human minds.We may logically assume that the intellectual cosmic integrity of the timeless, sublime integral of absolute perfection must continually test its integrity o£ eternal regenerativity; wherefore the integral that we inadequately identify as god requires a plurality of local sensing monitors to be omnideployed in the time-distance-differentiated, nonsimultaneously conceptual, serial Universe to continually observe the local Universe events, while also being progressively advantaged with an ever larger inventory of the discovered laws governing cosmic regeneration integrity, and thus equipped, to cope metaphysically with each of the profusion of unprecedentedly unique regenerative complexities that we speak of as problems. In effect god differentiates cosmic integrity into a time-distance-differentiated plurality of limited, local, metaphysical, intellectual experiences with which to test the capability of ‘‘god’’ to reintegrate and restore its timeless zerophase unity.320.00 Scenario Universe
83 321.03 Humans have always tried to conform their concepts of Universe to their own human prototype. Humans stop and start; sleep and wake; are bom, grow, decay, and die: so humans thought the Universe must also have a beginning and an end. Now astrophycists find this to be untrue. There could never have been a primordial chaos, simply because scientists now know that the proton and neutron always and only coexist in the most exquisite interorderliness. There could never have been a time when their integrity was not an integrity.
84 321.04 Universe is a scenario. Scenario Universe is the finite but nonuni- tarily conceptual aggregate of only partially overlapping and communicated experiences of humanity. Uni-verse is a momentarily glimpsed, special-case, systemic-episode takeout. When we start synergetically with wholes, we have to deal with the scenario within which we discover episodes—like the frog the snake is swallowing.
85 321.05 Time is only now. Time and size are always special-case, asymmetric episodes of now whose systemic aberrations are referenced to the cosmic hierarchy of primitive and symmetrical geometries through which they pulsate actively and passively but at which they never stop. The rest of Scenario Universe is shapeless: untuned-in. (See Sec. 982.62 for cosmic hierarchy and compare text at Sec. 1033.103.)
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86 Analogy of Rope-making and Film-strips325.11 As seen by .an individual human observer or as recorded by any humanly devised instruments, Scenario Universe is progressively reaggregated within the recorded, remembered, recalled, and progressively reconsidered information inventory of ever more macro-comprehensive-outward and micro-exquisite-inward ranges of the compositely growing individual’s experiencing of life-in-time.
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87 Scenario Universe is to any and all human observers very much like a rope-making experience—a rope that grows ever greater in total complexity but not in total diameter, and is comprised of ever more exquisitely di- ametered and ever stronger separate and differently lengthed fibers, a rope of which each of the myriad of progressive information events are in themselves terminal.Each fiber enters into the scenario of rope-making by being twisted with others into a small thread of successively introduced and only partially overlapping fibers. This composited thread in turn is twisted with other threads into more complex strands. The strands are twisted with strands—always consistendy clockwise or counterclockwise (never both)—until the totally twisted complex is brought together with a similarly twisted but turned-around and now oppositely directioned rope of equal complexity, whereat, when side by side, their respective tendencies to untwist interwhip them together to block one another’s untwisting and produce an overall stabilized rope.Employing the concept of individual fibers in this rope-making analogy and substituting for the word fibers the word photons, we can comprehend Einstein’s curved-space assumption of the manner in which the om- niremotely, entropically dispersed, individual energy increments, radiationally disassociated from former star sources at maximum remoteness from other entities, now progressively enter the gravitational neighborhood of radiation- ally disassociated energy increments—emanated from many sources—and become thereafter progressively reassociated with one another in forming new celestial aggregates, thereafter—as substantive matter—converging to a terminal complexity and density, thereafter once more to become radiandy dispersed.The balancing of the gravitational and radiational exchanges is again analogous to the patterns of rope-making. We simply splice together the ends of the stabilized overall ropes to produce a plurality of looped-back, cosmic rope-making in a Scenario Universe of nonsimultaneous, local, episode twistings and untwistings. While some loops are unraveling, their strayed- away strands got caught elsewhere in the new intertwinings.The whole analogy of the rope-making and unmaking can be retransformed into the cinema concept, and the words fibers or photons being replaced by the word atoms. 