Buckminster Fuller Cosmography Pdf Printer
For other uses, see. Synergetics is the study of systems in transformation, with an emphasis on total system behavior unpredicted by the behavior of any isolated components, including humanity's role as both participant and observer. Since systems are identifiable at every scale from the quantum level to the cosmic, and humanity both articulates the behavior of these systems and is composed of these systems, synergetics is a very broad discipline, and embraces a broad range of scientific and philosophical studies including tetrahedral and close-packed-sphere geometries,,,,,, and.
Despite a few mainstream endorsements such as articles by and the naming of a molecule ', synergetics remains an iconoclastic subject ignored by most traditional curricula and academic departments. (1895-1983) coined the term and attempted to define its scope in his two volume work Synergetics.
His oeuvre inspired many researchers to tackle branches of synergetics. Three examples: Haken explored self-organizing structures of open systems far from, Amy Edmondson explored tetrahedral and icosahedral geometry, tackled geodesics in the context of social dynamics, and Nystrom proposed a theory of computational cosmography. Many other researchers toil today on aspects of Synergetics, though many deliberately distance themselves from Fuller's broad all-encompassing definition, given its problematic attempt to differentiate and relate all aspects of reality including the ideal and the physically realized, the container and the contained, the one and the many, the observer and the observed, the human microcosm and the universal macrocosm. Contents • • • • • • • • • • • • • Definition [ ] 'Synergetics' is defined by (1895-1983) in his two books Synergetics: Explorations in the Geometry of Thinking and Synergetics 2: Explorations in the Geometry of Thinking as: A system of mensuration employing 60-degree vectorial coordination comprehensive to both physics and chemistry, and to both arithmetic and geometry, in rational whole numbers. Synergetics explains much that has not been previously illuminated.
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Synergetics follows the cosmic logic of the structural mathematics strategies of nature, which employ the paired sets of the six angular degrees of freedom, frequencies, and vectorially economical actions and their multi-alternative, equi-economical action options. Synergetics discloses the excruciating awkwardness characterizing present-day mathematical treatment of the interrelationships of the independent scientific disciplines as originally occasioned by their mutual and separate lacks of awareness of the existence of a comprehensive, rational, coordinating system inherent in nature. Other passages in Synergetics that outline the subject are its introduction (The Wellspring of Reality) and the section on Nature's Coordination (410.01). The chapter on Operational Mathematics (801.00-842.07) provides an easy to follow, easy to build introduction to some of Fuller's geometrical modeling techniques. So this chapter can help a new reader become familiar with Fuller's approach, style and geometry. One of Fuller's clearest expositions on 'the geometry of thinking' occurs in the two part essay 'Omnidirectional Halo' which appears in his book No More Secondhand God. Amy Edmondson describes synergetics 'in the broadest terms, as the study of spatial complexity, and as such is an inherently comprehensive discipline.'
In her PhD study, Cheryl Clark synthesizes the scope of synergetics as 'the study of how nature works, of the patterns inherent in nature, the geometry of environmental forces that impact on humanity.' Here's an abridged list of some of the discoveries Fuller claims for Synergetics again quoting directly: • The rational volumetric quantation or constant proportionality of the octahedron, the cube, the rhombic triacontahedron, and the rhombic dodecahedron when referenced to the tetrahedron as volumetric unity.
• The trigonometric identification of the great-circle trajectories of the seven axes of symmetry with the 120 basic disequilibrium LCD triangles of the spherical icosahedron. 1043.00.) • The rational identification of number with the hierarchy of all the geometries. Nisa Gama Pani Sariga Karaoke Free Download.
• The A and B Quanta Modules. • The volumetric hierarchy of Platonic and other symmetrical geometricals based on the tetrahedron and the A and B Quanta Modules as unity of coordinate mensuration. • The identification of the nucleus with the vector equilibrium.
• Omnirationality: the identification of triangling and tetrahedroning with second- and third-powering factors. • Omni-60-degree coordination versus 90-degree coordination.