'Vie. can conceive now of all the separate atoms in the chemical compounds comprising the photo-negative celluloid ribbon of long-ago-exposed, financially exploited, stored-and-forgotten footage, the significance of whose once novel special case information has long since been incorporated in popularly accepted generalized viewpoints. The old film-strip has been chemically dissolved and its atoms disassociatively dispersed, migrated, and subsequently reassociated in a new inventory of on-the-shelf, unexposed, film-strip footage upon which may be recorded the ever-changing but progressively increasing inventory of comprehensive human experiences of tomorrow’s today. In this analogy there is a plurality of fresh individual film-strips being nonsimultaneously and only overlappingly-in-time exposed for each individual observer in the Universe, as each is overlappingly intertwined into more complex information strands.Epistemography of Scenario UniverseSynergetics always commences its considerations and explorations with finite but nonunitarily conceptual Scenario Universe, which is inherendy nonsimultaneous. Scenario Universe is the totality of all humanity’s consciously apprehended and communicated experiences. It is inherendy prohibited for the totality of physical Universe to be quantitatively increased—ergo, in synergetics we have differentiation in the family of primitive generalized conceptual systems. Multiplication is always and only a special-case, relative time-size phenomenon—ergo, multiplication is accomplished always and only as special-case frequency of subdivision of the primitive epistemo- graphic family of interassociations of primitive concepts.All special-case multiplicity is considered and expressed in unique frequency, angle, vector, and topological quantation terms. The epistemography of synergetics discovers operationally, experientially, and experimentally that the most primitive of the conceptual systems to be divided or isolated from nonunitarily and nonsimultaneously conceptual Scenario Universe must inherendy consist of the simplest minimum considerability none of whose components can exist independendy of one another. The system components of minimum considerability are inherendy recollectable only because they are experientially components of observable otherness. The words to describe in- herencies of systems were invented by humans in spontaneous recognition of co-occurring observabilities. The word part could have been invented by humans only after having discovered a holistically considerable system.Within the time frame of any one given observer simultaneous means the unitary consideration of a plurality of experientially observable, concurrendy focal episodes with differendy occurring births, deaths, and longevities—but they are overlappingly co-occurring with their omnidirectionally comprehensive environment. Omnicircumstance conditions are often forgotten in the recall of only the focal episodes of the considered systems’ most prominent central memorabilities. Con-sideration—or the simultaneous co-reviewing of a plurality of stars—is always simultaneous. But simultaneous is not instantaneous. Apprehending and comprehending require a time lapse.Simultaneous is episodal in Scenario Universe. Because our sight is only a light-wave frequently phenomenon, instantaneous cannot accommodate apprehension because instantaneity inherently lacks time span or wavelength.
88 326.00 Universe as Metaphysical and Physical
89 •[326.00—326.50 Metaphysics Scenario]
90 326.01 The support of life on our planet consists of two kinds—metaphysical and physical. Both cosmic and terrestrial energetic regeneration, organic and inorganic, are physical; while the know-what of pure science and the know-how of applied science are both metaphysical. The know-what of science’s experimental evidence informs technology’s know-how to employ efficiendy the substantive resources and synergetic metaphysical patterns progressively found to be operative in Universe. These are essential to the maintenance of life on board our planet as well as in mounting local-Universe exploring excursions from our mother-spaceship Earth.
91 326.02 All that is physical is energetic. All that is metaphysical is synergetic.
92 326.03 All the energetic physical consists of two phases—(1) energy associative as matter, and (2) energy disassociative as radiation—with each being reconvertible into the other. All the synergetic metaphysical consists of two phases—(1) subjective information acquisition by pure science exploration, and (2) objectively employed information by applied science invention.