• The integration of geometry and philosophy in a single conceptual system providing a common language and accounting for both the physical and metaphysical. Significance [ ] Several authors have tried to characterize the importance of synergetics. Amy Edmonson asserts that 'Experience with synergetics encourages a new way of approaching and solving problems. Its emphasis on visual and spatial phenomena combined with Fuller's holistic approach fosters the kind of lateral thinking which so often leads to creative breakthroughs.' Cheryl Clark points out that 'In his thousands of lectures, Fuller urged his audiences to study synergetics, saying 'I am confident that humanity's survival depends on all of our willingness to comprehend feelingly the way nature works.'
' Tetrahedral accounting [ ] A chief hallmark of this system of mensuration was its unit of volume: a defined by four closest-packed unit-radius spheres. This tetrahedron anchored a set of concentrically arranged polyhedra proportioned in a canonical manner and inter-connected by a twisting-contracting, inside-outing dynamic named the Jitterbug Transformation. [ ] Shape Volume Properties A,B,T modules 1/24 tetrahedral voxels MITE 1/8 space-filler, 2As, 1B Tetrahedron 1 self dual Coupler 1 space filler Cuboctahedron 2.5 cb.h = 1/2, cb.v = 1/8 of 20 Duo-Tet Cube 3 24 MITEs Octahedron 4 dual of cube Rhombic Triacontahedron 5 radius rt.h. A & B modules Corresponding to Fuller's use of a regular tetrahedron as his unit of volume was his replacing the cube as his model of 3rd powering.() The relative size of a shape was indexed by its 'frequency,' a term he deliberately chose for its resonance with scientific meanings. 'Size and time are synonymous. Frequency and size are the same phenomenon.' () Shapes not having any size, because purely conceptual in the Platonic sense, were 'prefrequency' or 'subfrequency' in contrast.
Prime means sizeless, timeless, subfrequency. Prime is prehierarchical. Prime is prefrequency. Prime is generalized, a metaphysical conceptualization experience, not a special case. () Generalized principles (scientific laws), although communicated energetically, did not inhere in the 'special case' episodes, were considered 'metaphysical' in that sense. An energy event is always special case. Whenever we have experienced energy, we have special case.
The physicist's first definition of physical is that it is an experience that is extracorporeally, remotely, instrumentally apprehensible. Metaphysical includes all the experiences that are excluded by the definition of physical. Metaphysical is always generalized principle.() Tetrahedral mensuration also involved substituting what Fuller called the 'isotropic vector matrix' (IVM) for the standard XYZ coordinate system, as his principal conceptual backdrop for special case physicality: The synergetics coordinate system -- in contradistinction to the XYZ coordinate system -- is linearly referenced to the unit-vector-length edges of the regular tetrahedron, each of whose six unit vector edges occur in the isotropic vector matrix as the diagonals of the cube's six faces.
() The IVM scaffolding or skeletal framework was defined by cubic closest packed spheres (CCP), alternatively known as the FCC or face-centered cubic lattice, or as the octet truss in architecture (on which Fuller held a patent). The space-filling complementary tetrahedra and octahedra characterizing this matrix had prefrequency volumes 1 and 4 respectively (see above). A third consequence of switching to tetrahedral mensuration was Fuller's review of the standard 'dimension' concept. Whereas 'height, width and depth' have been promulgated as three distinct dimensions within the Euclidean context, each with its own independence, Fuller considered the tetrahedron a minimal starting point for spatial cognition. His use of '4D' was in many passages close to synonymous with the ordinary meaning of '3D,' with the dimensions of physicality (time, mass) considered additional dimensions. Geometers and 'schooled' people speak of length, breadth, and height as constituting a hierarchy of three independent dimensional states -- 'one-dimensional,' 'two-dimensional,' and 'three-dimensional' -- which can be conjoined like building blocks.
But length, breadth, and height simply do not exist independently of one another nor independently of all the inherent characteristics of all systems and of all systems' inherent complex of interrelationships with Scenario Universe. All conceptual consideration is inherently four-dimensional. Thus the primitive is a priori four-dimensional, always based on the four planes of reference of the tetrahedron. There can never be less than four primitive dimensions.
Any one of the stars or point-to-able 'points' is a system-ultratunable, tunable, or infratunable but inherently four-dimensional. (, ) Synergetics did not aim to replace or invalidate pre-existing geometry or mathematics, it was designed to carve out a new foundation with a language that would serve to provide a new source of insights.