93 326.04 We can refine all the tools and energy capability of single and commonwealth into two main constituents—the physical and the metaphysical. The physical consists of specific, measurable energy quantities; the metaphysical consists of specifically demonstrable know-how capabilities. Only the metaphysical can designedly organize the physical, landscape-forming events to human advantage, and do so while also maintaining
- (a)
- (b)
94 the regenerative integrity of the complex ecological-physiological support of human life aboard our planet, andthe integrity of the chemical-element inventory of which our planet, its biosphere and co-orbiting hydraulic, atmospheric, ozonic radiationshielding spheres, ionosphere, Van Allen belts, and other layerings all consist.326.05 Only the physical is alterable; the metaphysical is unalterable. All the physical is continually intertransforming in orderly ways discoverable only by the weightless metaphysical mind. The local physical systems are everywhere energy exportive, which is humanly misinterpreted to be entropic and dissynchronously expansive only because the exported energies are electro- magnetically (i.e., nonsubstantially) dispatched only as information—which is purely metaphysical—to be always eventually imported as information by electromagnetic reception in elsewhere-newborn, regenerative assemblages of cosmic systems. The local exportings appear to be dissynchronous only when viewed from too short a time span to permit the tuned-in occurrence of the next synchronous moment of the eons-apart frequencies often involved in celestial electromagnetics.*
95 326.06 We look at the stars, and they look very randomly scattered throughout the sky. But we can say that the number of direct and unique interrelationships between all the stars is always . This equation demonstrates the principle of order underlying all superficially appearing dis- orderliness or randomness (see Sec. 227) and tells us quite clearly and simply that we are mathematically justified in assuming order to be always present despite the superficially appearing disorder. This gives us a personal sense of the order-discovering and -employing power of the weightless mind and at the same time a sense of our human anatomy’s negligible magnitude in Universe when juxtaposed to the vast array of stars visible to the naked human eye. The stars observable on clear nights—the naked-eye-visible stars—constitute but a meager fraction of all the stars of our own ‘‘Milky Way’’ galaxy. Beyond this there is the 99.99 times greater array of the only-telescopically- visible 200 billion other already photographically identified galaxies, each consisting of an average of 100 billion stars, all coordinately operative within a 22-billion-light-year diameter sphere of Earth-planet-mounted instrumental observation and Earthians’ photographic recording. This spherical-sweepout sphere of astronomical observation by minuscule humans on Earth describes a sphere of 123-plus-21-zeros-miles in diameter, all of which adds up at the present moment to each of the four billion humans on Earth having an exclusive personal quota of 25 billion stars or suns operatively available to their energetic regeneration, just awaiting his metaphysical know-how development, with the metaphysical assurance already established that the Universe is eternally regenerative. Energy crises are crises of ignorance induced by lethal selfinterest.
96 326.07 This cosmic-accounting analysis discloses the omniuniversal orderliness that the scientist finds always to be underlying all of the only-ignorantly- apprehended illusions of randomness. This tells us that the seeming disorder of physical entropy is only superficial and explains why metaphysical thought
97 ‘Whether communication is by telephone hook-up or by wireless radio, what you and I transmit is only weightless metaphysical information. Metaphysical, information appreciative, you and I are nqt the telephones nor the wired or wireless means of the metaphysical information transmitting.
98 can always find the syntropic orderliness that cancels out all disorderliness. Disorderliriess is nonthinking. Exclusively energetic brain, which stores the sensorial input data of all the special-case experiences, cannot find the synergetic interrelationships existing only between and never in any of the specialcase systems considered only separately, any more than a library building in itself can find the unique interrelationships existing between the separate data that it houses. Only mind—the magnificent, weightless, metaphysical, pattern-seeking-and-apprehending function—has demonstrated the capability to intuitively apprehend and mathematically contrive the experimental means for identifying the significant, only-between-and-not-of, only mathematically expressible, eternal relationships, which altogether permit a seemingly inexhaustible variety of cosmic interrelationship patterning, and thereby human mind’s capability to participate in the ceaseless complex of orderly intertransformings in such a manner as continually to abet the human mind’s unique local-Universe functioning in maintenance of the cosmic integrity of eternal regeneration.