Starting with Universe [ ] Fuller's geometric explorations provided an experiential basis for designing and refining a philosophical language. His overarching concern was the co-occurring relationship between tensile and compressive tendencies within an eternally regenerative Universe. 'Universe' is a proper name he defined in terms of 'partially overlapping scenarios' while avoiding any static picture or model of same. His Universe was 'non-simultaneously conceptual': Because of the fundamental nonsimultaneity of universal structuring, a single, simultaneous, static model of Universe is inherently both nonexistent and conceptually impossible as well as unnecessary. Ergo, Universe does not have a shape. Do not waste your time, as man has been doing for ages, trying to think of a unit shape 'outside of which there must be something,' or 'within which, at center, there must be a smaller something.'
() U = MP described a first division of Universe into metaphysical and physical aspects, the former associated with invisibly cohesive tension, the latter with energy events, both associative as matter and disassociative as radiation. (162.00) Synergetics also distinguished between gravitational and precessional relationships among moving bodies, the latter referring to the vast majority of cosmic relationships, which are non-180-degree and do not involve bodies 'falling in' to one another (130.00 533.01, 1009.21).
'Precession' is a nuanced term in the synergetics vocabulary, relating to the behavior of gyroscopes, but also to side-effects. (326.13, 1009.92) Intuitive geometry [ ] Fuller took an intuitive approach to his studies, often going into exhaustive empirical detail while at the same time seeking to cast his findings in their most general philosophical context. For example, his sphere packing studies led him to generalize a formula for polyhedral numbers: 2 P F 2 + 2, where F stands for 'frequency' (the number of intervals between balls along an edge) and P for a product of low order primes (some integer). He then related the 'multiplicative 2' and 'additive 2' in this formula to the convex versus concave aspects of shapes, and to their polar spinnability respectively. These same polyhedra, developed through sphere packing and related by tetrahedral mensuration, he then spun around their various poles to form great circle networks and corresponding triangular tiles on the surface of a sphere. He exhaustively cataloged the central and surface angles of these spherical triangles and their related chord factors. Fuller was continually on the lookout for ways to connect the dots, often purely speculatively.
As an example of 'dot connecting' he sought to relate the 120 basic disequilibrium LCD triangles of the spherical icosahedron to the plane net of his A module.(915.11Fig. 913.01, Table 905.65) The Jitterbug Transformation provided a unifying dynamic in this work, with much significance attached to the doubling and quadrupling of edges that occurred, when a cuboctahedron is collapsed through icosahedral, octahedral and tetrahedral stages, then inside-outed and re-expanded in a complementary fashion.
The JT formed a bridge between 3,4-fold rotationally symmetric shapes, and the 5-fold family, such as a rhombic triacontahedron, which later he analyzed in terms of the T module, another tetrahedral wedge with the same volume as his A and B modules. He modeled energy transfer between systems by means of the double-edged octahedron and its ability to turn into a spiral (tetrahelix). Energy lost to one system always reappeared somewhere else in his Universe. He modeled a threshold between associative and disassociative energy patterns with his T-to-E module transformation ('E' for 'Einstein').(Fig 986.411A) 'Synergetics' is in some ways a library of potential 'science cartoons' (scenarios) described in prose and not heavily dependent upon mathematical notations. His demystification of a gyroscope's behavior in terms of a hammer thrower, pea shooter, and garden hose, is a good example of his commitment to using accessible metaphors.
826.02A) His modular dissection of a space-filling tetrahedron or MITE (minimum tetrahedron) into 2 A and 1 B module served as a basis for more speculations about energy, the former being more energy conservative, the latter more dissipative in his analysis.(986.422921.20, 921.30). His focus was reminiscent of later cellular automaton studies in that tessellating modules would affect their neighbors over successive time intervals. Social commentary [ ] Synergetics informed Fuller's social analysis of the human condition.