99 326.05 So long as humans progressively employ and develop their syntropic, energetic, metaphysical mind’s capability to locally abet cosmic integrity, just so long will that metaphysical capability continue to operate in this particular local Universe’s ecologically regenerative, planetary team aboard spaceship Earth. If, however, the entropic, energetically exploiting, antisynergetic, exclusively partisan profit motive—political or financial—continues to dominate and rule humans by force of arms, then the Earthian ecology team will become self-disqualifying for further continuance as a potentially effective local sustainer of cosmic-regeneration integrity. This is the net of what has now become metaphysically evidenced regarding the potential significance of humans aboard planet Earth. It is the nature of the contest between brain and mind. Brain is selfishly exclusive; mind is cosmically inclusive. Brain now commands the physical power to overwhelm humanity. But it is also the nature of mind’s design science capability to render all humanity physically successful, thus eliminating human preoccupation with the struggle and thereby freeing all humanity to become metaphysically preoccupied with fulfilling its cosmic-regeneration functioning.
100 326.09 The physical Universe is an aggregate of frequencies. The human brain’s senses are able to tune in direcdy only about one-millionth of the exclusively-mind-discovered and now experimentally proven and usable electromagnetic ranges of energetic reality. To this magnificent extent has the metaphysical brought humans into potential mastery of the physical. But thus far their physically most powerful political masters, misassuming ignorandy that there is fundamental inadequacy of life support, continue to exploit the fear that this induces in individuals, not for the individuals’ sake but for concern and love for their dependents. Thus individuals concerned for the welfare of their dependents fearfully yield their economic-strategy mandates to the power-wielding brains of exclusively partisan ideologists.
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101 Precession of Side Effects and Primary EffectsIn recognizing the residual ignorance of variously dominant Earthian power-structure partisans of this particular cosmic-history moment, we do not impute malevolence or wrongdoing; we are only recognizing the checks-and-balances mechanisms of nonsimultaneously occurring and only partially overlapping Scenario Universe’s vast variety of local conception-to- birth gestation rates. These gestations are the product of the associative energies’ frequency synchronizations as well as of the concomitant rate of local disassociative energies, the dyings-off.In the regenerative integrity of the cosmic design the locally supportive, human mind’s understanding operative on planet Earth has to be midwife at the birth and experiential development of critical information inventorying; it must also sustain the total—Garden of Eden—ecological re- generativity as naturally accomplished by intense high-frequency information transmitted by the electromagnetics of chemical elements of the star Sun and receivingly translated by the Earth’s land-borne vegetation and water-borne algae into photosynthetic sorting, reorganizing, and combining of the planet Earth’s inventory of carbon, hydrogen, and other chemical elements. Some of these energies are redistributed to the biosphere, and some reenter directly into the integral metabolic multiplication and proliferation by all biological organisms of the hydrocarbon molecules and their concomitant environmentally supportive, chemical exchanging events. To function successfully in gales and storms while exposing adequate leafage to the Sun, the dry Earth-borne vegetation must send into the soil and rocks roots that draw water from the soil to cool themselves against dehydration by the heat of radiation exposure as well as to provide the vegetation with noncompressible, hydraulic structuring as well as with hydraulic distribution of the many eccentric, locally concentrated energy stressings of the vegetation’s structure. Because the vegetation is rooted, it cannot reach the other vegetation to procreate. To solve this regenerative problem Universe inventively designed a vast variety of mobile creatures—such as birds, butterflies, worms and ants—to intertraffic and cross-pollinate the vast variety of vegetation involved in the biochemical refertilization complexities of ecology, as for instance does the honeybee buzz-enter the flowers to reach its honey while inadvertently cross-fertilizing the plants. Each biological specimen is structurally designed by the programmed codings of DNA-RNA and is chromosomically programmed to go directly to immediately rewarding targets while inadvertently, or unknowingly, producing (what are to it) ‘‘side effects’’ that inadvertently sustain the main objective of Universe, which is the sustenance of the synergetic circuitry of terrestrial ecology and thereby as well to sustain the cosmic regeneration.Humans, like the honeybee, are bom ignorant, preprogrammed with hunger, thirst, and respiratory drives to take in chemical elements in crystalline, liquid, and gaseous increments, as well as with procreativeness and parental-protectiveness drives. With their directly programmed drives humans inadvertently produce (what are to them) side effects, which results in their doing the right cosmic regenerative tasks for all the wrong reasons—or without any reason at all. This preliminary phase of preconditioned human reflexing, while lasting millions of years, is a gestative-phase behavior that becomes obsolete as humans’ metaphysical mind discovers the principles of precession and discovers—only through vast, cumulative trial and error—the pattern experience of both terrestrial and cosmic ecology; whereafter humans will progressively recommit their endeavors in support of the recycling and orbitally regenerative effects, precessionally interproduced by all independently orbiting cosmic systems. This abrupt 90-degree reorientation constitutes the evolutionary stage through which humanity is now passing, wherein humanity will progressively exchange its exclusive preoccupation with selfpreservation for that of supporting omniinclusive, cosmic integrity.Pyramid of GeneralizationsThe physical Universe is characterized by local-system entropy, an ever-increasing, locally expansive randomness, and an ever-increasing diffusion, as all the different and nonsimultaneous transformations and reorientations occur. While the entrophy and disorderliness of physically exportive Universe increase and expand, we have the metaphysical Universe countering syntropically with energy importing, orderly sorting, and comprehensive contraction and storage of energy. In the metaphysically organized, syntropic- importing phase of cosmic-energy events we have the human mind digesting and sorting out all the special-case experiences and generalizing therefrom the persistent relationships existing between and not in the special characteristics of all the special cases. All the eternal, weightless principles apparently governing both the physical and metaphysical Universe are experimentally detected and digested into mathematical generalizations, of which only a very few are as yet known.The whole process of generalizing generalizations forms a pyramid whose base consists of all the special cases of direct physical experiences. We can say, ‘‘We take a piece of rope and tense it,’’ when we do not in fact have a rope in our hands. We have all had so many rope experiences that we can generalize our communication of the concept. This is a first-degree generalization. The discovery of always and only coexisting tension and compression is a second-degree generalization. Finding a whole family of always and only coexisting phenomena is a third-degree generalization, and conceiving therefrom ‘‘relativity’’ is a fourth-degree generalization.In this pyramid of generalizations the human mind goes way beyond the biologicals in its development of the diminishing conceptual Universe—diminishing because, being progressively reduced and refined from a plurality of first-degree to a plurality of second-degree generalizations, and finally to as concise a form as E=Mc2, which may some day be even more economically expressed as it is synergetically digested into ever more comprehensive and exquisite cosmic comprehension by metaphysically evolving human minds. So we find the metaphysical not only comprehending the physical—which should have been expected—but also encompassing and omni-accounting all the physical with the tetrahedron and thereafter reducing Universe’s structural system myriadness to unity. The metaphysical, as with the circumferentially united, great-circle chord vectors of the vector equilibrium, masteringly coheres the physical by more effective use of the same quanta of energy. (See Sec. 440.08.)Discovery of an acceptable hypothesis for explaining the role of humans as an essential metaphysical function of Universe, along with discovery of the mathematical proof of the tetrahedron as the true minimum limit structural system of Universe and its subdivision of Universe into macro- and microcosms as the sizeless conceptual system basis for generalizing general system theory, all develop as a consequence of our asking ourselves the question: How may we organize our self-disciplining on behalf of all humanity and in support of the integrity of eternal cosmic regeneration to deal comprehensively and capably with the maximum and minimum of limiting factors of the combined and complementary metaphysical and physical prime subdivisions of Universe?326.23 The theory of functions holds for Universe itself. Universe consists at minimum of both the metaphysical and the physical. The inherent, uniquely differentiable, but constantly interproportional twoness of physical Universe was embraced in Einstein’s one-word metaphysical concept, ‘‘relativity,’’ and in a more specific and experimentally demonstrable way in the physicists’ concept of complementarity.