He identified 'ephemeralization' as the trend towards accomplishing more with less physical resources, as a result of increasing comprehension of such 'generalized principles' as E = Mc 2. He remained concerned that humanity's conditioned reflexes were not keeping pace with its engineering potential, emphasizing the 'touch and go' nature of our current predicament. Fuller hoped the streamlining effects of a more 60-degree-based approach within natural philosophy would help bridge the gap between C.P. Snow's 'two cultures' and result in a greater level of scientific literacy in the general population.
(935.24) Academic acceptance [ ] Fuller hoped to gain traction for his ideas and nomenclature by dedicating Synergetics to (with permission) and by citing page 71 of the latter's Regular Polytopes to suggest where his A & B modules (depicted above) might enter the literature (see Fig. Arthur Loeb provided a prologue and an appendix to Synergetics discussing its overlap with crystallography, chemistry and virology. Errata [ ] A major error, caught by Fuller himself, involved a misapplication of his Synergetics Constant in Synergetics 1, which led to the mistaken belief he had discovered a radius 1 sphere of 5 tetravolumes. He provided a correction in Synergetics 2 in the form of his T&E module thread. (986.206 - 986.212) About synergy [ ] Synergetics refers to: either the concept of the output of a not foreseen by the simple sum of the output of each system part, or simply — less used — another term for negative entropy —.
See also [ ] • • • • • • • Notes [ ]. • Synergetics, • Fuller, R. Buckminster (1963). No More Secondhand God. Carbondale and Edwardsville.
• CJ Fearnley,, p. Retrieved on 2010-01-26. • Nystrom, J. (October 1999).. Department of Electrical and Computer Engineering, University of Idaho. • Synergetics, Sec. Buckminster (1963).
No More Secondhand God. Carbondale and Edwardsville.
• Edmondson, Amy C. A Fuller Explanation: The Synergetic Geometry of R. Buckminster Fuller. Boston: Birkhauser. • Cheryl Clark, • Synergetics, Sec. Xiv References [ ] • R.
Buckminster Fuller (in collaboration with E.J. Applewhite, Synergetics: Explorations in the Geometry of Thinking, online edition hosted by R. Gray with permission, originally published by Macmillan, Vol. 1 in 1975 (with a preface and contribution by Arthur L. Loeb; ), and Vol.
2 in 1979 ( ), as two hard-bound volumes, re-editions in paperback. • Amy Edmondson,, EmergentWorld LLC, 2007.
External links [ ] •.
For the EP by Nerina Pallot, see. Buckminster Fuller Born Richard Buckminster Fuller ( 1895-07-12)July 12, 1895, United States Died July 1, 1983 ( 1983-07-01) (aged 87) Los Angeles, United States Education (expelled) Occupation Designer, author, inventor Spouse(s) Anne Hewlett ( m. 1917) Children Richard Buckminster ' Bucky' Fuller (; July 12, 1895 – July 1, 1983) was an American,, author, designer, and inventor. Fuller published more than 30 books, coining or popularizing terms such as ',, and. He also developed numerous inventions, mainly architectural designs, and popularized the widely known. Carbon molecules known as were later named by scientists for their structural and mathematical resemblance to geodesic spheres.
Fuller was the second World President of from 1974 to 1983. Guinea Pig B: I AM NOW CLOSE TO 88 and I am confident that the only thing important about me is that I am an average healthy human.
I am also a living case history of a thoroughly documented, half-century, search-and-research project designed to discover what, if anything, an unknown, moneyless individual, with a dependent wife and newborn child, might be able to do effectively on behalf of all humanity that could not be accomplished by great nations, great religions or private enterprise, no matter how rich or powerfully armed. — Bucky Fuller, 1983. In Carbondale International recognition began with the success of huge during the 1950s. Fuller lectured at in Raleigh in 1949, where he met James Fitzgibbon, who would become a close friend and colleague. Fitzgibbon was director of Geodesics, Inc. And Synergetics, Inc. The first licensees to design geodesic domes.
Howard was lead designer, architect and engineer for both companies. Fuller began working with architect in 1954, and in 1964 they co-founded the architectural firm Fuller & Sadao Inc., whose first project was to design the large for the at in. This building is now the '. From 1959 to 1970, Fuller taught at (SIU). Beginning as an assistant professor, he gained full professorship in 1968, in the School of Art and Design. Working as a designer, scientist, developer, and writer, he lectured for many years around the world. He collaborated at SIU with the designer.