102 326.30 Comprehensive Universe
103 326.31 Comprehensive Universe combines both the metaphysical Universe and the physical Universe. The local physical system is the one we experience sensorially: the conceptual metaphysical system is one we never experience physically but only consider in thought. As we discover in our grand synergetic strategy, we commence all problem-solving most advantageously at the supreme, terminally comprehensive level of Universe—that is, at the generalized-principle level. Thereafter we separate out from nonunitarily conceptual Scenario Universe one single, thinkable, experientially definable, holistic concept, which definition function inadvertendy discloses the inherent polyhedral geometry of all conceptually sizeless thought referencing. We go on to find out through topological mathematics how to demonstrate that the difference between the cosmically total metaphysical and physical Universe and anyone experiential physical system, or any one conceptually thinkable system, is just one (positive and negative) tetrahedron, or one unity- of-twoness. This is to say that the difference between the finite (because an aggregate of finites) but nonunitarily conceptual total Scenario Universe (which we used to call infinity) and the physical Scenario Universe of energy with which physics deals, is just one finitely positive and one complementary, finitely negative tetrahedron. The exclusively conceptual metaphysical Universe is also proven to be a finite scenario because it too is an aggregate of locally terminal—ergo, finite—intellectual conceptioning experiences. The total Universe is just one (plus and minus) tetrahedron more than either the exclusively physical or exclusively metaphysical conceptualized Universe. (See Sec. 620.12.)
104 326.32 What man used to call infinite, I call finite, but nonunitarily conceptual—ergo, nonsimultaneously thinkable. 'What man used to call finite, I call definite, i.e., definable, conceptually—ergo, thinkably definable. The plus and minus, sizelessly conceivable, tetrahedral differences are all finitely and rationally calculable.
105 326.40 Metaphysical and Physical: Summary
106 Metaphysical cogitates reliably in respect to equilibrium.
107 That which is communicated, i.e., understood, is metaphysical.
108 Metaphysical is unlimited and generalizable independent of time-spacesizing.
109 Metaphysical is unweighable, imponderable, and cannot move an electro- magnetically or mass-attracted, levered needle.
110 Physical abhors equilibrium.
111 The means of communication is physical.
112 Physical is limited, experienceable, and is always special-case time-spacesized.
113 Physical is always apprehensible by an instrument’s needle leverage actuated by weight, pressure, heat, or electromagnetics.
114 Metaphysical discoveries clarify ever more comprehensively, inclusively, and are more economically communicable in their progressive description of the eternally changeless, and the rate of the more economic restatability continually accelerates.
115 Humans are metaphysical. You and I are awareness, which is the identity of the weightless life.
116 Conceptioning is metaphysical.
117 Waves are metaphysical pattern integrities.
119 Equilibrium is metaphysical.
120 Conceptuality is metaphysical and weightless. Reality is metaphysically conceptualized information transmitted only through physical senses.
121 The metaphysical evolution of human awareness slows as it approaches the omniintegrated verity—physically unattainable by the only-physically- sensing, anatomical machine designed specifically only for limited operation with the highly specialized local Universe conditions of the Earthian biosphere.
122 Physical events are ever transforming and ever more acceleratingly en- tropic.
123 The physical, automatedly rebuilding, information-gathering device we sen- sorially apprehend as our anatomy, employed by metaphysical mind, consists entirely of inanimate atoms and is therefore entirely physical.
124 Sensing is physical, and the sensed is physical and always inherently specialcase.
125 Metaphysical pattern integrity waves articulate as physical phenomena such as water, air, or electromagnetic fields, and thus communicate their nonsen- sorially apprehensible presence through the displacement of the sensibly detectable physical phenomena.
127 Disequilibrium is physical.
128 Realizations are special case physical, brain-sensed phenomena.
129 Physical systems alone accelerate as they unravel entropically, ever approaching the speed of a noninter- fered-with electromagentic, spherically expansive wave (186,000 mps.) The generalized conceptions of metaphysical evolution tend ever to decelerate, simplify, consolidate, and ultimately unify.
130 Generalization is metaphysical: mind function. Design is generalized metaphysical conceptioning.
131 Theoretical and applied science is conceptually metaphysical.
132 Metaphysically operative mind cannot design a generalized tool of unlimited and eternal capability, which unlimited and eternal capability is manifest only in purely metaphysical, weightless principles. Principles have no beginning-ending or other temporal limitations. Principles are truths.
133 The special case transformings of physical evolution tend ever to accelerate, differentiate, and multiply.
134 Tools, artifacts, and all humanly contrived extracorporeal facilities designed by mind are always specialcase, brain-processed, physically sensible phenomena.
135 Applied science always results in special-case, brain-sensible, limitedlongevity phenomena.
136 We can invent only physical. The human mind, translating the generalized principles only through special-case, individual, brain-operated anatomical tools, can realize only phenomena of special-case, limited-capacity capability and durability.
137 326.50 Metaphysical and Physical: Cross-references
139 163 Metaphysical Experience
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140 Synergetics205.03 Vector Equilibrium
142 217.02 Prospects for Synergetics
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143 Principle of Irreversibility251.27 Discoveries of Synergetics
144 251.48 Discoveries of Synergetics
145 251.50 Discoveries of Synergetics
146 323 Scenario Universe (Same as 217.02) •
147 424.02 Isotropic Vector Matrix: Quantum
149 443 Vector Equilibrium as Equanimity Model
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150 Zerophase501.01 Symmetry & Asymmetry
151
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157158 Tetrahedron: Quantum (Same as 424.02)986.840 Primitive Hierarchy
160 1013.50 Visible and Invisible Tetrahedral Arrays
163 The design movement during the 1950s referred to as the Cranbrook experience often included both Cranbrook and the nearby University of Michigan College of Architecture and Design. Designers like the Eameses, the Saarinens, Harry Bertoia, and Carl Milles would interface with Fuller and form lifelong friendships. At the University of Michigan, young Saarinen, Yamasaki, Kahn, Birkerts, and occasionally Frank Lloyd Wright interacted with Bucky's ideas.
164 Bucky's assistant for the Dymaxion Deployment Unit, a converted grain bin called the Butler DDU was Walter Sanders, head of the Department of Architecture at the University of Michigan and later dean at the university. Here Bucky refined the 93- foot dome to enclose the Ford Motor Company's old Rotunda Building. Bucky's design was based on his octet truss, a 4-pound octahedral structure weighing only 2.5 pounds per square foot. It was an instant success. Recently, UM professor Joseph T. Lee donated a section of the octet truss to the Henry Ford Museum at Greenfield Village. Sanders, Oberdick, Eaton, Metcalf, Eero Saarinen's associate Glenn Paulsen (who would later become head of the Cranbrook Institute), and others would provide the basis of architectural studies at Michigan and stimulate Fuller's ideas. When Bucky was a visiting professor at Michigan, two of his students were Charles Correa and his wife, Monika, from Bombay, India. Other Michigan graduates—besides myself—included Charles Moore; Domino Pizza magnate Tom Monehan, a collector of Wright houses; and Raoul Wallenberg, later a Swedish diplomat and true humanitarian who would save the lives of thousands of Jews during World War II.
165 Charles Correa's essay on Bucky was originally written for a commemorative book that was not published. It is published here for the first time. Included also is Bucky's poem in his own hand, about his friend Edward Durell Stone and the architect's U.S. Embassy building in New Delhi, India.