In 1965, Fuller inaugurated the World Design Science Decade (1965 to 1975) at the meeting of the in Paris, which was, in his own words, devoted to 'applying the principles of science to solving the problems of humanity.' Later in his SIU tenure, Fuller was also a visiting professor at, where he designed the dome for the campus Religious Center. Fuller believed human societies would soon rely mainly on renewable sources of energy, such as solar- and wind-derived electricity. He hoped for an age of 'omni-successful education and sustenance of all humanity.'
Fuller referred to himself as 'the property of universe' and during one radio interview he gave later in life, declared himself and his work 'the property of all humanity'. For his lifetime of work, the named him the 1969 Humanist of the Year. In 1976, Fuller was a key participant at, the first UN forum on human settlements. Honors [ ] Fuller was awarded 28 United States patents and many honorary doctorates. In 1960, he was awarded the from.
Fuller was elected as an honorary member of in 1967, on the occasion of the 50th year reunion of his Harvard class of 1917 (from which he was expelled in his first year). He was elected a Fellow of the in 1968. In 1968 he was elected into the as an Associate member, and became a full Academician in 1970. In 1970 he received the award from the. In 1976, he received the from the Library Associates.
He also received numerous other awards, including the presented to him on February 23, 1983, by President. A geodesic sphere The geodesic dome [ ] Fuller was most famous for his –, which have been used as parts of military radar stations, civic buildings, environmental protest camps and exhibition attractions. An examination of the geodesic design by for the, built some 20 years prior to Fuller's work, reveals that Fuller's Geodesic Dome patent (U.S. 2,682,235; awarded in 1954), follows the same design as Bauersfeld's.
Their construction is based on extending some basic principles to build simple ' structures (tetrahedron,, and the closest packing of spheres), making them lightweight and stable. The geodesic dome was a result of Fuller's exploration of nature's constructing principles to find design solutions. The Fuller Dome is referenced in the -winning novel by, in which a geodesic dome is said to cover the entire island of, and it floats on air due to the hot-air balloon effect of the large air-mass under the dome (and perhaps its construction of lightweight materials). Transportation [ ]. The Omni-Media-Transport: With such a vehicle at our disposal, [Fuller] felt that human travel, like that of birds, would no longer be confined to airports, roads, and other bureaucratic boundaries, and that autonomous free-thinking human beings could live and prosper wherever they chose. Sieden, Bucky Fuller's Universe, 2000 To his young daughter Allegra: Fuller described the Dymaxion as a ' zoom-mobile, explaining that it could hop off the road at will, fly about, then, as deftly as a bird, settle back into a place in traffic.' The Dymaxion car, c.1933, artist shown entering the car, carrying coat The was a vehicle designed by Fuller, featured prominently at Chicago's 1933-1934 World's Fair.
During the, Fuller formed the Dymaxion Corporation and built three prototypes with noted naval architect and a team of 27 workmen — using donated money as well as a family inheritance. Fuller associated the word Dymaxion with much of his work, a of the words dynamic, maximum, and tens ion to sum up the goal of his study, 'maximum gain of advantage from minimal energy input.' The Dymaxion was not an automobile per se, but rather the 'ground-taxying mode' of a vehicle that might one day be designed to fly, land and drive — an 'Omni-Medium Transport' for air, land and water.
Fuller focused on the landing and taxiing qualities, and noted severe limitations in its handling. The team made constant improvements and refinements to the platform, and Fuller noted the Dymaxion 'was an invention that could not be made available to the general public without considerable improvements.' The bodywork was aerodynamically designed for increased fuel efficiency and speed as well as light weight, and its featured a lightweight cromoly-steel hinged chassis, rear-mounted V8 engine, front-drive and three-wheels. The vehicle was steered via the third wheel at the rear, capable of 90°. Thus able to steer in a tight circle, the Dymaxion often caused a sensation, bringing nearby traffic to a halt.
Shortly after launch, a prototype crashed after being hit by another car, killing the Dymaxion's driver. The other car was driven by a local politician and was illegally removed from the accident scene, leaving reporters who arrived subsequently to blame the Dymaxion's unconventional design — though investigations exonerated the prototype. Fuller would himself later crash another prototype with his young daughter aboard. Despite courting the interest of important figures from the auto industry, Fuller used his family inheritance to finish the second and third prototypes — eventually selling all three, dissolving Dymaxion Corporation and maintaining the Dymaxion was never intended as a commercial venture. One of the three original prototypes survives. A Dymaxion house at Fuller's energy-efficient and inexpensive garnered much interest, but only two prototypes were ever produced. Here the term 'Dymaxion' is used in effect to signify a 'radically strong and light tensegrity structure'.
One of Fuller's Dymaxion Houses is on display as a permanent exhibit at the in. Designed and developed during the mid-1940s, this prototype is a round structure (not a dome), shaped something like the flattened 'bell' of certain jellyfish. It has several innovative features, including revolving dresser drawers, and a fine-mist shower that reduces water consumption. According to Fuller biographer Steve Crooks, the house was designed to be delivered in two cylindrical packages, with interior color panels available at local dealers.
A circular structure at the top of the house was designed to rotate around a central mast to use natural winds for cooling and air circulation. Conceived nearly two decades earlier, and developed in, the house was designed to be lightweight, adapted to windy climates, cheap to produce and easy to assemble. Because of its light weight and portability, the Dymaxion House was intended to be the ideal housing for individuals and families who wanted the option of easy mobility. The design included a 'Go-Ahead-With-Life Room' stocked with maps, charts, and helpful tools for travel 'through time and space.' It was to be produced using factories, workers, and technologies that had produced World War II aircraft. It looked ultramodern at the time, built of metal, and sheathed in polished aluminum. The basic model enclosed 90 m 2 (970 sq ft) of floor area.
Due to publicity, there were many orders during the early Post-War years, but the company that Fuller and others had formed to produce the houses failed due to management problems. In 1967, Fuller developed a concept for an offshore floating city named and published a report on the design the following year.
Models of the city aroused the interest of President who, after leaving office, had them placed in the. In 1969, Fuller began the Otisco Project, named after its location in.
The project developed and demonstrated concrete spray with mesh-covered wireforms for producing large-scale, load-bearing spanning structures built on-site, without the use of pouring molds, other adjacent surfaces or hoisting. The initial method used a circular concrete footing in which anchor posts were set. Tubes cut to length and with ends flattened were then bolted together to form a duodeca-rhombicahedron (22-sided hemisphere) geodesic structure with spans ranging to 60 feet (18 m). The form was then draped with layers of ¼-inch wire mesh attached by twist ties.
Concrete was sprayed onto the structure, building up a solid layer which, when cured, would support additional concrete to be added by a variety of traditional means. Fuller referred to these buildings as monolithic ferroconcrete geodesic domes. However, the tubular frame form proved problematic for setting windows and doors. It was replaced by an iron set vertically in the concrete footing and then bent inward and welded in place to create the dome's wireform structure and performed satisfactorily. Domes up to three stories tall built with this method proved to be remarkably strong.
Other shapes such as cones, pyramids and arches proved equally adaptable. The project was enabled by a grant underwritten by and sponsored by (rebar), the Johnson Wire Corp, (mesh) and Portland Cement Company (concrete).
The ability to build large complex load bearing concrete spanning structures in free space would open many possibilities in architecture, and is considered as one of Fuller's greatest contributions. Dymaxion map and World Game [ ] Fuller, along with co-cartographer, also designed an alternative projection map, called the. This was designed to show Earth's continents with minimum distortion when projected or printed on a flat surface. In the 1960s, Fuller developed the, a collaborative simulation game played on a 70-by-35-foot Dymaxion map, in which players attempt to solve world problems. The object of the simulation game is, in Fuller's words, to “make the world work, for 100% of humanity, in the shortest possible time, through spontaneous cooperation, without ecological offense or the disadvantage of anyone.” Appearance and style [ ] Buckminster Fuller wore thick-lensed to correct his extreme, a condition that went undiagnosed for the first five years of his life.
Fuller's hearing was damaged during his Naval service in World War I and deteriorated during the 1960s.